Four solvency frameworks × four borrower types:
| Framework | Solvency Definition | Columns |
|---|---|---|
| A. Full Sample | No split (all banks) | 4 columns: AnyFed, BTFP, DW, FHLB |
| B. Jiang MTM | AE = Book Equity/TA − MTM/TA ≥ 0 | 8 columns: 4 × {Solvent, Insolvent} |
| C. Jiang IDCR-100% | (MV Assets − Uninsured − Insured) / Insured ≥ 0 | 8 columns: 4 × {Solvent, Insolvent} |
| D. DSSW Franchise | AE + DFV ≥ 0, where DFV = (1−β)×D/TA | Diagnostic table (prediction: 0 insolvent) |
| Test | Description | Solvency Splits |
|---|---|---|
| Temporal | BTFP & DW: Crisis vs. Arbitrage | Full + Jiang + IDCR-100% |
| Deposit Beta | Triple interaction: MTM × Uninsured × β^U | Full + Jiang + IDCR-100% |
| Facility Complementarity | Multinomial choice, DW→BTFP complement, substitution | Full sample |
The DSSW (2023/2025) deposit franchise value for bank \(i\) in cross-section: \[\text{DFV}_i = (1 - \beta_i) \times \frac{D_i}{TA_i}\]
Full formula: \(F = D \times [(1-\beta) - c/r] \times [1 - 1/(1+r)^T]\) where \(c \approx 2\%\), \(r\) = long rate, \(T\) = deposit runoff horizon. Since \(c\), \(r\), \(T\) are constant cross-sectionally, all bank-level variation comes from \(\beta_i\) and \(D_i/TA_i\).
Key insight: DFV exists only in the no-run equilibrium. If depositors run, the uninsured franchise is destroyed. A bank that is DSSW-solvent absent a run can become insolvent during one — this is the panic region.
rm(list = ls())
library(data.table)
library(dplyr)
library(tidyr)
library(stringr)
library(lubridate)
library(purrr)
library(tibble)
library(ggrepel)
library(fixest)
library(marginaleffects)
library(nnet)
library(broom)
library(modelsummary)
library(knitr)
library(kableExtra)
library(DescTools)
library(ggplot2)
library(gridExtra)
library(scales)
library(patchwork)
library(readr)
library(readxl)
cat("All packages loaded.\n")## All packages loaded.winsorize <- function(x, probs = c(0.025, 0.975)) {
if (all(is.na(x))) return(x)
q <- quantile(x, probs = probs, na.rm = TRUE, names = FALSE)
pmax(pmin(x, q[2]), q[1])
}
standardize_z <- function(x) {
if (all(is.na(x))) return(x)
(x - mean(x, na.rm = TRUE)) / sd(x, na.rm = TRUE)
}
safe_div <- function(num, denom, default = NA_real_) {
ifelse(is.na(denom) | denom == 0, default, num / denom)
}
create_size_category_3 <- function(assets_thousands) {
assets_millions <- assets_thousands / 1000
case_when(
assets_millions >= 100000 ~ "Large (>$100B)",
assets_millions >= 1000 ~ "Medium ($1B-$100B)",
TRUE ~ "Small (<$1B)"
)
}
size_levels_3 <- c("Small (<$1B)", "Medium ($1B-$100B)", "Large (>$100B)")
format_pval <- function(p) {
case_when(is.na(p) ~ "", p < 0.01 ~ "***", p < 0.05 ~ "**", p < 0.10 ~ "*", TRUE ~ "")
}
safe_writeLines <- function(text, con, max_retries = 5, wait_sec = 2) {
for (i in seq_len(max_retries)) {
result <- tryCatch(
{ writeLines(text, con); TRUE },
error = function(e) {
if (i < max_retries) Sys.sleep(wait_sec)
FALSE
}
)
if (isTRUE(result)) return(invisible(NULL))
}
warning("Failed to write ", con, " after ", max_retries, " attempts.")
}
save_figure <- function(plot_obj, filename, width = 12, height = 8) {
ggsave(
file.path(FIG_PATH, paste0(filename, ".pdf")),
plot = plot_obj, width = width, height = height, device = "pdf"
)
message("Saved: ", filename, ".pdf")
}BASE_PATH <- "C:/Users/mohua/OneDrive - Louisiana State University/Finance_PhD/DW_Stigma_paper/Liquidity_project_2025"
DATA_PROC <- file.path(BASE_PATH, "01_data/processed")
OUTPUT_PATH <- file.path(BASE_PATH, "03_documentation/Comprehensive_Analysis")
TABLE_PATH <- file.path(OUTPUT_PATH, "tables")
FIG_PATH <- file.path(OUTPUT_PATH, "figures")
for (path in c(TABLE_PATH, FIG_PATH)) {
if (!dir.exists(path)) dir.create(path, recursive = TRUE)
}BASELINE_MAIN <- "2022Q4"
BASELINE_ARB <- "2023Q3"
CRISIS_START <- as.Date("2023-03-08")
CRISIS_END <- as.Date("2023-05-04")
ARB_START <- as.Date("2023-11-15")
ARB_END <- as.Date("2024-01-24")
DW_DATA_END <- as.Date("2023-12-31")
cat("Crisis:", format(CRISIS_START), "to", format(CRISIS_END), "\n")## Crisis: 2023-03-08 to 2023-05-04cat("Arbitrage:", format(ARB_START), "to", format(ARB_END), "\n")## Arbitrage: 2023-11-15 to 2024-01-24call_q <- read_csv(file.path(DATA_PROC, "final_call_gsib.csv"), show_col_types = FALSE) %>%
mutate(idrssd = as.character(idrssd))
btfp_loans_raw <- read_csv(file.path(DATA_PROC, "btfp_loan_bank_only.csv"), show_col_types = FALSE) %>%
mutate(rssd_id = as.character(rssd_id), btfp_loan_date = mdy(btfp_loan_date))
dw_loans_raw <- read_csv(file.path(DATA_PROC, "dw_loan_bank_2023.csv"), show_col_types = FALSE) %>%
mutate(rssd_id = as.character(rssd_id), dw_loan_date = ymd(dw_loan_date))
dssw_betas <- read_csv(file.path(DATA_PROC, "dssw_deposit_betas.csv"), show_col_types = FALSE) %>%
mutate(idrssd = as.character(idrssd))
dssw_beta_2022q4 <- dssw_betas %>% filter(estimation_date == "2022Q4") %>%
select(idrssd, beta_overall, beta_insured, beta_uninsured,
beta_insured_w, beta_uninsured_w, gamma_hat, alpha_hat)
# Public bank flag (from NY Fed CRSP-FRB link via NIC hierarchy)
public_flag <- read_csv(file.path(DATA_PROC, "public_bank_flag.csv"), show_col_types = FALSE) %>%
mutate(idrssd = as.character(idrssd)) %>%
select(idrssd, period, is_public)
cat("=== DATA LOADED ===\n")## === DATA LOADED ===cat("Call Report:", nrow(call_q), "obs |", n_distinct(call_q$idrssd), "banks\n")## Call Report: 75989 obs | 5074 bankscat("BTFP Loans:", nrow(btfp_loans_raw), "\n")## BTFP Loans: 6734cat("DW Loans:", nrow(dw_loans_raw), "\n")## DW Loans: 10008cat("Public flag:", n_distinct(public_flag$idrssd[public_flag$is_public == 1]), "public banks\n")## Public flag: 427 public banksexcluded_banks <- call_q %>%
filter(period == BASELINE_MAIN, failed_bank == 1 | gsib == 1) %>%
pull(idrssd)
btfp_loans <- btfp_loans_raw %>% filter(!rssd_id %in% excluded_banks)
dw_loans <- dw_loans_raw %>% filter(!rssd_id %in% excluded_banks)
cat("Excluded banks:", length(excluded_banks), "\n")## Excluded banks: 41create_borrower_indicator <- function(loans_df, date_col, id_col, amount_col,
start_date, end_date, prefix) {
loans_df %>%
filter(!!sym(date_col) >= start_date, !!sym(date_col) <= end_date) %>%
group_by(!!sym(id_col)) %>%
summarise(
"{prefix}" := 1L,
"{prefix}_amt" := sum(!!sym(amount_col), na.rm = TRUE),
"{prefix}_first" := min(!!sym(date_col)),
.groups = "drop"
) %>%
rename(idrssd = !!sym(id_col))
}
btfp_crisis <- create_borrower_indicator(btfp_loans, "btfp_loan_date", "rssd_id", "btfp_loan_amount", CRISIS_START, CRISIS_END, "btfp_crisis")
btfp_arb <- create_borrower_indicator(btfp_loans, "btfp_loan_date", "rssd_id", "btfp_loan_amount", ARB_START, ARB_END, "btfp_arb")
dw_crisis <- create_borrower_indicator(dw_loans, "dw_loan_date", "rssd_id", "dw_loan_amount", CRISIS_START, min(CRISIS_END, DW_DATA_END), "dw_crisis")
dw_arb <- create_borrower_indicator(dw_loans, "dw_loan_date", "rssd_id", "dw_loan_amount", ARB_START, DW_DATA_END, "dw_arb")
cat("BTFP Crisis:", nrow(btfp_crisis), "| Arb:", nrow(btfp_arb), "\n")## BTFP Crisis: 526 | Arb: 780cat("DW Crisis:", nrow(dw_crisis), "| Arb:", nrow(dw_arb), "\n")## DW Crisis: 459 | Arb: 389construct_analysis_vars <- function(baseline_data) {
baseline_data %>%
mutate(
# === RAW VARIABLES ===
mtm_total_raw = mtm_loss_to_total_asset,
mtm_btfp_raw = mtm_loss_omo_eligible_to_total_asset,
mtm_other_raw = mtm_loss_non_omo_eligible_to_total_asset,
uninsured_lev_raw = uninsured_deposit_to_total_asset,
insured_lev_raw = r_insured_deposit,
uninsured_share_raw = uninsured_to_deposit,
ln_assets_raw = log(total_asset),
cash_ratio_raw = cash_to_total_asset,
securities_ratio_raw = security_to_total_asset,
loan_ratio_raw = total_loan_to_total_asset,
book_equity_ratio_raw = book_equity_to_total_asset,
roa_raw = roa,
fhlb_ratio_raw = fhlb_to_total_asset,
loan_to_deposit_raw = loan_to_deposit,
wholesale_raw = safe_div(
fed_fund_purchase + repo + replace_na(other_borrowed_less_than_1yr, 0),
total_liability, 0) * 100,
# === SOLVENCY FRAMEWORK A: Jiang MTM Adjusted Equity ===
adjusted_equity_raw = book_equity_to_total_asset - mtm_loss_to_total_asset,
mtm_insolvent = as.integer(adjusted_equity_raw < 0),
mtm_solvent = as.integer(adjusted_equity_raw >= 0),
# === SOLVENCY FRAMEWORK B: Jiang IDCR (100% uninsured run) ===
mv_assets = total_asset * (1 - mtm_loss_to_total_asset / 100),
idcr_100 = safe_div(
mv_assets - uninsured_deposit - insured_deposit,
insured_deposit, NA_real_
),
insolvent_idcr_100 = as.integer(idcr_100 < 0),
solvent_idcr_100 = as.integer(idcr_100 >= 0),
# === SOLVENCY FRAMEWORK C: DSSW Deposit Franchise Value ===
# DFV_i = (1 - β_i) × D_i / TA_i (cross-sectional DSSW simplification)
# Full: F = D × [(1-β) - c/r] × [1 - 1/(1+r)^T]; c,r,T constant cross-sectionally
# CRITICAL: DFV exists ONLY in the no-run equilibrium.
# If depositors run, uninsured franchise is destroyed → back to Jiang measure.
dfv_raw = ifelse(!is.na(beta_overall),
(1 - beta_overall) * (dom_deposit / total_asset) * 100, NA_real_),
adjusted_equity_dssw_raw = ifelse(!is.na(dfv_raw),
book_equity_to_total_asset - mtm_loss_to_total_asset + dfv_raw, NA_real_),
dssw_insolvent = as.integer(!is.na(adjusted_equity_dssw_raw) & adjusted_equity_dssw_raw < 0),
dssw_solvent = as.integer(!is.na(adjusted_equity_dssw_raw) & adjusted_equity_dssw_raw >= 0),
# === UNINSURED DEPOSIT BETA (for triple interaction) ===
# Use truly raw (unwinsorized) beta from DSSW decomposition;
# the Rmd's own winsorize() at 2.5/97.5 is the single winsorization step,
# consistent with all other variables in the pipeline.
uninsured_beta_raw = ifelse(!is.na(beta_uninsured), beta_uninsured, NA_real_),
# === WINSORIZED ===
mtm_total_w = winsorize(mtm_total_raw),
mtm_btfp_w = winsorize(mtm_btfp_raw),
mtm_other_w = winsorize(mtm_other_raw),
uninsured_lev_w = winsorize(uninsured_lev_raw),
insured_lev_w = winsorize(r_insured_deposit),
adjusted_equity_w = winsorize(adjusted_equity_raw),
dfv_w = winsorize(dfv_raw),
adjusted_equity_dssw_w = winsorize(adjusted_equity_dssw_raw),
uninsured_beta_w = winsorize(uninsured_beta_raw),
ln_assets_w = winsorize(ln_assets_raw),
cash_ratio_w = winsorize(cash_ratio_raw),
book_equity_ratio_w = winsorize(book_equity_ratio_raw),
roa_w = winsorize(roa_raw),
loan_to_deposit_w = winsorize(loan_to_deposit_raw),
wholesale_w = winsorize(wholesale_raw),
# === Z-STANDARDIZED ===
mtm_total = standardize_z(mtm_total_w),
uninsured_lev = standardize_z(uninsured_lev_w),
insured_lev = standardize_z(insured_lev_w),
adjusted_equity = standardize_z(adjusted_equity_w),
dfv = standardize_z(dfv_w),
adjusted_equity_dssw = standardize_z(adjusted_equity_dssw_w),
uninsured_beta = standardize_z(uninsured_beta_w),
ln_assets = standardize_z(ln_assets_w),
cash_ratio = standardize_z(cash_ratio_w),
book_equity_ratio = standardize_z(book_equity_ratio_w),
roa = standardize_z(roa_w),
loan_to_deposit = standardize_z(loan_to_deposit_w),
wholesale = standardize_z(wholesale_w),
# === INTERACTIONS ===
mtm_x_uninsured = mtm_total * uninsured_lev,
mtm_x_insured = mtm_total * insured_lev,
mtm_x_unins_beta = mtm_total * uninsured_beta,
unins_x_unins_beta = uninsured_lev * uninsured_beta,
mtm_x_unins_x_beta = mtm_total * uninsured_lev * uninsured_beta,
# === PAR BENEFIT & COLLATERAL ===
par_benefit_raw = safe_div(mtm_btfp_raw,
mtm_btfp_raw + 100 * safe_div(omo_eligible, total_asset * 1000, 0), NA_real_),
collateral_capacity_raw = safe_div(omo_eligible, total_asset * 1000, 0) * 100,
size_cat = factor(create_size_category_3(total_asset), levels = size_levels_3)
) %>%
mutate(
par_benefit_w = winsorize(par_benefit_raw),
par_benefit = standardize_z(par_benefit_w),
collateral_capacity_w = winsorize(collateral_capacity_raw),
collateral_capacity = standardize_z(collateral_capacity_w),
par_x_uninsured = par_benefit * uninsured_lev,
# === PAR RECAPITALIZATION (BTFP par lending − market value) / TA ===
# This is the actual capital injection from BTFP's face-value lending:
# a bank pledging OMO-eligible securities with MTM losses gets
# par_recap dollars of extra liquidity per dollar of TA vs. market lending (DW).
par_recap = standardize_z(mtm_btfp_w),
par_recap_x_unins = par_recap * uninsured_lev,
par_recap_x_mtm_ui = par_recap * mtm_x_uninsured
)
}df_2022q4 <- call_q %>%
filter(period == BASELINE_MAIN, !idrssd %in% excluded_banks,
!is.na(omo_eligible) & omo_eligible > 0) %>%
left_join(dssw_beta_2022q4, by = "idrssd") %>%
left_join(public_flag %>% filter(period == "2022Q4") %>% select(idrssd, is_public),
by = "idrssd") %>%
mutate(is_public = replace_na(is_public, 0L)) %>%
construct_analysis_vars()
df_2023q3 <- call_q %>%
filter(period == BASELINE_ARB, !idrssd %in% excluded_banks,
!is.na(omo_eligible) & omo_eligible > 0) %>%
left_join(dssw_beta_2022q4, by = "idrssd") %>%
left_join(public_flag %>% filter(period == "2023Q3") %>% select(idrssd, is_public),
by = "idrssd") %>%
mutate(is_public = replace_na(is_public, 0L)) %>%
construct_analysis_vars()
cat("=== BASELINES ===\n")## === BASELINES ===cat("2022Q4:", nrow(df_2022q4), "banks\n")## 2022Q4: 4292 bankscat(" MTM Insolvent:", sum(df_2022q4$mtm_insolvent, na.rm=TRUE), "\n")## MTM Insolvent: 825cat(" IDCR-100% Insolvent:", sum(df_2022q4$insolvent_idcr_100, na.rm=TRUE), "\n")## IDCR-100% Insolvent: 364cat(" DSSW Insolvent:", sum(df_2022q4$dssw_insolvent, na.rm=TRUE), "\n")## DSSW Insolvent: 0cat(" Beta coverage:", sum(!is.na(df_2022q4$beta_overall)), "\n")## Beta coverage: 4226cat(" Public banks:", sum(df_2022q4$is_public, na.rm=TRUE), "\n")## Public banks: 311cat(" Non-public banks:", sum(df_2022q4$is_public == 0, na.rm=TRUE), "\n")## Non-public banks: 3981join_all_borrowers <- function(df_base, btfp_df, dw_df, btfp_var, dw_var) {
df_base %>%
left_join(btfp_df %>% select(idrssd, starts_with(btfp_var)), by = "idrssd") %>%
left_join(dw_df %>% select(idrssd, starts_with(dw_var)), by = "idrssd") %>%
mutate(
"{btfp_var}" := replace_na(!!sym(btfp_var), 0L),
"{dw_var}" := replace_na(!!sym(dw_var), 0L),
fhlb_user = as.integer(abnormal_fhlb_borrowing_10pct == 1),
any_fed = as.integer(!!sym(btfp_var) == 1 | !!sym(dw_var) == 1),
both_fed = as.integer(!!sym(btfp_var) == 1 & !!sym(dw_var) == 1),
user_group = factor(case_when(
both_fed == 1 ~ "Both",
!!sym(btfp_var) == 1 ~ "BTFP_Only",
!!sym(dw_var) == 1 ~ "DW_Only",
TRUE ~ "Neither"
), levels = c("Neither", "BTFP_Only", "DW_Only", "Both")),
non_user = as.integer(any_fed == 0 & fhlb_user == 0)
)
}
# Crisis
df_crisis <- join_all_borrowers(df_2022q4, btfp_crisis, dw_crisis, "btfp_crisis", "dw_crisis") %>%
mutate(
btfp_pct = ifelse(btfp_crisis == 1 & btfp_crisis_amt > 0,
100 * btfp_crisis_amt / (total_asset * 1000), NA_real_),
dw_pct = ifelse(dw_crisis == 1 & dw_crisis_amt > 0,
100 * dw_crisis_amt / (total_asset * 1000), NA_real_)
)
# Arbitrage
df_arb <- df_2023q3 %>%
left_join(btfp_arb %>% select(idrssd, btfp_arb, btfp_arb_amt), by = "idrssd") %>%
left_join(dw_arb %>% select(idrssd, dw_arb), by = "idrssd") %>%
mutate(
btfp_arb = replace_na(btfp_arb, 0L),
dw_arb = replace_na(dw_arb, 0L),
fhlb_user = as.integer(abnormal_fhlb_borrowing_10pct == 1),
any_fed = as.integer(btfp_arb == 1 | dw_arb == 1),
non_user = as.integer(any_fed == 0 & fhlb_user == 0),
user_group = factor(case_when(
btfp_arb == 1 & dw_arb == 1 ~ "Both",
btfp_arb == 1 ~ "BTFP_Only",
dw_arb == 1 ~ "DW_Only",
TRUE ~ "Neither"
), levels = c("Neither", "BTFP_Only", "DW_Only", "Both"))
)
cat("=== PERIOD COUNTS ===\n")## === PERIOD COUNTS ===cat("Crisis:", nrow(df_crisis), "| BTFP:", sum(df_crisis$btfp_crisis),
"| DW:", sum(df_crisis$dw_crisis), "| Any:", sum(df_crisis$any_fed), "\n")## Crisis: 4292 | BTFP: 501 | DW: 433 | Any: 828cat("Arb:", nrow(df_arb), "| BTFP:", sum(df_arb$btfp_arb),
"| DW:", sum(df_arb$dw_arb), "\n")## Arb: 4214 | BTFP: 749 | DW: 362CONTROLS <- "ln_assets + cash_ratio + loan_to_deposit + book_equity_ratio + wholesale + roa"
EXPL_BASE <- "mtm_total + uninsured_lev + mtm_x_uninsured"
# Triple interaction for deposit beta channel
EXPL_BETA_FULL <- paste0(
"mtm_total + uninsured_lev + uninsured_beta + ",
"mtm_x_uninsured + mtm_x_unins_beta + unins_x_unins_beta + ",
"mtm_x_unins_x_beta")
EXPL_BETA_NESTED <- paste0(
"mtm_total + uninsured_lev + uninsured_beta + ",
"mtm_x_uninsured + mtm_x_unins_beta + unins_x_unins_beta")
# Facility choice
EXPL_FACILITY <- "mtm_total + uninsured_lev + mtm_x_uninsured + par_benefit + collateral_capacity"
setFixest_dict(c(
mtm_total = "MTM Loss (z)",
uninsured_lev = "Uninsured Leverage (z)",
insured_lev = "Insured Leverage (z)",
uninsured_beta = "Uninsured $\\beta$ (z)",
mtm_x_uninsured = "MTM $\\times$ Uninsured",
mtm_x_insured = "MTM $\\times$ Insured",
mtm_x_unins_beta = "MTM $\\times$ Unins. $\\beta$",
unins_x_unins_beta = "Uninsured $\\times$ Unins. $\\beta$",
mtm_x_unins_x_beta = "MTM $\\times$ Uninsured $\\times$ $\\beta^U$",
par_benefit = "Par Benefit (z)",
collateral_capacity = "OMO Collateral (z)",
par_x_uninsured = "Par $\\times$ Uninsured",
par_recap = "Par Recap (z)",
par_recap_x_unins = "Par Recap $\\times$ Uninsured",
par_recap_x_mtm_ui = "Par Recap $\\times$ MTM $\\times$ UI",
btfp_util = "BTFP Utilization (z)",
btfp_exhausted = "BTFP Exhausted (>80\\%)",
also_btfp = "Also BTFP",
also_dw = "Also DW",
adv_rate_z = "Advance Rate (z)",
dw_share_omo_z = "DW OMO Share (z)",
dw_share_loans_z = "DW Loan Share (z)",
ln_assets = "Log(Assets)",
cash_ratio = "Cash Ratio",
loan_to_deposit = "Loan-to-Deposit",
book_equity_ratio = "Book Equity Ratio",
wholesale = "Wholesale Funding",
roa = "ROA"
))
COEF_ORDER <- c("Constant", "MTM Loss", "Uninsured Leverage", "Uninsured.*beta",
"MTM.*Uninsured$", "MTM.*Unins.*beta", "Uninsured.*Unins",
"MTM.*Uninsured.*beta", "Par Benefit", "OMO Collateral")
# --- Model runner with safety ---
run_model <- function(data, dv, explanatory, family_type = "lpm", controls = CONTROLS) {
ff <- as.formula(paste(dv, "~", explanatory, "+", controls))
if (family_type == "lpm") {
feols(ff, data = data, vcov = "hetero")
} else {
feglm(ff, data = data, family = binomial("logit"), vcov = "hetero")
}
}
safe_run <- function(data, dv, explanatory, family_type = "lpm",
controls = CONTROLS, min_n = 30, min_dv1 = 5) {
n_obs <- sum(!is.na(data[[dv]]))
n_dv1 <- sum(data[[dv]] == 1, na.rm = TRUE)
if (n_obs < min_n || n_dv1 < min_dv1) {
message(" Skip: N=", n_obs, " DV=1:", n_dv1, " for ", dv)
return(NULL)
}
tryCatch(
run_model(data, dv, explanatory, family_type, controls),
error = function(e) { message(" Error: ", e$message); NULL }
)
}
# --- Save etable ---
save_etable <- function(models, filename, title_text, notes_text,
fitstat_use = ~ n + r2, extra_lines = NULL) {
models <- models[!sapply(models, is.null)]
if (length(models) == 0) { message("No models for ", filename); return(invisible(NULL)) }
# Auto-compute N(DV=1) for each model
dv1_counts <- sapply(models, function(m) {
dv_vec <- tryCatch(model.matrix(m, type = "lhs"), error = function(e) NULL)
if (!is.null(dv_vec)) sum(dv_vec == 1, na.rm = TRUE) else "—"
})
dv1_line <- c("N(DV=1)", dv1_counts)
extra_lines <- c(list(dv1_line), extra_lines)
etable(models, title = title_text, notes = notes_text,
fitstat = fitstat_use, order = COEF_ORDER, extralines = extra_lines,
se.below = TRUE, tex = TRUE,
file = file.path(TABLE_PATH, paste0(filename, ".tex")),
replace = TRUE, style.tex = style.tex("aer"))
message("Saved: ", filename, ".tex")
}
theme_paper <- theme_minimal(base_size = 12) +
theme(plot.title = element_text(face = "bold", size = 13, hjust = 0),
plot.subtitle = element_text(size = 10, color = "grey40", hjust = 0),
legend.position = "bottom", panel.grid.minor = element_blank(),
strip.text = element_text(face = "bold", size = 11))
cat("=== INFRASTRUCTURE READY ===\n")## === INFRASTRUCTURE READY ===# === Pure comparison samples (Crisis) ===
df_btfp_s <- df_crisis %>% filter(btfp_crisis == 1 | non_user == 1)
df_dw_s <- df_crisis %>% filter(dw_crisis == 1 | non_user == 1)
df_anyfed_s <- df_crisis %>% filter(any_fed == 1 | non_user == 1)
df_fhlb_s <- df_crisis %>% filter(fhlb_user == 1 | non_user == 1)
# === Arbitrage samples ===
df_btfp_arb_s <- df_arb %>% filter(btfp_arb == 1 | non_user == 1)
df_dw_arb_s <- df_arb %>% filter(dw_arb == 1 | non_user == 1)
cat("=== CRISIS SAMPLES ===\n")## === CRISIS SAMPLES ===cat("BTFP:", nrow(df_btfp_s), "(", sum(df_btfp_s$btfp_crisis), "borrowers)\n")## BTFP: 3727 ( 501 borrowers)cat("DW:", nrow(df_dw_s), "(", sum(df_dw_s$dw_crisis), "borrowers)\n")## DW: 3659 ( 433 borrowers)cat("AnyFed:", nrow(df_anyfed_s), "(", sum(df_anyfed_s$any_fed), "borrowers)\n")## AnyFed: 4054 ( 828 borrowers)cat("FHLB:", nrow(df_fhlb_s), "(", sum(df_fhlb_s$fhlb_user), "borrowers)\n")## FHLB: 3528 ( 302 borrowers)# === Solvency sub-sample counts ===
cat("\n=== SOLVENCY DISTRIBUTIONS IN ANYFED SAMPLE ===\n")##
## === SOLVENCY DISTRIBUTIONS IN ANYFED SAMPLE ===cat("Jiang MTM: Solvent=", sum(df_anyfed_s$mtm_solvent, na.rm=T),
" Insolvent=", sum(df_anyfed_s$mtm_insolvent, na.rm=T), "\n")## Jiang MTM: Solvent= 3252 Insolvent= 792cat("IDCR-100%: Solvent=", sum(df_anyfed_s$solvent_idcr_100, na.rm=T),
" Insolvent=", sum(df_anyfed_s$insolvent_idcr_100, na.rm=T), "\n")## IDCR-100%: Solvent= 3661 Insolvent= 352cat("DSSW: Solvent=", sum(df_anyfed_s$dssw_solvent, na.rm=T),
" Insolvent=", sum(df_anyfed_s$dssw_insolvent, na.rm=T), "\n")## DSSW: Solvent= 3991 Insolvent= 0cat("=== MAIN A: FULL SAMPLE (CRISIS) ===\n")## === MAIN A: FULL SAMPLE (CRISIS) ===mod_A_any <- run_model(df_anyfed_s, "any_fed", EXPL_BASE)
mod_A_btfp <- run_model(df_btfp_s, "btfp_crisis", EXPL_BASE)
mod_A_dw <- run_model(df_dw_s, "dw_crisis", EXPL_BASE)
mod_A_fhlb <- run_model(df_fhlb_s, "fhlb_user", EXPL_BASE)
models_A <- list(
"Any Fed" = mod_A_any, "BTFP" = mod_A_btfp,
"DW" = mod_A_dw, "FHLB" = mod_A_fhlb)
save_etable(models_A, "MainA_full_sample",
title_text = "Main Results A: Full Sample — Extensive Margin (Crisis Period)",
notes_text = "LPM. DV=1 if borrowed, 0 if pure non-borrower. Crisis: Mar 8--May 4, 2023. FHLB: falsification. Robust SEs. z-standardized.",
extra_lines = list(
c("Borrowers", sum(df_anyfed_s$any_fed), sum(df_btfp_s$btfp_crisis),
sum(df_dw_s$dw_crisis), sum(df_fhlb_s$fhlb_user)),
c("Mean DV", round(mean(df_anyfed_s$any_fed),3), round(mean(df_btfp_s$btfp_crisis),3),
round(mean(df_dw_s$dw_crisis),3), round(mean(df_fhlb_s$fhlb_user),3))))
etable(models_A, fitstat = ~ n + r2, se.below = TRUE)## Any Fed BTFP DW FHLB
## Dependent Var.: any_fed btfp_crisis dw_crisis fhlb_user
##
## Constant 0.2081*** 0.1435*** 0.1272*** 0.0908***
## (0.0060) (0.0056) (0.0054) (0.0050)
## MTM Loss (z) 0.0300*** 0.0249*** 0.0158** 0.0039
## (0.0070) (0.0062) (0.0061) (0.0056)
## Uninsured Leverage (z) 0.0198** 0.0214** 0.0126 0.0064
## (0.0076) (0.0070) (0.0067) (0.0051)
## MTM $\times$ Uninsured 0.0199*** 0.0193*** 0.0170*** -0.0039
## (0.0057) (0.0052) (0.0051) (0.0043)
## Log(Assets) 0.1064*** 0.0713*** 0.0920*** 0.0266***
## (0.0082) (0.0077) (0.0077) (0.0065)
## Cash Ratio -0.0246*** -0.0285*** -0.0043 -0.0214***
## (0.0061) (0.0048) (0.0053) (0.0039)
## Loan-to-Deposit -0.0035 -0.0107 -0.0007 0.0244***
## (0.0067) (0.0057) (0.0057) (0.0050)
## Book Equity Ratio -0.0135* -0.0118* -0.0006 0.0101*
## (0.0055) (0.0047) (0.0044) (0.0041)
## Wholesale Funding 0.0297*** 0.0263*** 0.0204** 0.0019
## (0.0069) (0.0065) (0.0063) (0.0051)
## ROA -0.0019 -0.0059 -0.0029 -0.0091*
## (0.0057) (0.0049) (0.0048) (0.0043)
## ______________________ __________ ___________ __________ __________
## S.E. type Hete.-rob. Heter.-rob. Hete.-rob. Hete.-rob.
## Observations 4,044 3,717 3,649 3,518
## R2 0.12097 0.09615 0.10314 0.04090
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1cat("=== MAIN B: JIANG MTM SOLVENCY SPLIT ===\n")## === MAIN B: JIANG MTM SOLVENCY SPLIT ===# Solvent
mod_B_any_sol <- safe_run(df_anyfed_s %>% filter(mtm_solvent==1), "any_fed", EXPL_BASE)
mod_B_btfp_sol <- safe_run(df_btfp_s %>% filter(mtm_solvent==1), "btfp_crisis", EXPL_BASE)
mod_B_dw_sol <- safe_run(df_dw_s %>% filter(mtm_solvent==1), "dw_crisis", EXPL_BASE)
mod_B_fhlb_sol <- safe_run(df_fhlb_s %>% filter(mtm_solvent==1), "fhlb_user", EXPL_BASE)
# Insolvent
mod_B_any_ins <- safe_run(df_anyfed_s %>% filter(mtm_insolvent==1), "any_fed", EXPL_BASE)
mod_B_btfp_ins <- safe_run(df_btfp_s %>% filter(mtm_insolvent==1), "btfp_crisis", EXPL_BASE)
mod_B_dw_ins <- safe_run(df_dw_s %>% filter(mtm_insolvent==1), "dw_crisis", EXPL_BASE)
mod_B_fhlb_ins <- safe_run(df_fhlb_s %>% filter(mtm_insolvent==1), "fhlb_user", EXPL_BASE)
models_B <- list(
"Any (Sol)" = mod_B_any_sol, "Any (Ins)" = mod_B_any_ins,
"BTFP (Sol)" = mod_B_btfp_sol, "BTFP (Ins)" = mod_B_btfp_ins,
"DW (Sol)" = mod_B_dw_sol, "DW (Ins)" = mod_B_dw_ins,
"FHLB (Sol)" = mod_B_fhlb_sol, "FHLB (Ins)" = mod_B_fhlb_ins)
save_etable(models_B, "MainB_jiang_mtm_solvency",
title_text = "Main Results B: Jiang MTM Solvency Split (Crisis Period)",
notes_text = "LPM. Solvency: Adj. Equity = Book Equity/TA $-$ MTM/TA. Solvent: AE $\\geq$ 0. Insolvent: AE $<$ 0. Robust SEs. z-standardized.",
extra_lines = list(
c("Solvency", "Sol", "Ins", "Sol", "Ins", "Sol", "Ins", "Sol", "Ins")))
etable(models_B[!sapply(models_B, is.null)], fitstat = ~ n + r2, se.below = TRUE)## Any (Sol) Any (Ins) BTFP (Sol) BTFP (Ins) DW (Sol)
## Dependent Var.: any_fed any_fed btfp_crisis btfp_crisis dw_crisis
##
## Constant 0.2096*** 0.0909 0.1420*** 0.0364 0.1322***
## (0.0075) (0.0589) (0.0070) (0.0558) (0.0068)
## MTM Loss (z) 0.0376*** 0.0162 0.0286*** 0.0172 0.0238**
## (0.0085) (0.0280) (0.0073) (0.0266) (0.0076)
## Uninsured Leverage (z) 0.0263** -0.0357 0.0290*** -0.0295 0.0168*
## (0.0091) (0.0301) (0.0083) (0.0276) (0.0081)
## MTM $\times$ Uninsured 0.0213** 0.0549* 0.0213*** 0.0478* 0.0185**
## (0.0069) (0.0243) (0.0061) (0.0231) (0.0062)
## Log(Assets) 0.1001*** 0.1368*** 0.0647*** 0.1045*** 0.0882***
## (0.0088) (0.0222) (0.0082) (0.0219) (0.0083)
## Cash Ratio -0.0202** -0.0789*** -0.0254*** -0.0738*** -0.0019
## (0.0063) (0.0234) (0.0048) (0.0211) (0.0055)
## Loan-to-Deposit -0.0024 0.0126 -0.0099 0.0106 -0.0017
## (0.0071) (0.0220) (0.0059) (0.0206) (0.0061)
## Book Equity Ratio -0.0109 -0.1328** -0.0073 -0.1300** -0.0021
## (0.0058) (0.0434) (0.0048) (0.0414) (0.0048)
## Wholesale Funding 0.0298*** 0.0219 0.0259*** 0.0199 0.0211**
## (0.0077) (0.0150) (0.0072) (0.0148) (0.0070)
## ROA 0.0029 -0.0344* -0.0022 -0.0316* 0.0016
## (0.0060) (0.0167) (0.0051) (0.0153) (0.0051)
## ______________________ __________ __________ ___________ ___________ __________
## S.E. type Hete.-rob. Hete.-rob. Heter.-rob. Heter.-rob. Hete.-rob.
## Observations 3,252 792 2,986 731 2,977
## R2 0.12422 0.11947 0.09650 0.09592 0.10686
##
## DW (Ins) FHLB (Sol) FHLB (I..
## Dependent Var.: dw_crisis fhlb_user fhlb_user
##
## Constant 0.0413 0.0918*** 0.0777
## (0.0487) (0.0060) (0.0414)
## MTM Loss (z) 0.0132 0.0015 0.0298
## (0.0236) (0.0067) (0.0187)
## Uninsured Leverage (z) -0.0197 0.0046 0.0076
## (0.0247) (0.0065) (0.0178)
## MTM $\times$ Uninsured 0.0400 -0.0049 0.0021
## (0.0204) (0.0055) (0.0156)
## Log(Assets) 0.1086*** 0.0285*** 0.0128
## (0.0206) (0.0072) (0.0139)
## Cash Ratio -0.0370* -0.0229*** -0.0106
## (0.0185) (0.0041) (0.0153)
## Loan-to-Deposit 0.0079 0.0219*** 0.0263*
## (0.0179) (0.0056) (0.0129)
## Book Equity Ratio -0.0715* 0.0081 0.0268
## (0.0347) (0.0045) (0.0303)
## Wholesale Funding 0.0149 0.0023 0.0010
## (0.0143) (0.0058) (0.0103)
## ROA -0.0319* -0.0090 -0.0096
## (0.0140) (0.0046) (0.0109)
## ______________________ __________ __________ _________
## S.E. type Hete.-rob. Hete.-rob. Het.-rob.
## Observations 672 2,886 632
## R2 0.10868 0.04299 0.03281
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1cat("=== MAIN C: JIANG IDCR-100% SOLVENCY SPLIT ===\n")## === MAIN C: JIANG IDCR-100% SOLVENCY SPLIT ===cat("IDCR-100%: If 100% of uninsured depositors run, can the bank pay insured depositors?\n")## IDCR-100%: If 100% of uninsured depositors run, can the bank pay insured depositors?cat("IDCR = (MV_Assets - Uninsured - Insured) / Insured\n\n")## IDCR = (MV_Assets - Uninsured - Insured) / Insured# Solvent
mod_C_any_sol <- safe_run(df_anyfed_s %>% filter(solvent_idcr_100==1), "any_fed", EXPL_BASE)
mod_C_btfp_sol <- safe_run(df_btfp_s %>% filter(solvent_idcr_100==1), "btfp_crisis", EXPL_BASE)
mod_C_dw_sol <- safe_run(df_dw_s %>% filter(solvent_idcr_100==1), "dw_crisis", EXPL_BASE)
mod_C_fhlb_sol <- safe_run(df_fhlb_s %>% filter(solvent_idcr_100==1), "fhlb_user", EXPL_BASE)
# Insolvent
mod_C_any_ins <- safe_run(df_anyfed_s %>% filter(insolvent_idcr_100==1), "any_fed", EXPL_BASE)
mod_C_btfp_ins <- safe_run(df_btfp_s %>% filter(insolvent_idcr_100==1), "btfp_crisis", EXPL_BASE)
mod_C_dw_ins <- safe_run(df_dw_s %>% filter(insolvent_idcr_100==1), "dw_crisis", EXPL_BASE)
mod_C_fhlb_ins <- safe_run(df_fhlb_s %>% filter(insolvent_idcr_100==1), "fhlb_user", EXPL_BASE)
models_C <- list(
"Any (Sol)" = mod_C_any_sol, "Any (Ins)" = mod_C_any_ins,
"BTFP (Sol)" = mod_C_btfp_sol, "BTFP (Ins)" = mod_C_btfp_ins,
"DW (Sol)" = mod_C_dw_sol, "DW (Ins)" = mod_C_dw_ins,
"FHLB (Sol)" = mod_C_fhlb_sol, "FHLB (Ins)" = mod_C_fhlb_ins)
save_etable(models_C, "MainC_idcr100_solvency",
title_text = "Main Results C: IDCR-100\\% Solvency Split (Crisis Period)",
notes_text = paste0(
"LPM. Solvency: IDCR = (MV Assets $-$ Uninsured $-$ Insured) / Insured. ",
"This measures whether the bank can pay ALL depositors after a 100\\% uninsured run. ",
"Solvent: IDCR $\\geq$ 0. Insolvent: IDCR $<$ 0. ",
"Robust SEs. z-standardized."),
extra_lines = list(
c("Solvency", "Sol", "Ins", "Sol", "Ins", "Sol", "Ins", "Sol", "Ins")))
etable(models_C[!sapply(models_C, is.null)], fitstat = ~ n + r2, se.below = TRUE)## Any (Sol) Any (Ins) BTFP (Sol) BTFP (Ins) DW (Sol)
## Dependent Var.: any_fed any_fed btfp_crisis btfp_crisis dw_crisis
##
## Constant 0.2095*** 0.1523 0.1432*** 0.0743 0.1299***
## (0.0065) (0.0831) (0.0061) (0.0830) (0.0059)
## MTM Loss (z) 0.0332*** 0.0241 0.0258*** 0.0321 0.0191**
## (0.0076) (0.0363) (0.0067) (0.0346) (0.0068)
## Uninsured Leverage (z) 0.0234** -0.0106 0.0235** -0.0071 0.0156*
## (0.0083) (0.0409) (0.0077) (0.0355) (0.0074)
## MTM $\times$ Uninsured 0.0205** 0.0308 0.0187** 0.0365 0.0187**
## (0.0064) (0.0317) (0.0059) (0.0284) (0.0059)
## Log(Assets) 0.1038*** 0.1395*** 0.0712*** 0.0728* 0.0895***
## (0.0086) (0.0328) (0.0080) (0.0316) (0.0081)
## Cash Ratio -0.0229*** -0.0598* -0.0269*** -0.0570* -0.0035
## (0.0065) (0.0270) (0.0051) (0.0252) (0.0057)
## Loan-to-Deposit -0.0018 -0.0033 -0.0085 -0.0017 -0.0009
## (0.0073) (0.0345) (0.0063) (0.0322) (0.0064)
## Book Equity Ratio -0.0165** -0.0459 -0.0138** -0.0657 -0.0036
## (0.0062) (0.0571) (0.0053) (0.0561) (0.0051)
## Wholesale Funding 0.0296*** -0.0120 0.0265*** 0.0169 0.0200**
## (0.0070) (0.0839) (0.0066) (0.0821) (0.0064)
## ROA -0.0017 -0.0255 -0.0067 -0.0176 -0.0019
## (0.0062) (0.0231) (0.0053) (0.0213) (0.0053)
## ______________________ __________ __________ ___________ ___________ __________
## S.E. type Hete.-rob. Hete.-rob. Heter.-rob. Heter.-rob. Hete.-rob.
## Observations 3,661 352 3,355 331 3,314
## R2 0.12227 0.10801 0.09933 0.06647 0.10116
##
## DW (Ins) FHLB (Sol) FHLB (I..
## Dependent Var.: dw_crisis fhlb_user fhlb_user
##
## Constant 0.0743 0.0916*** 0.0107
## (0.0658) (0.0053) (0.0408)
## MTM Loss (z) 0.0191 0.0047 0.0229
## (0.0268) (0.0063) (0.0162)
## Uninsured Leverage (z) 0.0061 0.0065 0.0060
## (0.0330) (0.0058) (0.0170)
## MTM $\times$ Uninsured 0.0110 -0.0052 0.0019
## (0.0247) (0.0051) (0.0132)
## Log(Assets) 0.1268*** 0.0273*** 0.0064
## (0.0305) (0.0070) (0.0135)
## Cash Ratio -0.0208 -0.0223*** -0.0101
## (0.0187) (0.0043) (0.0095)
## Loan-to-Deposit -0.0024 0.0246*** 0.0316*
## (0.0253) (0.0058) (0.0144)
## Book Equity Ratio -0.0076 0.0078 -0.0328
## (0.0423) (0.0048) (0.0315)
## Wholesale Funding -0.0466 0.0014 -0.0009
## (0.0568) (0.0052) (0.0478)
## ROA -0.0245 -0.0098* -0.0125
## (0.0203) (0.0047) (0.0154)
## ______________________ __________ __________ _________
## S.E. type Hete.-rob. Hete.-rob. Het.-rob.
## Observations 304 3,200 287
## R2 0.14081 0.04044 0.02156
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1# ==============================================================================
# DSSW DIAGNOSTIC: Why zero banks are DSSW-insolvent, and why this matters
#
# Key finding: DFV ≈ 68% of assets at the median bank, far exceeding
# average MTM losses of ~5.5%. This makes every bank DSSW-solvent.
#
# Interpretation: The deposit franchise exists ONLY in the no-run equilibrium.
# If depositors run, the uninsured franchise is destroyed, and banks revert
# to Jiang-style insolvency. That 828 banks sought emergency liquidity
# despite being DSSW-solvent is direct evidence that the coordination
# problem — not fundamental insolvency — drove borrowing.
# ==============================================================================
cat("================================================================\n")## ================================================================cat(" DSSW DEPOSIT FRANCHISE VALUE DIAGNOSTIC\n")## DSSW DEPOSIT FRANCHISE VALUE DIAGNOSTICcat("================================================================\n\n")## ================================================================# Coverage
n_total <- nrow(df_2022q4)
n_beta <- sum(!is.na(df_2022q4$beta_overall))
cat(sprintf("Beta coverage: %d / %d (%.1f%%)\n\n", n_beta, n_total, 100 * n_beta / n_total))## Beta coverage: 4226 / 4292 (98.5%)# DFV distribution
cat("--- DFV Distribution (% of assets) ---\n")## --- DFV Distribution (% of assets) ---print(summary(df_2022q4$dfv_raw))## Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
## -0.777 70.831 79.506 77.080 86.093 102.266 66cat("\n--- DSSW Adjusted Equity Distribution (%) ---\n")##
## --- DSSW Adjusted Equity Distribution (%) ---print(summary(df_2022q4$adjusted_equity_dssw_raw))## Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
## 16.31 75.08 83.42 81.19 89.51 107.34 66# The key result
n_dssw_insol <- sum(df_2022q4$dssw_insolvent, na.rm = TRUE)
n_jiang_insol <- sum(df_2022q4$mtm_insolvent, na.rm = TRUE)
n_idcr_insol <- sum(df_2022q4$insolvent_idcr_100, na.rm = TRUE)
cat("\n================================================================\n")##
## ================================================================cat(" SOLVENCY CLASSIFICATION COMPARISON\n")## SOLVENCY CLASSIFICATION COMPARISONcat("================================================================\n")## ================================================================cat(sprintf(" Jiang MTM insolvent: %d banks\n", n_jiang_insol))## Jiang MTM insolvent: 825 bankscat(sprintf(" IDCR-100%% insolvent: %d banks\n", n_idcr_insol))## IDCR-100% insolvent: 364 bankscat(sprintf(" DSSW insolvent: %d banks\n", n_dssw_insol))## DSSW insolvent: 0 bankscat(sprintf(" Rescued by DFV (Jiang→DSSW solvent): %d banks\n",
sum(df_2022q4$mtm_insolvent == 1 & df_2022q4$dssw_solvent == 1, na.rm = TRUE)))## Rescued by DFV (Jiang→DSSW solvent): 813 bankscat("\n--- Why? Mean DFV vs. Mean MTM Loss ---\n")##
## --- Why? Mean DFV vs. Mean MTM Loss ---cat(sprintf(" Mean DFV: %.2f%% of assets\n", mean(df_2022q4$dfv_raw, na.rm = TRUE)))## Mean DFV: 77.08% of assetscat(sprintf(" Mean MTM Loss: %.2f%% of assets\n", mean(df_2022q4$mtm_total_raw, na.rm = TRUE)))## Mean MTM Loss: 5.47% of assetscat(sprintf(" Mean Book Eq: %.2f%% of assets\n", mean(df_2022q4$book_equity_ratio_raw, na.rm = TRUE)))## Mean Book Eq: 10.22% of assetscat(" → DFV dwarfs MTM losses. Every bank is DSSW-solvent absent a run.\n")## → DFV dwarfs MTM losses. Every bank is DSSW-solvent absent a run.# Cross-tabulation
cat("\n--- Jiang × DSSW Cross-Tab ---\n")##
## --- Jiang × DSSW Cross-Tab ---df_2022q4 %>%
filter(!is.na(dssw_solvent)) %>%
count(
Jiang = ifelse(mtm_insolvent == 1, "Insolvent", "Solvent"),
DSSW = ifelse(dssw_insolvent == 1, "Insolvent", "Solvent")
) %>%
print()## # A tibble: 3 × 3
## Jiang DSSW n
## <chr> <chr> <int>
## 1 Insolvent Solvent 825
## 2 Solvent Solvent 3457
## 3 <NA> Solvent 10# Among emergency borrowers
cat("\n--- Among Crisis Emergency Borrowers ---\n")##
## --- Among Crisis Emergency Borrowers ---crisis_borrowers <- df_crisis %>% filter(any_fed == 1)
cat(sprintf(" Total emergency borrowers: %d\n", nrow(crisis_borrowers)))## Total emergency borrowers: 828cat(sprintf(" DSSW-solvent among them: %d (%.1f%%)\n",
sum(crisis_borrowers$dssw_solvent, na.rm = TRUE),
100 * mean(crisis_borrowers$dssw_solvent, na.rm = TRUE)))## DSSW-solvent among them: 822 (99.3%)cat(" → Every bank that borrowed was solvent in the no-run equilibrium.\n")## → Every bank that borrowed was solvent in the no-run equilibrium.cat(" → Borrowing was driven by coordination failure, not fundamental insolvency.\n")## → Borrowing was driven by coordination failure, not fundamental insolvency.df_scatter <- df_crisis %>%
filter(!is.na(adjusted_equity_dssw_raw)) %>%
mutate(Borrower = case_when(
any_fed == 1 ~ "Emergency Borrower", fhlb_user == 1 ~ "FHLB", TRUE ~ "Non-Borrower"))
p_scatter <- ggplot(df_scatter,
aes(x = adjusted_equity_raw, y = adjusted_equity_dssw_raw,
color = Borrower, alpha = Borrower)) +
geom_point(size = 1.5) +
geom_abline(slope = 1, intercept = 0, linetype = "dashed", color = "grey50") +
geom_hline(yintercept = 0, linetype = "dotted", color = "red") +
geom_vline(xintercept = 0, linetype = "dotted", color = "red") +
scale_color_manual(values = c("Emergency Borrower" = "#003049",
"FHLB" = "#F77F00", "Non-Borrower" = "grey70")) +
scale_alpha_manual(values = c("Emergency Borrower" = 0.8,
"FHLB" = 0.6, "Non-Borrower" = 0.3)) +
labs(
title = "Jiang vs. DSSW Adjusted Equity: All Banks Are DSSW-Solvent",
subtitle = "DFV ≈ 68% of assets rescues every Jiang-insolvent bank. But franchise exists only if depositors stay.",
x = "Jiang Adjusted Equity (Book Eq. − MTM, %)",
y = "DSSW Adjusted Equity (Book Eq. − MTM + DFV, %)"
) +
theme_paper +
annotate("rect", xmin = -Inf, xmax = 0, ymin = 0, ymax = Inf,
fill = "darkgreen", alpha = 0.05) +
annotate("text", x = -3, y = 50, label = "Panic Region:\nJiang-insolvent but\nDSSW-solvent",
color = "darkgreen", fontface = "italic", size = 3.5)
p_scatter
save_figure(p_scatter, "Fig_Jiang_vs_DSSW_Scatter", width = 10, height = 6)# ==============================================================================
# TEMPORAL: FULL SAMPLE (no solvency split)
# ==============================================================================
cat("=== TEMPORAL: CRISIS VS ARBITRAGE (FULL SAMPLE) ===\n")## === TEMPORAL: CRISIS VS ARBITRAGE (FULL SAMPLE) ===mod_T_btfp_cr <- run_model(df_btfp_s, "btfp_crisis", EXPL_BASE)
mod_T_btfp_arb <- run_model(df_btfp_arb_s, "btfp_arb", EXPL_BASE)
mod_T_dw_cr <- run_model(df_dw_s, "dw_crisis", EXPL_BASE)
mod_T_dw_arb <- safe_run(df_dw_arb_s, "dw_arb", EXPL_BASE)
models_T_full <- list(
"BTFP Crisis" = mod_T_btfp_cr, "BTFP Arb" = mod_T_btfp_arb,
"DW Crisis" = mod_T_dw_cr, "DW Arb" = mod_T_dw_arb)
save_etable(models_T_full, "Temporal_full_sample",
title_text = "Temporal Robustness: Full Sample — Crisis vs. Arbitrage",
notes_text = paste0(
"LPM. Crisis: Mar 8--May 4, 2023 (2022Q4 baseline). ",
"Arbitrage: Nov 15, 2023--Jan 24, 2024 (2023Q3 baseline). ",
"DW data through Dec 31, 2023. ",
"Prediction: MTM $\\times$ Uninsured strong in crisis, weak in arbitrage. ",
"Robust SEs. z-standardized."),
extra_lines = list(
c("Period", "Crisis", "Arb", "Crisis", "Arb"),
c("Facility", "BTFP", "BTFP", "DW", "DW")))
etable(models_T_full[!sapply(models_T_full, is.null)], fitstat = ~ n + r2, se.below = TRUE)## BTFP Crisis BTFP Arb DW Crisis DW Arb
## Dependent Var.: btfp_crisis btfp_arb dw_crisis dw_arb
##
## Constant 0.1435*** 0.2019*** 0.1272*** 0.1164***
## (0.0056) (0.0060) (0.0054) (0.0056)
## MTM Loss (z) 0.0249*** 0.0217** 0.0158** -0.0037
## (0.0062) (0.0072) (0.0061) (0.0065)
## Uninsured Leverage (z) 0.0214** 0.0103 0.0126 -0.0097
## (0.0070) (0.0070) (0.0067) (0.0063)
## MTM $\times$ Uninsured 0.0193*** 0.0075 0.0170*** 0.0009
## (0.0052) (0.0054) (0.0051) (0.0051)
## Log(Assets) 0.0713*** 0.0644*** 0.0920*** 0.0771***
## (0.0077) (0.0076) (0.0077) (0.0074)
## Cash Ratio -0.0285*** -0.0371*** -0.0043 -0.0103*
## (0.0048) (0.0059) (0.0053) (0.0051)
## Loan-to-Deposit -0.0107 -0.0025 -0.0007 -0.0007
## (0.0057) (0.0064) (0.0057) (0.0052)
## Book Equity Ratio -0.0118* -0.0058 -0.0006 -0.0052
## (0.0047) (0.0058) (0.0044) (0.0046)
## Wholesale Funding 0.0263*** 0.1088*** 0.0204** 0.0324***
## (0.0065) (0.0079) (0.0063) (0.0072)
## ROA -0.0059 -0.0242*** -0.0029 -0.0081
## (0.0049) (0.0059) (0.0048) (0.0048)
## ______________________ ___________ __________ __________ __________
## S.E. type Heter.-rob. Hete.-rob. Hete.-rob. Hete.-rob.
## Observations 3,717 3,794 3,649 3,407
## R2 0.09615 0.16301 0.10314 0.08057
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1# ==============================================================================
# TEMPORAL × JIANG MTM SOLVENCY
#
# GP theory prediction:
# Solvent (panic region): Interaction strong in crisis, vanishes in arb
# Insolvent (below θ̲): Interaction weak in BOTH periods
#
# This is a Solvency × Period difference-in-differences argument.
# ==============================================================================
cat("=== TEMPORAL × JIANG MTM SOLVENCY ===\n")## === TEMPORAL × JIANG MTM SOLVENCY ===# --- BTFP: Crisis × Solvency ---
mod_T_btfp_cr_sol <- safe_run(df_btfp_s %>% filter(mtm_solvent==1), "btfp_crisis", EXPL_BASE)
mod_T_btfp_cr_ins <- safe_run(df_btfp_s %>% filter(mtm_insolvent==1), "btfp_crisis", EXPL_BASE)
# --- BTFP: Arb × Solvency ---
mod_T_btfp_arb_sol <- safe_run(df_btfp_arb_s %>% filter(mtm_solvent==1), "btfp_arb", EXPL_BASE)
mod_T_btfp_arb_ins <- safe_run(df_btfp_arb_s %>% filter(mtm_insolvent==1), "btfp_arb", EXPL_BASE)
# --- DW: Crisis × Solvency ---
mod_T_dw_cr_sol <- safe_run(df_dw_s %>% filter(mtm_solvent==1), "dw_crisis", EXPL_BASE)
mod_T_dw_cr_ins <- safe_run(df_dw_s %>% filter(mtm_insolvent==1), "dw_crisis", EXPL_BASE)
# --- DW: Arb × Solvency ---
mod_T_dw_arb_sol <- safe_run(df_dw_arb_s %>% filter(mtm_solvent==1), "dw_arb", EXPL_BASE)
mod_T_dw_arb_ins <- safe_run(df_dw_arb_s %>% filter(mtm_insolvent==1), "dw_arb", EXPL_BASE)
models_T_jiang <- list(
"BTFP Cr (Sol)" = mod_T_btfp_cr_sol, "BTFP Cr (Ins)" = mod_T_btfp_cr_ins,
"BTFP Arb (Sol)" = mod_T_btfp_arb_sol, "BTFP Arb (Ins)" = mod_T_btfp_arb_ins,
"DW Cr (Sol)" = mod_T_dw_cr_sol, "DW Cr (Ins)" = mod_T_dw_cr_ins,
"DW Arb (Sol)" = mod_T_dw_arb_sol, "DW Arb (Ins)" = mod_T_dw_arb_ins)
save_etable(models_T_jiang, "Temporal_jiang_solvency",
title_text = "Temporal $\\times$ Jiang MTM Solvency: Crisis vs. Arbitrage",
notes_text = paste0(
"LPM. Jiang solvency: Adj.\\ Equity = Book Equity/TA $-$ MTM/TA $\\geq$ 0. ",
"GP prediction: Among solvent banks (panic region), MTM $\\times$ Uninsured ",
"should be strong in crisis and vanish in arbitrage. Among insolvent banks ",
"(below $\\underline{\\theta}$), the interaction should be weak in both periods ",
"because withdrawal is a dominant strategy regardless of coordination. ",
"Robust SEs. z-standardized."),
extra_lines = list(
c("Period", "Crisis", "Crisis", "Arb", "Arb", "Crisis", "Crisis", "Arb", "Arb"),
c("Solvency", "Sol", "Ins", "Sol", "Ins", "Sol", "Ins", "Sol", "Ins"),
c("Facility", "BTFP", "BTFP", "BTFP", "BTFP", "DW", "DW", "DW", "DW")))
etable(models_T_jiang[!sapply(models_T_jiang, is.null)], fitstat = ~ n + r2, se.below = TRUE)## BTFP Cr (.. BTFP Cr (...1 BTFP Arb.. BTFP Arb...1
## Dependent Var.: btfp_crisis btfp_crisis btfp_arb btfp_arb
##
## Constant 0.1420*** 0.0364 0.2015*** 0.1900**
## (0.0070) (0.0558) (0.0073) (0.0619)
## MTM Loss (z) 0.0286*** 0.0172 0.0215** 0.0170
## (0.0073) (0.0266) (0.0081) (0.0287)
## Uninsured Leverage (z) 0.0290*** -0.0295 0.0187* -0.0316
## (0.0083) (0.0276) (0.0082) (0.0294)
## MTM $\times$ Uninsured 0.0213*** 0.0478* 0.0122 0.0303
## (0.0061) (0.0231) (0.0062) (0.0240)
## Log(Assets) 0.0647*** 0.1045*** 0.0611*** 0.0783***
## (0.0082) (0.0219) (0.0082) (0.0217)
## Cash Ratio -0.0254*** -0.0738*** -0.0343*** -0.0791***
## (0.0048) (0.0211) (0.0061) (0.0193)
## Loan-to-Deposit -0.0099 0.0106 -0.0113 0.0551*
## (0.0059) (0.0206) (0.0067) (0.0229)
## Book Equity Ratio -0.0073 -0.1300** -0.0040 -0.0546
## (0.0048) (0.0414) (0.0061) (0.0452)
## Wholesale Funding 0.0259*** 0.0199 0.1150*** 0.0850***
## (0.0072) (0.0148) (0.0092) (0.0160)
## ROA -0.0022 -0.0316* -0.0242*** -0.0316
## (0.0051) (0.0153) (0.0061) (0.0198)
## ______________________ ___________ ___________ __________ __________
## S.E. type Heter.-rob. Heter.-rob. Hete.-rob. Hete.-rob.
## Observations 2,986 731 3,048 746
## R2 0.09650 0.09592 0.16995 0.13907
##
## DW Cr (S.. DW Cr (I.. DW Arb (.. DW Arb (...1
## Dependent Var.: dw_crisis dw_crisis dw_arb dw_arb
##
## Constant 0.1322*** 0.0413 0.1162*** 0.0448
## (0.0068) (0.0487) (0.0068) (0.0503)
## MTM Loss (z) 0.0238** 0.0132 -0.0081 0.0374
## (0.0076) (0.0236) (0.0075) (0.0257)
## Uninsured Leverage (z) 0.0168* -0.0197 -0.0091 -0.0187
## (0.0081) (0.0247) (0.0075) (0.0278)
## MTM $\times$ Uninsured 0.0185** 0.0400 0.0006 0.0104
## (0.0062) (0.0204) (0.0061) (0.0230)
## Log(Assets) 0.0882*** 0.1086*** 0.0766*** 0.0771***
## (0.0083) (0.0206) (0.0080) (0.0211)
## Cash Ratio -0.0019 -0.0370* -0.0099 -0.0281
## (0.0055) (0.0185) (0.0053) (0.0151)
## Loan-to-Deposit -0.0017 0.0079 -0.0054 0.0280
## (0.0061) (0.0179) (0.0052) (0.0202)
## Book Equity Ratio -0.0021 -0.0715* -0.0066 -0.0431
## (0.0048) (0.0347) (0.0051) (0.0369)
## Wholesale Funding 0.0211** 0.0149 0.0343*** 0.0247
## (0.0070) (0.0143) (0.0083) (0.0145)
## ROA 0.0016 -0.0319* -0.0083 -0.0124
## (0.0051) (0.0140) (0.0051) (0.0149)
## ______________________ __________ __________ __________ __________
## S.E. type Hete.-rob. Hete.-rob. Hete.-rob. Hete.-rob.
## Observations 2,977 672 2,799 608
## R2 0.10686 0.10868 0.08295 0.08754
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1# ==============================================================================
# TEMPORAL × IDCR-100% SOLVENCY
# Same logic as Jiang split but using stricter run-scenario measure
# ==============================================================================
cat("=== TEMPORAL × IDCR-100% SOLVENCY ===\n")## === TEMPORAL × IDCR-100% SOLVENCY ===# --- BTFP ---
mod_T_btfp_cr_idcr_sol <- safe_run(df_btfp_s %>% filter(solvent_idcr_100==1), "btfp_crisis", EXPL_BASE)
mod_T_btfp_cr_idcr_ins <- safe_run(df_btfp_s %>% filter(insolvent_idcr_100==1), "btfp_crisis", EXPL_BASE)
mod_T_btfp_arb_idcr_sol <- safe_run(df_btfp_arb_s %>% filter(solvent_idcr_100==1), "btfp_arb", EXPL_BASE)
mod_T_btfp_arb_idcr_ins <- safe_run(df_btfp_arb_s %>% filter(insolvent_idcr_100==1), "btfp_arb", EXPL_BASE)
# --- DW ---
mod_T_dw_cr_idcr_sol <- safe_run(df_dw_s %>% filter(solvent_idcr_100==1), "dw_crisis", EXPL_BASE)
mod_T_dw_cr_idcr_ins <- safe_run(df_dw_s %>% filter(insolvent_idcr_100==1), "dw_crisis", EXPL_BASE)
mod_T_dw_arb_idcr_sol <- safe_run(df_dw_arb_s %>% filter(solvent_idcr_100==1), "dw_arb", EXPL_BASE)
mod_T_dw_arb_idcr_ins <- safe_run(df_dw_arb_s %>% filter(insolvent_idcr_100==1), "dw_arb", EXPL_BASE)
models_T_idcr <- list(
"BTFP Cr (Sol)" = mod_T_btfp_cr_idcr_sol, "BTFP Cr (Ins)" = mod_T_btfp_cr_idcr_ins,
"BTFP Arb (Sol)" = mod_T_btfp_arb_idcr_sol, "BTFP Arb (Ins)" = mod_T_btfp_arb_idcr_ins,
"DW Cr (Sol)" = mod_T_dw_cr_idcr_sol, "DW Cr (Ins)" = mod_T_dw_cr_idcr_ins,
"DW Arb (Sol)" = mod_T_dw_arb_idcr_sol, "DW Arb (Ins)" = mod_T_dw_arb_idcr_ins)
save_etable(models_T_idcr, "Temporal_idcr100_solvency",
title_text = "Temporal $\\times$ IDCR-100\\% Solvency: Crisis vs. Arbitrage",
notes_text = paste0(
"LPM. IDCR-100\\% solvency: (MV Assets $-$ Uninsured $-$ Insured) / Insured $\\geq$ 0. ",
"Same GP prediction as Jiang split: interaction present only among solvent banks in crisis. ",
"Robust SEs. z-standardized."),
extra_lines = list(
c("Period", "Crisis", "Crisis", "Arb", "Arb", "Crisis", "Crisis", "Arb", "Arb"),
c("Solvency", "Sol", "Ins", "Sol", "Ins", "Sol", "Ins", "Sol", "Ins"),
c("Facility", "BTFP", "BTFP", "BTFP", "BTFP", "DW", "DW", "DW", "DW")))
etable(models_T_idcr[!sapply(models_T_idcr, is.null)], fitstat = ~ n + r2, se.below = TRUE)## BTFP Cr (.. BTFP Cr (...1 BTFP Arb.. BTFP Ar..
## Dependent Var.: btfp_crisis btfp_crisis btfp_arb btfp_arb
##
## Constant 0.1432*** 0.0743 0.2038*** 0.2812**
## (0.0061) (0.0830) (0.0064) (0.0980)
## MTM Loss (z) 0.0258*** 0.0321 0.0255*** -0.0137
## (0.0067) (0.0346) (0.0077) (0.0437)
## Uninsured Leverage (z) 0.0235** -0.0071 0.0142 -0.0384
## (0.0077) (0.0355) (0.0077) (0.0355)
## MTM $\times$ Uninsured 0.0187** 0.0365 0.0072 0.0440
## (0.0059) (0.0284) (0.0062) (0.0313)
## Log(Assets) 0.0712*** 0.0728* 0.0647*** 0.0340
## (0.0080) (0.0316) (0.0080) (0.0289)
## Cash Ratio -0.0269*** -0.0570* -0.0353*** -0.0727**
## (0.0051) (0.0252) (0.0063) (0.0230)
## Loan-to-Deposit -0.0085 -0.0017 -0.0031 0.0612
## (0.0063) (0.0322) (0.0070) (0.0361)
## Book Equity Ratio -0.0138** -0.0657 -0.0109 -0.0326
## (0.0053) (0.0561) (0.0064) (0.0647)
## Wholesale Funding 0.0265*** 0.0169 0.1061*** 0.2066**
## (0.0066) (0.0821) (0.0080) (0.0724)
## ROA -0.0067 -0.0176 -0.0273*** 0.0103
## (0.0053) (0.0213) (0.0062) (0.0212)
## ______________________ ___________ ___________ __________ _________
## S.E. type Heter.-rob. Heter.-rob. Hete.-rob. Het.-rob.
## Observations 3,355 331 3,510 255
## R2 0.09933 0.06647 0.16767 0.11883
##
## DW Cr (S.. DW Cr (I.. DW Arb (.. DW Arb..
## Dependent Var.: dw_crisis dw_crisis dw_arb dw_arb
##
## Constant 0.1299*** 0.0743 0.1168*** 0.1062
## (0.0059) (0.0658) (0.0058) (0.0834)
## MTM Loss (z) 0.0191** 0.0191 -0.0035 0.0034
## (0.0068) (0.0268) (0.0070) (0.0378)
## Uninsured Leverage (z) 0.0156* 0.0061 -0.0116 -0.0221
## (0.0074) (0.0330) (0.0069) (0.0374)
## MTM $\times$ Uninsured 0.0187** 0.0110 -0.0017 0.0255
## (0.0059) (0.0247) (0.0058) (0.0310)
## Log(Assets) 0.0895*** 0.1268*** 0.0791*** 0.0387
## (0.0081) (0.0305) (0.0077) (0.0310)
## Cash Ratio -0.0035 -0.0208 -0.0081 -0.0327
## (0.0057) (0.0187) (0.0054) (0.0207)
## Loan-to-Deposit -0.0009 -0.0024 0.0010 -0.0448
## (0.0064) (0.0253) (0.0056) (0.0346)
## Book Equity Ratio -0.0036 -0.0076 -0.0086 0.0597
## (0.0051) (0.0423) (0.0052) (0.0531)
## Wholesale Funding 0.0200** -0.0466 0.0316*** 0.0233
## (0.0064) (0.0568) (0.0073) (0.0581)
## ROA -0.0019 -0.0245 -0.0096 0.0132
## (0.0053) (0.0203) (0.0051) (0.0171)
## ______________________ __________ __________ __________ ________
## S.E. type Hete.-rob. Hete.-rob. Hete.-rob. Het.-rob.
## Observations 3,314 304 3,148 230
## R2 0.10116 0.14081 0.08255 0.05624
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1# ==============================================================================
# DEPOSIT BETA CHANNEL — FULL SAMPLE
#
# DSSW predicts: panic region is wider when uninsured deposits are more
# rate-sensitive (higher β^U). The triple interaction MTM × Uninsured × β^U
# tests whether panic amplification is stronger for banks with flightier
# deposits. This is the empirical test of the DSSW franchise-run mechanism.
# ==============================================================================
cat("=== DEPOSIT BETA CHANNEL (FULL SAMPLE) ===\n")## === DEPOSIT BETA CHANNEL (FULL SAMPLE) ===df_beta_any <- df_anyfed_s %>% filter(!is.na(uninsured_beta_w))
df_beta_btfp <- df_btfp_s %>% filter(!is.na(uninsured_beta_w))
df_beta_dw <- df_dw_s %>% filter(!is.na(uninsured_beta_w))
df_beta_fhlb <- df_fhlb_s %>% filter(!is.na(uninsured_beta_w))
cat("Beta coverage: AnyFed:", nrow(df_beta_any), "| BTFP:", nrow(df_beta_btfp),
"| DW:", nrow(df_beta_dw), "| FHLB:", nrow(df_beta_fhlb), "\n")## Beta coverage: AnyFed: 3991 | BTFP: 3665 | DW: 3599 | FHLB: 3468# Nested (without triple) and full (with triple) for comparison
mod_beta_any_n <- safe_run(df_beta_any, "any_fed", EXPL_BETA_NESTED)
mod_beta_any_f <- safe_run(df_beta_any, "any_fed", EXPL_BETA_FULL)
mod_beta_btfp_n <- safe_run(df_beta_btfp, "btfp_crisis", EXPL_BETA_NESTED)
mod_beta_btfp_f <- safe_run(df_beta_btfp, "btfp_crisis", EXPL_BETA_FULL)
mod_beta_dw_n <- safe_run(df_beta_dw, "dw_crisis", EXPL_BETA_NESTED)
mod_beta_dw_f <- safe_run(df_beta_dw, "dw_crisis", EXPL_BETA_FULL)
mod_beta_fhlb_f <- safe_run(df_beta_fhlb, "fhlb_user", EXPL_BETA_FULL)
models_beta_full <- list(
"Any (nested)" = mod_beta_any_n, "Any (full)" = mod_beta_any_f,
"BTFP (nested)" = mod_beta_btfp_n, "BTFP (full)" = mod_beta_btfp_f,
"DW (nested)" = mod_beta_dw_n, "DW (full)" = mod_beta_dw_f,
"FHLB (full)" = mod_beta_fhlb_f)
save_etable(models_beta_full, "DepositBeta_full_sample",
title_text = "Deposit Beta Channel: Full Sample — Triple Interaction",
notes_text = paste0(
"LPM. $\\beta^U$ is the bank's uninsured deposit beta (DSSW 2017/2021). ",
"Triple: MTM $\\times$ Uninsured $\\times$ $\\beta^U$ tests whether ",
"panic amplification is stronger for banks with flightier deposits. ",
"FHLB: falsification. Robust SEs. z-standardized."),
extra_lines = list(
c("Triple $\\beta^U$", "No", "Yes", "No", "Yes", "No", "Yes", "Yes")))
etable(models_beta_full[!sapply(models_beta_full, is.null)], fitstat = ~ n + r2, se.below = TRUE)## Any (nes.. Any (full) BTFP (nes..
## Dependent Var.: any_fed any_fed btfp_crisis
##
## Constant 0.2079*** 0.2076*** 0.1436***
## (0.0062) (0.0062) (0.0058)
## MTM Loss (z) 0.0303*** 0.0292*** 0.0257***
## (0.0071) (0.0072) (0.0063)
## Uninsured Leverage (z) 0.0208** 0.0190* 0.0232**
## (0.0078) (0.0078) (0.0071)
## Uninsured $\beta$ (z) 0.0069 0.0066 0.0109
## (0.0074) (0.0074) (0.0068)
## MTM $\times$ Uninsured 0.0193** 0.0191** 0.0190***
## (0.0060) (0.0059) (0.0055)
## MTM $\times$ Unins. $\beta$ 0.0068 0.0071 0.0100
## (0.0062) (0.0062) (0.0056)
## Uninsured $\times$ Unins. $\beta$ -0.0024 -0.0080 -0.0022
## (0.0057) (0.0068) (0.0053)
## Log(Assets) 0.1072*** 0.1074*** 0.0713***
## (0.0084) (0.0084) (0.0079)
## Cash Ratio -0.0244*** -0.0241*** -0.0288***
## (0.0064) (0.0064) (0.0051)
## Loan-to-Deposit -0.0031 -0.0035 -0.0110
## (0.0073) (0.0073) (0.0062)
## Book Equity Ratio -0.0145* -0.0143* -0.0128*
## (0.0060) (0.0060) (0.0051)
## Wholesale Funding 0.0297*** 0.0303*** 0.0266***
## (0.0069) (0.0069) (0.0066)
## ROA -0.0030 -0.0029 -0.0069
## (0.0060) (0.0060) (0.0052)
## MTM $\times$ Uninsured $\times$ $\beta^U$ -0.0100
## (0.0056)
## ________________________________________ __________ __________ ___________
## S.E. type Hete.-rob. Hete.-rob. Heter.-rob.
## Observations 3,991 3,991 3,665
## R2 0.12031 0.12112 0.09721
##
## BTFP (full) DW (nest.. DW (full)
## Dependent Var.: btfp_crisis dw_crisis dw_crisis
##
## Constant 0.1434*** 0.1271*** 0.1268***
## (0.0058) (0.0055) (0.0055)
## MTM Loss (z) 0.0251*** 0.0153* 0.0144*
## (0.0064) (0.0062) (0.0062)
## Uninsured Leverage (z) 0.0224** 0.0120 0.0103
## (0.0072) (0.0068) (0.0068)
## Uninsured $\beta$ (z) 0.0107 8.99e-5 -0.0004
## (0.0068) (0.0065) (0.0065)
## MTM $\times$ Uninsured 0.0188*** 0.0171*** 0.0170**
## (0.0055) (0.0052) (0.0052)
## MTM $\times$ Unins. $\beta$ 0.0099 0.0018 0.0019
## (0.0057) (0.0055) (0.0054)
## Uninsured $\times$ Unins. $\beta$ -0.0047 0.0029 -0.0028
## (0.0067) (0.0052) (0.0063)
## Log(Assets) 0.0714*** 0.0935*** 0.0936***
## (0.0079) (0.0079) (0.0079)
## Cash Ratio -0.0286*** -0.0036 -0.0033
## (0.0051) (0.0055) (0.0055)
## Loan-to-Deposit -0.0112 -0.0001 -0.0003
## (0.0062) (0.0063) (0.0063)
## Book Equity Ratio -0.0127* -0.0010 -0.0008
## (0.0051) (0.0048) (0.0048)
## Wholesale Funding 0.0269*** 0.0202** 0.0207**
## (0.0066) (0.0064) (0.0063)
## ROA -0.0069 -0.0032 -0.0032
## (0.0052) (0.0052) (0.0052)
## MTM $\times$ Uninsured $\times$ $\beta^U$ -0.0044 -0.0094
## (0.0053) (0.0051)
## ________________________________________ ___________ __________ __________
## S.E. type Heter.-rob. Hete.-rob. Hete.-rob.
## Observations 3,665 3,599 3,599
## R2 0.09742 0.10270 0.10377
##
## FHLB (fu..
## Dependent Var.: fhlb_user
##
## Constant 0.0905***
## (0.0051)
## MTM Loss (z) 0.0065
## (0.0057)
## Uninsured Leverage (z) 0.0083
## (0.0054)
## Uninsured $\beta$ (z) 0.0154*
## (0.0061)
## MTM $\times$ Uninsured -0.0044
## (0.0046)
## MTM $\times$ Unins. $\beta$ 0.0040
## (0.0048)
## Uninsured $\times$ Unins. $\beta$ 0.0026
## (0.0055)
## Log(Assets) 0.0245***
## (0.0067)
## Cash Ratio -0.0196***
## (0.0041)
## Loan-to-Deposit 0.0216***
## (0.0054)
## Book Equity Ratio 0.0088
## (0.0045)
## Wholesale Funding 0.0032
## (0.0052)
## ROA -0.0092*
## (0.0045)
## MTM $\times$ Uninsured $\times$ $\beta^U$ -0.0026
## (0.0046)
## ________________________________________ __________
## S.E. type Hete.-rob.
## Observations 3,468
## R2 0.04378
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1# ==============================================================================
# DEPOSIT BETA × JIANG MTM SOLVENCY
#
# GP prediction:
# Solvent (panic region): Triple interaction β^U should be positive —
# banks with flightier deposits have wider panic region → stronger
# amplification of MTM × Uninsured
# Insolvent (below θ̲): Triple should be zero —
# β^U doesn't matter because withdrawal is dominant strategy
#
# Finding the triple ONLY among solvent banks confirms DSSW mechanism:
# franchise runs occur in the panic region, where franchise fragility (β^U)
# determines whether the good equilibrium holds.
# ==============================================================================
cat("=== DEPOSIT BETA × JIANG MTM SOLVENCY ===\n")## === DEPOSIT BETA × JIANG MTM SOLVENCY ===# Solvent samples (panic region)
df_beta_any_sol <- df_beta_any %>% filter(mtm_solvent == 1)
df_beta_btfp_sol <- df_beta_btfp %>% filter(mtm_solvent == 1)
df_beta_dw_sol <- df_beta_dw %>% filter(mtm_solvent == 1)
# Insolvent samples (below θ̲)
df_beta_any_ins <- df_beta_any %>% filter(mtm_insolvent == 1)
df_beta_btfp_ins <- df_beta_btfp %>% filter(mtm_insolvent == 1)
df_beta_dw_ins <- df_beta_dw %>% filter(mtm_insolvent == 1)
cat("Jiang Solvent — Any:", nrow(df_beta_any_sol), "| BTFP:", nrow(df_beta_btfp_sol),
"| DW:", nrow(df_beta_dw_sol), "\n")## Jiang Solvent — Any: 3210 | BTFP: 2944 | DW: 2936cat("Jiang Insolvent — Any:", nrow(df_beta_any_ins), "| BTFP:", nrow(df_beta_btfp_ins),
"| DW:", nrow(df_beta_dw_ins), "\n")## Jiang Insolvent — Any: 781 | BTFP: 721 | DW: 663# Solvent: full triple specification
mod_beta_any_sol_f <- safe_run(df_beta_any_sol, "any_fed", EXPL_BETA_FULL)
mod_beta_btfp_sol_f <- safe_run(df_beta_btfp_sol, "btfp_crisis", EXPL_BETA_FULL)
mod_beta_dw_sol_f <- safe_run(df_beta_dw_sol, "dw_crisis", EXPL_BETA_FULL)
# Insolvent: full triple specification
mod_beta_any_ins_f <- safe_run(df_beta_any_ins, "any_fed", EXPL_BETA_FULL)
mod_beta_btfp_ins_f <- safe_run(df_beta_btfp_ins, "btfp_crisis", EXPL_BETA_FULL)
mod_beta_dw_ins_f <- safe_run(df_beta_dw_ins, "dw_crisis", EXPL_BETA_FULL)
models_beta_jiang <- list(
"Any (Sol)" = mod_beta_any_sol_f, "Any (Ins)" = mod_beta_any_ins_f,
"BTFP (Sol)" = mod_beta_btfp_sol_f, "BTFP (Ins)" = mod_beta_btfp_ins_f,
"DW (Sol)" = mod_beta_dw_sol_f, "DW (Ins)" = mod_beta_dw_ins_f)
save_etable(models_beta_jiang, "DepositBeta_jiang_solvency",
title_text = "Deposit Beta $\\times$ Jiang Solvency: Triple Interaction",
notes_text = paste0(
"LPM with full triple interaction MTM $\\times$ Uninsured $\\times$ $\\beta^U$. ",
"Jiang solvency: AE = Book Equity/TA $-$ MTM/TA $\\geq$ 0. ",
"GP prediction: triple is positive among solvent (panic region) banks ",
"and zero among insolvent (below $\\underline{\\theta}$) banks. ",
"Finding the triple only among solvent banks confirms the DSSW mechanism: ",
"franchise runs occur where deposit stickiness ($\\beta^U$) determines ",
"whether the good equilibrium holds. Robust SEs. z-standardized."),
extra_lines = list(
c("Solvency", "Sol", "Ins", "Sol", "Ins", "Sol", "Ins")))
etable(models_beta_jiang[!sapply(models_beta_jiang, is.null)], fitstat = ~ n + r2, se.below = TRUE)## Any (Sol) Any (Ins) BTFP (Sol)
## Dependent Var.: any_fed any_fed btfp_crisis
##
## Constant 0.2101*** 0.1136 0.1431***
## (0.0075) (0.0622) (0.0071)
## MTM Loss (z) 0.0379*** 0.0004 0.0300***
## (0.0087) (0.0299) (0.0075)
## Uninsured Leverage (z) 0.0266** -0.0149 0.0303***
## (0.0092) (0.0355) (0.0084)
## Uninsured $\beta$ (z) 0.0137 -0.0038 0.0174*
## (0.0087) (0.0428) (0.0080)
## MTM $\times$ Uninsured 0.0218** 0.0355 0.0216***
## (0.0070) (0.0279) (0.0063)
## MTM $\times$ Unins. $\beta$ 0.0113 -0.0060 0.0152*
## (0.0074) (0.0314) (0.0068)
## Uninsured $\times$ Unins. $\beta$ -0.0141 0.0609 -0.0043
## (0.0081) (0.0373) (0.0079)
## MTM $\times$ Uninsured $\times$ $\beta^U$ -0.0143* -0.0524 -0.0033
## (0.0066) (0.0286) (0.0062)
## Log(Assets) 0.1005*** 0.1404*** 0.0643***
## (0.0091) (0.0221) (0.0084)
## Cash Ratio -0.0196** -0.0786** -0.0258***
## (0.0066) (0.0240) (0.0051)
## Loan-to-Deposit -0.0049 0.0152 -0.0129*
## (0.0078) (0.0224) (0.0065)
## Book Equity Ratio -0.0107 -0.1258** -0.0071
## (0.0064) (0.0444) (0.0053)
## Wholesale Funding 0.0315*** 0.0196 0.0271***
## (0.0078) (0.0152) (0.0072)
## ROA 0.0024 -0.0312 -0.0024
## (0.0064) (0.0168) (0.0054)
## ________________________________________ __________ __________ ___________
## S.E. type Hete.-rob. Hete.-rob. Heter.-rob.
## Observations 3,210 781 2,944
## R2 0.12558 0.12320 0.09884
##
## BTFP (Ins) DW (Sol) DW (Ins)
## Dependent Var.: btfp_crisis dw_crisis dw_crisis
##
## Constant 0.0571 0.1326*** 0.0607
## (0.0585) (0.0068) (0.0500)
## MTM Loss (z) 0.0021 0.0235** 0.0010
## (0.0282) (0.0077) (0.0237)
## Uninsured Leverage (z) -0.0181 0.0155 -0.0004
## (0.0334) (0.0082) (0.0282)
## Uninsured $\beta$ (z) 0.0118 0.0049 -0.0210
## (0.0420) (0.0077) (0.0303)
## MTM $\times$ Uninsured 0.0340 0.0194** 0.0225
## (0.0262) (0.0062) (0.0218)
## MTM $\times$ Unins. $\beta$ -0.0106 0.0041 0.0015
## (0.0303) (0.0067) (0.0221)
## Uninsured $\times$ Unins. $\beta$ 0.0266 -0.0093 0.0655*
## (0.0349) (0.0078) (0.0278)
## MTM $\times$ Uninsured $\times$ $\beta^U$ -0.0381 -0.0141* -0.0478*
## (0.0273) (0.0062) (0.0211)
## Log(Assets) 0.1067*** 0.0893*** 0.1120***
## (0.0222) (0.0085) (0.0207)
## Cash Ratio -0.0735*** -0.0006 -0.0392*
## (0.0216) (0.0058) (0.0190)
## Loan-to-Deposit 0.0125 -0.0029 0.0106
## (0.0210) (0.0067) (0.0180)
## Book Equity Ratio -0.1237** -0.0019 -0.0622
## (0.0422) (0.0054) (0.0354)
## Wholesale Funding 0.0190 0.0223** 0.0119
## (0.0149) (0.0071) (0.0144)
## ROA -0.0301 0.0013 -0.0272
## (0.0154) (0.0055) (0.0140)
## ________________________________________ ___________ __________ __________
## S.E. type Heter.-rob. Hete.-rob. Hete.-rob.
## Observations 721 2,936 663
## R2 0.10031 0.10861 0.11365
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1# ==============================================================================
# DEPOSIT BETA × IDCR-100% SOLVENCY
# Same logic, stricter solvency definition
# ==============================================================================
cat("=== DEPOSIT BETA × IDCR-100% SOLVENCY ===\n")## === DEPOSIT BETA × IDCR-100% SOLVENCY ===df_beta_any_idcr_sol <- df_beta_any %>% filter(solvent_idcr_100 == 1)
df_beta_any_idcr_ins <- df_beta_any %>% filter(insolvent_idcr_100 == 1)
df_beta_btfp_idcr_sol <- df_beta_btfp %>% filter(solvent_idcr_100 == 1)
df_beta_btfp_idcr_ins <- df_beta_btfp %>% filter(insolvent_idcr_100 == 1)
df_beta_dw_idcr_sol <- df_beta_dw %>% filter(solvent_idcr_100 == 1)
df_beta_dw_idcr_ins <- df_beta_dw %>% filter(insolvent_idcr_100 == 1)
cat("IDCR Solvent — Any:", nrow(df_beta_any_idcr_sol), "| BTFP:", nrow(df_beta_btfp_idcr_sol),
"| DW:", nrow(df_beta_dw_idcr_sol), "\n")## IDCR Solvent — Any: 3648 | BTFP: 3343 | DW: 3302cat("IDCR Insolvent — Any:", nrow(df_beta_any_idcr_ins), "| BTFP:", nrow(df_beta_btfp_idcr_ins),
"| DW:", nrow(df_beta_dw_idcr_ins), "\n")## IDCR Insolvent — Any: 343 | BTFP: 322 | DW: 297mod_beta_any_idcr_sol_f <- safe_run(df_beta_any_idcr_sol, "any_fed", EXPL_BETA_FULL)
mod_beta_any_idcr_ins_f <- safe_run(df_beta_any_idcr_ins, "any_fed", EXPL_BETA_FULL)
mod_beta_btfp_idcr_sol_f <- safe_run(df_beta_btfp_idcr_sol, "btfp_crisis", EXPL_BETA_FULL)
mod_beta_btfp_idcr_ins_f <- safe_run(df_beta_btfp_idcr_ins, "btfp_crisis", EXPL_BETA_FULL)
mod_beta_dw_idcr_sol_f <- safe_run(df_beta_dw_idcr_sol, "dw_crisis", EXPL_BETA_FULL)
mod_beta_dw_idcr_ins_f <- safe_run(df_beta_dw_idcr_ins, "dw_crisis", EXPL_BETA_FULL)
models_beta_idcr <- list(
"Any (Sol)" = mod_beta_any_idcr_sol_f, "Any (Ins)" = mod_beta_any_idcr_ins_f,
"BTFP (Sol)" = mod_beta_btfp_idcr_sol_f, "BTFP (Ins)" = mod_beta_btfp_idcr_ins_f,
"DW (Sol)" = mod_beta_dw_idcr_sol_f, "DW (Ins)" = mod_beta_dw_idcr_ins_f)
save_etable(models_beta_idcr, "DepositBeta_idcr100_solvency",
title_text = "Deposit Beta $\\times$ IDCR-100\\% Solvency: Triple Interaction",
notes_text = paste0(
"LPM with full triple interaction. IDCR-100\\% solvency: ",
"(MV Assets $-$ Uninsured $-$ Insured) / Insured $\\geq$ 0. ",
"Same GP prediction as Jiang split. Robust SEs. z-standardized."),
extra_lines = list(
c("Solvency", "Sol", "Ins", "Sol", "Ins", "Sol", "Ins")))
etable(models_beta_idcr[!sapply(models_beta_idcr, is.null)], fitstat = ~ n + r2, se.below = TRUE)## Any (Sol) Any (Ins) BTFP (Sol)
## Dependent Var.: any_fed any_fed btfp_crisis
##
## Constant 0.2098*** 0.1448 0.1443***
## (0.0066) (0.0827) (0.0062)
## MTM Loss (z) 0.0328*** 0.0087 0.0267***
## (0.0078) (0.0396) (0.0069)
## Uninsured Leverage (z) 0.0229** -0.0020 0.0244**
## (0.0084) (0.0466) (0.0078)
## Uninsured $\beta$ (z) 0.0088 -0.0069 0.0124
## (0.0079) (0.0700) (0.0073)
## MTM $\times$ Uninsured 0.0210** 0.0163 0.0197**
## (0.0064) (0.0350) (0.0060)
## MTM $\times$ Unins. $\beta$ 0.0078 -0.0025 0.0114
## (0.0067) (0.0506) (0.0062)
## Uninsured $\times$ Unins. $\beta$ -0.0085 0.0352 -0.0045
## (0.0073) (0.0503) (0.0072)
## MTM $\times$ Uninsured $\times$ $\beta^U$ -0.0100 -0.0454 -0.0037
## (0.0060) (0.0411) (0.0057)
## Log(Assets) 0.1034*** 0.1487*** 0.0706***
## (0.0088) (0.0330) (0.0082)
## Cash Ratio -0.0227*** -0.0616* -0.0272***
## (0.0066) (0.0277) (0.0052)
## Loan-to-Deposit -0.0045 0.0018 -0.0119
## (0.0075) (0.0360) (0.0064)
## Book Equity Ratio -0.0153* -0.0443 -0.0124*
## (0.0063) (0.0570) (0.0053)
## Wholesale Funding 0.0305*** -0.0797 0.0273***
## (0.0070) (0.0710) (0.0066)
## ROA -0.0013 -0.0239 -0.0061
## (0.0063) (0.0233) (0.0053)
## ________________________________________ __________ __________ ___________
## S.E. type Hete.-rob. Hete.-rob. Heter.-rob.
## Observations 3,648 343 3,343
## R2 0.12319 0.12269 0.10145
##
## BTFP (Ins) DW (Sol) DW (Ins)
## Dependent Var.: btfp_crisis dw_crisis dw_crisis
##
## Constant 0.0737 0.1302*** 0.0838
## (0.0784) (0.0060) (0.0640)
## MTM Loss (z) 0.0161 0.0185** 0.0026
## (0.0368) (0.0069) (0.0286)
## Uninsured Leverage (z) 0.0089 0.0142 0.0058
## (0.0416) (0.0075) (0.0422)
## Uninsured $\beta$ (z) 0.0051 0.0031 -0.0170
## (0.0671) (0.0071) (0.0391)
## MTM $\times$ Uninsured 0.0187 0.0194*** 0.0003
## (0.0318) (0.0058) (0.0288)
## MTM $\times$ Unins. $\beta$ -0.0005 0.0037 -0.0161
## (0.0472) (0.0060) (0.0308)
## Uninsured $\times$ Unins. $\beta$ 0.0442 -0.0022 0.0201
## (0.0502) (0.0070) (0.0378)
## MTM $\times$ Uninsured $\times$ $\beta^U$ -0.0490 -0.0087 -0.0317
## (0.0386) (0.0056) (0.0308)
## Log(Assets) 0.0788* 0.0896*** 0.1339***
## (0.0319) (0.0082) (0.0310)
## Cash Ratio -0.0571* -0.0028 -0.0247
## (0.0258) (0.0057) (0.0182)
## Loan-to-Deposit 0.0041 -0.0022 -0.0023
## (0.0337) (0.0065) (0.0261)
## Book Equity Ratio -0.0646 -0.0027 -0.0012
## (0.0531) (0.0052) (0.0416)
## Wholesale Funding -0.0461 0.0203** -0.0521
## (0.0709) (0.0064) (0.0568)
## ROA -0.0170 -0.0016 -0.0194
## (0.0214) (0.0053) (0.0201)
## ________________________________________ ___________ __________ __________
## S.E. type Heter.-rob. Hete.-rob. Hete.-rob.
## Observations 322 3,302 297
## R2 0.07291 0.10160 0.16578
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1cat("--- Uninsured Beta Distribution ---\n")## --- Uninsured Beta Distribution ---print(summary(df_2022q4$uninsured_beta_raw))## Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
## -0.08442 0.26609 0.31059 0.33127 0.37339 1.35983 66cat("\n--- Mean β^U by Jiang Solvency ---\n")##
## --- Mean β^U by Jiang Solvency ---df_2022q4 %>%
filter(!is.na(uninsured_beta_raw)) %>%
group_by(Jiang_Solvent = mtm_solvent) %>%
summarise(N = n(), Mean_BetaU = round(mean(uninsured_beta_raw, na.rm=T), 4),
SD = round(sd(uninsured_beta_raw, na.rm=T), 4), .groups = "drop") %>%
print()## # A tibble: 2 × 4
## Jiang_Solvent N Mean_BetaU SD
## <int> <int> <dbl> <dbl>
## 1 0 813 0.309 0.08
## 2 1 3413 0.337 0.111cat("\n--- Correlation Matrix ---\n")##
## --- Correlation Matrix ---cor_df <- df_2022q4 %>%
select(uninsured_beta_raw, beta_overall, uninsured_lev_raw, mtm_total_raw, dfv_raw) %>%
drop_na()
if (nrow(cor_df) > 10) print(round(cor(cor_df), 3))## uninsured_beta_raw beta_overall uninsured_lev_raw
## uninsured_beta_raw 1.000 0.925 -0.058
## beta_overall 0.925 1.000 0.298
## uninsured_lev_raw -0.058 0.298 1.000
## mtm_total_raw -0.134 -0.190 -0.155
## dfv_raw -0.765 -0.834 -0.133
## mtm_total_raw dfv_raw
## uninsured_beta_raw -0.134 -0.765
## beta_overall -0.190 -0.834
## uninsured_lev_raw -0.155 -0.133
## mtm_total_raw 1.000 0.184
## dfv_raw 0.184 1.000cat("=== FACILITY COMPLEMENTARITY ===\n\n")## === FACILITY COMPLEMENTARITY ===df_emerg <- df_crisis %>%
filter(any_fed == 1) %>%
mutate(facility_choice = factor(case_when(
both_fed == 1 ~ "Both",
btfp_crisis == 1 ~ "BTFP_Only",
dw_crisis == 1 ~ "DW_Only"),
levels = c("DW_Only", "BTFP_Only", "Both")))
cat("Facility choice (Crisis emergency borrowers):\n")## Facility choice (Crisis emergency borrowers):print(table(df_emerg$facility_choice))##
## DW_Only BTFP_Only Both
## 327 395 106ff_mnom <- as.formula(paste0("facility_choice ~ mtm_total + uninsured_lev + mtm_x_uninsured + par_benefit + collateral_capacity + ", CONTROLS))
mod4a <- tryCatch(multinom(ff_mnom, data = df_emerg, trace = FALSE),
error = function(e) { message("Multinom failed: ", e$message); NULL })
if (!is.null(mod4a)) {
cat("\nAIC:", AIC(mod4a), "\n\n")
tidy_m <- tidy(mod4a, conf.int = TRUE) %>%
mutate(stars = case_when(p.value < 0.01 ~ "***", p.value < 0.05 ~ "**",
p.value < 0.10 ~ "*", TRUE ~ ""),
disp = sprintf("%.3f%s (%.3f)", estimate, stars, std.error))
cat("--- Key Coefficients (Base = DW Only) ---\n")
tidy_m %>%
filter(term %in% c("mtm_total", "uninsured_lev", "mtm_x_uninsured",
"par_benefit", "collateral_capacity")) %>%
select(Outcome = y.level, Variable = term, Estimate = disp) %>%
print(n = 20)
}##
## AIC: 1567.913
##
## --- Key Coefficients (Base = DW Only) ---
## # A tibble: 10 × 3
## Outcome Variable Estimate
## <chr> <chr> <chr>
## 1 BTFP_Only mtm_total 0.120 (0.103)
## 2 BTFP_Only uninsured_lev 0.120 (0.093)
## 3 BTFP_Only mtm_x_uninsured -0.103 (0.086)
## 4 BTFP_Only par_benefit -0.342*** (0.131)
## 5 BTFP_Only collateral_capacity 0.240** (0.103)
## 6 Both mtm_total -0.196 (0.172)
## 7 Both uninsured_lev 0.286** (0.134)
## 8 Both mtm_x_uninsured 0.113 (0.129)
## 9 Both par_benefit 0.284 (0.380)
## 10 Both collateral_capacity 0.106 (0.149)df_dw_comp <- df_crisis %>%
filter(dw_crisis == 1) %>%
mutate(also_btfp = as.integer(btfp_crisis == 1))
cat("DW borrowers:", nrow(df_dw_comp), "| Also BTFP:", sum(df_dw_comp$also_btfp), "\n")## DW borrowers: 433 | Also BTFP: 106mod4b_base <- safe_run(df_dw_comp, "also_btfp", EXPL_BASE, min_n = 20)
mod4b_fac <- safe_run(df_dw_comp, "also_btfp", EXPL_FACILITY, min_n = 20)
models_4b <- list("Base" = mod4b_base, "Facility" = mod4b_fac)
save_etable(models_4b, "M4b_complementarity",
title_text = "Complementarity: Among DW Borrowers, What Drove Also-BTFP?",
notes_text = "LPM. Sample: DW borrowers (Crisis). DV=1 if also used BTFP. Robust SEs.")
etable(models_4b[!sapply(models_4b, is.null)], fitstat = ~ n + r2, se.below = TRUE)## Base Facility
## Dependent Var.: Also BTFP Also BTFP
##
## Constant 0.1686*** 0.1668***
## (0.0235) (0.0231)
## MTM Loss (z) -0.0219 -0.0186
## (0.0242) (0.0246)
## Uninsured Leverage (z) 0.0490* 0.0499*
## (0.0241) (0.0243)
## MTM $\times$ Uninsured 0.0200 0.0200
## (0.0212) (0.0214)
## Log(Assets) 0.0590* 0.0563*
## (0.0247) (0.0253)
## Cash Ratio -0.0472 -0.0422
## (0.0263) (0.0266)
## Loan-to-Deposit -0.0270 -0.0103
## (0.0285) (0.0338)
## Book Equity Ratio -0.0502 -0.0517
## (0.0261) (0.0264)
## Wholesale Funding 0.0244 0.0217
## (0.0176) (0.0177)
## ROA -0.0258 -0.0215
## (0.0236) (0.0240)
## Par Benefit (z) 0.0132
## (0.0154)
## OMO Collateral (z) 0.0261
## (0.0283)
## ______________________ __________ __________
## S.E. type Hete.-rob. Hete.-rob.
## Observations 433 433
## R2 0.08055 0.08293
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1df_subst <- df_crisis %>%
filter(user_group %in% c("BTFP_Only", "DW_Only")) %>%
mutate(chose_btfp = as.integer(user_group == "BTFP_Only"))
cat("BTFP-only:", sum(df_subst$chose_btfp), "| DW-only:", sum(df_subst$chose_btfp==0), "\n")## BTFP-only: 395 | DW-only: 327mod4c_base <- safe_run(df_subst, "chose_btfp", EXPL_BASE, min_n = 20)
mod4c_fac <- safe_run(df_subst, "chose_btfp", EXPL_FACILITY, min_n = 20)
mod4c_stig <- safe_run(df_subst, "chose_btfp",
paste0(EXPL_FACILITY, " + par_x_uninsured"), min_n = 20)
models_4c <- list("Base" = mod4c_base, "Facility" = mod4c_fac, "Stigma" = mod4c_stig)
save_etable(models_4c, "M4c_substitution",
title_text = "Substitution: BTFP-Only vs. DW-Only",
notes_text = "LPM. Sample: single-facility borrowers (Crisis). DV=1 if BTFP, 0 if DW. Robust SEs.")
etable(models_4c[!sapply(models_4c, is.null)], fitstat = ~ n + r2, se.below = TRUE)## Base Facility Stigma
## Dependent Var.: chose_btfp chose_btfp chose_btfp
##
## Constant 0.5364*** 0.5378*** 0.5341***
## (0.0243) (0.0242) (0.0245)
## MTM Loss (z) 0.0092 0.0277 0.0239
## (0.0240) (0.0243) (0.0245)
## Uninsured Leverage (z) 0.0274 0.0270 0.0257
## (0.0231) (0.0223) (0.0225)
## MTM $\times$ Uninsured -0.0193 -0.0197 -0.0135
## (0.0205) (0.0199) (0.0206)
## Log(Assets) -0.0808*** -0.0791*** -0.0739**
## (0.0233) (0.0229) (0.0236)
## Cash Ratio -0.1242*** -0.1201*** -0.1228***
## (0.0300) (0.0285) (0.0287)
## Loan-to-Deposit -0.0466 -0.0115 -0.0174
## (0.0276) (0.0301) (0.0304)
## Book Equity Ratio -0.0380 -0.0431 -0.0408
## (0.0284) (0.0287) (0.0288)
## Wholesale Funding 0.0058 0.0027 0.0028
## (0.0156) (0.0155) (0.0155)
## ROA -0.0080 -0.0037 -0.0005
## (0.0232) (0.0233) (0.0234)
## Par Benefit (z) -0.0675** -0.0505
## (0.0245) (0.0314)
## OMO Collateral (z) 0.0550* 0.0544*
## (0.0227) (0.0228)
## Par $\times$ Uninsured -0.0294
## (0.0225)
## ______________________ __________ __________ __________
## S.E. type Hete.-rob. Hete.-rob. Hete.-rob.
## Observations 722 722 722
## R2 0.06253 0.07826 0.08051
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1desc_vars <- c("mtm_total_raw", "mtm_btfp_raw", "uninsured_lev_raw",
"book_equity_ratio_raw", "adjusted_equity_raw", "dfv_raw",
"ln_assets_raw", "cash_ratio_raw", "par_benefit_raw", "collateral_capacity_raw")
cat("--- Mean Characteristics by Facility Choice ---\n")## --- Mean Characteristics by Facility Choice ---df_emerg %>%
group_by(facility_choice) %>%
summarise(N = n(), across(all_of(desc_vars), ~round(mean(., na.rm=T), 3)), .groups = "drop") %>%
print(width = Inf)## # A tibble: 3 × 12
## facility_choice N mtm_total_raw mtm_btfp_raw uninsured_lev_raw
## <fct> <int> <dbl> <dbl> <dbl>
## 1 DW_Only 327 5.72 0.728 26.8
## 2 BTFP_Only 395 6.18 0.875 26.2
## 3 Both 106 5.83 0.924 32.0
## book_equity_ratio_raw adjusted_equity_raw dfv_raw ln_assets_raw cash_ratio_raw
## <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 9.10 3.38 74.6 13.8 6.15
## 2 8.19 2.01 75.6 13.5 4.69
## 3 8.14 2.31 70.0 14.6 4.62
## par_benefit_raw collateral_capacity_raw
## <dbl> <dbl>
## 1 0.962 0.009
## 2 0.933 0.012
## 3 0.978 0.011# T-tests: BTFP-only vs DW-only
cat("\n--- T-Tests: BTFP-Only vs DW-Only ---\n")##
## --- T-Tests: BTFP-Only vs DW-Only ---btfp_only <- df_emerg %>% filter(facility_choice == "BTFP_Only")
dw_only <- df_emerg %>% filter(facility_choice == "DW_Only")
for (v in desc_vars) {
tt <- tryCatch(t.test(btfp_only[[v]], dw_only[[v]]), error = function(e) NULL)
if (!is.null(tt)) {
stars <- case_when(tt$p.value < 0.01 ~ "***", tt$p.value < 0.05 ~ "**",
tt$p.value < 0.10 ~ "*", TRUE ~ "")
cat(sprintf(" %-28s BTFP=%.3f DW=%.3f diff=%.3f t=%.2f %s\n", v,
mean(btfp_only[[v]], na.rm=T), mean(dw_only[[v]], na.rm=T),
mean(btfp_only[[v]], na.rm=T) - mean(dw_only[[v]], na.rm=T),
tt$statistic, stars))
}
}## mtm_total_raw BTFP=6.175 DW=5.718 diff=0.458 t=3.07 ***
## mtm_btfp_raw BTFP=0.875 DW=0.728 diff=0.147 t=2.15 **
## uninsured_lev_raw BTFP=26.154 DW=26.774 diff=-0.621 t=-0.71
## book_equity_ratio_raw BTFP=8.188 DW=9.097 diff=-0.909 t=-3.82 ***
## adjusted_equity_raw BTFP=2.012 DW=3.379 diff=-1.367 t=-4.36 ***
## dfv_raw BTFP=75.609 DW=74.630 diff=0.980 t=1.02
## ln_assets_raw BTFP=13.486 DW=13.833 diff=-0.347 t=-3.22 ***
## cash_ratio_raw BTFP=4.686 DW=6.151 diff=-1.465 t=-3.43 ***
## par_benefit_raw BTFP=0.933 DW=0.962 diff=-0.029 t=-2.15 **
## collateral_capacity_raw BTFP=0.012 DW=0.009 diff=0.002 t=3.15 ***# ==============================================================================
# Three-way solvency cross-tab and visualization
# ==============================================================================
cat("=== SOLVENCY COMPARISON ACROSS FRAMEWORKS ===\n\n")## === SOLVENCY COMPARISON ACROSS FRAMEWORKS ===# Full cross-tab
solv_tab <- df_2022q4 %>%
filter(!is.na(dssw_solvent)) %>%
count(
Jiang = ifelse(mtm_insolvent == 1, "Jiang-Ins", "Jiang-Sol"),
IDCR = ifelse(insolvent_idcr_100 == 1, "IDCR-Ins", "IDCR-Sol"),
DSSW = ifelse(dssw_insolvent == 1, "DSSW-Ins", "DSSW-Sol")
) %>%
arrange(Jiang, IDCR, DSSW)
cat("--- Three-Way Cross-Tab ---\n")## --- Three-Way Cross-Tab ---print(solv_tab)## # A tibble: 6 × 4
## Jiang IDCR DSSW n
## <chr> <chr> <chr> <int>
## 1 Jiang-Ins IDCR-Ins DSSW-Sol 355
## 2 Jiang-Ins IDCR-Sol DSSW-Sol 470
## 3 Jiang-Sol IDCR-Ins DSSW-Sol 9
## 4 Jiang-Sol IDCR-Sol DSSW-Sol 3417
## 5 Jiang-Sol <NA> DSSW-Sol 31
## 6 <NA> <NA> DSSW-Sol 10# Summary
cat("\n--- Classification Summary ---\n")##
## --- Classification Summary ---cat(sprintf(" Jiang-insolvent: %d (%.1f%%)\n",
sum(df_2022q4$mtm_insolvent, na.rm=T),
100 * mean(df_2022q4$mtm_insolvent, na.rm=T)))## Jiang-insolvent: 825 (19.3%)cat(sprintf(" IDCR-insolvent: %d (%.1f%%)\n",
sum(df_2022q4$insolvent_idcr_100, na.rm=T),
100 * mean(df_2022q4$insolvent_idcr_100, na.rm=T)))## IDCR-insolvent: 364 (8.6%)cat(sprintf(" DSSW-insolvent: %d (%.1f%%)\n",
sum(df_2022q4$dssw_insolvent, na.rm=T),
100 * mean(df_2022q4$dssw_insolvent, na.rm=T)))## DSSW-insolvent: 0 (0.0%)# Euler-style summary of how frameworks relate
cat("\n--- Theoretical Interpretation ---\n")##
## --- Theoretical Interpretation ---cat(" Jiang: Book Equity > MTM losses? (asset-side solvency)\n")## Jiang: Book Equity > MTM losses? (asset-side solvency)cat(" IDCR: Can bank pay ALL depositors after 100% uninsured run? (run-scenario)\n")## IDCR: Can bank pay ALL depositors after 100% uninsured run? (run-scenario)cat(" DSSW: Include franchise value (no-run equilibrium solvency)\n")## DSSW: Include franchise value (no-run equilibrium solvency)cat(" → IDCR is stricter than Jiang (accounts for deposit payoff priority)\n")## → IDCR is stricter than Jiang (accounts for deposit payoff priority)cat(" → DSSW is most lenient (adds intangible franchise value)\n")## → DSSW is most lenient (adds intangible franchise value)cat(" → The gap between DSSW-solvent and Jiang/IDCR-insolvent IS the panic region\n")## → The gap between DSSW-solvent and Jiang/IDCR-insolvent IS the panic region# Visualization: Adjusted Equity distributions by framework
df_kde_solv <- df_2022q4 %>%
filter(!is.na(adjusted_equity_dssw_raw)) %>%
select(adjusted_equity_raw, adjusted_equity_dssw_raw, idcr_100) %>%
pivot_longer(cols = c(adjusted_equity_raw, adjusted_equity_dssw_raw),
names_to = "Framework", values_to = "Value") %>%
mutate(Framework = case_when(
Framework == "adjusted_equity_raw" ~ "Jiang (Book Eq. − MTM)",
Framework == "adjusted_equity_dssw_raw" ~ "DSSW (+ Franchise Value)"))
p_solv <- ggplot(df_kde_solv, aes(x = Value, fill = Framework, color = Framework)) +
geom_density(alpha = 0.4, linewidth = 0.8) +
geom_vline(xintercept = 0, linetype = "dotted", color = "red", linewidth = 1) +
scale_fill_manual(values = c("Jiang (Book Eq. − MTM)" = "#D62828",
"DSSW (+ Franchise Value)" = "#2A9D8F")) +
scale_color_manual(values = c("Jiang (Book Eq. − MTM)" = "#D62828",
"DSSW (+ Franchise Value)" = "#2A9D8F")) +
labs(title = "Solvency Distributions: Jiang vs. DSSW",
subtitle = "DSSW shifts the entire distribution rightward by ~68pp. Zero banks are DSSW-insolvent.",
x = "Adjusted Equity (% of Assets)", y = "Density") +
theme_paper +
annotate("text", x = -3, y = 0.08, label = "Jiang\ninsolvent\nzone",
color = "#D62828", size = 3, fontface = "italic")
p_solv
save_figure(p_solv, "Fig_Solvency_Jiang_vs_DSSW_KDE", width = 10, height = 6)# ==============================================================================
# SIZE SPLIT: ≤ $10B vs. > $10B total assets
#
# Banks of different sizes face different run dynamics:
# - Small banks: more reliant on insured deposits, less market scrutiny
# - Large banks: more uninsured deposits, subject to market discipline
#
# We re-run the main regression for each size group separately.
# ==============================================================================
cat("=== SIZE SPLIT: ≤$10B vs. >$10B ===\n\n")## === SIZE SPLIT: ≤$10B vs. >$10B ===# total_asset is in $000s → $10B = 10,000,000 thousands
SIZE_CUTOFF <- 10e6 # $10B in $000s
# --- Create size flag on each sample ---
add_size_flag <- function(df) {
df %>% mutate(
size_group = ifelse(total_asset <= SIZE_CUTOFF, "Small (<=10B)", "Large (>10B)"),
size_group = factor(size_group, levels = c("Small (<=10B)", "Large (>10B)"))
)
}
df_anyfed_s <- add_size_flag(df_anyfed_s)
df_btfp_s <- add_size_flag(df_btfp_s)
df_dw_s <- add_size_flag(df_dw_s)
df_fhlb_s <- add_size_flag(df_fhlb_s)
# Counts
for (sz in c("Small (<=10B)", "Large (>10B)")) {
cat(sprintf(" %s:\n", sz))
cat(sprintf(" AnyFed: N=%d, Borrowers=%d\n",
sum(df_anyfed_s$size_group == sz),
sum(df_anyfed_s$any_fed[df_anyfed_s$size_group == sz])))
cat(sprintf(" BTFP: N=%d, Borrowers=%d\n",
sum(df_btfp_s$size_group == sz),
sum(df_btfp_s$btfp_crisis[df_btfp_s$size_group == sz])))
cat(sprintf(" DW: N=%d, Borrowers=%d\n",
sum(df_dw_s$size_group == sz),
sum(df_dw_s$dw_crisis[df_dw_s$size_group == sz])))
cat(sprintf(" FHLB: N=%d, Borrowers=%d\n",
sum(df_fhlb_s$size_group == sz),
sum(df_fhlb_s$fhlb_user[df_fhlb_s$size_group == sz])))
}## Small (<=10B):
## AnyFed: N=3928, Borrowers=759
## BTFP: N=3628, Borrowers=459
## DW: N=3552, Borrowers=383
## FHLB: N=3451, Borrowers=282
## Large (>10B):
## AnyFed: N=126, Borrowers=69
## BTFP: N=99, Borrowers=42
## DW: N=107, Borrowers=50
## FHLB: N=77, Borrowers=20cat("=== SMALL BANKS (≤$10B) ===\n")## === SMALL BANKS (≤$10B) ===mod_sz_any_sm <- safe_run(df_anyfed_s %>% filter(size_group == "Small (<=10B)"), "any_fed", EXPL_BASE)
mod_sz_btfp_sm <- safe_run(df_btfp_s %>% filter(size_group == "Small (<=10B)"), "btfp_crisis", EXPL_BASE)
mod_sz_dw_sm <- safe_run(df_dw_s %>% filter(size_group == "Small (<=10B)"), "dw_crisis", EXPL_BASE)
mod_sz_fhlb_sm <- safe_run(df_fhlb_s %>% filter(size_group == "Small (<=10B)"), "fhlb_user", EXPL_BASE)
models_sz_sm <- list(
"Any Fed" = mod_sz_any_sm, "BTFP" = mod_sz_btfp_sm,
"DW" = mod_sz_dw_sm, "FHLB" = mod_sz_fhlb_sm)
save_etable(models_sz_sm, "Size_small_le10B",
title_text = "Size Split: Small Banks ($\\leq$ \\$10B) — Extensive Margin (Crisis)",
notes_text = "LPM. Sample restricted to banks with total assets $\\leq$ \\$10B. Robust SEs. z-standardized.",
extra_lines = list(c("Size Group", "Small", "Small", "Small", "Small")))
etable(models_sz_sm[!sapply(models_sz_sm, is.null)], fitstat = ~ n + r2, se.below = TRUE)## Any Fed BTFP DW FHLB
## Dependent Var.: any_fed btfp_crisis dw_crisis fhlb_user
##
## Constant 0.2065*** 0.1404*** 0.1231*** 0.0885***
## (0.0063) (0.0059) (0.0057) (0.0051)
## MTM Loss (z) 0.0299*** 0.0260*** 0.0152* 0.0056
## (0.0070) (0.0061) (0.0061) (0.0055)
## Uninsured Leverage (z) 0.0110 0.0154* 0.0040 0.0032
## (0.0078) (0.0071) (0.0067) (0.0052)
## MTM $\times$ Uninsured 0.0202*** 0.0192*** 0.0162** -0.0005
## (0.0057) (0.0052) (0.0050) (0.0040)
## Log(Assets) 0.1068*** 0.0668*** 0.0869*** 0.0211**
## (0.0089) (0.0081) (0.0082) (0.0068)
## Cash Ratio -0.0215*** -0.0265*** -0.0014 -0.0199***
## (0.0061) (0.0047) (0.0052) (0.0039)
## Loan-to-Deposit -0.0042 -0.0105 -0.0005 0.0260***
## (0.0067) (0.0057) (0.0057) (0.0051)
## Book Equity Ratio -0.0163** -0.0137** -0.0050 0.0069
## (0.0054) (0.0046) (0.0043) (0.0040)
## Wholesale Funding 0.0307*** 0.0265*** 0.0195** 0.0040
## (0.0070) (0.0067) (0.0064) (0.0052)
## ROA -3.67e-5 -0.0045 -0.0005 -0.0080
## (0.0057) (0.0048) (0.0048) (0.0043)
## ______________________ __________ ___________ __________ __________
## S.E. type Hete.-rob. Heter.-rob. Hete.-rob. Hete.-rob.
## Observations 3,918 3,618 3,542 3,441
## R2 0.10423 0.08245 0.07826 0.03495
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1cat("=== LARGE BANKS (>$10B) ===\n")## === LARGE BANKS (>$10B) ===mod_sz_any_lg <- safe_run(df_anyfed_s %>% filter(size_group == "Large (>10B)"), "any_fed", EXPL_BASE)
mod_sz_btfp_lg <- safe_run(df_btfp_s %>% filter(size_group == "Large (>10B)"), "btfp_crisis", EXPL_BASE)
mod_sz_dw_lg <- safe_run(df_dw_s %>% filter(size_group == "Large (>10B)"), "dw_crisis", EXPL_BASE)
mod_sz_fhlb_lg <- safe_run(df_fhlb_s %>% filter(size_group == "Large (>10B)"), "fhlb_user", EXPL_BASE)
models_sz_lg <- list(
"Any Fed" = mod_sz_any_lg, "BTFP" = mod_sz_btfp_lg,
"DW" = mod_sz_dw_lg, "FHLB" = mod_sz_fhlb_lg)
save_etable(models_sz_lg, "Size_large_gt10B",
title_text = "Size Split: Large Banks ($>$ \\$10B) — Extensive Margin (Crisis)",
notes_text = "LPM. Sample restricted to banks with total assets $>$ \\$10B. Robust SEs. z-standardized.",
extra_lines = list(c("Size Group", "Large", "Large", "Large", "Large")))
etable(models_sz_lg[!sapply(models_sz_lg, is.null)], fitstat = ~ n + r2, se.below = TRUE)## Any Fed BTFP DW FHLB
## Dependent Var.: any_fed btfp_crisis dw_crisis fhlb_user
##
## Constant 3.932* 3.420 5.001* 0.9506
## (1.907) (2.704) (2.056) (2.876)
## MTM Loss (z) 0.0169 -0.0193 0.0667 0.0447
## (0.0717) (0.0713) (0.0631) (0.0585)
## Uninsured Leverage (z) 0.1605*** 0.1949*** 0.1524*** 0.0895*
## (0.0379) (0.0336) (0.0393) (0.0443)
## MTM $\times$ Uninsured 0.0178 0.0641 -0.0086 -0.0636
## (0.0404) (0.0414) (0.0390) (0.0361)
## Log(Assets) -1.382 -1.231 -1.827* -0.3064
## (0.7402) (1.044) (0.7985) (1.112)
## Cash Ratio -0.1297 -0.1123 -0.0946 0.0012
## (0.0684) (0.0661) (0.0668) (0.0616)
## Loan-to-Deposit 0.0115 0.0034 0.0680 0.0466
## (0.0775) (0.0737) (0.0684) (0.0595)
## Book Equity Ratio -0.0742 -0.1288 -0.0739 0.0795
## (0.0702) (0.0694) (0.0745) (0.0758)
## Wholesale Funding -0.0078 -0.0181 0.0097 -0.0754**
## (0.0369) (0.0395) (0.0389) (0.0275)
## ROA 0.0131 0.0546 0.0130 0.0184
## (0.0623) (0.0632) (0.0641) (0.0542)
## ______________________ __________ ___________ __________ _________
## S.E. type Hete.-rob. Heter.-rob. Hete.-rob. Het.-rob.
## Observations 126 99 107 77
## R2 0.20292 0.21343 0.23015 0.24397
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1models_sz_combined <- list(
"Any (Sm)" = mod_sz_any_sm, "Any (Lg)" = mod_sz_any_lg,
"BTFP (Sm)" = mod_sz_btfp_sm, "BTFP (Lg)" = mod_sz_btfp_lg,
"DW (Sm)" = mod_sz_dw_sm, "DW (Lg)" = mod_sz_dw_lg,
"FHLB (Sm)" = mod_sz_fhlb_sm, "FHLB (Lg)" = mod_sz_fhlb_lg)
save_etable(models_sz_combined, "Size_combined_10B",
title_text = "Size Split: Small ($\\leq$ \\$10B) vs. Large ($>$ \\$10B) — Crisis Period",
notes_text = paste0(
"LPM. Banks split at \\$10B total assets. Sm = $\\leq$ \\$10B; Lg = $>$ \\$10B. ",
"Robust SEs. z-standardized."),
extra_lines = list(
c("Size", "Sm", "Lg", "Sm", "Lg", "Sm", "Lg", "Sm", "Lg")))
etable(models_sz_combined[!sapply(models_sz_combined, is.null)], fitstat = ~ n + r2, se.below = TRUE)## Any (Sm) Any (Lg) BTFP (Sm) BTFP (Lg) DW (Sm)
## Dependent Var.: any_fed any_fed btfp_crisis btfp_crisis dw_crisis
##
## Constant 0.2065*** 3.932* 0.1404*** 3.420 0.1231***
## (0.0063) (1.907) (0.0059) (2.704) (0.0057)
## MTM Loss (z) 0.0299*** 0.0169 0.0260*** -0.0193 0.0152*
## (0.0070) (0.0717) (0.0061) (0.0713) (0.0061)
## Uninsured Leverage (z) 0.0110 0.1605*** 0.0154* 0.1949*** 0.0040
## (0.0078) (0.0379) (0.0071) (0.0336) (0.0067)
## MTM $\times$ Uninsured 0.0202*** 0.0178 0.0192*** 0.0641 0.0162**
## (0.0057) (0.0404) (0.0052) (0.0414) (0.0050)
## Log(Assets) 0.1068*** -1.382 0.0668*** -1.231 0.0869***
## (0.0089) (0.7402) (0.0081) (1.044) (0.0082)
## Cash Ratio -0.0215*** -0.1297 -0.0265*** -0.1123 -0.0014
## (0.0061) (0.0684) (0.0047) (0.0661) (0.0052)
## Loan-to-Deposit -0.0042 0.0115 -0.0105 0.0034 -0.0005
## (0.0067) (0.0775) (0.0057) (0.0737) (0.0057)
## Book Equity Ratio -0.0163** -0.0742 -0.0137** -0.1288 -0.0050
## (0.0054) (0.0702) (0.0046) (0.0694) (0.0043)
## Wholesale Funding 0.0307*** -0.0078 0.0265*** -0.0181 0.0195**
## (0.0070) (0.0369) (0.0067) (0.0395) (0.0064)
## ROA -3.67e-5 0.0131 -0.0045 0.0546 -0.0005
## (0.0057) (0.0623) (0.0048) (0.0632) (0.0048)
## ______________________ __________ __________ ___________ ___________ __________
## S.E. type Hete.-rob. Hete.-rob. Heter.-rob. Heter.-rob. Hete.-rob.
## Observations 3,918 126 3,618 99 3,542
## R2 0.10423 0.20292 0.08245 0.21343 0.07826
##
## DW (Lg) FHLB (Sm) FHLB (Lg)
## Dependent Var.: dw_crisis fhlb_user fhlb_user
##
## Constant 5.001* 0.0885*** 0.9506
## (2.056) (0.0051) (2.876)
## MTM Loss (z) 0.0667 0.0056 0.0447
## (0.0631) (0.0055) (0.0585)
## Uninsured Leverage (z) 0.1524*** 0.0032 0.0895*
## (0.0393) (0.0052) (0.0443)
## MTM $\times$ Uninsured -0.0086 -0.0005 -0.0636
## (0.0390) (0.0040) (0.0361)
## Log(Assets) -1.827* 0.0211** -0.3064
## (0.7985) (0.0068) (1.112)
## Cash Ratio -0.0946 -0.0199*** 0.0012
## (0.0668) (0.0039) (0.0616)
## Loan-to-Deposit 0.0680 0.0260*** 0.0466
## (0.0684) (0.0051) (0.0595)
## Book Equity Ratio -0.0739 0.0069 0.0795
## (0.0745) (0.0040) (0.0758)
## Wholesale Funding 0.0097 0.0040 -0.0754**
## (0.0389) (0.0052) (0.0275)
## ROA 0.0130 -0.0080 0.0184
## (0.0641) (0.0043) (0.0542)
## ______________________ __________ __________ _________
## S.E. type Hete.-rob. Hete.-rob. Het.-rob.
## Observations 107 3,441 77
## R2 0.23015 0.03495 0.24397
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1# ==============================================================================
# THRESHOLD GRADIENT
#
# At low levels of mark-to-market (MTM) losses, banks with higher uninsured
# leverage are expected to borrow more to preempt run risk. We test this
# threshold effect by splitting the sample into Uninsured terciles
# (Low, Medium, High) and estimating the extensive margin separately for
# each group k ∈ {L, M, H}:
#
# Borrower_i = α^(k) + β^(k) · mtm_loss_i + γ X_i + ε_i
#
# Prediction: β^(H) >> β^(M) > β^(L) — the MTM coefficient should be
# strongest among high-uninsured banks, where run risk is most acute.
# ==============================================================================
cat("=== THRESHOLD GRADIENT: UNINSURED TERCILE REGRESSIONS ===\n\n")## === THRESHOLD GRADIENT: UNINSURED TERCILE REGRESSIONS ===# Create terciles on the full crisis sample (before sample splits)
tercile_breaks <- quantile(df_crisis$uninsured_lev_raw, probs = c(1/3, 2/3), na.rm = TRUE)
cat(sprintf(" Uninsured leverage tercile cuts: %.2f%%, %.2f%%\n",
tercile_breaks[1], tercile_breaks[2]))## Uninsured leverage tercile cuts: 17.71%, 26.99%add_tercile <- function(df) {
df %>% mutate(
uninsured_tercile = case_when(
uninsured_lev_raw <= tercile_breaks[1] ~ "Low",
uninsured_lev_raw <= tercile_breaks[2] ~ "Medium",
TRUE ~ "High"
),
uninsured_tercile = factor(uninsured_tercile, levels = c("Low", "Medium", "High"))
)
}
df_anyfed_s <- add_tercile(df_anyfed_s)
df_btfp_s <- add_tercile(df_btfp_s)
df_dw_s <- add_tercile(df_dw_s)
df_fhlb_s <- add_tercile(df_fhlb_s)
# Tercile-specific regression spec: no interaction, just MTM + controls
EXPL_TERCILE <- "mtm_total"
for (terc in c("Low", "Medium", "High")) {
cat(sprintf(" %s tercile:\n", terc))
cat(sprintf(" AnyFed: N=%d, Borrowers=%d\n",
sum(df_anyfed_s$uninsured_tercile == terc, na.rm=TRUE),
sum(df_anyfed_s$any_fed[df_anyfed_s$uninsured_tercile == terc], na.rm=TRUE)))
cat(sprintf(" BTFP: N=%d, Borrowers=%d\n",
sum(df_btfp_s$uninsured_tercile == terc, na.rm=TRUE),
sum(df_btfp_s$btfp_crisis[df_btfp_s$uninsured_tercile == terc], na.rm=TRUE)))
cat(sprintf(" DW: N=%d, Borrowers=%d\n",
sum(df_dw_s$uninsured_tercile == terc, na.rm=TRUE),
sum(df_dw_s$dw_crisis[df_dw_s$uninsured_tercile == terc], na.rm=TRUE)))
}## Low tercile:
## AnyFed: N=1361, Borrowers=175
## BTFP: N=1289, Borrowers=103
## DW: N=1272, Borrowers=86
## Medium tercile:
## AnyFed: N=1343, Borrowers=286
## BTFP: N=1230, Borrowers=173
## DW: N=1200, Borrowers=143
## High tercile:
## AnyFed: N=1350, Borrowers=367
## BTFP: N=1208, Borrowers=225
## DW: N=1187, Borrowers=204cat("=== TERCILE: ANY FED ===\n")## === TERCILE: ANY FED ===mod_terc_any_L <- safe_run(df_anyfed_s %>% filter(uninsured_tercile == "Low"), "any_fed", EXPL_TERCILE)
mod_terc_any_M <- safe_run(df_anyfed_s %>% filter(uninsured_tercile == "Medium"), "any_fed", EXPL_TERCILE)
mod_terc_any_H <- safe_run(df_anyfed_s %>% filter(uninsured_tercile == "High"), "any_fed", EXPL_TERCILE)
models_terc_any <- list("Low UI" = mod_terc_any_L, "Med UI" = mod_terc_any_M, "High UI" = mod_terc_any_H)
save_etable(models_terc_any, "Tercile_AnyFed",
title_text = "Threshold Gradient: Any Fed Borrowing by Uninsured Tercile",
notes_text = paste0(
"LPM. Sample split into terciles of uninsured leverage (\\% of assets). ",
"Each column estimates Borrower$_i = \\alpha^{(k)} + \\beta^{(k)} \\cdot$ MTM$_i + \\gamma \\mathbf{X}_i + \\varepsilon_i$ ",
"within tercile $k \\in \\{L, M, H\\}$. ",
"Prediction: $\\beta^{(H)} >> \\beta^{(M)} > \\beta^{(L)}$. ",
"Robust SEs. z-standardized."),
extra_lines = list(
c("UI Tercile", "Low", "Medium", "High"),
c("Mean UI Lev (\\%)",
round(mean(df_anyfed_s$uninsured_lev_raw[df_anyfed_s$uninsured_tercile=="Low"], na.rm=T), 1),
round(mean(df_anyfed_s$uninsured_lev_raw[df_anyfed_s$uninsured_tercile=="Medium"], na.rm=T), 1),
round(mean(df_anyfed_s$uninsured_lev_raw[df_anyfed_s$uninsured_tercile=="High"], na.rm=T), 1))))
etable(models_terc_any[!sapply(models_terc_any, is.null)], fitstat = ~ n + r2, se.below = TRUE)## Low UI Med UI High UI
## Dependent Var.: any_fed any_fed any_fed
##
## Constant 0.1826*** 0.2023*** 0.2167***
## (0.0132) (0.0105) (0.0126)
## MTM Loss (z) 0.0138 0.0170 0.0486***
## (0.0088) (0.0128) (0.0145)
## Log(Assets) 0.1015*** 0.0841*** 0.1267***
## (0.0135) (0.0157) (0.0129)
## Cash Ratio -0.0107 -0.0229 -0.0385**
## (0.0084) (0.0120) (0.0119)
## Loan-to-Deposit -0.0046 0.0044 -0.0115
## (0.0087) (0.0151) (0.0139)
## Book Equity Ratio -0.0144* -0.0365* -0.0075
## (0.0064) (0.0144) (0.0140)
## Wholesale Funding 0.0071 0.0585*** 0.0257
## (0.0089) (0.0132) (0.0138)
## ROA -0.0101 0.0146 0.0014
## (0.0080) (0.0115) (0.0112)
## _________________ __________ __________ __________
## S.E. type Hete.-rob. Hete.-rob. Hete.-rob.
## Observations 1,358 1,342 1,344
## R2 0.09509 0.08502 0.13289
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1cat("=== TERCILE: BTFP ===\n")## === TERCILE: BTFP ===mod_terc_btfp_L <- safe_run(df_btfp_s %>% filter(uninsured_tercile == "Low"), "btfp_crisis", EXPL_TERCILE)
mod_terc_btfp_M <- safe_run(df_btfp_s %>% filter(uninsured_tercile == "Medium"), "btfp_crisis", EXPL_TERCILE)
mod_terc_btfp_H <- safe_run(df_btfp_s %>% filter(uninsured_tercile == "High"), "btfp_crisis", EXPL_TERCILE)
models_terc_btfp <- list("Low UI" = mod_terc_btfp_L, "Med UI" = mod_terc_btfp_M, "High UI" = mod_terc_btfp_H)
save_etable(models_terc_btfp, "Tercile_BTFP",
title_text = "Threshold Gradient: BTFP Borrowing by Uninsured Tercile",
notes_text = paste0(
"LPM. Sample split into terciles of uninsured leverage. Robust SEs. z-standardized."),
extra_lines = list(c("UI Tercile", "Low", "Medium", "High")))
etable(models_terc_btfp[!sapply(models_terc_btfp, is.null)], fitstat = ~ n + r2, se.below = TRUE)## Low UI Med UI High UI
## Dependent Var.: btfp_crisis btfp_crisis btfp_crisis
##
## Constant 0.1203*** 0.1338*** 0.1583***
## (0.0119) (0.0093) (0.0118)
## MTM Loss (z) 0.0099 0.0075 0.0384**
## (0.0072) (0.0105) (0.0134)
## Log(Assets) 0.0718*** 0.0576*** 0.0855***
## (0.0120) (0.0145) (0.0132)
## Cash Ratio -0.0117 -0.0360*** -0.0408***
## (0.0062) (0.0096) (0.0099)
## Loan-to-Deposit -0.0032 -0.0216 -0.0135
## (0.0072) (0.0131) (0.0127)
## Book Equity Ratio -0.0097 -0.0263* -0.0184
## (0.0053) (0.0128) (0.0122)
## Wholesale Funding 0.0028 0.0562*** 0.0247
## (0.0067) (0.0136) (0.0138)
## ROA -0.0121 0.0079 -0.0027
## (0.0066) (0.0099) (0.0097)
## _________________ ___________ ___________ ___________
## S.E. type Heter.-rob. Heter.-rob. Heter.-rob.
## Observations 1,286 1,229 1,202
## R2 0.07578 0.07991 0.10071
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1cat("=== TERCILE: DW ===\n")## === TERCILE: DW ===mod_terc_dw_L <- safe_run(df_dw_s %>% filter(uninsured_tercile == "Low"), "dw_crisis", EXPL_TERCILE)
mod_terc_dw_M <- safe_run(df_dw_s %>% filter(uninsured_tercile == "Medium"), "dw_crisis", EXPL_TERCILE)
mod_terc_dw_H <- safe_run(df_dw_s %>% filter(uninsured_tercile == "High"), "dw_crisis", EXPL_TERCILE)
models_terc_dw <- list("Low UI" = mod_terc_dw_L, "Med UI" = mod_terc_dw_M, "High UI" = mod_terc_dw_H)
save_etable(models_terc_dw, "Tercile_DW",
title_text = "Threshold Gradient: DW Borrowing by Uninsured Tercile",
notes_text = paste0(
"LPM. Sample split into terciles of uninsured leverage. Robust SEs. z-standardized."),
extra_lines = list(c("UI Tercile", "Low", "Medium", "High")))
etable(models_terc_dw[!sapply(models_terc_dw, is.null)], fitstat = ~ n + r2, se.below = TRUE)## Low UI Med UI High UI
## Dependent Var.: dw_crisis dw_crisis dw_crisis
##
## Constant 0.1070*** 0.1207*** 0.1212***
## (0.0117) (0.0093) (0.0105)
## MTM Loss (z) 0.0014 0.0116 0.0325*
## (0.0070) (0.0112) (0.0129)
## Log(Assets) 0.0684*** 0.0690*** 0.1280***
## (0.0122) (0.0140) (0.0126)
## Cash Ratio -0.0027 0.0099 -0.0152
## (0.0072) (0.0106) (0.0105)
## Loan-to-Deposit -0.0070 0.0243 -0.0179
## (0.0069) (0.0132) (0.0124)
## Book Equity Ratio -0.0072 -0.0190 0.0098
## (0.0049) (0.0109) (0.0126)
## Wholesale Funding 0.0061 0.0336* 0.0243
## (0.0076) (0.0131) (0.0132)
## ROA -0.0041 0.0049 -0.0005
## (0.0067) (0.0098) (0.0099)
## _________________ __________ __________ __________
## S.E. type Hete.-rob. Hete.-rob. Hete.-rob.
## Observations 1,269 1,199 1,181
## R2 0.06042 0.05993 0.13873
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1models_terc_combined <- list(
"Any (L)" = mod_terc_any_L, "Any (M)" = mod_terc_any_M, "Any (H)" = mod_terc_any_H,
"BTFP (L)" = mod_terc_btfp_L, "BTFP (M)" = mod_terc_btfp_M, "BTFP (H)" = mod_terc_btfp_H,
"DW (L)" = mod_terc_dw_L, "DW (M)" = mod_terc_dw_M, "DW (H)" = mod_terc_dw_H)
save_etable(models_terc_combined, "Tercile_combined",
title_text = "Threshold Gradient: All Facilities by Uninsured Tercile (Crisis)",
notes_text = paste0(
"LPM. Borrower$_i = \\alpha^{(k)} + \\beta^{(k)} \\cdot$ MTM$_i + \\gamma \\mathbf{X}_i + \\varepsilon_i$ ",
"estimated separately for each uninsured leverage tercile $k$. ",
"Robust SEs. z-standardized."),
extra_lines = list(
c("UI Tercile", "L", "M", "H", "L", "M", "H", "L", "M", "H"),
c("Facility", "Any", "Any", "Any", "BTFP", "BTFP", "BTFP", "DW", "DW", "DW")))
etable(models_terc_combined[!sapply(models_terc_combined, is.null)], fitstat = ~ n + r2, se.below = TRUE)## Any (L) Any (M) Any (H) BTFP (L) BTFP (M)
## Dependent Var.: any_fed any_fed any_fed btfp_crisis btfp_crisis
##
## Constant 0.1826*** 0.2023*** 0.2167*** 0.1203*** 0.1338***
## (0.0132) (0.0105) (0.0126) (0.0119) (0.0093)
## MTM Loss (z) 0.0138 0.0170 0.0486*** 0.0099 0.0075
## (0.0088) (0.0128) (0.0145) (0.0072) (0.0105)
## Log(Assets) 0.1015*** 0.0841*** 0.1267*** 0.0718*** 0.0576***
## (0.0135) (0.0157) (0.0129) (0.0120) (0.0145)
## Cash Ratio -0.0107 -0.0229 -0.0385** -0.0117 -0.0360***
## (0.0084) (0.0120) (0.0119) (0.0062) (0.0096)
## Loan-to-Deposit -0.0046 0.0044 -0.0115 -0.0032 -0.0216
## (0.0087) (0.0151) (0.0139) (0.0072) (0.0131)
## Book Equity Ratio -0.0144* -0.0365* -0.0075 -0.0097 -0.0263*
## (0.0064) (0.0144) (0.0140) (0.0053) (0.0128)
## Wholesale Funding 0.0071 0.0585*** 0.0257 0.0028 0.0562***
## (0.0089) (0.0132) (0.0138) (0.0067) (0.0136)
## ROA -0.0101 0.0146 0.0014 -0.0121 0.0079
## (0.0080) (0.0115) (0.0112) (0.0066) (0.0099)
## _________________ __________ __________ __________ ___________ ___________
## S.E. type Hete.-rob. Hete.-rob. Hete.-rob. Heter.-rob. Heter.-rob.
## Observations 1,358 1,342 1,344 1,286 1,229
## R2 0.09509 0.08502 0.13289 0.07578 0.07991
##
## BTFP (H) DW (L) DW (M) DW (H)
## Dependent Var.: btfp_crisis dw_crisis dw_crisis dw_crisis
##
## Constant 0.1583*** 0.1070*** 0.1207*** 0.1212***
## (0.0118) (0.0117) (0.0093) (0.0105)
## MTM Loss (z) 0.0384** 0.0014 0.0116 0.0325*
## (0.0134) (0.0070) (0.0112) (0.0129)
## Log(Assets) 0.0855*** 0.0684*** 0.0690*** 0.1280***
## (0.0132) (0.0122) (0.0140) (0.0126)
## Cash Ratio -0.0408*** -0.0027 0.0099 -0.0152
## (0.0099) (0.0072) (0.0106) (0.0105)
## Loan-to-Deposit -0.0135 -0.0070 0.0243 -0.0179
## (0.0127) (0.0069) (0.0132) (0.0124)
## Book Equity Ratio -0.0184 -0.0072 -0.0190 0.0098
## (0.0122) (0.0049) (0.0109) (0.0126)
## Wholesale Funding 0.0247 0.0061 0.0336* 0.0243
## (0.0138) (0.0076) (0.0131) (0.0132)
## ROA -0.0027 -0.0041 0.0049 -0.0005
## (0.0097) (0.0067) (0.0098) (0.0099)
## _________________ ___________ __________ __________ __________
## S.E. type Heter.-rob. Hete.-rob. Hete.-rob. Hete.-rob.
## Observations 1,202 1,269 1,199 1,181
## R2 0.10071 0.06042 0.05993 0.13873
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1# ==============================================================================
# UNINSURED BETA CHANNEL
#
# Banks with low uninsured deposit betas (below median β^U) have deposits
# that are less rate-sensitive — "sticky" uninsured deposits. DSSW shows
# these banks have the highest franchise value but are also the most
# vulnerable to coordination failures: depositors don't leave for higher
# rates, but they WILL leave if they fear the bank is insolvent.
#
# Specification:
# Borrower_i = α + β₁·mtm + β₂·UI + β₃·UI×low_beta_UI
# + β₄·mtm×UI×low_beta_UI + γ·X_i + ε_i
#
# where low_beta_UI = 1 if bank's β^U is below the median.
#
# β₃ > 0: banks with sticky uninsured deposits borrow MORE (higher franchise
# value at risk, hence more precautionary borrowing)
# β₄ > 0: the MTM × Uninsured amplification is STRONGER for low-beta banks
# (franchise value is larger → more to lose from a run)
# ==============================================================================
cat("=== UNINSURED BETA CHANNEL: LOW β^U INTERACTION ===\n\n")## === UNINSURED BETA CHANNEL: LOW β^U INTERACTION ===# Define low_beta_UI = below median uninsured beta
beta_median <- median(df_crisis$uninsured_beta_raw, na.rm = TRUE)
cat(sprintf(" Median uninsured beta (β^U): %.4f\n", beta_median))## Median uninsured beta (β^U): 0.3106add_low_beta <- function(df) {
df %>% mutate(
low_beta_UI = as.integer(!is.na(uninsured_beta_raw) & uninsured_beta_raw <= beta_median),
# Interactions
UI_x_lowbeta = uninsured_lev * low_beta_UI,
mtm_x_UI_x_lowbeta = mtm_total * uninsured_lev * low_beta_UI
)
}
df_anyfed_s <- add_low_beta(df_anyfed_s)
df_btfp_s <- add_low_beta(df_btfp_s)
df_dw_s <- add_low_beta(df_dw_s)
df_fhlb_s <- add_low_beta(df_fhlb_s)
# Spec: mtm + UI + UI*low_beta + mtm*UI*low_beta
EXPL_LOWBETA <- "mtm_total + uninsured_lev + UI_x_lowbeta + mtm_x_UI_x_lowbeta"
# Register labels
setFixest_dict(c(
low_beta_UI = "Low $\\beta^U$ (below median)",
UI_x_lowbeta = "Uninsured $\\times$ Low $\\beta^U$",
mtm_x_UI_x_lowbeta = "MTM $\\times$ UI $\\times$ Low $\\beta^U$"
))
# Filter to banks with beta coverage
df_lowbeta_any <- df_anyfed_s %>% filter(!is.na(uninsured_beta_raw))
df_lowbeta_btfp <- df_btfp_s %>% filter(!is.na(uninsured_beta_raw))
df_lowbeta_dw <- df_dw_s %>% filter(!is.na(uninsured_beta_raw))
df_lowbeta_fhlb <- df_fhlb_s %>% filter(!is.na(uninsured_beta_raw))
cat(sprintf(" Low β^U banks: %d / %d (%.1f%%)\n",
sum(df_lowbeta_any$low_beta_UI), nrow(df_lowbeta_any),
100 * mean(df_lowbeta_any$low_beta_UI)))## Low β^U banks: 2029 / 3991 (50.8%)cat(sprintf(" Beta coverage: AnyFed=%d, BTFP=%d, DW=%d, FHLB=%d\n",
nrow(df_lowbeta_any), nrow(df_lowbeta_btfp),
nrow(df_lowbeta_dw), nrow(df_lowbeta_fhlb)))## Beta coverage: AnyFed=3991, BTFP=3665, DW=3599, FHLB=3468cat("=== LOW β^U: FULL SAMPLE ===\n")## === LOW β^U: FULL SAMPLE ===mod_lb_any <- safe_run(df_lowbeta_any, "any_fed", EXPL_LOWBETA)
mod_lb_btfp <- safe_run(df_lowbeta_btfp, "btfp_crisis", EXPL_LOWBETA)
mod_lb_dw <- safe_run(df_lowbeta_dw, "dw_crisis", EXPL_LOWBETA)
mod_lb_fhlb <- safe_run(df_lowbeta_fhlb, "fhlb_user", EXPL_LOWBETA)
models_lb_full <- list(
"Any Fed" = mod_lb_any, "BTFP" = mod_lb_btfp,
"DW" = mod_lb_dw, "FHLB" = mod_lb_fhlb)
save_etable(models_lb_full, "LowBeta_full_sample",
title_text = "Uninsured Beta Channel: Low $\\beta^U$ Interaction (Full Sample, Crisis)",
notes_text = paste0(
"LPM. Low $\\beta^U$ = below-median uninsured deposit beta. ",
"Specification: MTM + UI + UI $\\times$ Low $\\beta^U$ + MTM $\\times$ UI $\\times$ Low $\\beta^U$ + Controls. ",
"DSSW prediction: banks with sticky uninsured deposits (low $\\beta^U$) have larger franchise value ",
"but wider panic region. FHLB: falsification. Robust SEs. z-standardized."),
extra_lines = list(
c("Median $\\beta^U$", round(beta_median, 3), round(beta_median, 3),
round(beta_median, 3), round(beta_median, 3))))
etable(models_lb_full[!sapply(models_lb_full, is.null)], fitstat = ~ n + r2, se.below = TRUE)## Any Fed BTFP DW
## Dependent Var.: any_fed btfp_crisis dw_crisis
##
## Constant 0.2059*** 0.1412*** 0.1258***
## (0.0060) (0.0056) (0.0054)
## MTM Loss (z) 0.0272*** 0.0220*** 0.0132*
## (0.0068) (0.0059) (0.0058)
## Uninsured Leverage (z) 0.0086 0.0130 0.0056
## (0.0101) (0.0093) (0.0090)
## Uninsured $\times$ Low $\beta^U$ 0.0201 0.0153 0.0095
## (0.0122) (0.0112) (0.0109)
## MTM $\times$ UI $\times$ Low $\beta^U$ 0.0296*** 0.0270*** 0.0239***
## (0.0073) (0.0069) (0.0065)
## Log(Assets) 0.1079*** 0.0726*** 0.0934***
## (0.0083) (0.0078) (0.0078)
## Cash Ratio -0.0245*** -0.0287*** -0.0039
## (0.0064) (0.0050) (0.0055)
## Loan-to-Deposit -0.0032 -0.0100 -0.0012
## (0.0071) (0.0062) (0.0061)
## Book Equity Ratio -0.0158** -0.0142** -0.0019
## (0.0059) (0.0050) (0.0048)
## Wholesale Funding 0.0303*** 0.0273*** 0.0208**
## (0.0069) (0.0066) (0.0063)
## ROA -0.0030 -0.0071 -0.0029
## (0.0060) (0.0052) (0.0051)
## ______________________________________ __________ ___________ __________
## S.E. type Hete.-rob. Heter.-rob. Hete.-rob.
## Observations 3,991 3,665 3,599
## R2 0.12086 0.09665 0.10290
##
## FHLB
## Dependent Var.: fhlb_user
##
## Constant 0.0906***
## (0.0050)
## MTM Loss (z) 0.0056
## (0.0054)
## Uninsured Leverage (z) 0.0125
## (0.0074)
## Uninsured $\times$ Low $\beta^U$ -0.0094
## (0.0095)
## MTM $\times$ UI $\times$ Low $\beta^U$ -0.0016
## (0.0056)
## Log(Assets) 0.0275***
## (0.0065)
## Cash Ratio -0.0202***
## (0.0041)
## Loan-to-Deposit 0.0261***
## (0.0054)
## Book Equity Ratio 0.0089*
## (0.0045)
## Wholesale Funding 0.0021
## (0.0051)
## ROA -0.0105*
## (0.0045)
## ______________________________________ __________
## S.E. type Hete.-rob.
## Observations 3,468
## R2 0.04081
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1cat("=== LOW β^U: SMALL BANKS (≤$10B) ===\n")## === LOW β^U: SMALL BANKS (≤$10B) ===mod_lb_any_sm <- safe_run(df_lowbeta_any %>% filter(size_group == "Small (<=10B)"), "any_fed", EXPL_LOWBETA)
mod_lb_btfp_sm <- safe_run(df_lowbeta_btfp %>% filter(size_group == "Small (<=10B)"), "btfp_crisis", EXPL_LOWBETA)
mod_lb_dw_sm <- safe_run(df_lowbeta_dw %>% filter(size_group == "Small (<=10B)"), "dw_crisis", EXPL_LOWBETA)
mod_lb_fhlb_sm <- safe_run(df_lowbeta_fhlb %>% filter(size_group == "Small (<=10B)"), "fhlb_user", EXPL_LOWBETA)
models_lb_sm <- list(
"Any Fed" = mod_lb_any_sm, "BTFP" = mod_lb_btfp_sm,
"DW" = mod_lb_dw_sm, "FHLB" = mod_lb_fhlb_sm)
save_etable(models_lb_sm, "LowBeta_small_le10B",
title_text = "Low $\\beta^U$ Interaction: Small Banks ($\\leq$ \\$10B)",
notes_text = "LPM. Banks $\\leq$ \\$10B with uninsured beta coverage. Robust SEs. z-standardized.",
extra_lines = list(c("Size Group", "Small", "Small", "Small", "Small")))
etable(models_lb_sm[!sapply(models_lb_sm, is.null)], fitstat = ~ n + r2, se.below = TRUE)## Any Fed BTFP DW
## Dependent Var.: any_fed btfp_crisis dw_crisis
##
## Constant 0.2042*** 0.1380*** 0.1216***
## (0.0063) (0.0058) (0.0056)
## MTM Loss (z) 0.0268*** 0.0229*** 0.0124*
## (0.0068) (0.0059) (0.0058)
## Uninsured Leverage (z) -0.0018 0.0044 -0.0038
## (0.0103) (0.0094) (0.0089)
## Uninsured $\times$ Low $\beta^U$ 0.0229 0.0205 0.0105
## (0.0124) (0.0111) (0.0107)
## MTM $\times$ UI $\times$ Low $\beta^U$ 0.0289*** 0.0263*** 0.0202**
## (0.0074) (0.0068) (0.0064)
## Log(Assets) 0.1083*** 0.0679*** 0.0882***
## (0.0091) (0.0082) (0.0083)
## Cash Ratio -0.0219*** -0.0271*** -0.0015
## (0.0063) (0.0050) (0.0054)
## Loan-to-Deposit -0.0044 -0.0101 -0.0013
## (0.0072) (0.0062) (0.0061)
## Book Equity Ratio -0.0181** -0.0157** -0.0059
## (0.0059) (0.0050) (0.0047)
## Wholesale Funding 0.0313*** 0.0275*** 0.0198**
## (0.0070) (0.0067) (0.0064)
## ROA -0.0008 -0.0056 -0.0001
## (0.0060) (0.0051) (0.0051)
## ______________________________________ __________ ___________ __________
## S.E. type Hete.-rob. Heter.-rob. Hete.-rob.
## Observations 3,866 3,567 3,493
## R2 0.10365 0.08271 0.07700
##
## FHLB
## Dependent Var.: fhlb_user
##
## Constant 0.0877***
## (0.0051)
## MTM Loss (z) 0.0061
## (0.0054)
## Uninsured Leverage (z) 0.0051
## (0.0074)
## Uninsured $\times$ Low $\beta^U$ -0.0030
## (0.0092)
## MTM $\times$ UI $\times$ Low $\beta^U$ -0.0021
## (0.0055)
## Log(Assets) 0.0222**
## (0.0069)
## Cash Ratio -0.0192***
## (0.0040)
## Loan-to-Deposit 0.0272***
## (0.0055)
## Book Equity Ratio 0.0054
## (0.0043)
## Wholesale Funding 0.0044
## (0.0053)
## ROA -0.0091*
## (0.0045)
## ______________________________________ __________
## S.E. type Hete.-rob.
## Observations 3,392
## R2 0.03474
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1cat("=== LOW β^U: LARGE BANKS (>$10B) ===\n")## === LOW β^U: LARGE BANKS (>$10B) ===mod_lb_any_lg <- safe_run(df_lowbeta_any %>% filter(size_group == "Large (>10B)"), "any_fed", EXPL_LOWBETA)
mod_lb_btfp_lg <- safe_run(df_lowbeta_btfp %>% filter(size_group == "Large (>10B)"), "btfp_crisis", EXPL_LOWBETA)
mod_lb_dw_lg <- safe_run(df_lowbeta_dw %>% filter(size_group == "Large (>10B)"), "dw_crisis", EXPL_LOWBETA)
mod_lb_fhlb_lg <- safe_run(df_lowbeta_fhlb %>% filter(size_group == "Large (>10B)"), "fhlb_user", EXPL_LOWBETA)
models_lb_lg <- list(
"Any Fed" = mod_lb_any_lg, "BTFP" = mod_lb_btfp_lg,
"DW" = mod_lb_dw_lg, "FHLB" = mod_lb_fhlb_lg)
save_etable(models_lb_lg, "LowBeta_large_gt10B",
title_text = "Low $\\beta^U$ Interaction: Large Banks ($>$ \\$10B)",
notes_text = "LPM. Banks $>$ \\$10B with uninsured beta coverage. Robust SEs. z-standardized.",
extra_lines = list(c("Size Group", "Large", "Large", "Large", "Large")))
etable(models_lb_lg[!sapply(models_lb_lg, is.null)], fitstat = ~ n + r2, se.below = TRUE)## Any Fed BTFP DW
## Dependent Var.: any_fed btfp_crisis dw_crisis
##
## Constant 3.242 3.096 3.961
## (2.039) (2.741) (2.311)
## MTM Loss (z) 0.0288 0.0007 0.0640
## (0.0747) (0.0782) (0.0685)
## Uninsured Leverage (z) 0.1368** 0.1506*** 0.1373**
## (0.0414) (0.0432) (0.0408)
## Uninsured $\times$ Low $\beta^U$ 0.0956 0.0796 0.1255
## (0.0554) (0.0676) (0.0746)
## MTM $\times$ UI $\times$ Low $\beta^U$ -0.0155 0.0063 -0.0411
## (0.0511) (0.0654) (0.0700)
## Log(Assets) -1.121 -1.109 -1.434
## (0.7912) (1.060) (0.8965)
## Cash Ratio -0.1171 -0.1097 -0.0856
## (0.0754) (0.0772) (0.0727)
## Loan-to-Deposit 0.0232 0.0202 0.0761
## (0.0756) (0.0787) (0.0669)
## Book Equity Ratio -0.0728 -0.1164 -0.0844
## (0.0703) (0.0751) (0.0770)
## Wholesale Funding -0.0084 -0.0092 0.0045
## (0.0365) (0.0407) (0.0371)
## ROA 0.0252 0.0694 0.0221
## (0.0634) (0.0658) (0.0653)
## ______________________________________ _________ ___________ _________
## S.E. type Het.-rob. Heter.-rob. Het.-rob.
## Observations 125 98 106
## R2 0.20759 0.19790 0.24392
##
## FHLB
## Dependent Var.: fhlb_user
##
## Constant 0.6629
## (3.138)
## MTM Loss (z) 0.0283
## (0.0720)
## Uninsured Leverage (z) 0.1309**
## (0.0405)
## Uninsured $\times$ Low $\beta^U$ 0.0316
## (0.1013)
## MTM $\times$ UI $\times$ Low $\beta^U$ -0.0608
## (0.1148)
## Log(Assets) -0.1943
## (1.212)
## Cash Ratio 0.0142
## (0.0733)
## Loan-to-Deposit 0.0269
## (0.0650)
## Book Equity Ratio 0.0672
## (0.0790)
## Wholesale Funding -0.0835**
## (0.0280)
## ROA 0.0269
## (0.0541)
## ______________________________________ _________
## S.E. type Het.-rob.
## Observations 76
## R2 0.21737
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1models_lb_combined <- list(
"Any (Full)" = mod_lb_any, "Any (Sm)" = mod_lb_any_sm, "Any (Lg)" = mod_lb_any_lg,
"BTFP (Full)" = mod_lb_btfp, "BTFP (Sm)" = mod_lb_btfp_sm, "BTFP (Lg)" = mod_lb_btfp_lg,
"DW (Full)" = mod_lb_dw, "DW (Sm)" = mod_lb_dw_sm, "DW (Lg)" = mod_lb_dw_lg)
save_etable(models_lb_combined, "LowBeta_combined_size",
title_text = "Low $\\beta^U$ Interaction: Full Sample $\\times$ Size Split (Crisis)",
notes_text = paste0(
"LPM. Low $\\beta^U$ = below-median uninsured deposit beta (median = ",
round(beta_median, 3), "). ",
"Full = all banks; Sm = $\\leq$ \\$10B; Lg = $>$ \\$10B. ",
"DSSW prediction: MTM $\\times$ UI $\\times$ Low $\\beta^U > 0$ — panic amplification ",
"is stronger for banks with stickier (lower-beta) uninsured deposits. ",
"Robust SEs. z-standardized."),
extra_lines = list(
c("Sample", "Full", "Sm", "Lg", "Full", "Sm", "Lg", "Full", "Sm", "Lg"),
c("Facility", "Any", "Any", "Any", "BTFP", "BTFP", "BTFP", "DW", "DW", "DW")))
etable(models_lb_combined[!sapply(models_lb_combined, is.null)], fitstat = ~ n + r2, se.below = TRUE)## Any (Full) Any (Sm) Any (Lg)
## Dependent Var.: any_fed any_fed any_fed
##
## Constant 0.2059*** 0.2042*** 3.242
## (0.0060) (0.0063) (2.039)
## MTM Loss (z) 0.0272*** 0.0268*** 0.0288
## (0.0068) (0.0068) (0.0747)
## Uninsured Leverage (z) 0.0086 -0.0018 0.1368**
## (0.0101) (0.0103) (0.0414)
## Uninsured $\times$ Low $\beta^U$ 0.0201 0.0229 0.0956
## (0.0122) (0.0124) (0.0554)
## MTM $\times$ UI $\times$ Low $\beta^U$ 0.0296*** 0.0289*** -0.0155
## (0.0073) (0.0074) (0.0511)
## Log(Assets) 0.1079*** 0.1083*** -1.121
## (0.0083) (0.0091) (0.7912)
## Cash Ratio -0.0245*** -0.0219*** -0.1171
## (0.0064) (0.0063) (0.0754)
## Loan-to-Deposit -0.0032 -0.0044 0.0232
## (0.0071) (0.0072) (0.0756)
## Book Equity Ratio -0.0158** -0.0181** -0.0728
## (0.0059) (0.0059) (0.0703)
## Wholesale Funding 0.0303*** 0.0313*** -0.0084
## (0.0069) (0.0070) (0.0365)
## ROA -0.0030 -0.0008 0.0252
## (0.0060) (0.0060) (0.0634)
## ______________________________________ __________ __________ _________
## S.E. type Hete.-rob. Hete.-rob. Het.-rob.
## Observations 3,991 3,866 125
## R2 0.12086 0.10365 0.20759
##
## BTFP (Full) BTFP (Sm) BTFP (Lg)
## Dependent Var.: btfp_crisis btfp_crisis btfp_crisis
##
## Constant 0.1412*** 0.1380*** 3.096
## (0.0056) (0.0058) (2.741)
## MTM Loss (z) 0.0220*** 0.0229*** 0.0007
## (0.0059) (0.0059) (0.0782)
## Uninsured Leverage (z) 0.0130 0.0044 0.1506***
## (0.0093) (0.0094) (0.0432)
## Uninsured $\times$ Low $\beta^U$ 0.0153 0.0205 0.0796
## (0.0112) (0.0111) (0.0676)
## MTM $\times$ UI $\times$ Low $\beta^U$ 0.0270*** 0.0263*** 0.0063
## (0.0069) (0.0068) (0.0654)
## Log(Assets) 0.0726*** 0.0679*** -1.109
## (0.0078) (0.0082) (1.060)
## Cash Ratio -0.0287*** -0.0271*** -0.1097
## (0.0050) (0.0050) (0.0772)
## Loan-to-Deposit -0.0100 -0.0101 0.0202
## (0.0062) (0.0062) (0.0787)
## Book Equity Ratio -0.0142** -0.0157** -0.1164
## (0.0050) (0.0050) (0.0751)
## Wholesale Funding 0.0273*** 0.0275*** -0.0092
## (0.0066) (0.0067) (0.0407)
## ROA -0.0071 -0.0056 0.0694
## (0.0052) (0.0051) (0.0658)
## ______________________________________ ___________ ___________ ___________
## S.E. type Heter.-rob. Heter.-rob. Heter.-rob.
## Observations 3,665 3,567 98
## R2 0.09665 0.08271 0.19790
##
## DW (Full) DW (Sm) DW (Lg)
## Dependent Var.: dw_crisis dw_crisis dw_crisis
##
## Constant 0.1258*** 0.1216*** 3.961
## (0.0054) (0.0056) (2.311)
## MTM Loss (z) 0.0132* 0.0124* 0.0640
## (0.0058) (0.0058) (0.0685)
## Uninsured Leverage (z) 0.0056 -0.0038 0.1373**
## (0.0090) (0.0089) (0.0408)
## Uninsured $\times$ Low $\beta^U$ 0.0095 0.0105 0.1255
## (0.0109) (0.0107) (0.0746)
## MTM $\times$ UI $\times$ Low $\beta^U$ 0.0239*** 0.0202** -0.0411
## (0.0065) (0.0064) (0.0700)
## Log(Assets) 0.0934*** 0.0882*** -1.434
## (0.0078) (0.0083) (0.8965)
## Cash Ratio -0.0039 -0.0015 -0.0856
## (0.0055) (0.0054) (0.0727)
## Loan-to-Deposit -0.0012 -0.0013 0.0761
## (0.0061) (0.0061) (0.0669)
## Book Equity Ratio -0.0019 -0.0059 -0.0844
## (0.0048) (0.0047) (0.0770)
## Wholesale Funding 0.0208** 0.0198** 0.0045
## (0.0063) (0.0064) (0.0371)
## ROA -0.0029 -0.0001 0.0221
## (0.0051) (0.0051) (0.0653)
## ______________________________________ __________ __________ _________
## S.E. type Hete.-rob. Hete.-rob. Het.-rob.
## Observations 3,599 3,493 106
## R2 0.10290 0.07700 0.24392
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1# ==============================================================================
# PUBLIC vs. NON-PUBLIC BANK SPLIT
#
# Public banks (traded on equity markets) face dual market discipline:
# 1. Equity market: stock price declines signal distress → may trigger runs
# 2. Deposit market: uninsured depositors withdraw
#
# Non-public banks face only the deposit channel. If the coordination
# failure story holds, the MTM × Uninsured interaction should be strong
# across BOTH groups — the fundamental mechanism is depositor coordination,
# not equity market signaling.
#
# However, public banks may show STRONGER effects because equity price
# declines provide a publicly visible signal that helps depositors
# coordinate on the "run" equilibrium.
#
# Public status identified via NY Fed CRSP-FRB Link → NIC BHC hierarchy
# → CRSP PERMCO match (time-valid).
# ==============================================================================
cat("=== PUBLIC vs. NON-PUBLIC BANKS ===\n\n")## === PUBLIC vs. NON-PUBLIC BANKS ===# Ensure is_public is available on regression samples
cat(sprintf(" Crisis sample (df_crisis): %d public, %d non-public\n",
sum(df_crisis$is_public == 1, na.rm = TRUE),
sum(df_crisis$is_public == 0, na.rm = TRUE)))## Crisis sample (df_crisis): 311 public, 3981 non-public# Counts per regression sample
for (nm in c("df_anyfed_s", "df_btfp_s", "df_dw_s", "df_fhlb_s")) {
d <- get(nm)
cat(sprintf(" %s: %d public (borrowers: %d), %d non-public (borrowers: %d)\n",
nm,
sum(d$is_public == 1, na.rm = TRUE),
sum(d$is_public == 1 & d[[ifelse(nm == "df_anyfed_s", "any_fed",
ifelse(nm == "df_btfp_s", "btfp_crisis",
ifelse(nm == "df_dw_s", "dw_crisis", "fhlb_user")))]] == 1, na.rm = TRUE),
sum(d$is_public == 0, na.rm = TRUE),
sum(d$is_public == 0 & d[[ifelse(nm == "df_anyfed_s", "any_fed",
ifelse(nm == "df_btfp_s", "btfp_crisis",
ifelse(nm == "df_dw_s", "dw_crisis", "fhlb_user")))]] == 1, na.rm = TRUE)))
}## df_anyfed_s: 288 public (borrowers: 106), 3766 non-public (borrowers: 722)
## df_btfp_s: 230 public (borrowers: 48), 3497 non-public (borrowers: 453)
## df_dw_s: 265 public (borrowers: 83), 3394 non-public (borrowers: 350)
## df_fhlb_s: 222 public (borrowers: 40), 3306 non-public (borrowers: 262)cat("=== PUBLIC BANKS ===\n")## === PUBLIC BANKS ===mod_pub_any <- safe_run(df_anyfed_s %>% filter(is_public == 1), "any_fed", EXPL_BASE)
mod_pub_btfp <- safe_run(df_btfp_s %>% filter(is_public == 1), "btfp_crisis", EXPL_BASE)
mod_pub_dw <- safe_run(df_dw_s %>% filter(is_public == 1), "dw_crisis", EXPL_BASE)
mod_pub_fhlb <- safe_run(df_fhlb_s %>% filter(is_public == 1), "fhlb_user", EXPL_BASE)
models_pub <- list(
"Any Fed" = mod_pub_any, "BTFP" = mod_pub_btfp,
"DW" = mod_pub_dw, "FHLB" = mod_pub_fhlb)
save_etable(models_pub, "Public_banks_crisis",
title_text = "Public Banks: Extensive Margin (Crisis Period)",
notes_text = paste0(
"LPM. Sample restricted to publicly traded banks (NY Fed CRSP-FRB Link via NIC hierarchy). ",
"Public banks face dual discipline: equity market price signals AND depositor runs. ",
"FHLB: falsification. Robust SEs. z-standardized."),
extra_lines = list(
c("Listed", "Yes", "Yes", "Yes", "Yes")))
etable(models_pub[!sapply(models_pub, is.null)], fitstat = ~ n + r2, se.below = TRUE)## Any Fed BTFP DW FHLB
## Dependent Var.: any_fed btfp_crisis dw_crisis fhlb_user
##
## Constant 0.0994 -0.0580 0.0936 0.0026
## (0.0645) (0.0526) (0.0631) (0.0494)
## MTM Loss (z) 0.0605 0.0463 0.0384 0.0259
## (0.0311) (0.0290) (0.0296) (0.0260)
## Uninsured Leverage (z) 0.1158*** 0.0828** 0.1062*** 0.0546*
## (0.0280) (0.0277) (0.0282) (0.0234)
## MTM $\times$ Uninsured 0.0087 -0.0028 0.0253 -0.0142
## (0.0246) (0.0235) (0.0238) (0.0173)
## Log(Assets) 0.1005** 0.1060** 0.0875* 0.0659*
## (0.0350) (0.0320) (0.0341) (0.0303)
## Cash Ratio -0.0767 -0.0634 -0.0721 -0.0523*
## (0.0443) (0.0341) (0.0425) (0.0263)
## Loan-to-Deposit -0.0356 -0.0237 -0.0444 0.0080
## (0.0309) (0.0271) (0.0302) (0.0231)
## Book Equity Ratio 0.0500 0.0183 0.0493 0.1062**
## (0.0397) (0.0364) (0.0390) (0.0336)
## Wholesale Funding 0.0157 0.0191 0.0238 -0.0185
## (0.0296) (0.0282) (0.0302) (0.0276)
## ROA -0.0210 0.0412 -0.0414 -0.0235
## (0.0425) (0.0359) (0.0404) (0.0374)
## ______________________ __________ ___________ __________ _________
## S.E. type Hete.-rob. Heter.-rob. Hete.-rob. Het.-rob.
## Observations 288 230 265 222
## R2 0.13486 0.13655 0.12435 0.09231
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1cat("=== NON-PUBLIC BANKS ===\n")## === NON-PUBLIC BANKS ===mod_npub_any <- safe_run(df_anyfed_s %>% filter(is_public == 0), "any_fed", EXPL_BASE)
mod_npub_btfp <- safe_run(df_btfp_s %>% filter(is_public == 0), "btfp_crisis", EXPL_BASE)
mod_npub_dw <- safe_run(df_dw_s %>% filter(is_public == 0), "dw_crisis", EXPL_BASE)
mod_npub_fhlb <- safe_run(df_fhlb_s %>% filter(is_public == 0), "fhlb_user", EXPL_BASE)
models_npub <- list(
"Any Fed" = mod_npub_any, "BTFP" = mod_npub_btfp,
"DW" = mod_npub_dw, "FHLB" = mod_npub_fhlb)
save_etable(models_npub, "NonPublic_banks_crisis",
title_text = "Non-Public Banks: Extensive Margin (Crisis Period)",
notes_text = paste0(
"LPM. Sample restricted to non-publicly-traded banks. ",
"These banks face only the deposit channel (no equity price signal). ",
"If MTM $\\times$ Uninsured is significant here, the coordination problem ",
"operates through depositor-level information, not equity market signals. ",
"FHLB: falsification. Robust SEs. z-standardized."),
extra_lines = list(
c("Listed", "No", "No", "No", "No")))
etable(models_npub[!sapply(models_npub, is.null)], fitstat = ~ n + r2, se.below = TRUE)## Any Fed BTFP DW FHLB
## Dependent Var.: any_fed btfp_crisis dw_crisis fhlb_user
##
## Constant 0.2130*** 0.1504*** 0.1243*** 0.0879***
## (0.0066) (0.0062) (0.0060) (0.0053)
## MTM Loss (z) 0.0268*** 0.0230*** 0.0127* 0.0039
## (0.0072) (0.0063) (0.0061) (0.0057)
## Uninsured Leverage (z) 0.0098 0.0149* 0.0027 0.0027
## (0.0079) (0.0073) (0.0069) (0.0053)
## MTM $\times$ Uninsured 0.0202*** 0.0212*** 0.0145** -0.0040
## (0.0059) (0.0053) (0.0051) (0.0043)
## Log(Assets) 0.1191*** 0.0851*** 0.0905*** 0.0213**
## (0.0093) (0.0088) (0.0087) (0.0070)
## Cash Ratio -0.0228*** -0.0282*** -0.0012 -0.0197***
## (0.0062) (0.0049) (0.0052) (0.0039)
## Loan-to-Deposit -0.0042 -0.0122* 0.0010 0.0252***
## (0.0068) (0.0059) (0.0058) (0.0052)
## Book Equity Ratio -0.0153** -0.0115* -0.0049 0.0055
## (0.0055) (0.0047) (0.0043) (0.0041)
## Wholesale Funding 0.0292*** 0.0256*** 0.0180** 0.0027
## (0.0071) (0.0067) (0.0064) (0.0052)
## ROA -0.0007 -0.0065 -0.0002 -0.0080
## (0.0058) (0.0049) (0.0049) (0.0043)
## ______________________ __________ ___________ __________ __________
## S.E. type Hete.-rob. Heter.-rob. Hete.-rob. Hete.-rob.
## Observations 3,756 3,487 3,384 3,296
## R2 0.11435 0.09783 0.08008 0.03363
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1models_pub_combined <- list(
"Any (Pub)" = mod_pub_any, "Any (NP)" = mod_npub_any,
"BTFP (Pub)" = mod_pub_btfp, "BTFP (NP)" = mod_npub_btfp,
"DW (Pub)" = mod_pub_dw, "DW (NP)" = mod_npub_dw,
"FHLB (Pub)" = mod_pub_fhlb, "FHLB (NP)" = mod_npub_fhlb)
save_etable(models_pub_combined, "Public_NonPublic_combined",
title_text = "Public vs. Non-Public Banks: Extensive Margin (Crisis Period)",
notes_text = paste0(
"LPM. Pub = publicly traded (CRSP-linked); NP = non-public. ",
"Public banks face dual discipline (equity + deposits); non-public face deposits only. ",
"If MTM $\\times$ Uninsured is significant among non-public banks, the coordination ",
"failure operates through depositor-level information rather than equity market signals. ",
"FHLB: falsification. Robust SEs. z-standardized."),
extra_lines = list(
c("Listed", "Pub", "NP", "Pub", "NP", "Pub", "NP", "Pub", "NP")))
etable(models_pub_combined[!sapply(models_pub_combined, is.null)], fitstat = ~ n + r2, se.below = TRUE)## Any (Pub) Any (NP) BTFP (Pub) BTFP (NP) DW (Pub)
## Dependent Var.: any_fed any_fed btfp_crisis btfp_crisis dw_crisis
##
## Constant 0.0994 0.2130*** -0.0580 0.1504*** 0.0936
## (0.0645) (0.0066) (0.0526) (0.0062) (0.0631)
## MTM Loss (z) 0.0605 0.0268*** 0.0463 0.0230*** 0.0384
## (0.0311) (0.0072) (0.0290) (0.0063) (0.0296)
## Uninsured Leverage (z) 0.1158*** 0.0098 0.0828** 0.0149* 0.1062***
## (0.0280) (0.0079) (0.0277) (0.0073) (0.0282)
## MTM $\times$ Uninsured 0.0087 0.0202*** -0.0028 0.0212*** 0.0253
## (0.0246) (0.0059) (0.0235) (0.0053) (0.0238)
## Log(Assets) 0.1005** 0.1191*** 0.1060** 0.0851*** 0.0875*
## (0.0350) (0.0093) (0.0320) (0.0088) (0.0341)
## Cash Ratio -0.0767 -0.0228*** -0.0634 -0.0282*** -0.0721
## (0.0443) (0.0062) (0.0341) (0.0049) (0.0425)
## Loan-to-Deposit -0.0356 -0.0042 -0.0237 -0.0122* -0.0444
## (0.0309) (0.0068) (0.0271) (0.0059) (0.0302)
## Book Equity Ratio 0.0500 -0.0153** 0.0183 -0.0115* 0.0493
## (0.0397) (0.0055) (0.0364) (0.0047) (0.0390)
## Wholesale Funding 0.0157 0.0292*** 0.0191 0.0256*** 0.0238
## (0.0296) (0.0071) (0.0282) (0.0067) (0.0302)
## ROA -0.0210 -0.0007 0.0412 -0.0065 -0.0414
## (0.0425) (0.0058) (0.0359) (0.0049) (0.0404)
## ______________________ __________ __________ ___________ ___________ __________
## S.E. type Hete.-rob. Hete.-rob. Heter.-rob. Heter.-rob. Hete.-rob.
## Observations 288 3,756 230 3,487 265
## R2 0.13486 0.11435 0.13655 0.09783 0.12435
##
## DW (NP) FHLB (P.. FHLB (NP)
## Dependent Var.: dw_crisis fhlb_user fhlb_user
##
## Constant 0.1243*** 0.0026 0.0879***
## (0.0060) (0.0494) (0.0053)
## MTM Loss (z) 0.0127* 0.0259 0.0039
## (0.0061) (0.0260) (0.0057)
## Uninsured Leverage (z) 0.0027 0.0546* 0.0027
## (0.0069) (0.0234) (0.0053)
## MTM $\times$ Uninsured 0.0145** -0.0142 -0.0040
## (0.0051) (0.0173) (0.0043)
## Log(Assets) 0.0905*** 0.0659* 0.0213**
## (0.0087) (0.0303) (0.0070)
## Cash Ratio -0.0012 -0.0523* -0.0197***
## (0.0052) (0.0263) (0.0039)
## Loan-to-Deposit 0.0010 0.0080 0.0252***
## (0.0058) (0.0231) (0.0052)
## Book Equity Ratio -0.0049 0.1062** 0.0055
## (0.0043) (0.0336) (0.0041)
## Wholesale Funding 0.0180** -0.0185 0.0027
## (0.0064) (0.0276) (0.0052)
## ROA -0.0002 -0.0235 -0.0080
## (0.0049) (0.0374) (0.0043)
## ______________________ __________ _________ __________
## S.E. type Hete.-rob. Het.-rob. Hete.-rob.
## Observations 3,384 222 3,296
## R2 0.08008 0.09231 0.03363
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1cat("--- Mean Characteristics: Public vs. Non-Public (2022Q4 Baseline) ---\n\n")## --- Mean Characteristics: Public vs. Non-Public (2022Q4 Baseline) ---desc_pub_vars <- c("mtm_total_raw", "uninsured_lev_raw", "uninsured_beta_raw",
"adjusted_equity_raw", "dfv_raw", "ln_assets_raw", "cash_ratio_raw",
"book_equity_ratio_raw", "roa_raw", "wholesale_raw")
pub_desc <- df_2022q4 %>%
group_by(Public = ifelse(is_public == 1, "Public", "Non-Public")) %>%
summarise(
N = n(),
across(all_of(desc_pub_vars), ~round(mean(., na.rm = TRUE), 3)),
.groups = "drop"
)
print(pub_desc, width = Inf)## # A tibble: 2 × 12
## Public N mtm_total_raw uninsured_lev_raw uninsured_beta_raw
## <chr> <int> <dbl> <dbl> <dbl>
## 1 Non-Public 3981 5.48 23.0 0.328
## 2 Public 311 5.28 31.7 0.372
## adjusted_equity_raw dfv_raw ln_assets_raw cash_ratio_raw book_equity_ratio_raw
## <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 4.58 77.8 12.7 8.42 10.2
## 2 5.82 68.0 15.5 4.63 11.1
## roa_raw wholesale_raw
## <dbl> <dbl>
## 1 1.13 0.983
## 2 1.62 1.23# T-tests
cat("\n--- T-Tests: Public vs. Non-Public ---\n")##
## --- T-Tests: Public vs. Non-Public ---df_pub <- df_2022q4 %>% filter(is_public == 1)
df_npub <- df_2022q4 %>% filter(is_public == 0)
for (v in desc_pub_vars) {
tt <- tryCatch(t.test(df_pub[[v]], df_npub[[v]]), error = function(e) NULL)
if (!is.null(tt)) {
stars <- case_when(tt$p.value < 0.01 ~ "***", tt$p.value < 0.05 ~ "**",
tt$p.value < 0.10 ~ "*", TRUE ~ "")
cat(sprintf(" %-25s Pub=%.3f NP=%.3f diff=%.3f t=%.2f %s\n", v,
mean(df_pub[[v]], na.rm = TRUE), mean(df_npub[[v]], na.rm = TRUE),
mean(df_pub[[v]], na.rm = TRUE) - mean(df_npub[[v]], na.rm = TRUE),
tt$statistic, stars))
}
}## mtm_total_raw Pub=5.276 NP=5.482 diff=-0.207 t=-1.67 *
## uninsured_lev_raw Pub=31.738 NP=22.976 diff=8.762 t=11.65 ***
## uninsured_beta_raw Pub=0.372 NP=0.328 diff=0.044 t=5.88 ***
## adjusted_equity_raw Pub=5.824 NP=4.581 diff=1.242 t=2.00 **
## dfv_raw Pub=67.979 NP=77.788 diff=-9.809 t=-12.09 ***
## ln_assets_raw Pub=15.544 NP=12.674 diff=2.870 t=33.48 ***
## cash_ratio_raw Pub=4.626 NP=8.423 diff=-3.797 t=-8.64 ***
## book_equity_ratio_raw Pub=11.099 NP=10.152 diff=0.948 t=1.63
## roa_raw Pub=1.619 NP=1.128 diff=0.491 t=2.08 **
## wholesale_raw Pub=1.227 NP=0.983 diff=0.245 t=1.57# Borrowing rates by public status
cat("\n--- Borrowing Rates by Public Status (Crisis) ---\n")##
## --- Borrowing Rates by Public Status (Crisis) ---df_crisis %>%
group_by(Public = ifelse(is_public == 1, "Public", "Non-Public")) %>%
summarise(
N = n(),
AnyFed_pct = round(100 * mean(any_fed, na.rm = TRUE), 2),
BTFP_pct = round(100 * mean(btfp_crisis, na.rm = TRUE), 2),
DW_pct = round(100 * mean(dw_crisis, na.rm = TRUE), 2),
FHLB_pct = round(100 * mean(fhlb_user, na.rm = TRUE), 2),
.groups = "drop"
) %>%
print()## # A tibble: 2 × 6
## Public N AnyFed_pct BTFP_pct DW_pct FHLB_pct
## <chr> <int> <dbl> <dbl> <dbl> <dbl>
## 1 Non-Public 3981 18.1 11.4 8.79 6.58
## 2 Public 311 34.1 15.4 26.7 12.9# ==============================================================================
# SVB CASE STUDY
#
# Silicon Valley Bank (RSSD = 802866) is the defining case of the 2023
# banking crisis. Excluded from regressions as a failed bank, but its
# pre-crisis characteristics illustrate the model's predictions.
#
# This section:
# 1. SVB reference values and beta decomposition
# 2. Original SVB-like regressions (β^U × uninsured share)
# 3. Improved Approach 1: Redefined indicator (orthogonal to interaction)
# 4. Improved Approach 2: Continuous Mahalanobis proximity
# 5. Approach 2b: Euclidean robustness
# 6. Summary comparison table
# 7. Visualizations
# ==============================================================================
SVB_RSSD <- "802866"
svb_call <- call_q %>% filter(idrssd == SVB_RSSD, period == "2022Q4")
svb_beta <- dssw_betas %>% filter(idrssd == SVB_RSSD, estimation_date == "2022Q4")
stopifnot(nrow(svb_call) == 1, nrow(svb_beta) == 1)
svb_ref <- list(
beta_u = svb_beta$beta_uninsured,
beta_o = svb_beta$beta_overall,
beta_i = svb_beta$beta_insured,
s_u = svb_beta$uninsured_share,
securities_rat = svb_call$security_to_total_asset,
cash_rat = svb_call$cash_to_total_asset,
mtm_omo_rat = svb_call$mtm_loss_omo_eligible_to_total_asset,
mtm_total_rat = svb_call$mtm_loss_to_total_asset,
uninsured_lev = svb_call$uninsured_deposit_to_total_asset,
book_eq = svb_call$book_equity_to_total_asset,
total_assets = svb_call$total_asset
)
cat("=== SVB REFERENCE VALUES (2022Q4) ===\n\n")## === SVB REFERENCE VALUES (2022Q4) ===cat(sprintf(" Total assets: $%.1fB\n", svb_ref$total_assets / 1e6))## Total assets: $209.0Bcat(sprintf(" MTM loss / TA: %.2f%%\n", svb_ref$mtm_total_rat))## MTM loss / TA: 7.40%cat(sprintf(" Uninsured / TA: %.2f%%\n", svb_ref$uninsured_lev))## Uninsured / TA: 70.52%cat(sprintf(" Book equity / TA: %.2f%%\n", svb_ref$book_eq))## Book equity / TA: 7.39%cat(sprintf(" β_overall: %.4f\n", svb_ref$beta_o))## β_overall: 0.3410cat(sprintf(" β_insured: %.4f\n", svb_ref$beta_i))## β_insured: 0.0535cat(sprintf(" β_uninsured: %.4f\n", svb_ref$beta_u))## β_uninsured: 0.3661cat(sprintf(" Uninsured share: %.1f%%\n", svb_ref$s_u * 100))## Uninsured share: 92.0%cat(sprintf(" Securities / TA: %.2f%%\n", svb_ref$securities_rat))## Securities / TA: 54.20%cat(sprintf(" Cash / TA: %.2f%%\n", svb_ref$cash_rat))## Cash / TA: 5.99%# DSSW decomposition check
cat(sprintf("\n DSSW check: s_U×β^U + (1-s_U)×β^I = %.4f×%.4f + %.4f×%.4f = %.4f\n",
svb_ref$s_u, svb_ref$beta_u, 1 - svb_ref$s_u, svb_ref$beta_i,
svb_ref$s_u * svb_ref$beta_u + (1 - svb_ref$s_u) * svb_ref$beta_i))##
## DSSW check: s_U×β^U + (1-s_U)×β^I = 0.9198×0.3661 + 0.0802×0.0535 = 0.3410cat(sprintf(" β_overall = %.4f ✓\n", svb_ref$beta_o))## β_overall = 0.3410 ✓# Solvency
d_ta <- svb_call$dom_deposit[1] / svb_call$total_asset[1]
dfv_svb <- (1 - svb_ref$beta_o) * d_ta * 100
ae_jiang <- svb_ref$book_eq - svb_ref$mtm_total_rat
ae_dssw <- ae_jiang + dfv_svb
cat(sprintf("\n DFV (DSSW) = (1 - %.4f) × %.2f%% = %.2f%% of TA\n",
svb_ref$beta_o, d_ta * 100, dfv_svb))##
## DFV (DSSW) = (1 - 0.3410) × 77.25% = 50.91% of TAcat(sprintf(" Jiang AE = %.2f%% → %s\n", ae_jiang,
ifelse(ae_jiang < 0, "INSOLVENT", "Solvent")))## Jiang AE = -0.00% → INSOLVENTcat(sprintf(" DSSW AE = %.2f%% → %s\n", ae_dssw,
ifelse(ae_dssw < 0, "INSOLVENT", "Solvent")))## DSSW AE = 50.91% → Solventcat("\n KEY: SVB was DSSW-solvent in the no-run equilibrium.\n")##
## KEY: SVB was DSSW-solvent in the no-run equilibrium.cat(" Its extreme uninsured share (92%) made the franchise fragile.\n")## Its extreme uninsured share (92%) made the franchise fragile.cat(" Once depositors coordinated, the franchise was destroyed.\n")## Once depositors coordinated, the franchise was destroyed.# ==============================================================================
# APPROACH 1: REDEFINED SVB-LIKE INDICATOR
#
# SVB-like = above-median β^U AND above-median securities/TA AND below-median cash/TA
#
# Why: These variables are ORTHOGONAL to MTM × Uninsured.
# Uninsured leverage varies freely within each group.
# ==============================================================================
cat("=== APPROACH 1: REDEFINED SVB-LIKE (ORTHOGONAL) ===\n\n")## === APPROACH 1: REDEFINED SVB-LIKE (ORTHOGONAL) ===med_beta_u_v2 <- median(df_crisis$uninsured_beta_raw, na.rm = TRUE)
med_sec_ratio <- median(df_crisis$securities_ratio_raw, na.rm = TRUE)
med_cash_ratio <- median(df_crisis$cash_ratio_raw, na.rm = TRUE)
cat(sprintf(" Median β^U: %.4f\n", med_beta_u_v2))## Median β^U: 0.3106cat(sprintf(" Median Securities / TA: %.2f%%\n", med_sec_ratio))## Median Securities / TA: 23.32%cat(sprintf(" Median Cash / TA: %.2f%%\n", med_cash_ratio))## Median Cash / TA: 5.03%cat(sprintf("\n SVB qualifies? β^U>med: %s | Sec>med: %s | Cash<med: %s → %s\n",
ifelse(svb_ref$beta_u > med_beta_u_v2, "YES", "NO"),
ifelse(svb_ref$securities_rat > med_sec_ratio, "YES", "NO"),
ifelse(svb_ref$cash_rat < med_cash_ratio, "YES", "NO"),
ifelse(svb_ref$beta_u > med_beta_u_v2 &
svb_ref$securities_rat > med_sec_ratio &
svb_ref$cash_rat < med_cash_ratio, "YES ✓", "NO ✗")))##
## SVB qualifies? β^U>med: YES | Sec>med: YES | Cash<med: NO → NO ✗add_svb_like_v2 <- function(df) {
df %>% mutate(
svb_like_v2 = case_when(
is.na(uninsured_beta_raw) | is.na(securities_ratio_raw) |
is.na(cash_ratio_raw) ~ NA_integer_,
uninsured_beta_raw > med_beta_u_v2 &
securities_ratio_raw > med_sec_ratio &
cash_ratio_raw < med_cash_ratio ~ 1L,
TRUE ~ 0L
)
)
}
df_anyfed_s <- add_svb_like_v2(df_anyfed_s)
df_btfp_s <- add_svb_like_v2(df_btfp_s)
df_dw_s <- add_svb_like_v2(df_dw_s)
df_fhlb_s <- add_svb_like_v2(df_fhlb_s)
df_crisis <- add_svb_like_v2(df_crisis)
cat("\n--- SVB-Like v2 Counts ---\n")##
## --- SVB-Like v2 Counts ---for (grp in c("SVB-like (1)", "SVB-unlike (0)")) {
val <- ifelse(grp == "SVB-like (1)", 1L, 0L)
cat(sprintf(" %s:\n", grp))
cat(sprintf(" AnyFed: N=%d, Borrowers=%d\n",
sum(df_anyfed_s$svb_like_v2 == val, na.rm = TRUE),
sum(df_anyfed_s$any_fed[df_anyfed_s$svb_like_v2 == val], na.rm = TRUE)))
cat(sprintf(" BTFP: N=%d, Borrowers=%d\n",
sum(df_btfp_s$svb_like_v2 == val, na.rm = TRUE),
sum(df_btfp_s$btfp_crisis[df_btfp_s$svb_like_v2 == val], na.rm = TRUE)))
}## SVB-like (1):
## AnyFed: N=502, Borrowers=155
## BTFP: N=448, Borrowers=101
## SVB-unlike (0):
## AnyFed: N=3489, Borrowers=667
## BTFP: N=3217, Borrowers=395# --- Verify uninsured leverage variation is PRESERVED ---
cat("\n--- Uninsured Leverage Variation by SVB-Like v2 ---\n")##
## --- Uninsured Leverage Variation by SVB-Like v2 ---cat(" (SD should be similar across groups — no restriction of range)\n")## (SD should be similar across groups — no restriction of range)df_crisis %>%
filter(!is.na(svb_like_v2)) %>%
group_by(SVB_Like_v2 = ifelse(svb_like_v2 == 1, "Like", "Unlike")) %>%
summarise(N = n(), Mean_UI = round(mean(uninsured_lev_raw, na.rm=T), 2),
SD_UI = round(sd(uninsured_lev_raw, na.rm=T), 2),
P10_UI = round(quantile(uninsured_lev_raw, .10, na.rm=T), 2),
P90_UI = round(quantile(uninsured_lev_raw, .90, na.rm=T), 2),
.groups = "drop") %>% print()## # A tibble: 2 × 6
## SVB_Like_v2 N Mean_UI SD_UI P10_UI P90_UI
## <chr> <int> <dbl> <dbl> <dbl> <dbl>
## 1 Like 530 22.6 10.4 10.7 35.2
## 2 Unlike 3696 23.9 12.2 9.74 40.0# --- Regressions ---
mod_svbv2_any_like <- safe_run(df_anyfed_s %>% filter(svb_like_v2 == 1), "any_fed", EXPL_BASE)
mod_svbv2_btfp_like <- safe_run(df_btfp_s %>% filter(svb_like_v2 == 1), "btfp_crisis", EXPL_BASE)
mod_svbv2_dw_like <- safe_run(df_dw_s %>% filter(svb_like_v2 == 1), "dw_crisis", EXPL_BASE)
mod_svbv2_fhlb_like <- safe_run(df_fhlb_s %>% filter(svb_like_v2 == 1), "fhlb_user", EXPL_BASE)
mod_svbv2_any_unlike <- safe_run(df_anyfed_s %>% filter(svb_like_v2 == 0), "any_fed", EXPL_BASE)
mod_svbv2_btfp_unlike <- safe_run(df_btfp_s %>% filter(svb_like_v2 == 0), "btfp_crisis", EXPL_BASE)
mod_svbv2_dw_unlike <- safe_run(df_dw_s %>% filter(svb_like_v2 == 0), "dw_crisis", EXPL_BASE)
mod_svbv2_fhlb_unlike <- safe_run(df_fhlb_s %>% filter(svb_like_v2 == 0), "fhlb_user", EXPL_BASE)
models_svbv2_combined <- list(
"Any (Like)" = mod_svbv2_any_like, "Any (Unlike)" = mod_svbv2_any_unlike,
"BTFP (Like)" = mod_svbv2_btfp_like, "BTFP (Unlike)" = mod_svbv2_btfp_unlike,
"DW (Like)" = mod_svbv2_dw_like, "DW (Unlike)" = mod_svbv2_dw_unlike,
"FHLB (Like)" = mod_svbv2_fhlb_like, "FHLB (Unlike)" = mod_svbv2_fhlb_unlike)
save_etable(models_svbv2_combined, "SVBlike_v2_combined",
title_text = "SVB-Like v2 (Orthogonal): Asset-Side Vulnerability Profile (Crisis)",
notes_text = paste0(
"LPM. SVB-like v2 = above-median $\\beta^U$ AND above-median securities/TA ",
"AND below-median cash/TA. These variables are orthogonal to MTM $\\times$ Uninsured, ",
"preserving within-group variation in uninsured leverage. ",
"FHLB: falsification. Robust SEs. z-standardized."),
extra_lines = list(
c("SVB-Like v2", "Yes", "No", "Yes", "No", "Yes", "No", "Yes", "No")))
etable(models_svbv2_combined[!sapply(models_svbv2_combined, is.null)],
fitstat = ~ n + r2, se.below = TRUE)## Any (Like) Any (Unl.. BTFP (Like) BTFP (Unl.. DW (Like)
## Dependent Var.: any_fed any_fed btfp_crisis btfp_crisis dw_crisis
##
## Constant 0.1094 0.2001*** 0.0165 0.1366*** 0.0355
## (0.0933) (0.0066) (0.0838) (0.0061) (0.0846)
## MTM Loss (z) 0.0272 0.0303*** 0.0233 0.0250*** 0.0095
## (0.0246) (0.0073) (0.0229) (0.0064) (0.0225)
## Uninsured Leverage (z) 0.0094 0.0210** 0.0209 0.0226** 0.0008
## (0.0256) (0.0081) (0.0241) (0.0075) (0.0237)
## MTM $\times$ Uninsured 0.0481* 0.0160** 0.0371 0.0157** 0.0416*
## (0.0221) (0.0062) (0.0211) (0.0057) (0.0198)
## Log(Assets) 0.1379*** 0.1010*** 0.1036*** 0.0658*** 0.1338***
## (0.0258) (0.0087) (0.0252) (0.0081) (0.0251)
## Cash Ratio -0.2371 -0.0208** -0.2676* -0.0273*** -0.1801
## (0.1340) (0.0065) (0.1221) (0.0051) (0.1214)
## Loan-to-Deposit 0.0518 -0.0013 0.0557 -0.0102 0.0115
## (0.0335) (0.0074) (0.0312) (0.0063) (0.0305)
## Book Equity Ratio -0.0297 -0.0125* -0.0366* -0.0098 0.0056
## (0.0221) (0.0060) (0.0184) (0.0052) (0.0207)
## Wholesale Funding 0.0302 0.0280*** 0.0404* 0.0219** 0.0165
## (0.0172) (0.0076) (0.0166) (0.0070) (0.0171)
## ROA -0.0273 -0.0002 -0.0319 -0.0046 -0.0283
## (0.0255) (0.0061) (0.0234) (0.0052) (0.0232)
## ______________________ __________ __________ ___________ ___________ __________
## S.E. type Hete.-rob. Hete.-rob. Heter.-rob. Heter.-rob. Hete.-rob.
## Observations 502 3,489 448 3,217 420
## R2 0.13608 0.11358 0.13177 0.08769 0.13557
##
## DW (Unli.. FHLB (L.. FHLB (Un..
## Dependent Var.: dw_crisis fhlb_user fhlb_user
##
## Constant 0.1225*** 0.1089 0.0890***
## (0.0058) (0.0697) (0.0053)
## MTM Loss (z) 0.0163* 0.0081 0.0038
## (0.0064) (0.0199) (0.0059)
## Uninsured Leverage (z) 0.0128 0.0077 0.0058
## (0.0072) (0.0192) (0.0056)
## MTM $\times$ Uninsured 0.0142** 0.0083 -0.0065
## (0.0055) (0.0149) (0.0048)
## Log(Assets) 0.0867*** 0.0331 0.0273***
## (0.0082) (0.0246) (0.0068)
## Cash Ratio -0.0010 0.0091 -0.0213***
## (0.0056) (0.1026) (0.0042)
## Loan-to-Deposit 0.0023 0.0372 0.0249***
## (0.0063) (0.0244) (0.0056)
## Book Equity Ratio -0.0019 -0.0051 0.0097*
## (0.0048) (0.0152) (0.0047)
## Wholesale Funding 0.0206** 0.0092 0.0012
## (0.0069) (0.0133) (0.0056)
## ROA -0.0007 -0.0206 -0.0096*
## (0.0052) (0.0215) (0.0046)
## ______________________ __________ _________ __________
## S.E. type Hete.-rob. Het.-rob. Hete.-rob.
## Observations 3,179 385 3,083
## R2 0.09766 0.02065 0.04431
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1# ==============================================================================
# APPROACH 2: CONTINUOUS MAHALANOBIS DISTANCE TO SVB
#
# No sample splitting. Compute each bank's Mahalanobis distance from SVB's
# profile on (β^U, securities/TA, cash/TA) — all orthogonal to interaction.
# Interact this continuous SVB-proximity score with MTM × Uninsured.
# ==============================================================================
cat("=== APPROACH 2: CONTINUOUS SVB-PROXIMITY (MAHALANOBIS) ===\n\n")## === APPROACH 2: CONTINUOUS SVB-PROXIMITY (MAHALANOBIS) ===profile_vars <- c("uninsured_beta_raw", "securities_ratio_raw", "cash_ratio_raw")
svb_vec <- c(svb_ref$beta_u, svb_ref$securities_rat, svb_ref$cash_rat)
names(svb_vec) <- profile_vars
cat("SVB reference vector:\n")## SVB reference vector:print(round(svb_vec, 4))## uninsured_beta_raw securities_ratio_raw cash_ratio_raw
## 0.3661 54.2019 5.9854add_svb_proximity <- function(df) {
profile_mat <- df %>% select(all_of(profile_vars)) %>% as.matrix()
complete_idx <- complete.cases(profile_mat)
Sigma <- cov(profile_mat[complete_idx, ], use = "complete.obs")
mahal_dist <- rep(NA_real_, nrow(df))
mahal_dist[complete_idx] <- mahalanobis(
x = profile_mat[complete_idx, ], center = svb_vec, cov = Sigma)
df %>% mutate(
svb_mahal_dist = mahal_dist,
svb_prox_raw = -mahal_dist,
svb_prox_w = winsorize(svb_prox_raw),
svb_prox = standardize_z(svb_prox_w),
mtm_x_ui_x_svbprox = mtm_total * uninsured_lev * svb_prox,
svb_prox_x_mtm = svb_prox * mtm_total,
svb_prox_x_ui = svb_prox * uninsured_lev
)
}
df_anyfed_s <- add_svb_proximity(df_anyfed_s)
df_btfp_s <- add_svb_proximity(df_btfp_s)
df_dw_s <- add_svb_proximity(df_dw_s)
df_fhlb_s <- add_svb_proximity(df_fhlb_s)
df_crisis <- add_svb_proximity(df_crisis)
# Diagnostics
cat("\n--- SVB Proximity Distribution (AnyFed sample) ---\n")##
## --- SVB Proximity Distribution (AnyFed sample) ---print(summary(df_anyfed_s$svb_prox))## Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
## -2.9717 -0.6133 0.1358 0.0000 0.7971 1.3975 63cat("\n--- Corr(SVB_prox, uninsured_lev) ---\n")##
## --- Corr(SVB_prox, uninsured_lev) ---cat(sprintf(" r = %.3f (should be modest — profile is orthogonal to UI)\n",
cor(df_anyfed_s$svb_prox, df_anyfed_s$uninsured_lev, use = "complete.obs")))## r = -0.106 (should be modest — profile is orthogonal to UI)cat("\n--- SVB Proximity by Borrower Status ---\n")##
## --- SVB Proximity by Borrower Status ---df_anyfed_s %>%
group_by(Borrower = ifelse(any_fed == 1, "Fed Borrower", "Non-Borrower")) %>%
summarise(N = n(), Mean_Prox = round(mean(svb_prox, na.rm=T), 3),
Mean_Dist = round(mean(svb_mahal_dist, na.rm=T), 2), .groups = "drop") %>%
print()## # A tibble: 2 × 4
## Borrower N Mean_Prox Mean_Dist
## <chr> <int> <dbl> <dbl>
## 1 Fed Borrower 828 0.13 6.27
## 2 Non-Borrower 3226 -0.034 7.23# Regressions
setFixest_dict(c(
svb_prox = "SVB Proximity (z)",
svb_prox_x_mtm = "SVB Prox $\\times$ MTM",
svb_prox_x_ui = "SVB Prox $\\times$ Uninsured",
mtm_x_ui_x_svbprox = "MTM $\\times$ UI $\\times$ SVB Prox"
))
EXPL_SVB_PROX <- paste0(
"mtm_total + uninsured_lev + mtm_x_uninsured + ",
"svb_prox + svb_prox_x_mtm + svb_prox_x_ui + ",
"mtm_x_ui_x_svbprox")
mod_prox_any <- safe_run(df_anyfed_s, "any_fed", EXPL_SVB_PROX)
mod_prox_btfp <- safe_run(df_btfp_s, "btfp_crisis", EXPL_SVB_PROX)
mod_prox_dw <- safe_run(df_dw_s, "dw_crisis", EXPL_SVB_PROX)
mod_prox_fhlb <- safe_run(df_fhlb_s, "fhlb_user", EXPL_SVB_PROX)
models_prox <- list("Any Fed" = mod_prox_any, "BTFP" = mod_prox_btfp,
"DW" = mod_prox_dw, "FHLB" = mod_prox_fhlb)
save_etable(models_prox, "SVB_proximity_continuous",
title_text = "SVB Proximity: Continuous Mahalanobis Distance (Crisis Period)",
notes_text = paste0(
"LPM. SVB Proximity = negative Mahalanobis distance from SVB's profile ",
"($\\beta^U$, securities/TA, cash/TA), z-standardized. Higher = more SVB-like. ",
"Profile is orthogonal to MTM $\\times$ Uninsured. ",
"FHLB: falsification. Robust SEs. z-standardized."),
extra_lines = list(c("Sample", "Full", "Full", "Full", "Full")))
etable(models_prox[!sapply(models_prox, is.null)], fitstat = ~ n + r2, se.below = TRUE)## Any Fed BTFP DW FHLB
## Dependent Var.: any_fed btfp_crisis dw_crisis fhlb_user
##
## Constant 0.2027*** 0.1372*** 0.1261*** 0.0898***
## (0.0063) (0.0058) (0.0057) (0.0053)
## MTM Loss (z) 0.0284*** 0.0226*** 0.0150* 0.0035
## (0.0071) (0.0063) (0.0062) (0.0056)
## Uninsured Leverage (z) 0.0181* 0.0212** 0.0094 0.0048
## (0.0081) (0.0073) (0.0072) (0.0057)
## MTM $\times$ Uninsured 0.0200** 0.0167** 0.0190** -0.0066
## (0.0066) (0.0062) (0.0059) (0.0052)
## SVB Proximity (z) 0.0220* 0.0240** 0.0067 0.0020
## (0.0101) (0.0090) (0.0088) (0.0079)
## SVB Prox $\times$ MTM 0.0118* 0.0143** 0.0016 0.0007
## (0.0056) (0.0048) (0.0050) (0.0042)
## SVB Prox $\times$ Uninsured 0.0074 0.0112 0.0012 0.0079
## (0.0065) (0.0060) (0.0059) (0.0048)
## MTM $\times$ UI $\times$ SVB Prox 0.0090 0.0084* 0.0061 0.0056
## (0.0049) (0.0043) (0.0045) (0.0037)
## Log(Assets) 0.1084*** 0.0725*** 0.0943*** 0.0283***
## (0.0083) (0.0078) (0.0078) (0.0066)
## Cash Ratio -0.0139 -0.0178* -0.0004 -0.0202**
## (0.0092) (0.0075) (0.0079) (0.0064)
## Loan-to-Deposit 0.0136 0.0076 0.0041 0.0256***
## (0.0100) (0.0087) (0.0085) (0.0073)
## Book Equity Ratio -0.0143* -0.0130* -0.0004 0.0088
## (0.0060) (0.0051) (0.0048) (0.0045)
## Wholesale Funding 0.0277*** 0.0247*** 0.0197** 0.0025
## (0.0070) (0.0066) (0.0064) (0.0052)
## ROA -0.0043 -0.0084 -0.0036 -0.0106*
## (0.0060) (0.0052) (0.0051) (0.0046)
## _________________________________ __________ ___________ __________ __________
## S.E. type Hete.-rob. Heter.-rob. Hete.-rob. Hete.-rob.
## Observations 3,991 3,665 3,599 3,468
## R2 0.12155 0.09876 0.10318 0.04164
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1# Nested comparison
cat("\n=== NESTED COMPARISON: Base → +Proximity → +Triple ===\n")##
## === NESTED COMPARISON: Base → +Proximity → +Triple ===EXPL_SVB_PROX_NESTED <- paste0(
"mtm_total + uninsured_lev + mtm_x_uninsured + ",
"svb_prox + svb_prox_x_mtm + svb_prox_x_ui")
mod_prox_btfp_nested <- safe_run(df_btfp_s, "btfp_crisis", EXPL_SVB_PROX_NESTED)
models_nested <- list(
"BTFP (Base)" = mod_A_btfp,
"BTFP (+ Prox)" = mod_prox_btfp_nested,
"BTFP (+ Triple)" = mod_prox_btfp)
save_etable(models_nested, "SVB_proximity_nested",
title_text = "Nested: BTFP with SVB Proximity (Crisis)",
notes_text = paste0(
"LPM. Col 1: baseline. Col 2: + SVB Proximity and two-way interactions. ",
"Col 3: + triple MTM $\\times$ UI $\\times$ SVB Prox. Robust SEs. z-standardized."))
etable(models_nested[!sapply(models_nested, is.null)], fitstat = ~ n + r2, se.below = TRUE)## BTFP (Base) BTFP (+ P.. BTFP (+ T..
## Dependent Var.: btfp_crisis btfp_crisis btfp_crisis
##
## Constant 0.1435*** 0.1376*** 0.1372***
## (0.0056) (0.0057) (0.0058)
## MTM Loss (z) 0.0249*** 0.0230*** 0.0226***
## (0.0062) (0.0063) (0.0063)
## Uninsured Leverage (z) 0.0214** 0.0249*** 0.0212**
## (0.0070) (0.0072) (0.0073)
## MTM $\times$ Uninsured 0.0193*** 0.0150* 0.0167**
## (0.0052) (0.0060) (0.0062)
## Log(Assets) 0.0713*** 0.0715*** 0.0725***
## (0.0077) (0.0077) (0.0078)
## Cash Ratio -0.0285*** -0.0177* -0.0178*
## (0.0048) (0.0075) (0.0075)
## Loan-to-Deposit -0.0107 0.0073 0.0076
## (0.0057) (0.0087) (0.0087)
## Book Equity Ratio -0.0118* -0.0138** -0.0130*
## (0.0047) (0.0051) (0.0051)
## Wholesale Funding 0.0263*** 0.0248*** 0.0247***
## (0.0065) (0.0066) (0.0066)
## ROA -0.0059 -0.0080 -0.0084
## (0.0049) (0.0052) (0.0052)
## SVB Proximity (z) 0.0220* 0.0240**
## (0.0088) (0.0090)
## SVB Prox $\times$ MTM 0.0124** 0.0143**
## (0.0046) (0.0048)
## SVB Prox $\times$ Uninsured 0.0064 0.0112
## (0.0050) (0.0060)
## MTM $\times$ UI $\times$ SVB Prox 0.0084*
## (0.0043)
## _________________________________ ___________ ___________ ___________
## S.E. type Heter.-rob. Heter.-rob. Heter.-rob.
## Observations 3,717 3,665 3,665
## R2 0.09615 0.09797 0.09876
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1# ==============================================================================
# APPROACH 2b: EUCLIDEAN DISTANCE ON Z-SCORES (simpler alternative)
# ==============================================================================
cat("=== APPROACH 2b: EUCLIDEAN DISTANCE ===\n\n")## === APPROACH 2b: EUCLIDEAN DISTANCE ===add_svb_euclidean <- function(df) {
beta_u_z <- standardize_z(winsorize(df$uninsured_beta_raw))
sec_z <- standardize_z(winsorize(df$securities_ratio_raw))
cash_z <- standardize_z(winsorize(df$cash_ratio_raw))
svb_beta_z <- (svb_ref$beta_u - mean(df$uninsured_beta_raw, na.rm=T)) /
sd(df$uninsured_beta_raw, na.rm=T)
svb_sec_z <- (svb_ref$securities_rat - mean(df$securities_ratio_raw, na.rm=T)) /
sd(df$securities_ratio_raw, na.rm=T)
svb_cash_z <- (svb_ref$cash_rat - mean(df$cash_ratio_raw, na.rm=T)) /
sd(df$cash_ratio_raw, na.rm=T)
euc_dist <- sqrt((beta_u_z - svb_beta_z)^2 + (sec_z - svb_sec_z)^2 + (cash_z - svb_cash_z)^2)
df %>% mutate(
svb_euc_dist = euc_dist,
svb_euc_prox_raw = -euc_dist,
svb_euc_prox_w = winsorize(svb_euc_prox_raw),
svb_euc_prox = standardize_z(svb_euc_prox_w),
mtm_x_ui_x_eucprox = mtm_total * uninsured_lev * svb_euc_prox,
euc_prox_x_mtm = svb_euc_prox * mtm_total,
euc_prox_x_ui = svb_euc_prox * uninsured_lev
)
}
df_anyfed_s <- add_svb_euclidean(df_anyfed_s)
df_btfp_s <- add_svb_euclidean(df_btfp_s)
df_dw_s <- add_svb_euclidean(df_dw_s)
df_fhlb_s <- add_svb_euclidean(df_fhlb_s)
setFixest_dict(c(
svb_euc_prox = "SVB Proximity (Eucl., z)",
euc_prox_x_mtm = "SVB Prox (E) $\\times$ MTM",
euc_prox_x_ui = "SVB Prox (E) $\\times$ Uninsured",
mtm_x_ui_x_eucprox = "MTM $\\times$ UI $\\times$ SVB Prox (E)"
))
EXPL_SVB_EUC <- paste0(
"mtm_total + uninsured_lev + mtm_x_uninsured + ",
"svb_euc_prox + euc_prox_x_mtm + euc_prox_x_ui + ",
"mtm_x_ui_x_eucprox")
mod_euc_any <- safe_run(df_anyfed_s, "any_fed", EXPL_SVB_EUC)
mod_euc_btfp <- safe_run(df_btfp_s, "btfp_crisis", EXPL_SVB_EUC)
mod_euc_dw <- safe_run(df_dw_s, "dw_crisis", EXPL_SVB_EUC)
mod_euc_fhlb <- safe_run(df_fhlb_s, "fhlb_user", EXPL_SVB_EUC)
models_euc <- list("Any Fed" = mod_euc_any, "BTFP" = mod_euc_btfp,
"DW" = mod_euc_dw, "FHLB" = mod_euc_fhlb)
save_etable(models_euc, "SVB_euclidean_continuous",
title_text = "SVB Proximity (Euclidean): Robustness (Crisis Period)",
notes_text = paste0(
"LPM. Euclidean distance on z-standardized ($\\beta^U$, securities/TA, cash/TA). ",
"Simpler alternative to Mahalanobis. FHLB: falsification. Robust SEs. z-standardized."),
extra_lines = list(c("Metric", "Euclidean", "Euclidean", "Euclidean", "Euclidean")))
etable(models_euc[!sapply(models_euc, is.null)], fitstat = ~ n + r2, se.below = TRUE)## Any Fed BTFP DW
## Dependent Var.: any_fed btfp_crisis dw_crisis
##
## Constant 0.2038*** 0.1387*** 0.1268***
## (0.0065) (0.0059) (0.0058)
## MTM Loss (z) 0.0281*** 0.0221*** 0.0157*
## (0.0072) (0.0064) (0.0063)
## Uninsured Leverage (z) 0.0166* 0.0208** 0.0076
## (0.0083) (0.0075) (0.0073)
## MTM $\times$ Uninsured 0.0181** 0.0149* 0.0183**
## (0.0068) (0.0064) (0.0060)
## SVB Proximity (Eucl., z) 0.0131 0.0173 -0.0037
## (0.0120) (0.0110) (0.0101)
## SVB Prox (E) $\times$ MTM 0.0086 0.0099 0.0003
## (0.0059) (0.0052) (0.0052)
## SVB Prox (E) $\times$ Uninsured 0.0102 0.0128* 0.0023
## (0.0066) (0.0062) (0.0058)
## MTM $\times$ UI $\times$ SVB Prox (E) 0.0107* 0.0079 0.0079
## (0.0053) (0.0048) (0.0047)
## Log(Assets) 0.1086*** 0.0730*** 0.0941***
## (0.0083) (0.0078) (0.0078)
## Cash Ratio -0.0180 -0.0196* -0.0072
## (0.0110) (0.0094) (0.0093)
## Loan-to-Deposit 0.0074 0.0034 -0.0036
## (0.0113) (0.0099) (0.0096)
## Book Equity Ratio -0.0146* -0.0135** -0.0004
## (0.0060) (0.0051) (0.0048)
## Wholesale Funding 0.0286*** 0.0253*** 0.0206**
## (0.0070) (0.0067) (0.0064)
## ROA -0.0044 -0.0084 -0.0037
## (0.0060) (0.0052) (0.0052)
## _____________________________________ __________ ___________ __________
## S.E. type Hete.-rob. Heter.-rob. Hete.-rob.
## Observations 3,991 3,665 3,599
## R2 0.12127 0.09804 0.10332
##
## FHLB
## Dependent Var.: fhlb_user
##
## Constant 0.0912***
## (0.0054)
## MTM Loss (z) 0.0042
## (0.0057)
## Uninsured Leverage (z) 0.0039
## (0.0059)
## MTM $\times$ Uninsured -0.0077
## (0.0054)
## SVB Proximity (Eucl., z) -0.0108
## (0.0092)
## SVB Prox (E) $\times$ MTM -0.0018
## (0.0044)
## SVB Prox (E) $\times$ Uninsured 0.0073
## (0.0048)
## MTM $\times$ UI $\times$ SVB Prox (E) 0.0040
## (0.0040)
## Log(Assets) 0.0281***
## (0.0066)
## Cash Ratio -0.0289***
## (0.0080)
## Loan-to-Deposit 0.0158
## (0.0081)
## Book Equity Ratio 0.0090*
## (0.0045)
## Wholesale Funding 0.0036
## (0.0052)
## ROA -0.0104*
## (0.0045)
## _____________________________________ __________
## S.E. type Hete.-rob.
## Observations 3,468
## R2 0.04199
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1# ==============================================================================
# COMBINED SUMMARY: Original vs. v2 Indicator vs. Mahalanobis vs. Euclidean
# All objects now exist from chunks above.
# ==============================================================================
cat("=== SUMMARY: ALL SVB-LIKE APPROACHES (BTFP) ===\n\n")## === SUMMARY: ALL SVB-LIKE APPROACHES (BTFP) ===models_svb_summary <- list(
"Orig (Like)" = mod_svb_btfp_like,
"Orig (Unlike)" = mod_svb_btfp_unlike,
"v2 (Like)" = mod_svbv2_btfp_like,
"v2 (Unlike)" = mod_svbv2_btfp_unlike,
"Mahalanobis" = mod_prox_btfp,
"Euclidean" = mod_euc_btfp)
save_etable(models_svb_summary, "SVB_all_approaches_BTFP",
title_text = "SVB-Like Approaches Compared: BTFP (Crisis Period)",
notes_text = paste0(
"LPM. Cols 1--2: original (above-median $\\beta^U$ $\\cap$ above-median uninsured share). ",
"Cols 3--4: v2 (above-median $\\beta^U$ $\\cap$ above-median securities/TA $\\cap$ below-median cash/TA). ",
"Cols 5--6: continuous proximity on full sample. v2 and continuous approaches preserve ",
"uninsured leverage variation, fixing the restriction-of-range problem. ",
"Robust SEs. z-standardized."),
extra_lines = list(
c("Approach", "Orig", "Orig", "v2", "v2", "Mahal", "Euclid"),
c("SVB-Like", "Yes", "No", "Yes", "No", "Full", "Full")))
etable(models_svb_summary[!sapply(models_svb_summary, is.null)],
fitstat = ~ n + r2, se.below = TRUE)## Orig (Like) Orig (Unl.. v2 (Like)
## Dependent Var.: btfp_crisis btfp_crisis btfp_crisis
##
## Constant 0.1594*** 0.1382*** 0.0165
## (0.0195) (0.0071) (0.0838)
## MTM Loss (z) 0.0266 0.0212** 0.0233
## (0.0197) (0.0073) (0.0229)
## Uninsured Leverage (z) 0.0086 0.0211** 0.0209
## (0.0219) (0.0081) (0.0241)
## MTM $\times$ Uninsured 0.0181 0.0152* 0.0371
## (0.0191) (0.0063) (0.0211)
## Log(Assets) 0.0774*** 0.0694*** 0.1036***
## (0.0169) (0.0087) (0.0252)
## Cash Ratio -0.0337* -0.0278*** -0.2676*
## (0.0156) (0.0052) (0.1221)
## Loan-to-Deposit -0.0175 -0.0068 0.0557
## (0.0170) (0.0065) (0.0312)
## Book Equity Ratio -0.0174 -0.0126* -0.0366*
## (0.0157) (0.0053) (0.0184)
## Wholesale Funding 0.0668*** 0.0126 0.0404*
## (0.0165) (0.0066) (0.0166)
## ROA -0.0038 -0.0071 -0.0319
## (0.0129) (0.0056) (0.0234)
## SVB Proximity (z)
##
## SVB Prox $\times$ MTM
##
## SVB Prox $\times$ Uninsured
##
## MTM $\times$ UI $\times$ SVB Prox
##
## SVB Proximity (Eucl., z)
##
## SVB Prox (E) $\times$ MTM
##
## SVB Prox (E) $\times$ Uninsured
##
## MTM $\times$ UI $\times$ SVB Prox (E)
##
## _____________________________________ ___________ ___________ ___________
## S.E. type Heter.-rob. Heter.-rob. Heter.-rob.
## Observations 862 2,803 448
## R2 0.10453 0.08357 0.13177
##
## v2 (Unlike) Mahalanobis Euclidean
## Dependent Var.: btfp_crisis btfp_crisis btfp_crisis
##
## Constant 0.1366*** 0.1372*** 0.1387***
## (0.0061) (0.0058) (0.0059)
## MTM Loss (z) 0.0250*** 0.0226*** 0.0221***
## (0.0064) (0.0063) (0.0064)
## Uninsured Leverage (z) 0.0226** 0.0212** 0.0208**
## (0.0075) (0.0073) (0.0075)
## MTM $\times$ Uninsured 0.0157** 0.0167** 0.0149*
## (0.0057) (0.0062) (0.0064)
## Log(Assets) 0.0658*** 0.0725*** 0.0730***
## (0.0081) (0.0078) (0.0078)
## Cash Ratio -0.0273*** -0.0178* -0.0196*
## (0.0051) (0.0075) (0.0094)
## Loan-to-Deposit -0.0102 0.0076 0.0034
## (0.0063) (0.0087) (0.0099)
## Book Equity Ratio -0.0098 -0.0130* -0.0135**
## (0.0052) (0.0051) (0.0051)
## Wholesale Funding 0.0219** 0.0247*** 0.0253***
## (0.0070) (0.0066) (0.0067)
## ROA -0.0046 -0.0084 -0.0084
## (0.0052) (0.0052) (0.0052)
## SVB Proximity (z) 0.0240**
## (0.0090)
## SVB Prox $\times$ MTM 0.0143**
## (0.0048)
## SVB Prox $\times$ Uninsured 0.0112
## (0.0060)
## MTM $\times$ UI $\times$ SVB Prox 0.0084*
## (0.0043)
## SVB Proximity (Eucl., z) 0.0173
## (0.0110)
## SVB Prox (E) $\times$ MTM 0.0099
## (0.0052)
## SVB Prox (E) $\times$ Uninsured 0.0128*
## (0.0062)
## MTM $\times$ UI $\times$ SVB Prox (E) 0.0079
## (0.0048)
## _____________________________________ ___________ ___________ ___________
## S.E. type Heter.-rob. Heter.-rob. Heter.-rob.
## Observations 3,217 3,665 3,665
## R2 0.08769 0.09876 0.09804
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1# ==============================================================================
# SVB VISUALIZATIONS — 4-panel figure
# ==============================================================================
# --- Build borrower ID set for coloring ---
fed_borrower_ids <- df_crisis %>% filter(any_fed == 1) %>% pull(idrssd)
# --- Panel A: SVB in MTM × Uninsured scatter ---
svb_pt <- data.frame(
mtm_total_raw = svb_ref$mtm_total_rat,
uninsured_lev_raw = svb_ref$uninsured_lev
)
df_plot_a <- df_2022q4 %>%
mutate(group = ifelse(idrssd %in% fed_borrower_ids, "Emergency Borrower", "Non-Borrower"))
p_a <- ggplot(df_plot_a, aes(x = mtm_total_raw, y = uninsured_lev_raw)) +
geom_point(aes(color = group, alpha = group), size = 1.2) +
geom_point(data = svb_pt, size = 5, shape = 18, color = "red") +
annotate("text", x = svb_pt$mtm_total_raw + 0.3, y = svb_pt$uninsured_lev_raw + 2,
label = "SVB", color = "red", fontface = "bold", size = 4) +
scale_color_manual(values = c("Emergency Borrower" = "#003049", "Non-Borrower" = "grey70")) +
scale_alpha_manual(values = c("Emergency Borrower" = 0.5, "Non-Borrower" = 0.2)) +
labs(title = "A. SVB in MTM × Uninsured Space",
subtitle = "SVB sits at the extreme of both risk dimensions",
x = "MTM Loss (% of TA)", y = "Uninsured Leverage (% of TA)", color = NULL) +
theme_paper + guides(alpha = "none")
# --- Panel B: β^U distribution with SVB highlighted ---
df_beta_dist <- df_2022q4 %>% filter(!is.na(uninsured_beta_raw))
p_b <- ggplot(df_beta_dist, aes(x = uninsured_beta_raw)) +
geom_histogram(bins = 50, fill = "steelblue", alpha = 0.6, color = "white") +
geom_vline(xintercept = svb_ref$beta_u, color = "red", linewidth = 1.2) +
geom_vline(xintercept = median(df_beta_dist$uninsured_beta_raw, na.rm = TRUE),
color = "grey40", linewidth = 0.8, linetype = "dashed") +
annotate("text", x = svb_ref$beta_u + 0.02, y = Inf,
label = sprintf("SVB β^U = %.3f", svb_ref$beta_u),
hjust = 0, vjust = 2, color = "red", fontface = "bold", size = 3.5) +
annotate("text", x = median(df_beta_dist$uninsured_beta_raw, na.rm = TRUE) - 0.02,
y = Inf, label = "Median", hjust = 1, vjust = 4,
color = "grey40", fontface = "italic", size = 3) +
labs(title = "B. Distribution of Uninsured Deposit Beta (β^U)",
subtitle = sprintf("SVB at %.0fth percentile",
100 * mean(df_beta_dist$uninsured_beta_raw <= svb_ref$beta_u, na.rm = TRUE)),
x = "Uninsured Deposit Beta (β^U)", y = "Count") +
theme_paper
# --- Panel C: SVB-Like v2 — UI leverage overlap ---
df_ui_v2 <- df_crisis %>%
filter(!is.na(svb_like_v2)) %>%
mutate(SVB_Group = ifelse(svb_like_v2 == 1, "SVB-Like (v2)", "SVB-Unlike (v2)"))
p_c <- ggplot(df_ui_v2, aes(x = uninsured_lev_raw, fill = SVB_Group)) +
geom_density(alpha = 0.4, linewidth = 0.7) +
scale_fill_manual(values = c("SVB-Like (v2)" = "#D62828", "SVB-Unlike (v2)" = "#2A9D8F")) +
labs(title = "C. Uninsured Leverage: SVB-Like v2 vs. Unlike",
subtitle = "v2 definition preserves full overlap in uninsured leverage (no restriction of range)",
x = "Uninsured Leverage (% of TA)", y = "Density", fill = NULL) +
theme_paper
# --- Panel D: SVB Proximity (Mahalanobis) by borrower status ---
df_prox_plot <- df_anyfed_s %>%
filter(!is.na(svb_prox)) %>%
mutate(Borrower = ifelse(any_fed == 1, "Fed Borrower", "Non-Borrower"))
p_d <- ggplot(df_prox_plot, aes(x = svb_prox, fill = Borrower)) +
geom_density(alpha = 0.4, linewidth = 0.7) +
scale_fill_manual(values = c("Fed Borrower" = "#003049", "Non-Borrower" = "grey70")) +
geom_vline(xintercept = 0, linetype = "dashed", color = "grey40") +
labs(title = "D. SVB Proximity (Mahalanobis) by Borrower Status",
subtitle = "Borrowers are closer to SVB's profile (higher proximity)",
x = "SVB Proximity (z-standardized; higher = more SVB-like)", y = "Density", fill = NULL) +
theme_paper
# --- Combine ---
p_combined <- (p_a + p_b) / (p_c + p_d) +
plot_annotation(
title = "SVB Case Study: Position in Cross-Section and Improved Definitions",
theme = theme(plot.title = element_text(face = "bold", size = 14, hjust = 0))
)
print(p_combined)
save_figure(p_combined, "Fig_SVB_CaseStudy_4Panel", width = 14, height = 12)
# --- Also save individual panels ---
save_figure(p_a, "Fig_SVB_MTM_Uninsured_Scatter", width = 10, height = 7)
save_figure(p_b, "Fig_SVB_BetaU_Distribution", width = 10, height = 6)
save_figure(p_c, "Fig_SVB_v2_UILeverage_Overlap", width = 10, height = 6)
save_figure(p_d, "Fig_SVB_Proximity_Borrower", width = 10, height = 6)# ==============================================================================
# DIAGNOSTIC: Why the original split fails (restriction of range)
# Side-by-side density of uninsured leverage for original vs. v2 definitions
# ==============================================================================
df_ror <- df_crisis %>%
filter(!is.na(svb_like) & !is.na(svb_like_v2)) %>%
select(uninsured_lev_raw, svb_like, svb_like_v2) %>%
pivot_longer(cols = c(svb_like, svb_like_v2),
names_to = "Definition", values_to = "SVB_Like") %>%
mutate(
Definition = factor(ifelse(Definition == "svb_like",
"Original (β^U × UI Share)", "v2 (β^U × Securities × Cash)"),
levels = c("Original (β^U × UI Share)", "v2 (β^U × Securities × Cash)")),
Group = ifelse(SVB_Like == 1, "SVB-Like", "SVB-Unlike")
)
p_ror <- ggplot(df_ror, aes(x = uninsured_lev_raw, fill = Group)) +
geom_density(alpha = 0.4, linewidth = 0.7) +
facet_wrap(~ Definition) +
scale_fill_manual(values = c("SVB-Like" = "#D62828", "SVB-Unlike" = "#2A9D8F")) +
labs(
title = "Restriction of Range: Original vs. Improved SVB-Like Definition",
subtitle = paste0(
"Left: original definition splits on uninsured share → groups barely overlap on UI leverage.\n",
"Right: v2 definition uses orthogonal variables → full overlap preserved."),
x = "Uninsured Leverage (% of TA)", y = "Density", fill = NULL
) + theme_paper
print(p_ror)
save_figure(p_ror, "Fig_SVB_RestrictionOfRange_Diagnostic", width = 12, height = 6)# ==============================================================================
# INTENSIVE MARGIN ANALYSIS
#
# The extensive margin asks WHO borrows; the intensive margin asks HOW MUCH.
# Conditional on borrowing, what bank characteristics determine the size of
# emergency lending? We estimate:
#
# Borrow_Amount_i / TA_i = α + β₁·MTM + β₂·UI + β₃·MTM×UI + γ·X + ε
#
# DV: borrowing amount as % of total assets (btfp_pct, dw_pct).
# Sample: borrowers only (conditional on extensive margin = 1).
#
# --- Four model specifications, building progressively ---
#
# M1. RUN PRESSURE (baseline):
# MTM + Uninsured + MTM×Uninsured + Controls
# Banks facing more severe run pressure need more emergency liquidity.
# Controls include anticipated liquidity need proxies:
# - Cash ratio (liquid buffer)
# - Loan-to-deposit (illiquidity)
# - Wholesale funding (rollover risk)
#
# M2. + DEPOSIT BETA CHANNEL:
# Full triple interaction (MTM × UI × β^U)
# Banks with flightier (higher β^U) uninsured deposits face faster,
# larger runs → need more emergency liquidity.
#
# M3. + COLLATERAL / PAR SUPPLY CONSTRAINT:
# Par benefit + Collateral capacity (BTFP-specific: par_benefit)
# BTFP lends at par on OMO-eligible securities, so banks with larger
# unrealized losses on eligible collateral have a bigger par subsidy
# → incentive to borrow more. DW has no par feature.
# Collateral capacity constrains maximum borrowing for both facilities.
#
# M4. FULL SPECIFICATION:
# All channels combined: run pressure + deposit beta + collateral.
#
# Robustness: log(dollar amount) as alternative DV (right-skewed amounts).
# ==============================================================================
cat("=== INTENSIVE MARGIN: BORROWING AMOUNTS (CRISIS) ===\n\n")## === INTENSIVE MARGIN: BORROWING AMOUNTS (CRISIS) ===# --- Samples: borrowers only ---
df_btfp_intensive <- df_crisis %>% filter(btfp_crisis == 1, !is.na(btfp_pct), btfp_pct > 0)
df_dw_intensive <- df_crisis %>% filter(dw_crisis == 1, !is.na(dw_pct), dw_pct > 0)
# Log-transformed DVs (add small constant not needed — already > 0)
df_btfp_intensive <- df_btfp_intensive %>%
mutate(log_btfp_amt = log(btfp_crisis_amt),
log_btfp_pct = log(btfp_pct))
df_dw_intensive <- df_dw_intensive %>%
mutate(log_dw_amt = log(dw_crisis_amt),
log_dw_pct = log(dw_pct))
cat(sprintf(" BTFP borrowers: %d banks\n", nrow(df_btfp_intensive)))## BTFP borrowers: 501 bankscat(sprintf(" Mean amount: $%.1fM | Median: $%.1fM\n",
mean(df_btfp_intensive$btfp_crisis_amt, na.rm = TRUE) / 1e6,
median(df_btfp_intensive$btfp_crisis_amt, na.rm = TRUE) / 1e6))## Mean amount: $260.9M | Median: $22.5Mcat(sprintf(" Mean %%TA: %.2f%% | Median: %.2f%%\n",
mean(df_btfp_intensive$btfp_pct, na.rm = TRUE),
median(df_btfp_intensive$btfp_pct, na.rm = TRUE)))## Mean %TA: 6.62% | Median: 3.86%cat(sprintf(" SD %%TA: %.2f%% | Skewness: %.2f\n",
sd(df_btfp_intensive$btfp_pct, na.rm = TRUE),
(mean((df_btfp_intensive$btfp_pct - mean(df_btfp_intensive$btfp_pct))^3, na.rm=T)) /
sd(df_btfp_intensive$btfp_pct, na.rm=T)^3))## SD %TA: 10.07% | Skewness: 7.67cat(sprintf("\n DW borrowers: %d banks\n", nrow(df_dw_intensive)))##
## DW borrowers: 433 bankscat(sprintf(" Mean amount: $%.1fM | Median: $%.1fM\n",
mean(df_dw_intensive$dw_crisis_amt, na.rm = TRUE) / 1e6,
median(df_dw_intensive$dw_crisis_amt, na.rm = TRUE) / 1e6))## Mean amount: $1240.9M | Median: $0.1Mcat(sprintf(" Mean %%TA: %.2f%% | Median: %.2f%%\n",
mean(df_dw_intensive$dw_pct, na.rm = TRUE),
median(df_dw_intensive$dw_pct, na.rm = TRUE)))## Mean %TA: 8.23% | Median: 0.01%cat(sprintf(" SD %%TA: %.2f%%\n",
sd(df_dw_intensive$dw_pct, na.rm = TRUE)))## SD %TA: 34.78%# --- Explanatory variable sets ---
# M1: Run Pressure
INTENS_M1 <- EXPL_BASE # "mtm_total + uninsured_lev + mtm_x_uninsured"
# M2: + Deposit Beta (full triple)
INTENS_M2 <- EXPL_BETA_FULL
# M3: + Collateral/Par (BTFP gets par_benefit; DW does not)
INTENS_M3_BTFP <- paste0(EXPL_BASE, " + par_benefit + collateral_capacity")
INTENS_M3_DW <- paste0(EXPL_BASE, " + collateral_capacity")
# M4: Full
INTENS_M4_BTFP <- paste0(EXPL_BETA_FULL, " + par_benefit + collateral_capacity")
INTENS_M4_DW <- paste0(EXPL_BETA_FULL, " + collateral_capacity")
# Register additional labels for intensive-margin context
setFixest_dict(c(
btfp_pct = "BTFP / TA (\\%)",
dw_pct = "DW / TA (\\%)",
log_btfp_pct = "log(BTFP / TA)",
log_dw_pct = "log(DW / TA)",
log_btfp_amt = "log(BTFP \\$)",
log_dw_amt = "log(DW \\$)"
))cat("=== BTFP INTENSIVE MARGIN ===\n\n")## === BTFP INTENSIVE MARGIN ===# --- Levels: btfp_pct (% of TA) ---
mod_int_btfp_m1 <- safe_run(df_btfp_intensive, "btfp_pct", INTENS_M1, min_n = 20, min_dv1 = 0)
mod_int_btfp_m2 <- safe_run(df_btfp_intensive %>% filter(!is.na(uninsured_beta_w)),
"btfp_pct", INTENS_M2, min_n = 20, min_dv1 = 0)
mod_int_btfp_m3 <- safe_run(df_btfp_intensive, "btfp_pct", INTENS_M3_BTFP, min_n = 20, min_dv1 = 0)
mod_int_btfp_m4 <- safe_run(df_btfp_intensive %>% filter(!is.na(uninsured_beta_w)),
"btfp_pct", INTENS_M4_BTFP, min_n = 20, min_dv1 = 0)
# --- Log: log(amount in $) ---
mod_int_btfp_log_m1 <- safe_run(df_btfp_intensive, "log_btfp_amt", INTENS_M1, min_n = 20, min_dv1 = 0)
mod_int_btfp_log_m4 <- safe_run(df_btfp_intensive %>% filter(!is.na(uninsured_beta_w)),
"log_btfp_amt", INTENS_M4_BTFP, min_n = 20, min_dv1 = 0)
models_int_btfp <- list(
"M1: Run" = mod_int_btfp_m1, "M2: +Beta" = mod_int_btfp_m2,
"M3: +Collat" = mod_int_btfp_m3, "M4: Full" = mod_int_btfp_m4,
"M1 log($)" = mod_int_btfp_log_m1, "M4 log($)" = mod_int_btfp_log_m4)
save_etable(models_int_btfp, "Intensive_BTFP_crisis",
title_text = "Intensive Margin: BTFP Borrowing Amount (Crisis Period)",
notes_text = paste0(
"OLS. DV cols 1--4: BTFP amount / TA ($\\times 100$). DV cols 5--6: log(BTFP \\$). ",
"Sample: BTFP borrowers only (conditional on extensive margin). ",
"M1: Run pressure (MTM $\\times$ Uninsured). ",
"M2: + Deposit beta channel ($\\beta^U$ triple). ",
"M3: + Collateral/par supply (par benefit + OMO capacity). ",
"M4: Full specification. ",
"Controls: log(assets), cash ratio, loan-to-deposit, book equity, wholesale, ROA. ",
"Robust SEs. z-standardized explanatory variables."),
extra_lines = list(
c("DV", "\\%TA", "\\%TA", "\\%TA", "\\%TA", "log(\\$)", "log(\\$)"),
c("$\\beta^U$ channel", "No", "Yes", "No", "Yes", "No", "Yes"),
c("Par/Collateral", "No", "No", "Yes", "Yes", "No", "Yes")))
etable(models_int_btfp[!sapply(models_int_btfp, is.null)], fitstat = ~ n + r2, se.below = TRUE)## M1: Run M2: +Beta
## Dependent Var.: BTFP / TA (\%) BTFP / TA (\%)
##
## Constant 7.791*** 6.896***
## (1.113) (0.7387)
## MTM Loss (z) -1.199 -0.3225
## (1.026) (0.5904)
## Uninsured Leverage (z) -1.622 0.0880
## (1.477) (0.6376)
## MTM $\times$ Uninsured 1.392 0.4027
## (0.9568) (0.5987)
## Log(Assets) 1.742 0.4455
## (1.287) (0.6155)
## Cash Ratio 2.072 1.092
## (1.626) (1.314)
## Loan-to-Deposit -2.639 -2.829*
## (1.565) (1.273)
## Book Equity Ratio 0.8910 0.6620
## (0.8683) (0.7616)
## Wholesale Funding 0.6748 0.6836*
## (0.3504) (0.3222)
## ROA -0.1763 -1.009*
## (0.8310) (0.5060)
## Uninsured $\beta$ (z) 2.398**
## (0.9241)
## MTM $\times$ Unins. $\beta$ -2.547*
## (1.106)
## Uninsured $\times$ Unins. $\beta$ -1.140*
## (0.5610)
## MTM $\times$ Uninsured $\times$ $\beta^U$ 2.025*
## (0.9979)
## Par Benefit (z)
##
## OMO Collateral (z)
##
## ________________________________________ ______________ ______________
## S.E. type Heterosk.-rob. Heterosk.-rob.
## Observations 501 496
## R2 0.11747 0.26411
##
## M3: +Collat M4: Full
## Dependent Var.: BTFP / TA (\%) BTFP / TA (\%)
##
## Constant 7.618*** 6.852***
## (0.9117) (0.6817)
## MTM Loss (z) -0.2800 0.4714
## (0.6812) (0.4961)
## Uninsured Leverage (z) -1.816 -0.2002
## (1.388) (0.6654)
## MTM $\times$ Uninsured 1.565 0.6966
## (0.8867) (0.5609)
## Log(Assets) 1.806 0.4780
## (1.216) (0.6356)
## Cash Ratio 1.815 1.076
## (1.335) (1.182)
## Loan-to-Deposit -1.189 -1.441
## (1.110) (1.014)
## Book Equity Ratio 0.5872 0.4828
## (0.7001) (0.6809)
## Wholesale Funding 0.5540 0.5188
## (0.3433) (0.3196)
## ROA -0.0109 -0.6455
## (0.7475) (0.4922)
## Uninsured $\beta$ (z) 2.340**
## (0.7875)
## MTM $\times$ Unins. $\beta$ -2.236*
## (0.9118)
## Uninsured $\times$ Unins. $\beta$ -0.8717
## (0.4451)
## MTM $\times$ Uninsured $\times$ $\beta^U$ 1.844*
## (0.8260)
## Par Benefit (z) -3.621* -2.594*
## (1.840) (1.147)
## OMO Collateral (z) 1.956** 2.087***
## (0.6647) (0.5810)
## ________________________________________ ______________ ______________
## S.E. type Heterosk.-rob. Heterosk.-rob.
## Observations 501 496
## R2 0.20082 0.31816
##
## M1 log($) M4 log($)
## Dependent Var.: log(BTFP \$) log(BTFP \$)
##
## Constant 15.79*** 15.76***
## (0.2105) (0.1928)
## MTM Loss (z) 0.0653 0.2778
## (0.1738) (0.1792)
## Uninsured Leverage (z) -0.1417 -0.0363
## (0.2021) (0.1897)
## MTM $\times$ Uninsured 0.1489 0.1718
## (0.1790) (0.1667)
## Log(Assets) 0.7499*** 0.6611**
## (0.2124) (0.2182)
## Cash Ratio -0.6273 -0.6373
## (0.3778) (0.3448)
## Loan-to-Deposit 0.0708 0.2220
## (0.2001) (0.2321)
## Book Equity Ratio -0.2564 -0.2842
## (0.2280) (0.2258)
## Wholesale Funding 0.2280** 0.1990*
## (0.0864) (0.0894)
## ROA -0.1980 -0.1971
## (0.1837) (0.1724)
## Uninsured $\beta$ (z) 0.2324
## (0.1338)
## MTM $\times$ Unins. $\beta$ 0.0325
## (0.1498)
## Uninsured $\times$ Unins. $\beta$ -0.0891
## (0.1192)
## MTM $\times$ Uninsured $\times$ $\beta^U$ 0.0747
## (0.1280)
## Par Benefit (z) -0.4150*
## (0.1753)
## OMO Collateral (z) 0.3781*
## (0.1763)
## ________________________________________ ____________ ____________
## S.E. type Hetero.-rob. Hetero.-rob.
## Observations 501 496
## R2 0.11225 0.13684
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1cat("=== DW INTENSIVE MARGIN ===\n\n")## === DW INTENSIVE MARGIN ===# --- Levels: dw_pct (% of TA) ---
mod_int_dw_m1 <- safe_run(df_dw_intensive, "dw_pct", INTENS_M1, min_n = 20, min_dv1 = 0)
mod_int_dw_m2 <- safe_run(df_dw_intensive %>% filter(!is.na(uninsured_beta_w)),
"dw_pct", INTENS_M2, min_n = 20, min_dv1 = 0)
mod_int_dw_m3 <- safe_run(df_dw_intensive, "dw_pct", INTENS_M3_DW, min_n = 20, min_dv1 = 0)
mod_int_dw_m4 <- safe_run(df_dw_intensive %>% filter(!is.na(uninsured_beta_w)),
"dw_pct", INTENS_M4_DW, min_n = 20, min_dv1 = 0)
# --- Log: log(amount in $) ---
mod_int_dw_log_m1 <- safe_run(df_dw_intensive, "log_dw_amt", INTENS_M1, min_n = 20, min_dv1 = 0)
mod_int_dw_log_m4 <- safe_run(df_dw_intensive %>% filter(!is.na(uninsured_beta_w)),
"log_dw_amt", INTENS_M4_DW, min_n = 20, min_dv1 = 0)
models_int_dw <- list(
"M1: Run" = mod_int_dw_m1, "M2: +Beta" = mod_int_dw_m2,
"M3: +Collat" = mod_int_dw_m3, "M4: Full" = mod_int_dw_m4,
"M1 log($)" = mod_int_dw_log_m1, "M4 log($)" = mod_int_dw_log_m4)
save_etable(models_int_dw, "Intensive_DW_crisis",
title_text = "Intensive Margin: DW Borrowing Amount (Crisis Period)",
notes_text = paste0(
"OLS. DV cols 1--4: DW amount / TA ($\\times 100$). DV cols 5--6: log(DW \\$). ",
"Sample: DW borrowers only (conditional on extensive margin). ",
"No par benefit for DW (lends at market value, not par). ",
"M1: Run pressure. M2: + Deposit beta. M3: + Collateral capacity. M4: Full. ",
"Robust SEs. z-standardized."),
extra_lines = list(
c("DV", "\\%TA", "\\%TA", "\\%TA", "\\%TA", "log(\\$)", "log(\\$)"),
c("$\\beta^U$ channel", "No", "Yes", "No", "Yes", "No", "Yes"),
c("Collateral", "No", "No", "Yes", "Yes", "No", "Yes")))
etable(models_int_dw[!sapply(models_int_dw, is.null)], fitstat = ~ n + r2, se.below = TRUE)## M1: Run M2: +Beta
## Dependent Var.: DW / TA (\%) DW / TA (\%)
##
## Constant 3.943** 4.492**
## (1.512) (1.464)
## MTM Loss (z) 0.6626 1.395
## (1.993) (2.174)
## Uninsured Leverage (z) 2.280 2.742
## (2.036) (2.033)
## MTM $\times$ Uninsured 1.861 2.590
## (1.444) (1.780)
## Log(Assets) 3.102 2.753
## (1.844) (1.725)
## Cash Ratio -2.279 -2.108
## (1.457) (1.569)
## Loan-to-Deposit -0.6124 -1.277
## (2.508) (2.629)
## Book Equity Ratio -0.2767 0.1705
## (2.008) (2.026)
## Wholesale Funding 2.524* 2.517*
## (1.265) (1.208)
## ROA -0.0455 -0.0425
## (1.059) (1.094)
## Uninsured $\beta$ (z) 1.155
## (2.152)
## MTM $\times$ Unins. $\beta$ -0.6384
## (2.316)
## Uninsured $\times$ Unins. $\beta$ 2.582
## (2.341)
## MTM $\times$ Uninsured $\times$ $\beta^U$ 2.067
## (1.724)
## OMO Collateral (z)
##
## ________________________________________ ____________ ____________
## S.E. type Hetero.-rob. Hetero.-rob.
## Observations 433 430
## R2 0.03726 0.05058
##
## M3: +Collat M4: Full M1 log($)
## Dependent Var.: DW / TA (\%) DW / TA (\%) log(DW \$)
##
## Constant 3.940** 4.493** 11.04***
## (1.520) (1.469) (0.2545)
## MTM Loss (z) 0.5858 1.427 -0.2730
## (1.857) (1.949) (0.2769)
## Uninsured Leverage (z) 2.259 2.753 1.016***
## (2.040) (2.024) (0.2632)
## MTM $\times$ Uninsured 1.875 2.589 0.2793
## (1.426) (1.776) (0.2195)
## Log(Assets) 3.137 2.735 0.3568
## (1.880) (1.702) (0.2734)
## Cash Ratio -2.357 -2.079 -1.634***
## (1.505) (1.654) (0.3015)
## Loan-to-Deposit -0.9054 -1.187 -0.2425
## (2.996) (3.142) (0.3378)
## Book Equity Ratio -0.2470 0.1642 -0.2963
## (1.990) (2.024) (0.3486)
## Wholesale Funding 2.569 2.504* 0.8106***
## (1.322) (1.265) (0.1881)
## ROA -0.1133 -0.0185 0.3510
## (0.9888) (0.9956) (0.2671)
## Uninsured $\beta$ (z) 1.188
## (2.057)
## MTM $\times$ Unins. $\beta$ -0.6352
## (2.333)
## Uninsured $\times$ Unins. $\beta$ 2.582
## (2.343)
## MTM $\times$ Uninsured $\times$ $\beta^U$ 2.068
## (1.726)
## OMO Collateral (z) -0.4756 0.1595
## (2.310) (2.249)
## ________________________________________ ____________ ____________ __________
## S.E. type Hetero.-rob. Hetero.-rob. Hete.-rob.
## Observations 433 430 433
## R2 0.03737 0.05060 0.19081
##
## M4 log($)
## Dependent Var.: log(DW \$)
##
## Constant 11.01***
## (0.2612)
## MTM Loss (z) -0.1442
## (0.2858)
## Uninsured Leverage (z) 1.192***
## (0.2735)
## MTM $\times$ Uninsured 0.2169
## (0.2337)
## Log(Assets) 0.2075
## (0.2820)
## Cash Ratio -1.604***
## (0.3140)
## Loan-to-Deposit -0.4419
## (0.3834)
## Book Equity Ratio -0.2663
## (0.3504)
## Wholesale Funding 0.8595***
## (0.1894)
## ROA 0.3635
## (0.2705)
## Uninsured $\beta$ (z) 0.6080*
## (0.2557)
## MTM $\times$ Unins. $\beta$ -0.1233
## (0.2314)
## Uninsured $\times$ Unins. $\beta$ -0.2956
## (0.2037)
## MTM $\times$ Uninsured $\times$ $\beta^U$ 0.0297
## (0.1746)
## OMO Collateral (z) -0.0450
## (0.3121)
## ________________________________________ __________
## S.E. type Hete.-rob.
## Observations 430
## R2 0.20170
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1# ==============================================================================
# Side-by-side BTFP vs. DW using the full specification:
# Key question: Do the same factors drive both, or do the facilities serve
# different intensive-margin purposes?
#
# Prediction:
# - MTM × Uninsured: positive for both (run pressure → more borrowing)
# - Par benefit: positive for BTFP, irrelevant for DW
# - β^U triple: positive for BTFP (demand-side), may differ for DW
# (DW carries stigma → banks minimize DW amounts regardless of need)
# - Collateral: positive constraint for both
# ==============================================================================
cat("=== BTFP vs. DW INTENSIVE MARGIN COMPARISON ===\n\n")## === BTFP vs. DW INTENSIVE MARGIN COMPARISON ===models_int_combined <- list(
"BTFP: M1" = mod_int_btfp_m1, "DW: M1" = mod_int_dw_m1,
"BTFP: M4" = mod_int_btfp_m4, "DW: M4" = mod_int_dw_m4)
save_etable(models_int_combined, "Intensive_BTFP_vs_DW",
title_text = "Intensive Margin Comparison: BTFP vs. DW (Crisis Period)",
notes_text = paste0(
"OLS. DV: borrowing amount / TA ($\\times 100$). Sample: borrowers only. ",
"M1: Run pressure baseline. M4: Full (+ $\\beta^U$ triple + collateral/par). ",
"BTFP lends at par on OMO-eligible $\\Rightarrow$ par benefit matters. ",
"DW has stigma $\\Rightarrow$ banks may minimize DW amounts unconditionally. ",
"Robust SEs. z-standardized."),
extra_lines = list(
c("Facility", "BTFP", "DW", "BTFP", "DW"),
c("Specification", "M1", "M1", "M4", "M4"),
c("N borrowers",
nrow(df_btfp_intensive), nrow(df_dw_intensive),
sum(!is.na(df_btfp_intensive$uninsured_beta_w)),
sum(!is.na(df_dw_intensive$uninsured_beta_w)))))
etable(models_int_combined[!sapply(models_int_combined, is.null)], fitstat = ~ n + r2, se.below = TRUE)## BTFP: M1 DW: M1
## Dependent Var.: BTFP / TA (\%) DW / TA (\%)
##
## Constant 7.791*** 3.943**
## (1.113) (1.512)
## MTM Loss (z) -1.199 0.6626
## (1.026) (1.993)
## Uninsured Leverage (z) -1.622 2.280
## (1.477) (2.036)
## MTM $\times$ Uninsured 1.392 1.861
## (0.9568) (1.444)
## Log(Assets) 1.742 3.102
## (1.287) (1.844)
## Cash Ratio 2.072 -2.279
## (1.626) (1.457)
## Loan-to-Deposit -2.639 -0.6124
## (1.565) (2.508)
## Book Equity Ratio 0.8910 -0.2767
## (0.8683) (2.008)
## Wholesale Funding 0.6748 2.524*
## (0.3504) (1.265)
## ROA -0.1763 -0.0455
## (0.8310) (1.059)
## Uninsured $\beta$ (z)
##
## MTM $\times$ Unins. $\beta$
##
## Uninsured $\times$ Unins. $\beta$
##
## MTM $\times$ Uninsured $\times$ $\beta^U$
##
## Par Benefit (z)
##
## OMO Collateral (z)
##
## ________________________________________ ______________ ____________
## S.E. type Heterosk.-rob. Hetero.-rob.
## Observations 501 433
## R2 0.11747 0.03726
##
## BTFP: M4 DW: M4
## Dependent Var.: BTFP / TA (\%) DW / TA (\%)
##
## Constant 6.852*** 4.493**
## (0.6817) (1.469)
## MTM Loss (z) 0.4714 1.427
## (0.4961) (1.949)
## Uninsured Leverage (z) -0.2002 2.753
## (0.6654) (2.024)
## MTM $\times$ Uninsured 0.6966 2.589
## (0.5609) (1.776)
## Log(Assets) 0.4780 2.735
## (0.6356) (1.702)
## Cash Ratio 1.076 -2.079
## (1.182) (1.654)
## Loan-to-Deposit -1.441 -1.187
## (1.014) (3.142)
## Book Equity Ratio 0.4828 0.1642
## (0.6809) (2.024)
## Wholesale Funding 0.5188 2.504*
## (0.3196) (1.265)
## ROA -0.6455 -0.0185
## (0.4922) (0.9956)
## Uninsured $\beta$ (z) 2.340** 1.188
## (0.7875) (2.057)
## MTM $\times$ Unins. $\beta$ -2.236* -0.6352
## (0.9118) (2.333)
## Uninsured $\times$ Unins. $\beta$ -0.8717 2.582
## (0.4451) (2.343)
## MTM $\times$ Uninsured $\times$ $\beta^U$ 1.844* 2.068
## (0.8260) (1.726)
## Par Benefit (z) -2.594*
## (1.147)
## OMO Collateral (z) 2.087*** 0.1595
## (0.5810) (2.249)
## ________________________________________ ______________ ____________
## S.E. type Heterosk.-rob. Hetero.-rob.
## Observations 496 430
## R2 0.31816 0.05060
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1cat("=== INTENSIVE MARGIN DESCRIPTIVE STATISTICS ===\n\n")## === INTENSIVE MARGIN DESCRIPTIVE STATISTICS ===# --- Distribution of borrowing amounts ---
cat("--- BTFP Borrowing Distribution ---\n")## --- BTFP Borrowing Distribution ---cat(sprintf(" N: %d\n", nrow(df_btfp_intensive)))## N: 501cat(sprintf(" Mean: $%.1fM (%.2f%% TA)\n",
mean(df_btfp_intensive$btfp_crisis_amt) / 1e6, mean(df_btfp_intensive$btfp_pct)))## Mean: $260.9M (6.62% TA)cat(sprintf(" Median: $%.1fM (%.2f%% TA)\n",
median(df_btfp_intensive$btfp_crisis_amt) / 1e6, median(df_btfp_intensive$btfp_pct)))## Median: $22.5M (3.86% TA)cat(sprintf(" P10: $%.1fM (%.2f%% TA)\n",
quantile(df_btfp_intensive$btfp_crisis_amt, .10) / 1e6,
quantile(df_btfp_intensive$btfp_pct, .10)))## P10: $1.0M (0.06% TA)cat(sprintf(" P90: $%.1fM (%.2f%% TA)\n",
quantile(df_btfp_intensive$btfp_crisis_amt, .90) / 1e6,
quantile(df_btfp_intensive$btfp_pct, .90)))## P90: $350.0M (14.79% TA)cat("\n--- DW Borrowing Distribution ---\n")##
## --- DW Borrowing Distribution ---cat(sprintf(" N: %d\n", nrow(df_dw_intensive)))## N: 433cat(sprintf(" Mean: $%.1fM (%.2f%% TA)\n",
mean(df_dw_intensive$dw_crisis_amt) / 1e6, mean(df_dw_intensive$dw_pct)))## Mean: $1240.9M (8.23% TA)cat(sprintf(" Median: $%.1fM (%.2f%% TA)\n",
median(df_dw_intensive$dw_crisis_amt) / 1e6, median(df_dw_intensive$dw_pct)))## Median: $0.1M (0.01% TA)cat(sprintf(" P10: $%.1fM (%.2f%% TA)\n",
quantile(df_dw_intensive$dw_crisis_amt, .10) / 1e6,
quantile(df_dw_intensive$dw_pct, .10)))## P10: $0.0M (0.00% TA)cat(sprintf(" P90: $%.1fM (%.2f%% TA)\n",
quantile(df_dw_intensive$dw_crisis_amt, .90) / 1e6,
quantile(df_dw_intensive$dw_pct, .90)))## P90: $226.2M (12.67% TA)# --- Correlation of borrowing with key risk variables ---
cat("\n--- Correlations: Borrowing Intensity vs. Risk Variables ---\n")##
## --- Correlations: Borrowing Intensity vs. Risk Variables ---cor_btfp <- df_btfp_intensive %>%
select(btfp_pct, mtm_total_raw, uninsured_lev_raw, uninsured_beta_raw,
cash_ratio_raw, collateral_capacity_raw, par_benefit_raw,
ln_assets_raw, wholesale_raw) %>%
drop_na()
if (nrow(cor_btfp) > 10) {
cat(" BTFP (N=", nrow(cor_btfp), "):\n")
r <- cor(cor_btfp)[1, -1]
for (i in seq_along(r)) cat(sprintf(" %-28s r = %+.3f\n", names(r)[i], r[i]))
}## BTFP (N= 496 ):
## mtm_total_raw r = -0.082
## uninsured_lev_raw r = -0.026
## uninsured_beta_raw r = +0.236
## cash_ratio_raw r = +0.177
## collateral_capacity_raw r = +0.314
## par_benefit_raw r = -0.256
## ln_assets_raw r = +0.035
## wholesale_raw r = +0.111cor_dw <- df_dw_intensive %>%
select(dw_pct, mtm_total_raw, uninsured_lev_raw, uninsured_beta_raw,
cash_ratio_raw, collateral_capacity_raw, ln_assets_raw, wholesale_raw) %>%
drop_na()
if (nrow(cor_dw) > 10) {
cat("\n DW (N=", nrow(cor_dw), "):\n")
r <- cor(cor_dw)[1, -1]
for (i in seq_along(r)) cat(sprintf(" %-28s r = %+.3f\n", names(r)[i], r[i]))
}##
## DW (N= 430 ):
## mtm_total_raw r = +0.047
## uninsured_lev_raw r = +0.107
## uninsured_beta_raw r = +0.037
## cash_ratio_raw r = -0.090
## collateral_capacity_raw r = +0.016
## ln_assets_raw r = +0.150
## wholesale_raw r = +0.053# --- Distribution plots ---
p_int_dist <- bind_rows(
df_btfp_intensive %>% transmute(Facility = "BTFP", pct = btfp_pct),
df_dw_intensive %>% transmute(Facility = "DW", pct = dw_pct)
) %>%
ggplot(aes(x = pct, fill = Facility)) +
geom_histogram(bins = 40, alpha = 0.6, position = "identity", color = "white") +
facet_wrap(~Facility, scales = "free") +
scale_fill_manual(values = c("BTFP" = "#2A9D8F", "DW" = "#D62828")) +
labs(
title = "Distribution of Borrowing Intensity: BTFP vs. DW (Crisis)",
subtitle = "Borrowing amount as % of total assets, conditional on borrowing",
x = "Borrowing Amount / Total Assets (%)", y = "Count"
) + theme_paper + theme(legend.position = "none")
p_int_dist
save_figure(p_int_dist, "Fig_Intensive_Margin_Distribution", width = 12, height = 6)
# --- Scatter: MTM loss vs. borrowing intensity ---
p_int_scatter <- bind_rows(
df_btfp_intensive %>% transmute(Facility = "BTFP", mtm = mtm_total_raw, pct = btfp_pct),
df_dw_intensive %>% transmute(Facility = "DW", mtm = mtm_total_raw, pct = dw_pct)
) %>%
ggplot(aes(x = mtm, y = pct, color = Facility)) +
geom_point(alpha = 0.5, size = 2) +
geom_smooth(method = "lm", se = TRUE, linewidth = 1) +
facet_wrap(~Facility, scales = "free_y") +
scale_color_manual(values = c("BTFP" = "#2A9D8F", "DW" = "#D62828")) +
labs(
title = "MTM Loss vs. Borrowing Intensity (Crisis Borrowers)",
subtitle = "Do banks with larger unrealized losses borrow more?",
x = "MTM Loss (% of Total Assets)", y = "Borrowing Amount / TA (%)"
) + theme_paper + theme(legend.position = "none")
p_int_scatter
save_figure(p_int_scatter, "Fig_Intensive_MTM_vs_Amount", width = 12, height = 6)BTFP lent at par (face) value of collateral, while DW lent at market value. For banks with unrealized losses on OMO-eligible securities, this par-value lending provides implicit recapitalization: \[\text{Par Recap}_i = \frac{\text{Face Value}_i - \text{Market Value}_i}{\text{TA}_i} = \frac{\text{MTM Loss on OMO-eligible}_i}{\text{TA}_i}\]
If BTFP complements DW, we should see: 1. Par recapitalization increases DW probability (not decreases) 2. BTFP borrowers with larger par wedge are more likely to also use DW 3. Joint (both) facility usage rises with par recapitalization
cat("=== BTFP PAR RECAPITALIZATION → DW COMPLEMENTARITY ===\n\n")## === BTFP PAR RECAPITALIZATION → DW COMPLEMENTARITY ===# --- Panel A: Full sample — does par recap increase DW probability? ---
# If BTFP substitutes for DW, par_recap should be NEGATIVE (banks use BTFP instead)
# If BTFP complements DW, par_recap should be POSITIVE (recapitalization enables more DW)
EXPL_RECAP_BASE <- paste0(EXPL_BASE, " + par_recap")
EXPL_RECAP_INT <- paste0(EXPL_BASE, " + par_recap + par_recap_x_unins")
EXPL_RECAP_FULL <- paste0(EXPL_BASE, " + par_recap + par_recap_x_unins + collateral_capacity")
mod_recap_dw_m1 <- run_model(df_dw_s, "dw_crisis", EXPL_BASE)
mod_recap_dw_m2 <- run_model(df_dw_s, "dw_crisis", EXPL_RECAP_BASE)
mod_recap_dw_m3 <- run_model(df_dw_s, "dw_crisis", EXPL_RECAP_INT)
mod_recap_dw_m4 <- run_model(df_dw_s, "dw_crisis", EXPL_RECAP_FULL)
models_recap_dw <- list(
"DW (Base)" = mod_recap_dw_m1,
"DW + Recap" = mod_recap_dw_m2,
"DW + Recap×UI" = mod_recap_dw_m3,
"DW Full" = mod_recap_dw_m4)
save_etable(models_recap_dw, "ParRecap_DW_complementarity",
title_text = "BTFP Par Recapitalization → DW Borrowing (Complementarity Test)",
notes_text = paste0(
"LPM. DV = dw\\_crisis. Sample: DW borrowers + non-users (Crisis). ",
"Par Recap = MTM loss on OMO-eligible / TA (z). ",
"Positive par recap coefficient = BTFP complements DW. Robust SEs."))
etable(models_recap_dw, fitstat = ~ n + r2, se.below = TRUE)## DW (Base) DW + Recap DW + Rec.. DW Full
## Dependent Var.: dw_crisis dw_crisis dw_crisis dw_crisis
##
## Constant 0.1272*** 0.1273*** 0.1271*** 0.1271***
## (0.0054) (0.0054) (0.0054) (0.0054)
## MTM Loss (z) 0.0158** 0.0149* 0.0146* 0.0133*
## (0.0061) (0.0062) (0.0062) (0.0067)
## Uninsured Leverage (z) 0.0126 0.0129 0.0128 0.0127
## (0.0067) (0.0067) (0.0067) (0.0067)
## MTM $\times$ Uninsured 0.0170*** 0.0169*** 0.0159** 0.0158**
## (0.0051) (0.0051) (0.0053) (0.0053)
## Log(Assets) 0.0920*** 0.0907*** 0.0905*** 0.0902***
## (0.0077) (0.0077) (0.0077) (0.0077)
## Cash Ratio -0.0043 -0.0034 -0.0035 -0.0039
## (0.0053) (0.0053) (0.0053) (0.0054)
## Loan-to-Deposit -0.0007 0.0022 0.0021 0.0007
## (0.0057) (0.0061) (0.0061) (0.0065)
## Book Equity Ratio -0.0006 -0.0004 -0.0004 -2.82e-5
## (0.0044) (0.0044) (0.0044) (0.0045)
## Wholesale Funding 0.0204** 0.0199** 0.0198** 0.0199**
## (0.0063) (0.0063) (0.0063) (0.0063)
## ROA -0.0029 -0.0021 -0.0021 -0.0024
## (0.0048) (0.0049) (0.0049) (0.0049)
## Par Recap (z) 0.0068 0.0069 0.0100
## (0.0060) (0.0061) (0.0076)
## Par Recap $\times$ Uninsured 0.0031 0.0031
## (0.0054) (0.0054)
## OMO Collateral (z) -0.0045
## (0.0066)
## ____________________________ __________ __________ __________ __________
## S.E. type Hete.-rob. Hete.-rob. Hete.-rob. Hete.-rob.
## Observations 3,649 3,649 3,649 3,649
## R2 0.10314 0.10347 0.10356 0.10363
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1cat("\n--- Interpretation ---\n")##
## --- Interpretation ---cat("Par Recap > 0 → BTFP recapitalization INCREASES DW probability (complement)\n")## Par Recap > 0 → BTFP recapitalization INCREASES DW probability (complement)cat("Par Recap < 0 → BTFP recapitalization DECREASES DW probability (substitute)\n")## Par Recap < 0 → BTFP recapitalization DECREASES DW probability (substitute)cat("Par Recap × Uninsured > 0 → recapitalization amplifies coordination channel\n")## Par Recap × Uninsured > 0 → recapitalization amplifies coordination channelcat("=== AMONG BTFP BORROWERS: PAR RECAP → ALSO DW? ===\n\n")## === AMONG BTFP BORROWERS: PAR RECAP → ALSO DW? ===# Among banks that already accessed BTFP (got par recapitalization),
# does the SIZE of that recapitalization predict also using DW?
df_btfp_comp <- df_crisis %>%
filter(btfp_crisis == 1) %>%
mutate(also_dw = as.integer(dw_crisis == 1))
cat("BTFP borrowers:", nrow(df_btfp_comp), "| Also DW:", sum(df_btfp_comp$also_dw),
sprintf("(%.1f%%)\n", 100 * mean(df_btfp_comp$also_dw)))## BTFP borrowers: 501 | Also DW: 106 (21.2%)mod_btfp2dw_m1 <- safe_run(df_btfp_comp, "also_dw", EXPL_BASE, min_n = 20, min_dv1 = 5)
mod_btfp2dw_m2 <- safe_run(df_btfp_comp, "also_dw", EXPL_RECAP_BASE, min_n = 20, min_dv1 = 5)
mod_btfp2dw_m3 <- safe_run(df_btfp_comp, "also_dw",
paste0(EXPL_BASE, " + par_recap + collateral_capacity"), min_n = 20, min_dv1 = 5)
mod_btfp2dw_m4 <- safe_run(df_btfp_comp, "also_dw",
paste0(EXPL_BASE, " + par_recap + par_recap_x_unins + collateral_capacity"),
min_n = 20, min_dv1 = 5)
models_btfp2dw <- list(
"Base" = mod_btfp2dw_m1,
"+ Recap" = mod_btfp2dw_m2,
"+ Recap + Coll" = mod_btfp2dw_m3,
"+ Recap×UI + Coll" = mod_btfp2dw_m4)
save_etable(models_btfp2dw, "ParRecap_BTFP_to_DW",
title_text = "Among BTFP Borrowers: Par Recapitalization → Also DW?",
notes_text = paste0(
"LPM. DV = 1 if BTFP borrower also used DW. Sample: BTFP borrowers (Crisis). ",
"Positive par recap → larger recapitalization predicts joint facility use. Robust SEs."),
extra_lines = list(
c("BTFP Borrowers", rep(nrow(df_btfp_comp), 4)),
c("Also DW", rep(sum(df_btfp_comp$also_dw), 4))))
etable(models_btfp2dw[!sapply(models_btfp2dw, is.null)],
fitstat = ~ n + r2, se.below = TRUE)## Base + Recap + Recap .. + Recap×..
## Dependent Var.: Also DW Also DW Also DW Also DW
##
## Constant 0.1466*** 0.1459*** 0.1480*** 0.1479***
## (0.0226) (0.0226) (0.0225) (0.0225)
## MTM Loss (z) -0.0283 -0.0273 -0.0357 -0.0356
## (0.0234) (0.0235) (0.0255) (0.0256)
## Uninsured Leverage (z) 0.0356 0.0357 0.0344 0.0346
## (0.0220) (0.0221) (0.0220) (0.0220)
## MTM $\times$ Uninsured 0.0198 0.0194 0.0189 0.0200
## (0.0192) (0.0192) (0.0193) (0.0217)
## Log(Assets) 0.1121*** 0.1158*** 0.1152*** 0.1158***
## (0.0224) (0.0228) (0.0225) (0.0232)
## Cash Ratio 0.0177 0.0137 0.0138 0.0139
## (0.0357) (0.0360) (0.0356) (0.0357)
## Loan-to-Deposit -0.0060 -0.0126 -0.0216 -0.0214
## (0.0282) (0.0291) (0.0312) (0.0312)
## Book Equity Ratio -0.0184 -0.0199 -0.0175 -0.0171
## (0.0228) (0.0231) (0.0234) (0.0236)
## Wholesale Funding 0.0145 0.0159 0.0165 0.0164
## (0.0143) (0.0143) (0.0143) (0.0143)
## ROA -0.0357 -0.0381 -0.0392 -0.0393
## (0.0241) (0.0245) (0.0245) (0.0245)
## Par Recap (z) -0.0136 0.0035 0.0046
## (0.0179) (0.0251) (0.0253)
## OMO Collateral (z) -0.0261 -0.0261
## (0.0288) (0.0288)
## Par Recap $\times$ Uninsured -0.0027
## (0.0194)
## ____________________________ __________ __________ __________ __________
## S.E. type Hete.-rob. Hete.-rob. Hete.-rob. Hete.-rob.
## Observations 501 501 501 501
## R2 0.10284 0.10384 0.10497 0.10502
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1cat("=== PAR RECAPITALIZATION → JOINT BTFP + DW USAGE ===\n\n")## === PAR RECAPITALIZATION → JOINT BTFP + DW USAGE ===# Direct test: does par recapitalization predict using BOTH facilities?
# DV = both_fed (1 if used both BTFP and DW during crisis)
# Sample: full crisis (all banks)
df_both_s <- df_crisis %>%
filter(both_fed == 1 | (btfp_crisis == 0 & dw_crisis == 0 & fhlb_user == 0))
cat("Both-Fed sample:", nrow(df_both_s),
"| Both users:", sum(df_both_s$both_fed),
"| Non-users:", sum(df_both_s$both_fed == 0), "\n")## Both-Fed sample: 3332 | Both users: 106 | Non-users: 3226mod_both_m1 <- safe_run(df_both_s, "both_fed", EXPL_BASE, min_n = 20, min_dv1 = 5)
mod_both_m2 <- safe_run(df_both_s, "both_fed", EXPL_RECAP_BASE, min_n = 20, min_dv1 = 5)
mod_both_m3 <- safe_run(df_both_s, "both_fed", EXPL_RECAP_FULL, min_n = 20, min_dv1 = 5)
# Also run on the full anyfed sample (both_fed vs single-facility vs none)
mod_both_full_m1 <- safe_run(df_anyfed_s, "both_fed", EXPL_BASE, min_n = 20, min_dv1 = 5)
mod_both_full_m2 <- safe_run(df_anyfed_s, "both_fed", EXPL_RECAP_FULL, min_n = 20, min_dv1 = 5)
models_both <- list(
"Both (clean)" = mod_both_m1,
"+ Recap" = mod_both_m2,
"+ Recap Full" = mod_both_m3,
"AnyFed Base" = mod_both_full_m1,
"AnyFed + Recap" = mod_both_full_m2)
save_etable(models_both, "ParRecap_BothFed",
title_text = "Par Recapitalization → Joint BTFP + DW Usage",
notes_text = paste0(
"LPM. DV = both\\_fed (1 if used BTFP and DW). ",
"Cols 1-3: Both users vs. pure non-users. Cols 4-5: Both users vs. AnyFed sample. ",
"Par Recap measures BTFP's implicit capital injection. Robust SEs."))
etable(models_both[!sapply(models_both, is.null)],
fitstat = ~ n + r2, se.below = TRUE)## Both (cl.. + Recap + Recap .. AnyFed B..
## Dependent Var.: both_fed both_fed both_fed both_fed
##
## Constant 0.0394*** 0.0395*** 0.0391*** 0.0273***
## (0.0036) (0.0036) (0.0036) (0.0026)
## MTM Loss (z) 0.0048 0.0042 0.0040 0.0019
## (0.0036) (0.0037) (0.0040) (0.0029)
## Uninsured Leverage (z) 0.0119** 0.0121** 0.0120** 0.0086*
## (0.0045) (0.0045) (0.0045) (0.0036)
## MTM $\times$ Uninsured 0.0118*** 0.0118*** 0.0096** 0.0076**
## (0.0034) (0.0034) (0.0036) (0.0027)
## Log(Assets) 0.0390*** 0.0381*** 0.0378*** 0.0268***
## (0.0055) (0.0055) (0.0054) (0.0042)
## Cash Ratio -0.0054* -0.0047 -0.0048 -0.0039
## (0.0026) (0.0026) (0.0026) (0.0023)
## Loan-to-Deposit -0.0069* -0.0049 -0.0048 -0.0049
## (0.0032) (0.0033) (0.0036) (0.0027)
## Book Equity Ratio 0.0011 0.0013 0.0011 2.86e-5
## (0.0021) (0.0021) (0.0022) (0.0018)
## Wholesale Funding 0.0118** 0.0115** 0.0112** 0.0078*
## (0.0041) (0.0040) (0.0040) (0.0031)
## ROA -0.0061* -0.0056* -0.0055* -0.0048*
## (0.0027) (0.0027) (0.0027) (0.0023)
## Par Recap (z) 0.0048 0.0044
## (0.0038) (0.0045)
## Par Recap $\times$ Uninsured 0.0069
## (0.0044)
## OMO Collateral (z) 0.0012
## (0.0035)
## ____________________________ __________ __________ __________ __________
## S.E. type Hete.-rob. Hete.-rob. Hete.-rob. Hete.-rob.
## Observations 3,322 3,322 3,322 4,044
## R2 0.06807 0.06862 0.07015 0.04246
##
## AnyFed +..
## Dependent Var.: both_fed
##
## Constant 0.0270***
## (0.0026)
## MTM Loss (z) 0.0015
## (0.0033)
## Uninsured Leverage (z) 0.0087*
## (0.0037)
## MTM $\times$ Uninsured 0.0063*
## (0.0029)
## Log(Assets) 0.0260***
## (0.0042)
## Cash Ratio -0.0036
## (0.0023)
## Loan-to-Deposit -0.0037
## (0.0031)
## Book Equity Ratio -4.46e-5
## (0.0019)
## Wholesale Funding 0.0075*
## (0.0030)
## ROA -0.0044
## (0.0023)
## Par Recap (z) 0.0018
## (0.0036)
## Par Recap $\times$ Uninsured 0.0040
## (0.0036)
## OMO Collateral (z) 0.0011
## (0.0031)
## ____________________________ __________
## S.E. type Hete.-rob.
## Observations 4,044
## R2 0.04329
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1cat("=== PAR RECAPITALIZATION → TOTAL FED BORROWING INTENSITY ===\n\n")## === PAR RECAPITALIZATION → TOTAL FED BORROWING INTENSITY ===# Among banks using ANY fed facility: total borrowing = BTFP + DW amount
df_total_int <- df_crisis %>%
filter(any_fed == 1) %>%
mutate(
btfp_amt_safe = replace_na(btfp_crisis_amt, 0),
dw_amt_safe = replace_na(dw_crisis_amt, 0),
total_fed_amt = btfp_amt_safe + dw_amt_safe,
total_fed_pct = 100 * total_fed_amt / (total_asset * 1000),
log_total_fed = log(pmax(total_fed_amt, 1))
)
cat(sprintf("Any-Fed borrowers: %d\n", nrow(df_total_int)))## Any-Fed borrowers: 828cat(sprintf(" Mean total fed / TA: %.2f%%\n", mean(df_total_int$total_fed_pct, na.rm=T)))## Mean total fed / TA: 8.31%cat(sprintf(" Median total fed / TA: %.2f%%\n", median(df_total_int$total_fed_pct, na.rm=T)))## Median total fed / TA: 2.27%cat(sprintf(" Mean total fed ($M): %.1f\n", mean(df_total_int$total_fed_amt, na.rm=T) / 1e6))## Mean total fed ($M): 806.8INTENS_RECAP_M1 <- EXPL_BASE
INTENS_RECAP_M2 <- paste0(EXPL_BASE, " + par_recap + collateral_capacity")
INTENS_RECAP_M3 <- paste0(EXPL_BASE, " + par_recap + par_recap_x_unins + collateral_capacity")
mod_total_m1 <- safe_run(df_total_int, "total_fed_pct", INTENS_RECAP_M1, min_n = 20, min_dv1 = 0)
mod_total_m2 <- safe_run(df_total_int, "total_fed_pct", INTENS_RECAP_M2, min_n = 20, min_dv1 = 0)
mod_total_m3 <- safe_run(df_total_int, "total_fed_pct", INTENS_RECAP_M3, min_n = 20, min_dv1 = 0)
mod_total_log_m1 <- safe_run(df_total_int, "log_total_fed", INTENS_RECAP_M1, min_n = 20, min_dv1 = 0)
mod_total_log_m2 <- safe_run(df_total_int, "log_total_fed", INTENS_RECAP_M3, min_n = 20, min_dv1 = 0)
models_total <- list(
"%TA Base" = mod_total_m1,
"%TA + Recap" = mod_total_m2,
"%TA + Recap×UI" = mod_total_m3,
"log($) Base" = mod_total_log_m1,
"log($) Full" = mod_total_log_m2)
save_etable(models_total, "ParRecap_TotalFed_Intensive",
title_text = "Par Recapitalization → Total Fed Borrowing (Intensive Margin)",
notes_text = paste0(
"OLS. DV: total fed borrowing (BTFP + DW) / TA (\\%) or log(\\$). ",
"Sample: AnyFed borrowers (Crisis). ",
"Par Recap > 0 → larger BTFP recapitalization increases total borrowing. Robust SEs."),
extra_lines = list(
c("Borrowers", rep(nrow(df_total_int), 5)),
c("Mean DV", round(mean(df_total_int$total_fed_pct, na.rm=T), 2),
round(mean(df_total_int$total_fed_pct, na.rm=T), 2),
round(mean(df_total_int$total_fed_pct, na.rm=T), 2),
round(mean(df_total_int$log_total_fed, na.rm=T), 2),
round(mean(df_total_int$log_total_fed, na.rm=T), 2))))
etable(models_total[!sapply(models_total, is.null)],
fitstat = ~ n + r2, se.below = TRUE)## %TA Base %TA + Recap %TA + Recap..
## Dependent Var.: total_fed_pct total_fed_pct total_fed_pct
##
## Constant 6.124*** 6.064*** 5.965***
## (0.8546) (0.8201) (0.8493)
## MTM Loss (z) -0.4515 0.6457 0.7256
## (1.269) (1.171) (1.193)
## Uninsured Leverage (z) 0.6744 0.8902 0.9699
## (1.477) (1.404) (1.435)
## MTM $\times$ Uninsured 1.961 2.041* 2.761*
## (1.022) (1.015) (1.190)
## Log(Assets) 3.304* 3.579* 3.941**
## (1.391) (1.425) (1.501)
## Cash Ratio -0.9301 -0.9716 -0.7937
## (1.153) (1.131) (1.136)
## Loan-to-Deposit -2.145 -1.363 -1.137
## (1.739) (1.830) (1.899)
## Book Equity Ratio 0.5655 0.3649 0.4575
## (1.140) (1.117) (1.100)
## Wholesale Funding 1.919** 1.922* 1.950**
## (0.7066) (0.7459) (0.7538)
## ROA -0.3661 -0.2762 -0.2426
## (0.7737) (0.7403) (0.7606)
## Par Recap (z) -2.978 -2.386
## (2.173) (2.075)
## OMO Collateral (z) 3.560 3.530
## (2.635) (2.634)
## Par Recap $\times$ Uninsured -1.671
## (1.244)
## ____________________________ _____________ _____________ _____________
## S.E. type Heteros.-rob. Heteros.-rob. Heteros.-rob.
## Observations 828 828 828
## R2 0.03451 0.03930 0.04316
##
## log($) Base log($) Full
## Dependent Var.: log_total_fed log_total_fed
##
## Constant 13.69*** 13.67***
## (0.1889) (0.1860)
## MTM Loss (z) -0.0680 0.1589
## (0.1968) (0.2121)
## Uninsured Leverage (z) 0.5303** 0.5798**
## (0.1959) (0.1857)
## MTM $\times$ Uninsured 0.0724 0.1204
## (0.1656) (0.1766)
## Log(Assets) 0.3988 0.4523*
## (0.2035) (0.2070)
## Cash Ratio -1.685*** -1.665***
## (0.2814) (0.2757)
## Loan-to-Deposit -0.3381 -0.1143
## (0.2375) (0.2539)
## Book Equity Ratio -0.3250 -0.3609
## (0.2243) (0.2249)
## Wholesale Funding 0.4740*** 0.4659***
## (0.1126) (0.1149)
## ROA 0.0003 0.0343
## (0.1797) (0.1818)
## Par Recap (z) -0.5129
## (0.2857)
## OMO Collateral (z) 0.7574*
## (0.3260)
## Par Recap $\times$ Uninsured -0.0764
## (0.1551)
## ____________________________ _____________ _____________
## S.E. type Heteros.-rob. Heteros.-rob.
## Observations 828 828
## R2 0.12827 0.13569
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1cat("=== DESCRIPTIVE: PAR RECAPITALIZATION BY FACILITY CHOICE ===\n\n")## === DESCRIPTIVE: PAR RECAPITALIZATION BY FACILITY CHOICE ===# --- Compare par recap across facility choice groups ---
df_choice_desc <- df_crisis %>%
filter(any_fed == 1 | (btfp_crisis == 0 & dw_crisis == 0)) %>%
mutate(group = factor(case_when(
both_fed == 1 ~ "Both BTFP+DW",
btfp_crisis == 1 ~ "BTFP Only",
dw_crisis == 1 ~ "DW Only",
TRUE ~ "Neither"),
levels = c("Neither", "DW Only", "BTFP Only", "Both BTFP+DW")))
desc_recap <- df_choice_desc %>%
group_by(group) %>%
summarise(
N = n(),
pct = sprintf("%.1f%%", 100 * n() / nrow(df_choice_desc)),
mtm_total_mean = round(mean(mtm_total_raw, na.rm=T), 3),
mtm_omo_mean = round(mean(mtm_btfp_raw, na.rm=T), 3),
uninsured_lev_mean = round(mean(uninsured_lev_raw, na.rm=T), 3),
collateral_mean = round(mean(collateral_capacity_raw, na.rm=T), 3),
par_benefit_mean = round(mean(par_benefit_raw, na.rm=T), 3),
book_equity_mean = round(mean(book_equity_ratio_raw, na.rm=T), 3),
ln_assets_mean = round(mean(ln_assets_raw, na.rm=T), 2),
.groups = "drop")
cat("--- Mean Characteristics by Facility Choice (Par Recap Focus) ---\n")## --- Mean Characteristics by Facility Choice (Par Recap Focus) ---print(desc_recap, width = Inf)## # A tibble: 4 × 10
## group N pct mtm_total_mean mtm_omo_mean uninsured_lev_mean
## <fct> <int> <chr> <dbl> <dbl> <dbl>
## 1 Neither 3464 80.7% 5.35 0.647 22.8
## 2 DW Only 327 7.6% 5.72 0.728 26.8
## 3 BTFP Only 395 9.2% 6.18 0.875 26.2
## 4 Both BTFP+DW 106 2.5% 5.83 0.924 32.0
## collateral_mean par_benefit_mean book_equity_mean ln_assets_mean
## <dbl> <dbl> <dbl> <dbl>
## 1 0.011 0.909 10.6 12.7
## 2 0.009 0.962 9.10 13.8
## 3 0.012 0.933 8.19 13.5
## 4 0.011 0.978 8.14 14.6# --- T-tests: Both vs. Single-facility users ---
cat("\n--- T-Tests: Joint (Both) vs. BTFP-Only Users ---\n")##
## --- T-Tests: Joint (Both) vs. BTFP-Only Users ---both_users <- df_choice_desc %>% filter(group == "Both BTFP+DW")
btfp_only_d <- df_choice_desc %>% filter(group == "BTFP Only")
dw_only_d <- df_choice_desc %>% filter(group == "DW Only")
recap_vars <- c("mtm_btfp_raw", "mtm_total_raw", "uninsured_lev_raw",
"collateral_capacity_raw", "par_benefit_raw",
"book_equity_ratio_raw", "ln_assets_raw")
for (v in recap_vars) {
tt <- tryCatch(t.test(both_users[[v]], btfp_only_d[[v]]), error = function(e) NULL)
if (!is.null(tt)) {
stars <- case_when(tt$p.value < 0.01 ~ "***", tt$p.value < 0.05 ~ "**",
tt$p.value < 0.10 ~ "*", TRUE ~ "")
cat(sprintf(" %-28s Both=%.3f BTFPonly=%.3f diff=%.3f t=%.2f %s\n", v,
mean(both_users[[v]], na.rm=T), mean(btfp_only_d[[v]], na.rm=T),
mean(both_users[[v]], na.rm=T) - mean(btfp_only_d[[v]], na.rm=T),
tt$statistic, stars))
}
}## mtm_btfp_raw Both=0.924 BTFPonly=0.875 diff=0.049 t=0.46
## mtm_total_raw Both=5.832 BTFPonly=6.175 diff=-0.344 t=-1.65
## uninsured_lev_raw Both=32.010 BTFPonly=26.154 diff=5.856 t=4.03 ***
## collateral_capacity_raw Both=0.011 BTFPonly=0.012 diff=-0.000 t=-0.36
## par_benefit_raw Both=0.978 BTFPonly=0.933 diff=0.045 t=4.09 ***
## book_equity_ratio_raw Both=8.138 BTFPonly=8.188 diff=-0.050 t=-0.16
## ln_assets_raw Both=14.577 BTFPonly=13.486 diff=1.091 t=5.82 ***cat("\n--- T-Tests: Joint (Both) vs. DW-Only Users ---\n")##
## --- T-Tests: Joint (Both) vs. DW-Only Users ---for (v in recap_vars) {
tt <- tryCatch(t.test(both_users[[v]], dw_only_d[[v]]), error = function(e) NULL)
if (!is.null(tt)) {
stars <- case_when(tt$p.value < 0.01 ~ "***", tt$p.value < 0.05 ~ "**",
tt$p.value < 0.10 ~ "*", TRUE ~ "")
cat(sprintf(" %-28s Both=%.3f DWonly=%.3f diff=%.3f t=%.2f %s\n", v,
mean(both_users[[v]], na.rm=T), mean(dw_only_d[[v]], na.rm=T),
mean(both_users[[v]], na.rm=T) - mean(dw_only_d[[v]], na.rm=T),
tt$statistic, stars))
}
}## mtm_btfp_raw Both=0.924 DWonly=0.728 diff=0.196 t=1.90 *
## mtm_total_raw Both=5.832 DWonly=5.718 diff=0.114 t=0.53
## uninsured_lev_raw Both=32.010 DWonly=26.774 diff=5.236 t=3.53 ***
## collateral_capacity_raw Both=0.011 DWonly=0.009 diff=0.002 t=1.84 *
## par_benefit_raw Both=0.978 DWonly=0.962 diff=0.016 t=1.70 *
## book_equity_ratio_raw Both=8.138 DWonly=9.097 diff=-0.959 t=-2.99 ***
## ln_assets_raw Both=14.577 DWonly=13.833 diff=0.744 t=3.89 ***# --- Figure: Par Recap Distribution by Facility Choice ---
p_recap_box <- df_choice_desc %>%
filter(group != "Neither") %>%
ggplot(aes(x = group, y = mtm_btfp_raw, fill = group)) +
geom_boxplot(alpha = 0.7, outlier.alpha = 0.3) +
scale_fill_manual(values = c("DW Only" = "#D62828",
"BTFP Only" = "#2A9D8F", "Both BTFP+DW" = "#6A0572")) +
labs(
title = "Par Recapitalization by Facility Choice",
subtitle = "MTM loss on OMO-eligible / TA (the par wedge banks capture from BTFP)",
x = NULL, y = "MTM Loss on OMO-Eligible (% of TA)"
) + theme_paper + theme(legend.position = "none")
p_recap_box
save_figure(p_recap_box, "Fig_ParRecap_by_FacilityChoice", width = 10, height = 7)
# --- Figure: Par Recap vs. DW probability (scatterplot with loess) ---
p_recap_dw <- df_crisis %>%
mutate(dw_label = ifelse(dw_crisis == 1, "DW Borrower", "Non-DW")) %>%
ggplot(aes(x = mtm_btfp_raw, y = dw_crisis)) +
geom_jitter(aes(color = dw_label), alpha = 0.3, height = 0.05, width = 0, size = 1.5) +
geom_smooth(method = "loess", se = TRUE, color = "black", linewidth = 1.2) +
scale_color_manual(values = c("Non-DW" = "grey60", "DW Borrower" = "#D62828")) +
labs(
title = "BTFP Par Recapitalization vs. DW Borrowing Probability",
subtitle = "Does larger par wedge increase DW usage? (loess fit)",
x = "Par Recapitalization (MTM Loss on OMO-Eligible / TA, %)",
y = "P(DW Borrowing)"
) + theme_paper
p_recap_dw
save_figure(p_recap_dw, "Fig_ParRecap_vs_DW_probability", width = 10, height = 7)
# --- Summary statistics ---
cat("\n--- Key Complementarity Statistics ---\n")##
## --- Key Complementarity Statistics ---n_both <- sum(df_crisis$both_fed, na.rm = TRUE)
n_btfp <- sum(df_crisis$btfp_crisis, na.rm = TRUE)
n_dw <- sum(df_crisis$dw_crisis, na.rm = TRUE)
cat(sprintf(" BTFP borrowers: %d\n", n_btfp))## BTFP borrowers: 501cat(sprintf(" DW borrowers: %d\n", n_dw))## DW borrowers: 433cat(sprintf(" Both: %d (%.1f%% of BTFP users, %.1f%% of DW users)\n",
n_both, 100 * n_both / n_btfp, 100 * n_both / n_dw))## Both: 106 (21.2% of BTFP users, 24.5% of DW users)cat(sprintf(" If independent: expected Both = %.1f\n",
n_btfp * n_dw / nrow(df_crisis)))## If independent: expected Both = 50.5cat(sprintf(" Observed / Expected ratio: %.2f\n",
n_both / (n_btfp * n_dw / nrow(df_crisis))))## Observed / Expected ratio: 2.10cat(" Ratio > 1 → positive association → complementarity\n")## Ratio > 1 → positive association → complementarityBTFP accepts only OMO-eligible securities (Treasury, Agency MBS/CMO/Debt) at par. DW accepts everything — securities, loans (CRE, C&I, consumer, residential) — at market value with haircuts.
This creates a natural collateral pecking order under run pressure: 1. Pledge OMO-eligible securities at BTFP (best terms, par value, no stigma) 2. If OMO capacity is exhausted, pledge remaining assets at DW (stigma, haircuts) 3. Banks pledging a larger fraction of their OMO portfolio → more severe liquidity need
Key variables from loan-level data: - BTFP utilization = Total BTFP collateral pledged / Bank’s OMO-eligible portfolio - DW collateral composition = Share of OMO-eligible vs. loan-based vs. other at DW - Advance rate = Loan amount / Collateral pledged (BTFP ≈ 1 at par; DW < 1 with haircuts) - Loan count = Number of trips to each facility (repeat borrowing intensity)
cat("=== LOAN-LEVEL COLLATERAL AGGREGATION ===\n\n")## === LOAN-LEVEL COLLATERAL AGGREGATION ===# --- BTFP: Aggregate to bank level (crisis period) ---
# Each BTFP loan encumbers specific securities (1-year term); summing is appropriate
btfp_coll_crisis <- btfp_loans %>%
filter(btfp_loan_date >= CRISIS_START & btfp_loan_date <= CRISIS_END) %>%
group_by(rssd_id) %>%
summarise(
btfp_n_loans = n(),
btfp_total_coll = sum(btfp_total_collateral, na.rm = TRUE),
btfp_coll_treasury = sum(btfp_treasury_sec, na.rm = TRUE),
btfp_coll_mbs = sum(btfp_agency_mbs, na.rm = TRUE),
btfp_coll_cmo = sum(btfp_agency_cmo, na.rm = TRUE),
btfp_coll_agdebt = sum(btfp_agency_debt, na.rm = TRUE),
btfp_total_lent = sum(btfp_loan_amount, na.rm = TRUE),
btfp_avg_rate = weighted.mean(btfp_interest_rate, btfp_loan_amount, na.rm = TRUE),
btfp_first_date = min(btfp_loan_date),
btfp_last_date = max(btfp_loan_date),
.groups = "drop"
) %>%
mutate(
btfp_advance_rate = btfp_total_lent / btfp_total_coll,
btfp_share_treasury = btfp_coll_treasury / btfp_total_coll,
btfp_share_mbs = btfp_coll_mbs / btfp_total_coll,
btfp_share_cmo = btfp_coll_cmo / btfp_total_coll,
btfp_share_agdebt = btfp_coll_agdebt / btfp_total_coll
) %>%
rename(idrssd = rssd_id)
cat(sprintf("BTFP crisis loans: %d from %d banks\n",
sum(btfp_coll_crisis$btfp_n_loans), nrow(btfp_coll_crisis)))## BTFP crisis loans: 1303 from 526 bankscat(sprintf(" Mean loans/bank: %.1f | Max: %d\n",
mean(btfp_coll_crisis$btfp_n_loans), max(btfp_coll_crisis$btfp_n_loans)))## Mean loans/bank: 2.5 | Max: 33cat(sprintf(" Advance rate: mean=%.3f, median=%.3f (1.0 = full par)\n",
mean(btfp_coll_crisis$btfp_advance_rate, na.rm=T),
median(btfp_coll_crisis$btfp_advance_rate, na.rm=T)))## Advance rate: mean=0.579, median=0.580 (1.0 = full par)# --- DW: Aggregate to bank level (crisis period) ---
# DW collateral is a maintained pool; max across loans = pool size
# Sum loan amounts = total liquidity drawn (may include rollovers)
dw_coll_crisis <- dw_loans %>%
filter(dw_loan_date >= CRISIS_START &
dw_loan_date <= min(CRISIS_END, DW_DATA_END)) %>%
group_by(rssd_id) %>%
summarise(
dw_n_loans = n(),
dw_max_coll = max(dw_total_collateral, na.rm = TRUE),
dw_max_omo = max(dw_omo_eligible, na.rm = TRUE),
dw_max_nonomo = max(dw_non_omo_eligible, na.rm = TRUE),
dw_max_comm = max(dw_comm_loans, na.rm = TRUE),
dw_max_resmort = max(dw_res_mortgages, na.rm = TRUE),
dw_max_cre = max(dw_cre_loans, na.rm = TRUE),
dw_max_consumer = max(dw_consumer_loans, na.rm = TRUE),
dw_max_treas_agency = max(dw_treasury_agency, na.rm = TRUE),
dw_max_mbs_agency = max(dw_mbs_agency, na.rm = TRUE),
dw_max_municipal = max(dw_municipal_sec, na.rm = TRUE),
dw_max_corporate = max(dw_corporate_instruments, na.rm = TRUE),
dw_total_lent = sum(dw_loan_amount, na.rm = TRUE),
dw_max_single_loan = max(dw_loan_amount, na.rm = TRUE),
dw_first_date = min(dw_loan_date),
dw_last_date = max(dw_loan_date),
.groups = "drop"
) %>%
mutate(
dw_advance_rate = dw_max_single_loan / dw_max_coll,
dw_share_omo = dw_max_omo / dw_max_coll,
dw_share_loans = (dw_max_comm + dw_max_resmort + dw_max_cre + dw_max_consumer) / dw_max_coll,
dw_share_treas = dw_max_treas_agency / dw_max_coll,
dw_share_mbs = dw_max_mbs_agency / dw_max_coll
) %>%
rename(idrssd = rssd_id)
cat(sprintf("\nDW crisis loans: %d from %d banks\n",
sum(dw_coll_crisis$dw_n_loans), nrow(dw_coll_crisis)))##
## DW crisis loans: 1842 from 459 bankscat(sprintf(" Mean loans/bank: %.1f | Max: %d\n",
mean(dw_coll_crisis$dw_n_loans), max(dw_coll_crisis$dw_n_loans)))## Mean loans/bank: 4.0 | Max: 42cat(sprintf(" Advance rate (max loan/max coll): mean=%.3f, median=%.3f\n",
mean(dw_coll_crisis$dw_advance_rate, na.rm=T),
median(dw_coll_crisis$dw_advance_rate, na.rm=T)))## Advance rate (max loan/max coll): mean=0.173, median=0.014cat(sprintf(" Share OMO-eligible at DW: mean=%.3f, median=%.3f\n",
mean(dw_coll_crisis$dw_share_omo, na.rm=T),
median(dw_coll_crisis$dw_share_omo, na.rm=T)))## Share OMO-eligible at DW: mean=0.332, median=0.000# --- Merge with crisis dataset ---
df_coll <- df_crisis %>%
left_join(btfp_coll_crisis, by = "idrssd") %>%
left_join(dw_coll_crisis, by = "idrssd") %>%
mutate(
# BTFP Utilization = collateral pledged / available OMO portfolio
# omo_eligible in call report is in thousands; btfp_total_coll in dollars
btfp_utilization_raw = ifelse(btfp_crisis == 1 & !is.na(omo_eligible) & omo_eligible > 0,
btfp_total_coll / (omo_eligible * 1000), NA_real_),
# Cap at reasonable max (>1 possible if bank pledged more than Q4 holdings)
btfp_utilization_raw = pmin(btfp_utilization_raw, 2.0),
# DW utilization = max collateral pool / total assets (in dollars)
dw_utilization_raw = ifelse(dw_crisis == 1 & !is.na(total_asset) & total_asset > 0,
dw_max_coll / (total_asset * 1000), NA_real_),
# Number of trips
btfp_n_loans = replace_na(btfp_n_loans, 0L),
dw_n_loans = replace_na(dw_n_loans, 0L),
total_n_loans = btfp_n_loans + dw_n_loans,
# Z-standardize for regressions (within borrowers)
btfp_util = standardize_z(btfp_utilization_raw),
dw_util = standardize_z(dw_utilization_raw),
dw_share_omo_z = standardize_z(dw_share_omo),
dw_share_loans_z = standardize_z(dw_share_loans)
)
cat(sprintf("\n--- BTFP Utilization (collateral / OMO portfolio) ---\n"))##
## --- BTFP Utilization (collateral / OMO portfolio) ---cat(sprintf(" Mean: %.3f | Median: %.3f | P25: %.3f | P75: %.3f\n",
mean(df_coll$btfp_utilization_raw, na.rm=T),
median(df_coll$btfp_utilization_raw, na.rm=T),
quantile(df_coll$btfp_utilization_raw, .25, na.rm=T),
quantile(df_coll$btfp_utilization_raw, .75, na.rm=T)))## Mean: 1.081 | Median: 0.961 | P25: 0.368 | P75: 2.000cat(sprintf(" Banks with utilization > 0.80: %d (%.1f%% of BTFP borrowers)\n",
sum(df_coll$btfp_utilization_raw > 0.80, na.rm=T),
100 * mean(df_coll$btfp_utilization_raw > 0.80, na.rm=T)))## Banks with utilization > 0.80: 270 (53.9% of BTFP borrowers)cat("=== COLLATERAL UTILIZATION = REVEALED RUN SEVERITY ===\n\n")## === COLLATERAL UTILIZATION = REVEALED RUN SEVERITY ===# Among BTFP borrowers: what predicts pledging a larger fraction of OMO portfolio?
# Higher utilization = more desperate for liquidity = more severe run pressure
df_btfp_util <- df_coll %>% filter(btfp_crisis == 1 & !is.na(btfp_util))
cat(sprintf("BTFP borrowers with utilization data: %d\n", nrow(df_btfp_util)))## BTFP borrowers with utilization data: 501# DV: btfp_utilization_raw (continuous 0-2)
UTIL_M1 <- EXPL_BASE
UTIL_M2 <- paste0(EXPL_BASE, " + collateral_capacity")
UTIL_M3 <- paste0(EXPL_BASE, " + collateral_capacity + uninsured_beta")
UTIL_M4 <- paste0(EXPL_BASE, " + collateral_capacity + uninsured_beta + mtm_x_unins_x_beta")
mod_util_m1 <- safe_run(df_btfp_util, "btfp_utilization_raw", UTIL_M1, min_n = 20, min_dv1 = 0)
mod_util_m2 <- safe_run(df_btfp_util, "btfp_utilization_raw", UTIL_M2, min_n = 20, min_dv1 = 0)
mod_util_m3 <- safe_run(df_btfp_util, "btfp_utilization_raw", UTIL_M3, min_n = 20, min_dv1 = 0)
mod_util_m4 <- safe_run(df_btfp_util, "btfp_utilization_raw", UTIL_M4, min_n = 20, min_dv1 = 0)
# Also: log(loan count) as alternative DV
df_btfp_util <- df_btfp_util %>%
mutate(log_n_loans = log(btfp_n_loans))
mod_nloans_m1 <- safe_run(df_btfp_util, "log_n_loans", UTIL_M1, min_n = 20, min_dv1 = 0)
mod_nloans_m2 <- safe_run(df_btfp_util, "log_n_loans", UTIL_M4, min_n = 20, min_dv1 = 0)
models_util <- list(
"Util M1" = mod_util_m1,
"Util M2" = mod_util_m2,
"Util M3" = mod_util_m3,
"Util Full" = mod_util_m4,
"log(Trips) M1" = mod_nloans_m1,
"log(Trips) Full" = mod_nloans_m2)
save_etable(models_util, "Collateral_Utilization_RunSeverity",
title_text = "Collateral Utilization as Revealed Run Severity (BTFP Borrowers)",
notes_text = paste0(
"OLS. Cols 1-4: DV = BTFP collateral pledged / OMO-eligible portfolio (0--2). ",
"Cols 5-6: DV = log(number of BTFP loans). ",
"Sample: BTFP crisis borrowers with call-report match. ",
"Higher utilization = bank pledged more of its capacity = more severe liquidity need. ",
"Robust SEs. z-standardized regressors."),
extra_lines = list(
c("Borrowers", rep(nrow(df_btfp_util), 6)),
c("Mean Util", rep(round(mean(df_btfp_util$btfp_utilization_raw, na.rm=T), 3), 4),
round(mean(df_btfp_util$log_n_loans, na.rm=T), 3),
round(mean(df_btfp_util$log_n_loans, na.rm=T), 3))))
etable(models_util[!sapply(models_util, is.null)],
fitstat = ~ n + r2, se.below = TRUE)## Util M1
## Dependent Var.: btfp_utilization_raw
##
## Constant 1.069***
## (0.0486)
## MTM Loss (z) 0.1357**
## (0.0454)
## Uninsured Leverage (z) 0.0206
## (0.0438)
## MTM $\times$ Uninsured 0.0139
## (0.0372)
## Log(Assets) -0.0476
## (0.0442)
## Cash Ratio 0.0622
## (0.0718)
## Loan-to-Deposit 0.1913***
## (0.0540)
## Book Equity Ratio -0.0006
## (0.0583)
## Wholesale Funding 0.0053
## (0.0265)
## ROA 0.0332
## (0.0423)
## OMO Collateral (z)
##
## Uninsured $\beta$ (z)
##
## MTM $\times$ Uninsured $\times$ $\beta^U$
##
## ________________________________________ ____________________
## S.E. type Heteroskedasti.-rob.
## Observations 501
## R2 0.04363
##
## Util M2
## Dependent Var.: btfp_utilization_raw
##
## Constant 1.083***
## (0.0492)
## MTM Loss (z) 0.0442
## (0.0433)
## Uninsured Leverage (z) 0.0058
## (0.0460)
## MTM $\times$ Uninsured 0.0006
## (0.0388)
## Log(Assets) 0.0045
## (0.0448)
## Cash Ratio -0.0016
## (0.0759)
## Loan-to-Deposit -0.0308
## (0.0569)
## Book Equity Ratio 0.0049
## (0.0549)
## Wholesale Funding 0.0350
## (0.0246)
## ROA -0.0204
## (0.0410)
## OMO Collateral (z) -0.3351***
## (0.0357)
## Uninsured $\beta$ (z)
##
## MTM $\times$ Uninsured $\times$ $\beta^U$
##
## ________________________________________ ____________________
## S.E. type Heteroskedasti.-rob.
## Observations 501
## R2 0.17489
##
## Util M3
## Dependent Var.: btfp_utilization_raw
##
## Constant 1.076***
## (0.0479)
## MTM Loss (z) 0.0575
## (0.0429)
## Uninsured Leverage (z) 0.0242
## (0.0436)
## MTM $\times$ Uninsured 0.0023
## (0.0379)
## Log(Assets) -0.0136
## (0.0429)
## Cash Ratio -0.0146
## (0.0734)
## Loan-to-Deposit -0.0561
## (0.0588)
## Book Equity Ratio 0.0025
## (0.0543)
## Wholesale Funding 0.0317
## (0.0248)
## ROA -0.0212
## (0.0404)
## OMO Collateral (z) -0.3258***
## (0.0370)
## Uninsured $\beta$ (z) 0.0648
## (0.0330)
## MTM $\times$ Uninsured $\times$ $\beta^U$
##
## ________________________________________ ____________________
## S.E. type Heteroskedasti.-rob.
## Observations 496
## R2 0.18056
##
## Util Full log(Trip..1
## Dependent Var.: btfp_utilization_raw log_n_loans
##
## Constant 1.076*** 0.5751***
## (0.0479) (0.0424)
## MTM Loss (z) 0.0559 0.0157
## (0.0425) (0.0396)
## Uninsured Leverage (z) 0.0221 -0.0345
## (0.0410) (0.0339)
## MTM $\times$ Uninsured 0.0029 0.0536
## (0.0373) (0.0351)
## Log(Assets) -0.0131 0.1175***
## (0.0426) (0.0346)
## Cash Ratio -0.0144 -0.0634
## (0.0736) (0.0645)
## Loan-to-Deposit -0.0563 -0.0812
## (0.0587) (0.0490)
## Book Equity Ratio 0.0019 0.0764
## (0.0549) (0.0510)
## Wholesale Funding 0.0316 0.0532*
## (0.0247) (0.0261)
## ROA -0.0201 -0.0593
## (0.0396) (0.0383)
## OMO Collateral (z) -0.3256***
## (0.0369)
## Uninsured $\beta$ (z) 0.0643
## (0.0339)
## MTM $\times$ Uninsured $\times$ $\beta^U$ -0.0058
## (0.0287)
## ________________________________________ ____________________ ___________
## S.E. type Heteroskedasti.-rob. Heter.-rob.
## Observations 496 501
## R2 0.18065 0.05749
##
## log(Trips..
## Dependent Var.: log_n_loans
##
## Constant 0.5691***
## (0.0423)
## MTM Loss (z) 0.0311
## (0.0418)
## Uninsured Leverage (z) -0.0262
## (0.0358)
## MTM $\times$ Uninsured 0.0531
## (0.0352)
## Log(Assets) 0.1138**
## (0.0356)
## Cash Ratio -0.0607
## (0.0663)
## Loan-to-Deposit -0.0699
## (0.0608)
## Book Equity Ratio 0.0705
## (0.0513)
## Wholesale Funding 0.0511
## (0.0265)
## ROA -0.0558
## (0.0379)
## OMO Collateral (z) 0.0220
## (0.0385)
## Uninsured $\beta$ (z) -0.0041
## (0.0313)
## MTM $\times$ Uninsured $\times$ $\beta^U$ 0.0054
## (0.0198)
## ________________________________________ ___________
## S.E. type Heter.-rob.
## Observations 496
## R2 0.06044
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1cat("=== BTFP COLLATERAL EXHAUSTION → DW COMPLEMENTARITY ===\n\n")## === BTFP COLLATERAL EXHAUSTION → DW COMPLEMENTARITY ===# KEY TEST: Among BTFP borrowers, does HIGH utilization predict also using DW?
# If yes → banks exhaust BTFP capacity, then turn to DW for additional liquidity
# This is the collateral-based complementarity mechanism
df_btfp_exh <- df_coll %>%
filter(btfp_crisis == 1 & !is.na(btfp_utilization_raw)) %>%
mutate(
also_dw = as.integer(dw_crisis == 1),
btfp_exhausted = as.integer(btfp_utilization_raw > 0.80),
btfp_high_util = as.integer(btfp_utilization_raw > median(btfp_utilization_raw, na.rm=T))
)
cat(sprintf("BTFP borrowers: %d\n", nrow(df_btfp_exh)))## BTFP borrowers: 501cat(sprintf(" Also DW: %d (%.1f%%)\n",
sum(df_btfp_exh$also_dw), 100 * mean(df_btfp_exh$also_dw)))## Also DW: 106 (21.2%)cat(sprintf(" BTFP Exhausted (>80%%): %d (%.1f%%)\n",
sum(df_btfp_exh$btfp_exhausted), 100 * mean(df_btfp_exh$btfp_exhausted)))## BTFP Exhausted (>80%): 270 (53.9%)cat(sprintf(" DW rate among exhausted: %.1f%%\n",
100 * mean(df_btfp_exh$also_dw[df_btfp_exh$btfp_exhausted == 1])))## DW rate among exhausted: 20.0%cat(sprintf(" DW rate among non-exhausted: %.1f%%\n",
100 * mean(df_btfp_exh$also_dw[df_btfp_exh$btfp_exhausted == 0])))## DW rate among non-exhausted: 22.5%# Regressions: does utilization predict also_dw?
EXH_M1 <- "btfp_util"
EXH_M2 <- paste0("btfp_util + ", EXPL_BASE)
EXH_M3 <- paste0("btfp_util + btfp_exhausted + ", EXPL_BASE)
EXH_M4 <- paste0("btfp_util + ", EXPL_BASE, " + collateral_capacity + uninsured_beta")
mod_exh_m1 <- safe_run(df_btfp_exh, "also_dw", EXH_M1, min_n = 20, min_dv1 = 5)
mod_exh_m2 <- safe_run(df_btfp_exh, "also_dw", EXH_M2, min_n = 20, min_dv1 = 5)
mod_exh_m3 <- safe_run(df_btfp_exh, "also_dw", EXH_M3, min_n = 20, min_dv1 = 5)
mod_exh_m4 <- safe_run(df_btfp_exh, "also_dw", EXH_M4, min_n = 20, min_dv1 = 5)
models_exh <- list(
"Util Only" = mod_exh_m1,
"+ Run Vars" = mod_exh_m2,
"+ Exhausted" = mod_exh_m3,
"Full" = mod_exh_m4)
# Add btfp_util and btfp_exhausted labels to fixest dict temporarily
save_etable(models_exh, "Collateral_BTFP_Exhaustion_to_DW",
title_text = "BTFP Collateral Exhaustion → DW Borrowing (Complementarity)",
notes_text = paste0(
"LPM. DV = also\\_dw (1 if BTFP borrower also used DW). ",
"Sample: BTFP crisis borrowers. ",
"BTFP Util = collateral pledged / OMO portfolio (z). ",
"Exhausted = 1 if utilization > 80\\%. ",
"Positive coefficient = banks that used more BTFP capacity also went to DW. Robust SEs."),
extra_lines = list(
c("BTFP Borrowers", rep(nrow(df_btfp_exh), 4)),
c("Also DW", rep(sum(df_btfp_exh$also_dw), 4)),
c("Mean DV", rep(round(mean(df_btfp_exh$also_dw), 3), 4))))
etable(models_exh[!sapply(models_exh, is.null)],
fitstat = ~ n + r2, se.below = TRUE)## Util Only + Run Vars + Exhaus.. Full
## Dependent Var.: Also DW Also DW Also DW Also DW
##
## Constant 0.1458*** 0.1466*** 0.1793*** 0.1425***
## (0.0215) (0.0226) (0.0460) (0.0230)
## BTFP Utilization (z) -0.0040 -0.0021 0.0253 -0.0072
## (0.0181) (0.0186) (0.0376) (0.0210)
## Log(Assets) 0.1294*** 0.1120*** 0.1115*** 0.1118***
## (0.0204) (0.0224) (0.0224) (0.0231)
## Cash Ratio 0.0379 0.0179 0.0172 0.0065
## (0.0328) (0.0359) (0.0360) (0.0359)
## Loan-to-Deposit -0.0066 -0.0055 -0.0048 -0.0193
## (0.0262) (0.0286) (0.0286) (0.0317)
## Book Equity Ratio -0.0210 -0.0184 -0.0187 -0.0147
## (0.0232) (0.0229) (0.0229) (0.0229)
## Wholesale Funding 0.0132 0.0146 0.0152 0.0173
## (0.0143) (0.0143) (0.0143) (0.0144)
## ROA -0.0207 -0.0356 -0.0347 -0.0355
## (0.0227) (0.0242) (0.0241) (0.0246)
## MTM Loss (z) -0.0279 -0.0282 -0.0342
## (0.0241) (0.0240) (0.0247)
## Uninsured Leverage (z) 0.0356 0.0361 0.0355
## (0.0221) (0.0221) (0.0225)
## MTM $\times$ Uninsured 0.0198 0.0195 0.0161
## (0.0192) (0.0192) (0.0192)
## BTFP Exhausted (>80\%) -0.0616
## (0.0733)
## OMO Collateral (z) -0.0187
## (0.0233)
## Uninsured $\beta$ (z) 0.0136
## (0.0193)
## ______________________ __________ __________ __________ __________
## S.E. type Hete.-rob. Hete.-rob. Hete.-rob. Hete.-rob.
## Observations 501 501 501 496
## R2 0.09104 0.10286 0.10399 0.10672
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1cat("=== DW COLLATERAL COMPOSITION: WHAT DID BANKS PLEDGE? ===\n\n")## === DW COLLATERAL COMPOSITION: WHAT DID BANKS PLEDGE? ===# Among DW borrowers: what fraction of collateral is OMO-eligible vs. loans?
# Banks that also used BTFP may have less OMO left → more loan-based DW collateral
df_dw_coll <- df_coll %>%
filter(dw_crisis == 1 & !is.na(dw_share_omo)) %>%
mutate(
also_btfp = as.integer(btfp_crisis == 1),
dw_loan_collateral = as.integer(dw_share_loans > 0.5), # majority loan-based
dw_pure_loan_coll = as.integer(dw_share_omo < 0.01) # almost no OMO at DW
)
cat(sprintf("DW borrowers with collateral data: %d\n", nrow(df_dw_coll)))## DW borrowers with collateral data: 433cat(sprintf(" Also BTFP: %d (%.1f%%)\n",
sum(df_dw_coll$also_btfp), 100 * mean(df_dw_coll$also_btfp)))## Also BTFP: 106 (24.5%)cat("\n--- DW Collateral Composition by Also-BTFP Status ---\n")##
## --- DW Collateral Composition by Also-BTFP Status ---df_dw_coll %>%
group_by(also_btfp) %>%
summarise(
N = n(),
share_omo = round(mean(dw_share_omo, na.rm=T), 3),
share_loans = round(mean(dw_share_loans, na.rm=T), 3),
share_treas = round(mean(dw_share_treas, na.rm=T), 3),
share_mbs = round(mean(dw_share_mbs, na.rm=T), 3),
advance_rate = round(mean(dw_advance_rate, na.rm=T), 3),
dw_max_coll_M = round(mean(dw_max_coll, na.rm=T) / 1e6, 1),
.groups = "drop"
) %>% print()## # A tibble: 2 × 8
## also_btfp N share_omo share_loans share_treas share_mbs advance_rate
## <int> <int> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 0 327 0.354 0.418 0.193 0.16 0.153
## 2 1 106 0.309 0.501 0.149 0.161 0.227
## # ℹ 1 more variable: dw_max_coll_M <dbl># T-test: do joint users pledge less OMO at DW?
tt_omo <- t.test(dw_share_omo ~ also_btfp, data = df_dw_coll)
cat(sprintf("\nT-test (OMO share at DW): DW-only=%.3f, Joint=%.3f, diff=%.3f, p=%.4f\n",
mean(df_dw_coll$dw_share_omo[df_dw_coll$also_btfp == 0], na.rm=T),
mean(df_dw_coll$dw_share_omo[df_dw_coll$also_btfp == 1], na.rm=T),
tt_omo$estimate[2] - tt_omo$estimate[1], tt_omo$p.value))##
## T-test (OMO share at DW): DW-only=0.354, Joint=0.309, diff=-0.045, p=0.3635tt_loans <- t.test(dw_share_loans ~ also_btfp, data = df_dw_coll)
cat(sprintf("T-test (Loan share at DW): DW-only=%.3f, Joint=%.3f, diff=%.3f, p=%.4f\n",
mean(df_dw_coll$dw_share_loans[df_dw_coll$also_btfp == 0], na.rm=T),
mean(df_dw_coll$dw_share_loans[df_dw_coll$also_btfp == 1], na.rm=T),
tt_loans$estimate[2] - tt_loans$estimate[1], tt_loans$p.value))## T-test (Loan share at DW): DW-only=0.418, Joint=0.501, diff=0.083, p=0.1235# Regressions: what predicts OMO share at DW?
DW_COMP_M1 <- "also_btfp"
DW_COMP_M2 <- paste0("also_btfp + ", EXPL_BASE)
DW_COMP_M3 <- paste0("also_btfp + ", EXPL_BASE, " + collateral_capacity + uninsured_beta")
mod_dwcomp_m1 <- safe_run(df_dw_coll, "dw_share_omo", DW_COMP_M1, min_n = 20, min_dv1 = 0)
mod_dwcomp_m2 <- safe_run(df_dw_coll, "dw_share_omo", DW_COMP_M2, min_n = 20, min_dv1 = 0)
mod_dwcomp_m3 <- safe_run(df_dw_coll, "dw_share_omo", DW_COMP_M3, min_n = 20, min_dv1 = 0)
# Also: what predicts using MORE loan-based collateral at DW?
mod_dwloan_m1 <- safe_run(df_dw_coll, "dw_share_loans", DW_COMP_M1, min_n = 20, min_dv1 = 0)
mod_dwloan_m2 <- safe_run(df_dw_coll, "dw_share_loans", DW_COMP_M3, min_n = 20, min_dv1 = 0)
models_dwcomp <- list(
"OMO Share M1" = mod_dwcomp_m1,
"OMO Share M2" = mod_dwcomp_m2,
"OMO Share Full" = mod_dwcomp_m3,
"Loan Share M1" = mod_dwloan_m1,
"Loan Share Full" = mod_dwloan_m2)
save_etable(models_dwcomp, "Collateral_DW_Composition",
title_text = "DW Collateral Composition: OMO-Eligible vs. Loan-Based",
notes_text = paste0(
"OLS. Cols 1-3: DV = share of DW collateral that is OMO-eligible (0--1). ",
"Cols 4-5: DV = share of DW collateral that is loan-based (0--1). ",
"Sample: DW crisis borrowers. Also\\_BTFP = 1 if bank also used BTFP. ",
"Negative Also\\_BTFP on OMO share = joint users lack OMO for DW → collateral exhaustion. ",
"Robust SEs."),
extra_lines = list(
c("DW Borrowers", rep(nrow(df_dw_coll), 5)),
c("Also BTFP", rep(sum(df_dw_coll$also_btfp), 5))))
etable(models_dwcomp[!sapply(models_dwcomp, is.null)],
fitstat = ~ n + r2, se.below = TRUE)## OMO Share M1 OMO Share M2 OMO Share .. Loan Share M1
## Dependent Var.: dw_share_omo dw_share_omo dw_share_omo dw_share_loans
##
## Constant 0.4326*** 0.4284*** 0.4272*** 0.3165***
## (0.0300) (0.0297) (0.0288) (0.0268)
## Also BTFP -0.0372 -0.0199 -0.0350 0.0767
## (0.0464) (0.0466) (0.0475) (0.0494)
## Log(Assets) -0.0638** -0.0286 -0.0332 0.1246***
## (0.0209) (0.0228) (0.0228) (0.0213)
## Cash Ratio -0.0352 0.0024 0.0213 0.0997***
## (0.0285) (0.0305) (0.0295) (0.0268)
## Loan-to-Deposit -0.1190*** -0.1101*** -0.0309 0.1596***
## (0.0290) (0.0294) (0.0344) (0.0268)
## Book Equity Ratio 0.0052 0.0058 0.0003 0.0370
## (0.0333) (0.0328) (0.0333) (0.0289)
## Wholesale Funding -0.0169 -0.0170 -0.0285 -0.0033
## (0.0169) (0.0169) (0.0163) (0.0174)
## ROA -0.0690** -0.0566* -0.0388 0.0282
## (0.0241) (0.0237) (0.0234) (0.0249)
## MTM Loss (z) 0.0397 0.0554*
## (0.0279) (0.0273)
## Uninsured Leverage (z) -0.0667** -0.0647**
## (0.0215) (0.0215)
## MTM $\times$ Uninsured 0.0115 0.0044
## (0.0197) (0.0193)
## OMO Collateral (z) 0.1199***
## (0.0289)
## Uninsured $\beta$ (z) -0.0061
## (0.0192)
## ______________________ ____________ ____________ ____________ ______________
## S.E. type Hetero.-rob. Hetero.-rob. Hetero.-rob. Heterosk.-rob.
## Observations 433 433 430 433
## R2 0.12424 0.14813 0.18269 0.22628
##
## Loan Share F..
## Dependent Var.: dw_share_loans
##
## Constant 0.3302***
## (0.0271)
## Also BTFP 0.0445
## (0.0506)
## Log(Assets) 0.0794**
## (0.0246)
## Cash Ratio 0.0703*
## (0.0293)
## Loan-to-Deposit 0.1631***
## (0.0331)
## Book Equity Ratio 0.0398
## (0.0280)
## Wholesale Funding -0.0040
## (0.0170)
## ROA 0.0167
## (0.0254)
## MTM Loss (z) -0.0423
## (0.0282)
## Uninsured Leverage (z) 0.0786***
## (0.0227)
## MTM $\times$ Uninsured 0.0142
## (0.0198)
## OMO Collateral (z) 0.0364
## (0.0261)
## Uninsured $\beta$ (z) 0.0288
## (0.0207)
## ______________________ ______________
## S.E. type Heterosk.-rob.
## Observations 430
## R2 0.25379
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1cat("=== ADVANCE RATE: BTFP (PAR) vs. DW (MARKET + HAIRCUT) ===\n\n")## === ADVANCE RATE: BTFP (PAR) vs. DW (MARKET + HAIRCUT) ===# BTFP advance rate ≈ 1 (par lending) vs. DW < 1 (haircuts)
# The gap = implicit recapitalization per dollar of collateral
cat("--- BTFP Advance Rate Distribution ---\n")## --- BTFP Advance Rate Distribution ---cat(sprintf(" N: %d | Mean: %.3f | Median: %.3f | P10: %.3f | P90: %.3f\n",
sum(!is.na(df_coll$btfp_advance_rate) & df_coll$btfp_crisis == 1),
mean(df_coll$btfp_advance_rate[df_coll$btfp_crisis == 1], na.rm=T),
median(df_coll$btfp_advance_rate[df_coll$btfp_crisis == 1], na.rm=T),
quantile(df_coll$btfp_advance_rate[df_coll$btfp_crisis == 1], .10, na.rm=T),
quantile(df_coll$btfp_advance_rate[df_coll$btfp_crisis == 1], .90, na.rm=T)))## N: 501 | Mean: 0.571 | Median: 0.564 | P10: 0.095 | P90: 1.000cat("\n--- DW Advance Rate Distribution ---\n")##
## --- DW Advance Rate Distribution ---cat(sprintf(" N: %d | Mean: %.3f | Median: %.3f | P10: %.3f | P90: %.3f\n",
sum(!is.na(df_coll$dw_advance_rate) & df_coll$dw_crisis == 1),
mean(df_coll$dw_advance_rate[df_coll$dw_crisis == 1], na.rm=T),
median(df_coll$dw_advance_rate[df_coll$dw_crisis == 1], na.rm=T),
quantile(df_coll$dw_advance_rate[df_coll$dw_crisis == 1], .10, na.rm=T),
quantile(df_coll$dw_advance_rate[df_coll$dw_crisis == 1], .90, na.rm=T)))## N: 433 | Mean: 0.171 | Median: 0.012 | P10: 0.000 | P90: 0.628# For BOTH-facility users: compare advance rates at each
df_both_users <- df_coll %>%
filter(both_fed == 1 & !is.na(btfp_advance_rate) & !is.na(dw_advance_rate))
if (nrow(df_both_users) > 10) {
cat(sprintf("\n--- Joint Users (Both BTFP + DW): %d banks ---\n", nrow(df_both_users)))
cat(sprintf(" BTFP advance rate: mean=%.3f, median=%.3f\n",
mean(df_both_users$btfp_advance_rate, na.rm=T),
median(df_both_users$btfp_advance_rate, na.rm=T)))
cat(sprintf(" DW advance rate: mean=%.3f, median=%.3f\n",
mean(df_both_users$dw_advance_rate, na.rm=T),
median(df_both_users$dw_advance_rate, na.rm=T)))
cat(sprintf(" Gap (BTFP - DW): mean=%.3f = %.1f%% recapitalization per dollar of collateral\n",
mean(df_both_users$btfp_advance_rate - df_both_users$dw_advance_rate, na.rm=T),
100 * mean(df_both_users$btfp_advance_rate - df_both_users$dw_advance_rate, na.rm=T)))
tt_adv <- t.test(df_both_users$btfp_advance_rate, df_both_users$dw_advance_rate, paired = TRUE)
cat(sprintf(" Paired t-test: t=%.2f, p=%.4f\n", tt_adv$statistic, tt_adv$p.value))
}##
## --- Joint Users (Both BTFP + DW): 106 banks ---
## BTFP advance rate: mean=0.490, median=0.476
## DW advance rate: mean=0.227, median=0.078
## Gap (BTFP - DW): mean=0.264 = 26.4% recapitalization per dollar of collateral
## Paired t-test: t=6.85, p=0.0000# Regression: does the advance rate gap predict total borrowing?
df_adv <- df_coll %>%
filter(any_fed == 1 & !is.na(btfp_advance_rate)) %>%
mutate(
adv_rate_z = standardize_z(btfp_advance_rate),
total_fed_pct = 100 * (replace_na(btfp_total_lent, 0) + replace_na(dw_total_lent, 0)) /
(total_asset * 1000)
)
if (nrow(df_adv) > 30) {
mod_adv_m1 <- safe_run(df_adv, "total_fed_pct",
paste0("adv_rate_z + ", EXPL_BASE), min_n = 20, min_dv1 = 0)
mod_adv_m2 <- safe_run(df_adv, "total_fed_pct",
paste0("adv_rate_z + ", EXPL_BASE, " + collateral_capacity"), min_n = 20, min_dv1 = 0)
models_adv <- list("+ Advance Rate" = mod_adv_m1, "Full" = mod_adv_m2)
save_etable(models_adv, "Collateral_AdvanceRate",
title_text = "BTFP Advance Rate and Total Fed Borrowing",
notes_text = paste0(
"OLS. DV = total fed borrowing (BTFP + DW) / TA (\\%). ",
"Sample: BTFP borrowers (crisis). ",
"Advance Rate = loan amount / collateral (higher = closer to par). Robust SEs."))
etable(models_adv[!sapply(models_adv, is.null)], fitstat = ~ n + r2, se.below = TRUE)
}## + Advance R.. Full
## Dependent Var.: total_fed_pct total_fed_pct
##
## Constant 7.737*** 7.713***
## (1.317) (1.289)
## Advance Rate (z) 3.081* 3.080*
## (1.258) (1.259)
## MTM Loss (z) -1.184 -1.032
## (1.450) (1.386)
## Uninsured Leverage (z) 0.4067 0.4311
## (2.166) (2.145)
## MTM $\times$ Uninsured 2.885* 2.907*
## (1.297) (1.293)
## Log(Assets) 5.856* 5.770*
## (2.271) (2.317)
## Cash Ratio 2.334 2.440
## (1.809) (1.794)
## Loan-to-Deposit -1.560 -1.193
## (2.202) (1.867)
## Book Equity Ratio 0.7734 0.7642
## (1.253) (1.244)
## Wholesale Funding 2.049* 2.000*
## (0.8665) (0.9115)
## ROA -0.6370 -0.5486
## (1.161) (1.151)
## OMO Collateral (z) 0.5536
## (1.166)
## ______________________ _____________ _____________
## S.E. type Heteros.-rob. Heteros.-rob.
## Observations 501 501
## R2 0.07249 0.07276
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1cat("=== REPEAT BORROWING: ESCALATION DYNAMICS ===\n\n")## === REPEAT BORROWING: ESCALATION DYNAMICS ===# Banks with multiple loans → escalating run pressure?
# Compare first-loan vs last-loan characteristics within BTFP borrowers
df_btfp_first_last <- btfp_loans %>%
filter(btfp_loan_date >= CRISIS_START & btfp_loan_date <= CRISIS_END) %>%
group_by(rssd_id) %>%
filter(n() > 1) %>%
arrange(btfp_loan_date) %>%
summarise(
n_loans = n(),
first_amount = first(btfp_loan_amount),
last_amount = last(btfp_loan_amount),
first_coll = first(btfp_total_collateral),
last_coll = last(btfp_total_collateral),
first_date = first(btfp_loan_date),
last_date = last(btfp_loan_date),
total_amount = sum(btfp_loan_amount),
.groups = "drop"
) %>%
mutate(
escalation_ratio = last_amount / first_amount,
coll_escalation = last_coll / first_coll,
days_span = as.numeric(last_date - first_date)
)
cat(sprintf("BTFP banks with multiple crisis loans: %d\n", nrow(df_btfp_first_last)))## BTFP banks with multiple crisis loans: 292cat(sprintf(" Mean escalation ratio (last/first amount): %.2f\n",
mean(df_btfp_first_last$escalation_ratio, na.rm=T)))## Mean escalation ratio (last/first amount): 90.44cat(sprintf(" Median: %.2f | Share with escalation > 1: %.1f%%\n",
median(df_btfp_first_last$escalation_ratio, na.rm=T),
100 * mean(df_btfp_first_last$escalation_ratio > 1, na.rm=T)))## Median: 1.00 | Share with escalation > 1: 36.0%# DW repeat borrowers
df_dw_first_last <- dw_loans %>%
filter(dw_loan_date >= CRISIS_START &
dw_loan_date <= min(CRISIS_END, DW_DATA_END)) %>%
group_by(rssd_id) %>%
filter(n() > 1) %>%
arrange(dw_loan_date) %>%
summarise(
n_loans = n(),
first_amount = first(dw_loan_amount),
last_amount = last(dw_loan_amount),
first_coll = first(dw_total_collateral),
last_coll = last(dw_total_collateral),
first_date = first(dw_loan_date),
last_date = last(dw_loan_date),
total_amount = sum(dw_loan_amount),
.groups = "drop"
) %>%
mutate(
escalation_ratio = last_amount / first_amount,
days_span = as.numeric(last_date - first_date)
)
cat(sprintf("\nDW banks with multiple crisis loans: %d\n", nrow(df_dw_first_last)))##
## DW banks with multiple crisis loans: 130cat(sprintf(" Mean escalation ratio (last/first amount): %.2f\n",
mean(df_dw_first_last$escalation_ratio, na.rm=T)))## Mean escalation ratio (last/first amount): 43.22# Regression: number of trips ~ run pressure
cat("\n--- Loan Count Regressions (All Borrowers) ---\n")##
## --- Loan Count Regressions (All Borrowers) ---df_trips <- df_coll %>%
filter(any_fed == 1) %>%
mutate(log_total_trips = log(pmax(total_n_loans, 1)))
mod_trips_m1 <- safe_run(df_trips, "log_total_trips", EXPL_BASE, min_n = 20, min_dv1 = 0)
mod_trips_m2 <- safe_run(df_trips, "log_total_trips",
paste0(EXPL_BASE, " + collateral_capacity + uninsured_beta"),
min_n = 20, min_dv1 = 0)
models_trips <- list("Base" = mod_trips_m1, "Full" = mod_trips_m2)
save_etable(models_trips, "Collateral_RepeatBorrowing",
title_text = "Repeat Borrowing: Number of Trips to Fed Facilities",
notes_text = paste0(
"OLS. DV = log(total number of BTFP + DW loans during crisis). ",
"Sample: any-fed borrowers (crisis). ",
"More trips = sustained/escalating liquidity demand. Robust SEs."),
extra_lines = list(
c("Borrowers", rep(nrow(df_trips), 2)),
c("Mean Trips", rep(round(mean(df_trips$total_n_loans), 1), 2))))
etable(models_trips[!sapply(models_trips, is.null)],
fitstat = ~ n + r2, se.below = TRUE)## Base Full
## Dependent Var.: log_total_trips log_total_trips
##
## Constant 0.5596*** 0.5535***
## (0.0354) (0.0352)
## MTM Loss (z) -0.0071 0.0061
## (0.0408) (0.0414)
## Uninsured Leverage (z) 0.0466 0.0547
## (0.0335) (0.0339)
## MTM $\times$ Uninsured 0.0493 0.0476
## (0.0332) (0.0334)
## Log(Assets) 0.0986** 0.0892*
## (0.0354) (0.0357)
## Cash Ratio -0.1703*** -0.1683***
## (0.0459) (0.0461)
## Loan-to-Deposit -0.0854 -0.0773
## (0.0488) (0.0554)
## Book Equity Ratio 0.0207 0.0212
## (0.0485) (0.0483)
## Wholesale Funding 0.1134*** 0.1121***
## (0.0288) (0.0294)
## ROA -0.0538 -0.0463
## (0.0351) (0.0344)
## OMO Collateral (z) 0.0259
## (0.0424)
## Uninsured $\beta$ (z) 0.0272
## (0.0321)
## ______________________ _______________ _______________
## S.E. type Heteroske.-rob. Heteroske.-rob.
## Observations 828 822
## R2 0.07261 0.07376
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1cat("=== COLLATERAL UTILIZATION FIGURES ===\n\n")## === COLLATERAL UTILIZATION FIGURES ===# --- Figure 1: BTFP Utilization Distribution ---
p_util_hist <- df_coll %>%
filter(btfp_crisis == 1 & !is.na(btfp_utilization_raw)) %>%
mutate(also_dw_label = ifelse(dw_crisis == 1, "Also DW", "BTFP Only")) %>%
ggplot(aes(x = btfp_utilization_raw, fill = also_dw_label)) +
geom_histogram(bins = 40, alpha = 0.7, position = "identity") +
geom_vline(xintercept = 0.80, linetype = "dashed", color = "red", linewidth = 1) +
scale_fill_manual(values = c("BTFP Only" = "#2A9D8F", "Also DW" = "#D62828")) +
annotate("text", x = 0.82, y = Inf, label = "80% exhaustion",
hjust = 0, vjust = 2, color = "red", size = 3.5) +
labs(
title = "BTFP Collateral Utilization (Collateral Pledged / OMO Portfolio)",
subtitle = "Red = banks that also used DW; dashed line = 80% exhaustion threshold",
x = "BTFP Utilization Rate", y = "Count", fill = NULL
) + theme_paper
p_util_hist
save_figure(p_util_hist, "Fig_BTFP_Utilization_Distribution", width = 12, height = 7)
# --- Figure 2: DW Collateral Composition by Also-BTFP ---
df_dw_comp_plot <- df_coll %>%
filter(dw_crisis == 1 & !is.na(dw_share_omo)) %>%
mutate(group = ifelse(btfp_crisis == 1, "Joint (BTFP+DW)", "DW Only")) %>%
select(group, dw_share_omo, dw_share_loans) %>%
pivot_longer(-group, names_to = "Collateral Type", values_to = "Share") %>%
mutate(`Collateral Type` = recode(`Collateral Type`,
"dw_share_omo" = "OMO-Eligible (Securities)",
"dw_share_loans" = "Loan-Based (C&I, CRE, etc.)"))
p_dw_comp <- df_dw_comp_plot %>%
ggplot(aes(x = group, y = Share, fill = `Collateral Type`)) +
geom_boxplot(alpha = 0.7) +
scale_fill_manual(values = c("OMO-Eligible (Securities)" = "#2A9D8F",
"Loan-Based (C&I, CRE, etc.)" = "#E76F51")) +
labs(
title = "DW Collateral Composition: Joint BTFP+DW vs. DW-Only Banks",
subtitle = "Do joint users have less OMO-eligible collateral left for DW?",
x = NULL, y = "Share of DW Collateral", fill = NULL
) + theme_paper
p_dw_comp
save_figure(p_dw_comp, "Fig_DW_CollateralComposition", width = 12, height = 7)
# --- Figure 3: BTFP Utilization vs. Run Pressure (hex scatter) ---
p_util_scatter <- df_coll %>%
filter(btfp_crisis == 1 & !is.na(btfp_utilization_raw)) %>%
ggplot(aes(x = mtm_total_raw, y = btfp_utilization_raw)) +
geom_point(aes(color = uninsured_lev_raw), alpha = 0.6, size = 2.5) +
geom_smooth(method = "lm", se = TRUE, color = "black", linewidth = 1.2) +
scale_color_viridis_c(option = "plasma", name = "Uninsured\nLeverage (%)") +
labs(
title = "MTM Loss vs. BTFP Collateral Utilization",
subtitle = "Color = uninsured deposit leverage; Higher utilization = more severe liquidity need",
x = "MTM Loss (% of Total Assets)", y = "BTFP Utilization (Collateral / OMO Portfolio)"
) + theme_paper
p_util_scatter
save_figure(p_util_scatter, "Fig_BTFP_Util_vs_MTM", width = 12, height = 8)
# --- Figure 4: Advance Rate Comparison ---
df_adv_plot <- bind_rows(
df_coll %>% filter(btfp_crisis == 1 & !is.na(btfp_advance_rate)) %>%
transmute(Facility = "BTFP (Par)", advance_rate = btfp_advance_rate),
df_coll %>% filter(dw_crisis == 1 & !is.na(dw_advance_rate)) %>%
transmute(Facility = "DW (Market)", advance_rate = dw_advance_rate)
)
p_adv_rate <- df_adv_plot %>%
ggplot(aes(x = Facility, y = advance_rate, fill = Facility)) +
geom_boxplot(alpha = 0.7, outlier.alpha = 0.2) +
geom_hline(yintercept = 1.0, linetype = "dashed", color = "grey50") +
scale_fill_manual(values = c("BTFP (Par)" = "#2A9D8F", "DW (Market)" = "#D62828")) +
labs(
title = "Advance Rate: BTFP (Par Valuation) vs. DW (Market + Haircuts)",
subtitle = "Advance rate = loan received / collateral pledged; gap = recapitalization benefit",
x = NULL, y = "Advance Rate (Loan / Collateral)"
) + theme_paper + theme(legend.position = "none")
p_adv_rate
save_figure(p_adv_rate, "Fig_AdvanceRate_BTFP_vs_DW", width = 10, height = 7)
# --- Figure 5: BTFP collateral composition (treemap-style bar) ---
btfp_agg_type <- df_coll %>%
filter(btfp_crisis == 1) %>%
summarise(
Treasury = sum(btfp_coll_treasury, na.rm=T),
`Agency MBS` = sum(btfp_coll_mbs, na.rm=T),
`Agency CMO` = sum(btfp_coll_cmo, na.rm=T),
`Agency Debt` = sum(btfp_coll_agdebt, na.rm=T)
) %>%
pivot_longer(everything(), names_to = "Type", values_to = "Amount") %>%
mutate(Share = Amount / sum(Amount))
dw_agg_type <- df_coll %>%
filter(dw_crisis == 1) %>%
summarise(
`Commercial` = sum(dw_max_comm, na.rm=T),
`Residential` = sum(dw_max_resmort, na.rm=T),
`CRE` = sum(dw_max_cre, na.rm=T),
`Consumer` = sum(dw_max_consumer, na.rm=T),
`Treasury/Agency` = sum(dw_max_treas_agency, na.rm=T),
`Agency MBS` = sum(dw_max_mbs_agency, na.rm=T),
`Municipal` = sum(dw_max_municipal, na.rm=T),
`Corporate` = sum(dw_max_corporate, na.rm=T)
) %>%
pivot_longer(everything(), names_to = "Type", values_to = "Amount") %>%
mutate(Share = Amount / sum(Amount)) %>%
filter(Share > 0.01)
p_coll_type <- bind_rows(
btfp_agg_type %>% mutate(Facility = "BTFP"),
dw_agg_type %>% mutate(Facility = "DW")
) %>%
ggplot(aes(x = reorder(Type, Share), y = Share, fill = Facility)) +
geom_col(alpha = 0.8, position = "dodge") +
scale_fill_manual(values = c("BTFP" = "#2A9D8F", "DW" = "#D62828")) +
scale_y_continuous(labels = percent_format()) +
coord_flip() +
labs(
title = "Collateral Composition: BTFP vs. DW",
subtitle = "BTFP: all OMO-eligible securities | DW: dominated by loans",
x = NULL, y = "Share of Total Collateral", fill = NULL
) + theme_paper
p_coll_type
save_figure(p_coll_type, "Fig_CollateralComposition_BTFP_vs_DW", width = 12, height = 8)cat("=== COLLATERAL UTILIZATION: KEY STATISTICS ===\n\n")## === COLLATERAL UTILIZATION: KEY STATISTICS ===# Comprehensive summary table
cat("--- By Facility Choice Group ---\n")## --- By Facility Choice Group ---df_coll %>%
filter(any_fed == 1 | (btfp_crisis == 0 & dw_crisis == 0 & fhlb_user == 0)) %>%
mutate(group = case_when(
both_fed == 1 ~ "Both",
btfp_crisis == 1 ~ "BTFP Only",
dw_crisis == 1 ~ "DW Only",
TRUE ~ "Neither"
)) %>%
filter(group != "Neither") %>%
group_by(group) %>%
summarise(
N = n(),
btfp_util_mean = round(mean(btfp_utilization_raw, na.rm=T), 3),
btfp_util_med = round(median(btfp_utilization_raw, na.rm=T), 3),
dw_util_mean = round(mean(dw_utilization_raw, na.rm=T), 3),
btfp_n_loans = round(mean(btfp_n_loans[btfp_n_loans > 0], na.rm=T), 1),
dw_n_loans = round(mean(dw_n_loans[dw_n_loans > 0], na.rm=T), 1),
btfp_adv_rate = round(mean(btfp_advance_rate, na.rm=T), 3),
dw_adv_rate = round(mean(dw_advance_rate, na.rm=T), 3),
dw_share_omo = round(mean(dw_share_omo, na.rm=T), 3),
dw_share_loans = round(mean(dw_share_loans, na.rm=T), 3),
.groups = "drop"
) %>%
print(width = Inf)## # A tibble: 3 × 11
## group N btfp_util_mean btfp_util_med dw_util_mean btfp_n_loans
## <chr> <int> <dbl> <dbl> <dbl> <dbl>
## 1 BTFP Only 395 1.09 0.967 NaN 2.4
## 2 Both 106 1.05 0.836 0.067 2.9
## 3 DW Only 327 NaN NA 0.063 NaN
## dw_n_loans btfp_adv_rate dw_adv_rate dw_share_omo dw_share_loans
## <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 NaN 0.593 NaN NaN NaN
## 2 5 0.49 0.227 0.309 0.501
## 3 3.8 NaN 0.153 0.354 0.418cat("\n--- Collateral Exhaustion & DW Transition ---\n")##
## --- Collateral Exhaustion & DW Transition ---btfp_b <- df_coll %>% filter(btfp_crisis == 1 & !is.na(btfp_utilization_raw))
n_exhausted <- sum(btfp_b$btfp_utilization_raw > 0.80, na.rm=T)
n_exhausted_also_dw <- sum(btfp_b$btfp_utilization_raw > 0.80 & btfp_b$dw_crisis == 1, na.rm=T)
n_nonexhausted_also_dw <- sum(btfp_b$btfp_utilization_raw <= 0.80 & btfp_b$dw_crisis == 1, na.rm=T)
cat(sprintf(" BTFP borrowers: %d\n", nrow(btfp_b)))## BTFP borrowers: 501cat(sprintf(" Exhausted (util > 80%%): %d (%.1f%%)\n",
n_exhausted, 100 * n_exhausted / nrow(btfp_b)))## Exhausted (util > 80%): 270 (53.9%)cat(sprintf(" Exhausted → Also DW: %d (%.1f%% of exhausted)\n",
n_exhausted_also_dw,
100 * n_exhausted_also_dw / max(n_exhausted, 1)))## Exhausted → Also DW: 54 (20.0% of exhausted)cat(sprintf(" Non-exhausted → Also DW: %d (%.1f%% of non-exhausted)\n",
n_nonexhausted_also_dw,
100 * n_nonexhausted_also_dw / max(nrow(btfp_b) - n_exhausted, 1)))## Non-exhausted → Also DW: 52 (22.5% of non-exhausted)if (n_exhausted > 5 & n_exhausted < nrow(btfp_b)) {
ft <- fisher.test(table(btfp_b$btfp_utilization_raw > 0.80, btfp_b$dw_crisis == 1))
cat(sprintf(" Fisher exact test (exhaustion → DW): OR=%.2f, p=%.4f\n",
ft$estimate, ft$p.value))
}## Fisher exact test (exhaustion → DW): OR=0.86, p=0.5117cat("\n--- Advance Rate Gap (Recapitalization) ---\n")##
## --- Advance Rate Gap (Recapitalization) ---btfp_ar <- mean(df_coll$btfp_advance_rate[df_coll$btfp_crisis == 1], na.rm=T)
dw_ar <- mean(df_coll$dw_advance_rate[df_coll$dw_crisis == 1], na.rm=T)
cat(sprintf(" BTFP mean advance rate: %.3f (close to 1 = par)\n", btfp_ar))## BTFP mean advance rate: 0.571 (close to 1 = par)cat(sprintf(" DW mean advance rate: %.3f (< 1 = haircut)\n", dw_ar))## DW mean advance rate: 0.171 (< 1 = haircut)cat(sprintf(" Gap: %.3f = %.1f%% recapitalization per $ of collateral\n",
btfp_ar - dw_ar, 100 * (btfp_ar - dw_ar)))## Gap: 0.400 = 40.0% recapitalization per $ of collateral# ==============================================================================
# DSSW TABLE A.10 — EXACT REPLICATION OF COLUMNS 1–5
#
# DSSW regress SVB beta on deposit fragility measures for 171 public banks.
# We replicate their 5-column structure but with DV = emergency borrowing
# and our full sample. "Uninsured share" in DSSW ≡ our uninsured_lev
# (uninsured deposits / total assets).
#
# Col 1: Uninsured leverage only
# Col 2: Uninsured leverage + β^U + (β^U × Uninsured leverage)
# Col 3: (1 − β^U) × Uninsured leverage [Proposition 4 product]
# Col 4: Uninsured deposit franchise / TA = (1 − β^U) × Uninsured_D / TA
# Col 5: Col 4 + Insured deposit franchise / TA = (1 − β^I) × Insured_D / TA
# ==============================================================================
cat("=== DSSW TABLE A.10 ANALOG (COLS 1–5) ===\n\n")## === DSSW TABLE A.10 ANALOG (COLS 1–5) ===# --- Construct DSSW-specific variables ---
add_dssw_a10_vars <- function(df) {
df %>% mutate(
# Col 3: (1 − β^U) × Uninsured leverage (raw → winsorize → z)
one_minus_betaU_x_unins_raw = (1 - uninsured_beta_raw) * uninsured_lev_raw,
one_minus_betaU_x_unins_w = winsorize(one_minus_betaU_x_unins_raw),
one_minus_betaU_x_unins = standardize_z(one_minus_betaU_x_unins_w),
# Col 4: Uninsured deposit franchise / TA = (1 − β^U) × Uninsured_D / TA
# Same economic quantity as Col 3 given our leverage definition;
# constructed identically for transparency
unins_franchise_raw = (1 - uninsured_beta_raw) * uninsured_lev_raw,
unins_franchise_w = winsorize(unins_franchise_raw),
unins_franchise = standardize_z(unins_franchise_w),
# Col 5: Insured deposit franchise / TA = (1 − β^I) × Insured_D / TA
ins_franchise_raw = (1 - beta_insured) * insured_lev_raw,
ins_franchise_w = winsorize(ins_franchise_raw),
ins_franchise = standardize_z(ins_franchise_w)
)
}
df_anyfed_s <- add_dssw_a10_vars(df_anyfed_s)
df_btfp_s <- add_dssw_a10_vars(df_btfp_s)
df_dw_s <- add_dssw_a10_vars(df_dw_s)
df_fhlb_s <- add_dssw_a10_vars(df_fhlb_s)
# Register labels for new variables
setFixest_dict(c(
one_minus_betaU_x_unins = "$(1 - \\beta^U) \\times$ Uninsured",
unins_franchise = "Uninsured Deposit Franchise",
ins_franchise = "Insured Deposit Franchise"
))
# --- Filter to banks with beta coverage ---
df_a10_any <- df_anyfed_s %>% filter(!is.na(uninsured_beta_w) & !is.na(beta_insured))
df_a10_btfp <- df_btfp_s %>% filter(!is.na(uninsured_beta_w) & !is.na(beta_insured))
df_a10_dw <- df_dw_s %>% filter(!is.na(uninsured_beta_w) & !is.na(beta_insured))
df_a10_fhlb <- df_fhlb_s %>% filter(!is.na(uninsured_beta_w) & !is.na(beta_insured))
cat(sprintf(" Beta coverage: Any=%d, BTFP=%d, DW=%d, FHLB=%d\n\n",
nrow(df_a10_any), nrow(df_a10_btfp), nrow(df_a10_dw), nrow(df_a10_fhlb)))## Beta coverage: Any=3991, BTFP=3665, DW=3599, FHLB=3468# --- Specifications matching DSSW Cols 1–5 ---
EXPL_C1 <- "uninsured_lev"
EXPL_C2 <- "uninsured_lev + uninsured_beta + unins_x_unins_beta"
EXPL_C3 <- "one_minus_betaU_x_unins"
EXPL_C4 <- "unins_franchise"
EXPL_C5 <- "unins_franchise + ins_franchise"
# =========================================================================
# Panel A: Any Fed (Cols 1–5)
# =========================================================================
cat("=== Panel A: Any Fed ===\n")## === Panel A: Any Fed ===mod_any_c1 <- safe_run(df_a10_any, "any_fed", EXPL_C1)
mod_any_c2 <- safe_run(df_a10_any, "any_fed", EXPL_C2)
mod_any_c3 <- safe_run(df_a10_any, "any_fed", EXPL_C3)
mod_any_c4 <- safe_run(df_a10_any, "any_fed", EXPL_C4)
mod_any_c5 <- safe_run(df_a10_any, "any_fed", EXPL_C5)
models_any_a10 <- list(
"(1)" = mod_any_c1, "(2)" = mod_any_c2, "(3)" = mod_any_c3,
"(4)" = mod_any_c4, "(5)" = mod_any_c5)
save_etable(models_any_a10, "DSSW_A10_AnyFed",
title_text = "DSSW Table A.10 Analog — Any Fed Borrowing (Crisis Period)",
notes_text = paste0(
"LPM. DV = 1 if borrowed from any Fed facility, 0 if non-borrower. ",
"Col~1: uninsured leverage. Col~2: + $\\beta^U$ + $\\beta^U \\times$ uninsured. ",
"Col~3: $(1-\\beta^U) \\times$ uninsured (Prop.~4). ",
"Col~4: uninsured deposit franchise$/TA$. Col~5: + insured deposit franchise$/TA$. ",
"Robust SEs. z-standardized. Controls: log(assets), cash, LTD, book equity, wholesale, ROA."),
extra_lines = list(
c("Spec", "C1", "C2", "C3", "C4", "C5")))
etable(models_any_a10[!sapply(models_any_a10, is.null)],
fitstat = ~ n + r2, se.below = TRUE)## (1) (2) (3) (4)
## Dependent Var.: any_fed any_fed any_fed any_fed
##
## Constant 0.2044*** 0.2042*** 0.2045*** 0.2045***
## (0.0060) (0.0060) (0.0060) (0.0060)
## Uninsured Leverage (z) 0.0114 0.0118
## (0.0073) (0.0073)
## Log(Assets) 0.1106*** 0.1102*** 0.1124*** 0.1124***
## (0.0082) (0.0083) (0.0079) (0.0079)
## Cash Ratio -0.0367*** -0.0370*** -0.0363*** -0.0363***
## (0.0058) (0.0059) (0.0059) (0.0059)
## Loan-to-Deposit -0.0098 -0.0099 -0.0093 -0.0093
## (0.0070) (0.0072) (0.0071) (0.0071)
## Book Equity Ratio -0.0209*** -0.0209*** -0.0213*** -0.0213***
## (0.0058) (0.0058) (0.0058) (0.0058)
## Wholesale Funding 0.0293*** 0.0294*** 0.0291*** 0.0291***
## (0.0070) (0.0070) (0.0070) (0.0070)
## ROA -0.0052 -0.0055 -0.0051 -0.0051
## (0.0060) (0.0060) (0.0060) (0.0060)
## Uninsured $\beta$ (z) 0.0020
## (0.0069)
## Uninsured $\times$ Unins. $\beta$ -0.0052
## (0.0058)
## $(1 - \beta^U) \times$ Uninsured 0.0092
## (0.0070)
## Uninsured Deposit Franchise 0.0092
## (0.0070)
## Insured Deposit Franchise
##
## _________________________________ __________ __________ __________ __________
## S.E. type Hete.-rob. Hete.-rob. Hete.-rob. Hete.-rob.
## Observations 3,991 3,991 3,991 3,991
## R2 0.11479 0.11500 0.11462 0.11462
##
## (5)
## Dependent Var.: any_fed
##
## Constant 0.2043***
## (0.0060)
## Uninsured Leverage (z)
##
## Log(Assets) 0.1068***
## (0.0084)
## Cash Ratio -0.0373***
## (0.0059)
## Loan-to-Deposit -0.0135
## (0.0071)
## Book Equity Ratio -0.0269***
## (0.0067)
## Wholesale Funding 0.0270***
## (0.0070)
## ROA -0.0051
## (0.0060)
## Uninsured $\beta$ (z)
##
## Uninsured $\times$ Unins. $\beta$
##
## $(1 - \beta^U) \times$ Uninsured
##
## Uninsured Deposit Franchise -0.0001
## (0.0084)
## Insured Deposit Franchise -0.0191*
## (0.0091)
## _________________________________ __________
## S.E. type Hete.-rob.
## Observations 3,991
## R2 0.11565
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1# =========================================================================
# Panel B: BTFP (Cols 1–5)
# =========================================================================
cat("\n=== Panel B: BTFP ===\n")##
## === Panel B: BTFP ===mod_btfp_c1 <- safe_run(df_a10_btfp, "btfp_crisis", EXPL_C1)
mod_btfp_c2 <- safe_run(df_a10_btfp, "btfp_crisis", EXPL_C2)
mod_btfp_c3 <- safe_run(df_a10_btfp, "btfp_crisis", EXPL_C3)
mod_btfp_c4 <- safe_run(df_a10_btfp, "btfp_crisis", EXPL_C4)
mod_btfp_c5 <- safe_run(df_a10_btfp, "btfp_crisis", EXPL_C5)
models_btfp_a10 <- list(
"(1)" = mod_btfp_c1, "(2)" = mod_btfp_c2, "(3)" = mod_btfp_c3,
"(4)" = mod_btfp_c4, "(5)" = mod_btfp_c5)
save_etable(models_btfp_a10, "DSSW_A10_BTFP",
title_text = "DSSW Table A.10 Analog — BTFP Borrowing (Crisis Period)",
notes_text = paste0(
"LPM. DV = 1 if BTFP borrower, 0 if non-borrower. ",
"Columns match DSSW Table A.10 Cols 1--5. Robust SEs. z-standardized."),
extra_lines = list(
c("Spec", "C1", "C2", "C3", "C4", "C5")))
etable(models_btfp_a10[!sapply(models_btfp_a10, is.null)],
fitstat = ~ n + r2, se.below = TRUE)## (1) (2) (3)
## Dependent Var.: btfp_crisis btfp_crisis btfp_crisis
##
## Constant 0.1395*** 0.1393*** 0.1395***
## (0.0055) (0.0055) (0.0055)
## Uninsured Leverage (z) 0.0141* 0.0149*
## (0.0066) (0.0066)
## Log(Assets) 0.0747*** 0.0735*** 0.0770***
## (0.0077) (0.0078) (0.0075)
## Cash Ratio -0.0384*** -0.0388*** -0.0379***
## (0.0047) (0.0047) (0.0047)
## Loan-to-Deposit -0.0154* -0.0167** -0.0148*
## (0.0061) (0.0062) (0.0062)
## Book Equity Ratio -0.0186*** -0.0187*** -0.0191***
## (0.0050) (0.0050) (0.0050)
## Wholesale Funding 0.0262*** 0.0264*** 0.0260***
## (0.0066) (0.0066) (0.0066)
## ROA -0.0087 -0.0089 -0.0085
## (0.0052) (0.0052) (0.0052)
## Uninsured $\beta$ (z) 0.0060
## (0.0062)
## Uninsured $\times$ Unins. $\beta$ -0.0045
## (0.0054)
## $(1 - \beta^U) \times$ Uninsured 0.0111
## (0.0064)
## Uninsured Deposit Franchise
##
## Insured Deposit Franchise
##
## _________________________________ ___________ ___________ ___________
## S.E. type Heter.-rob. Heter.-rob. Heter.-rob.
## Observations 3,665 3,665 3,665
## R2 0.09062 0.09101 0.09021
##
## (4) (5)
## Dependent Var.: btfp_crisis btfp_crisis
##
## Constant 0.1395*** 0.1385***
## (0.0055) (0.0055)
## Uninsured Leverage (z)
##
## Log(Assets) 0.0770*** 0.0686***
## (0.0075) (0.0078)
## Cash Ratio -0.0379*** -0.0392***
## (0.0047) (0.0047)
## Loan-to-Deposit -0.0148* -0.0207***
## (0.0062) (0.0062)
## Book Equity Ratio -0.0191*** -0.0275***
## (0.0050) (0.0059)
## Wholesale Funding 0.0260*** 0.0230***
## (0.0066) (0.0066)
## ROA -0.0085 -0.0085
## (0.0052) (0.0052)
## Uninsured $\beta$ (z)
##
## Uninsured $\times$ Unins. $\beta$
##
## $(1 - \beta^U) \times$ Uninsured
##
## Uninsured Deposit Franchise 0.0111 -0.0027
## (0.0064) (0.0077)
## Insured Deposit Franchise -0.0277***
## (0.0082)
## _________________________________ ___________ ___________
## S.E. type Heter.-rob. Heter.-rob.
## Observations 3,665 3,665
## R2 0.09021 0.09323
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1# =========================================================================
# Panel C: DW (Cols 1–5)
# =========================================================================
cat("\n=== Panel C: DW ===\n")##
## === Panel C: DW ===mod_dw_c1 <- safe_run(df_a10_dw, "dw_crisis", EXPL_C1)
mod_dw_c2 <- safe_run(df_a10_dw, "dw_crisis", EXPL_C2)
mod_dw_c3 <- safe_run(df_a10_dw, "dw_crisis", EXPL_C3)
mod_dw_c4 <- safe_run(df_a10_dw, "dw_crisis", EXPL_C4)
mod_dw_c5 <- safe_run(df_a10_dw, "dw_crisis", EXPL_C5)
models_dw_a10 <- list(
"(1)" = mod_dw_c1, "(2)" = mod_dw_c2, "(3)" = mod_dw_c3,
"(4)" = mod_dw_c4, "(5)" = mod_dw_c5)
save_etable(models_dw_a10, "DSSW_A10_DW",
title_text = "DSSW Table A.10 Analog — DW Borrowing (Crisis Period)",
notes_text = paste0(
"LPM. DV = 1 if DW borrower, 0 if non-borrower. ",
"Columns match DSSW Table A.10 Cols 1--5. Robust SEs. z-standardized."),
extra_lines = list(
c("Spec", "C1", "C2", "C3", "C4", "C5")))
etable(models_dw_a10[!sapply(models_dw_a10, is.null)],
fitstat = ~ n + r2, se.below = TRUE)## (1) (2) (3) (4)
## Dependent Var.: dw_crisis dw_crisis dw_crisis dw_crisis
##
## Constant 0.1241*** 0.1241*** 0.1240*** 0.1240***
## (0.0053) (0.0053) (0.0053) (0.0053)
## Uninsured Leverage (z) 0.0058 0.0056
## (0.0063) (0.0063)
## Log(Assets) 0.0945*** 0.0949*** 0.0958*** 0.0958***
## (0.0077) (0.0078) (0.0076) (0.0076)
## Cash Ratio -0.0098* -0.0098 -0.0095 -0.0095
## (0.0050) (0.0050) (0.0050) (0.0050)
## Loan-to-Deposit -0.0042 -0.0038 -0.0042 -0.0042
## (0.0060) (0.0061) (0.0061) (0.0061)
## Book Equity Ratio -0.0050 -0.0050 -0.0053 -0.0053
## (0.0047) (0.0047) (0.0047) (0.0047)
## Wholesale Funding 0.0204** 0.0204** 0.0203** 0.0203**
## (0.0064) (0.0064) (0.0064) (0.0064)
## ROA -0.0034 -0.0034 -0.0033 -0.0033
## (0.0051) (0.0051) (0.0051) (0.0051)
## Uninsured $\beta$ (z) -0.0017
## (0.0060)
## Uninsured $\times$ Unins. $\beta$ 0.0007
## (0.0052)
## $(1 - \beta^U) \times$ Uninsured 0.0038
## (0.0061)
## Uninsured Deposit Franchise 0.0038
## (0.0061)
## Insured Deposit Franchise
##
## _________________________________ __________ __________ __________ __________
## S.E. type Hete.-rob. Hete.-rob. Hete.-rob. Hete.-rob.
## Observations 3,599 3,599 3,599 3,599
## R2 0.09909 0.09912 0.09897 0.09897
##
## (5)
## Dependent Var.: dw_crisis
##
## Constant 0.1239***
## (0.0053)
## Uninsured Leverage (z)
##
## Log(Assets) 0.0942***
## (0.0079)
## Cash Ratio -0.0097
## (0.0050)
## Loan-to-Deposit -0.0054
## (0.0061)
## Book Equity Ratio -0.0070
## (0.0056)
## Wholesale Funding 0.0197**
## (0.0064)
## ROA -0.0033
## (0.0051)
## Uninsured $\beta$ (z)
##
## Uninsured $\times$ Unins. $\beta$
##
## $(1 - \beta^U) \times$ Uninsured
##
## Uninsured Deposit Franchise 0.0010
## (0.0076)
## Insured Deposit Franchise -0.0056
## (0.0081)
## _________________________________ __________
## S.E. type Hete.-rob.
## Observations 3,599
## R2 0.09911
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1# =========================================================================
# Panel D: FHLB — Falsification (Cols 1–5)
# =========================================================================
cat("\n=== Panel D: FHLB (Falsification) ===\n")##
## === Panel D: FHLB (Falsification) ===mod_fhlb_c1 <- safe_run(df_a10_fhlb, "fhlb_user", EXPL_C1)
mod_fhlb_c2 <- safe_run(df_a10_fhlb, "fhlb_user", EXPL_C2)
mod_fhlb_c3 <- safe_run(df_a10_fhlb, "fhlb_user", EXPL_C3)
mod_fhlb_c4 <- safe_run(df_a10_fhlb, "fhlb_user", EXPL_C4)
mod_fhlb_c5 <- safe_run(df_a10_fhlb, "fhlb_user", EXPL_C5)
models_fhlb_a10 <- list(
"(1)" = mod_fhlb_c1, "(2)" = mod_fhlb_c2, "(3)" = mod_fhlb_c3,
"(4)" = mod_fhlb_c4, "(5)" = mod_fhlb_c5)
save_etable(models_fhlb_a10, "DSSW_A10_FHLB",
title_text = "DSSW Table A.10 Analog — FHLB Falsification (Crisis Period)",
notes_text = paste0(
"LPM. DV = 1 if abnormal FHLB borrower, 0 if non-borrower. Falsification test. ",
"Columns match DSSW Table A.10 Cols 1--5. Robust SEs. z-standardized."),
extra_lines = list(
c("Spec", "C1", "C2", "C3", "C4", "C5")))
etable(models_fhlb_a10[!sapply(models_fhlb_a10, is.null)],
fitstat = ~ n + r2, se.below = TRUE)## (1) (2) (3) (4)
## Dependent Var.: fhlb_user fhlb_user fhlb_user fhlb_user
##
## Constant 0.0906*** 0.0907*** 0.0905*** 0.0905***
## (0.0049) (0.0049) (0.0049) (0.0049)
## Uninsured Leverage (z) 0.0068 0.0082
## (0.0050) (0.0050)
## Log(Assets) 0.0285*** 0.0255*** 0.0318*** 0.0318***
## (0.0065) (0.0066) (0.0065) (0.0065)
## Cash Ratio -0.0226*** -0.0222*** -0.0216*** -0.0216***
## (0.0034) (0.0034) (0.0034) (0.0034)
## Loan-to-Deposit 0.0249*** 0.0209*** 0.0242*** 0.0242***
## (0.0052) (0.0052) (0.0052) (0.0052)
## Book Equity Ratio 0.0083 0.0081 0.0073 0.0073
## (0.0045) (0.0044) (0.0045) (0.0045)
## Wholesale Funding 0.0019 0.0025 0.0014 0.0014
## (0.0051) (0.0051) (0.0052) (0.0052)
## ROA -0.0115* -0.0107* -0.0108* -0.0108*
## (0.0045) (0.0045) (0.0045) (0.0045)
## Uninsured $\beta$ (z) 0.0132*
## (0.0056)
## Uninsured $\times$ Unins. $\beta$ 0.0043
## (0.0044)
## $(1 - \beta^U) \times$ Uninsured 0.0002
## (0.0047)
## Uninsured Deposit Franchise 0.0002
## (0.0047)
## Insured Deposit Franchise
##
## _________________________________ __________ __________ __________ __________
## S.E. type Hete.-rob. Hete.-rob. Hete.-rob. Hete.-rob.
## Observations 3,468 3,468 3,468 3,468
## R2 0.04024 0.04259 0.03983 0.03983
##
## (5)
## Dependent Var.: fhlb_user
##
## Constant 0.0902***
## (0.0049)
## Uninsured Leverage (z)
##
## Log(Assets) 0.0283***
## (0.0067)
## Cash Ratio -0.0221***
## (0.0034)
## Loan-to-Deposit 0.0216***
## (0.0052)
## Book Equity Ratio 0.0037
## (0.0054)
## Wholesale Funding 0.0003
## (0.0053)
## ROA -0.0107*
## (0.0045)
## Uninsured $\beta$ (z)
##
## Uninsured $\times$ Unins. $\beta$
##
## $(1 - \beta^U) \times$ Uninsured
##
## Uninsured Deposit Franchise -0.0057
## (0.0061)
## Insured Deposit Franchise -0.0118
## (0.0069)
## _________________________________ __________
## S.E. type Hete.-rob.
## Observations 3,468
## R2 0.04066
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1# =========================================================================
# COMPACT TABLE: Col 2 across all facilities (key specification)
# =========================================================================
cat("\n=== Compact: Col 2 (Key Spec) Across Facilities ===\n")##
## === Compact: Col 2 (Key Spec) Across Facilities ===models_c2_compact <- list(
"Any Fed" = mod_any_c2, "BTFP" = mod_btfp_c2,
"DW" = mod_dw_c2, "FHLB" = mod_fhlb_c2)
save_etable(models_c2_compact, "DSSW_A10_Col2_compact",
title_text = "DSSW Col 2 Analog: $\\beta^U \\times$ Uninsured Across Facilities",
notes_text = paste0(
"LPM. Specification: Uninsured + $\\beta^U$ + ($\\beta^U \\times$ Uninsured) + Controls. ",
"FHLB: falsification. Robust SEs. z-standardized."))
etable(models_c2_compact[!sapply(models_c2_compact, is.null)],
fitstat = ~ n + r2, se.below = TRUE)## Any Fed BTFP DW FHLB
## Dependent Var.: any_fed btfp_crisis dw_crisis fhlb_user
##
## Constant 0.2042*** 0.1393*** 0.1241*** 0.0907***
## (0.0060) (0.0055) (0.0053) (0.0049)
## Uninsured Leverage (z) 0.0118 0.0149* 0.0056 0.0082
## (0.0073) (0.0066) (0.0063) (0.0050)
## Uninsured $\beta$ (z) 0.0020 0.0060 -0.0017 0.0132*
## (0.0069) (0.0062) (0.0060) (0.0056)
## Uninsured $\times$ Unins. $\beta$ -0.0052 -0.0045 0.0007 0.0043
## (0.0058) (0.0054) (0.0052) (0.0044)
## Log(Assets) 0.1102*** 0.0735*** 0.0949*** 0.0255***
## (0.0083) (0.0078) (0.0078) (0.0066)
## Cash Ratio -0.0370*** -0.0388*** -0.0098 -0.0222***
## (0.0059) (0.0047) (0.0050) (0.0034)
## Loan-to-Deposit -0.0099 -0.0167** -0.0038 0.0209***
## (0.0072) (0.0062) (0.0061) (0.0052)
## Book Equity Ratio -0.0209*** -0.0187*** -0.0050 0.0081
## (0.0058) (0.0050) (0.0047) (0.0044)
## Wholesale Funding 0.0294*** 0.0264*** 0.0204** 0.0025
## (0.0070) (0.0066) (0.0064) (0.0051)
## ROA -0.0055 -0.0089 -0.0034 -0.0107*
## (0.0060) (0.0052) (0.0051) (0.0045)
## _________________________________ __________ ___________ __________ __________
## S.E. type Hete.-rob. Heter.-rob. Hete.-rob. Hete.-rob.
## Observations 3,991 3,665 3,599 3,468
## R2 0.11500 0.09101 0.09912 0.04259
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1# ==============================================================================
# DSSW TABLE A.10 — NO CONTROLS
# DSSW Table A.10 does not include bank-level controls.
# This chunk replicates Cols 1–5 without controls for direct comparison.
# ==============================================================================
cat("=== DSSW TABLE A.10 — NO CONTROLS ===\n\n")## === DSSW TABLE A.10 — NO CONTROLS ===NO_CTRL <- "1" # intercept only (no additional controls)
# --- Specifications (same RHS, no controls) ---
run_nc <- function(data, dv, expl) {
ff <- as.formula(paste(dv, "~", expl))
feols(ff, data = data, vcov = "hetero")
}
safe_run_nc <- function(data, dv, expl, min_n = 30, min_dv1 = 5) {
n_obs <- sum(!is.na(data[[dv]]))
n_dv1 <- sum(data[[dv]] == 1, na.rm = TRUE)
if (n_obs < min_n || n_dv1 < min_dv1) {
message(" Skip: N=", n_obs, " DV=1:", n_dv1, " for ", dv)
return(NULL)
}
tryCatch(run_nc(data, dv, expl),
error = function(e) { message(" Error: ", e$message); NULL })
}
# --- Any Fed (Cols 1–5, no controls) ---
cat("=== Panel A: Any Fed (No Controls) ===\n")## === Panel A: Any Fed (No Controls) ===nc_any_c1 <- safe_run_nc(df_a10_any, "any_fed", "uninsured_lev")
nc_any_c2 <- safe_run_nc(df_a10_any, "any_fed", "uninsured_lev + uninsured_beta + unins_x_unins_beta")
nc_any_c3 <- safe_run_nc(df_a10_any, "any_fed", "one_minus_betaU_x_unins")
nc_any_c4 <- safe_run_nc(df_a10_any, "any_fed", "unins_franchise")
nc_any_c5 <- safe_run_nc(df_a10_any, "any_fed", "unins_franchise + ins_franchise")
models_nc_any <- list(
"(1)" = nc_any_c1, "(2)" = nc_any_c2, "(3)" = nc_any_c3,
"(4)" = nc_any_c4, "(5)" = nc_any_c5)
save_etable(models_nc_any, "DSSW_A10_AnyFed_nocontrols",
title_text = "DSSW Table A.10 Analog — Any Fed, No Controls",
notes_text = paste0(
"LPM. No controls (exact DSSW specification). ",
"Col~1: uninsured leverage. Col~2: + $\\beta^U$ + $\\beta^U \\times$ uninsured. ",
"Col~3: $(1-\\beta^U) \\times$ uninsured. ",
"Col~4: uninsured franchise$/TA$. Col~5: + insured franchise$/TA$. ",
"Robust SEs. z-standardized."),
extra_lines = list(c("Spec", "C1", "C2", "C3", "C4", "C5")))
etable(models_nc_any[!sapply(models_nc_any, is.null)],
fitstat = ~ n + r2, se.below = TRUE)## (1) (2) (3) (4)
## Dependent Var.: any_fed any_fed any_fed any_fed
##
## Constant 0.2052*** 0.2055*** 0.2060*** 0.2060***
## (0.0063) (0.0063) (0.0064) (0.0064)
## Uninsured Leverage (z) 0.0595*** 0.0612***
## (0.0064) (0.0064)
## Uninsured $\beta$ (z) 0.0299***
## (0.0067)
## Uninsured $\times$ Unins. $\beta$ -0.0052
## (0.0059)
## $(1 - \beta^U) \times$ Uninsured 0.0467***
## (0.0065)
## Uninsured Deposit Franchise 0.0467***
## (0.0065)
## Insured Deposit Franchise
##
## _________________________________ __________ __________ __________ __________
## S.E. type Hete.-rob. Hete.-rob. Hete.-rob. Hete.-rob.
## Observations 3,991 3,991 3,991 3,991
## R2 0.02143 0.02654 0.01333 0.01333
##
## (5)
## Dependent Var.: any_fed
##
## Constant 0.2060***
## (0.0063)
## Uninsured Leverage (z)
##
## Uninsured $\beta$ (z)
##
## Uninsured $\times$ Unins. $\beta$
##
## $(1 - \beta^U) \times$ Uninsured
##
## Uninsured Deposit Franchise 0.0179*
## (0.0076)
## Insured Deposit Franchise -0.0565***
## (0.0077)
## _________________________________ __________
## S.E. type Hete.-rob.
## Observations 3,991
## R2 0.02778
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1# --- BTFP (Cols 1–5, no controls) ---
cat("\n=== Panel B: BTFP (No Controls) ===\n")##
## === Panel B: BTFP (No Controls) ===nc_btfp_c1 <- safe_run_nc(df_a10_btfp, "btfp_crisis", "uninsured_lev")
nc_btfp_c2 <- safe_run_nc(df_a10_btfp, "btfp_crisis", "uninsured_lev + uninsured_beta + unins_x_unins_beta")
nc_btfp_c3 <- safe_run_nc(df_a10_btfp, "btfp_crisis", "one_minus_betaU_x_unins")
nc_btfp_c4 <- safe_run_nc(df_a10_btfp, "btfp_crisis", "unins_franchise")
nc_btfp_c5 <- safe_run_nc(df_a10_btfp, "btfp_crisis", "unins_franchise + ins_franchise")
models_nc_btfp <- list(
"(1)" = nc_btfp_c1, "(2)" = nc_btfp_c2, "(3)" = nc_btfp_c3,
"(4)" = nc_btfp_c4, "(5)" = nc_btfp_c5)
save_etable(models_nc_btfp, "DSSW_A10_BTFP_nocontrols",
title_text = "DSSW Table A.10 Analog — BTFP, No Controls",
notes_text = "LPM. No controls. Cols 1--5 match DSSW Table A.10. Robust SEs. z-standardized.",
extra_lines = list(c("Spec", "C1", "C2", "C3", "C4", "C5")))
etable(models_nc_btfp[!sapply(models_nc_btfp, is.null)],
fitstat = ~ n + r2, se.below = TRUE)## (1) (2) (3)
## Dependent Var.: btfp_crisis btfp_crisis btfp_crisis
##
## Constant 0.1358*** 0.1363*** 0.1353***
## (0.0056) (0.0056) (0.0056)
## Uninsured Leverage (z) 0.0447*** 0.0460***
## (0.0058) (0.0058)
## Uninsured $\beta$ (z) 0.0227***
## (0.0061)
## Uninsured $\times$ Unins. $\beta$ -0.0035
## (0.0055)
## $(1 - \beta^U) \times$ Uninsured 0.0356***
## (0.0058)
## Uninsured Deposit Franchise
##
## Insured Deposit Franchise
##
## _________________________________ ___________ ___________ ___________
## S.E. type Heter.-rob. Heter.-rob. Heter.-rob.
## Observations 3,665 3,665 3,665
## R2 0.01685 0.02094 0.01081
##
## (4) (5)
## Dependent Var.: btfp_crisis btfp_crisis
##
## Constant 0.1353*** 0.1353***
## (0.0056) (0.0056)
## Uninsured Leverage (z)
##
## Uninsured $\beta$ (z)
##
## Uninsured $\times$ Unins. $\beta$
##
## $(1 - \beta^U) \times$ Uninsured
##
## Uninsured Deposit Franchise 0.0356*** 0.0140*
## (0.0058) (0.0068)
## Insured Deposit Franchise -0.0423***
## (0.0069)
## _________________________________ ___________ ___________
## S.E. type Heter.-rob. Heter.-rob.
## Observations 3,665 3,665
## R2 0.01081 0.02210
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1# --- DW (Cols 1–5, no controls) ---
cat("\n=== Panel C: DW (No Controls) ===\n")##
## === Panel C: DW (No Controls) ===nc_dw_c1 <- safe_run_nc(df_a10_dw, "dw_crisis", "uninsured_lev")
nc_dw_c2 <- safe_run_nc(df_a10_dw, "dw_crisis", "uninsured_lev + uninsured_beta + unins_x_unins_beta")
nc_dw_c3 <- safe_run_nc(df_a10_dw, "dw_crisis", "one_minus_betaU_x_unins")
nc_dw_c4 <- safe_run_nc(df_a10_dw, "dw_crisis", "unins_franchise")
nc_dw_c5 <- safe_run_nc(df_a10_dw, "dw_crisis", "unins_franchise + ins_franchise")
models_nc_dw <- list(
"(1)" = nc_dw_c1, "(2)" = nc_dw_c2, "(3)" = nc_dw_c3,
"(4)" = nc_dw_c4, "(5)" = nc_dw_c5)
save_etable(models_nc_dw, "DSSW_A10_DW_nocontrols",
title_text = "DSSW Table A.10 Analog — DW, No Controls",
notes_text = "LPM. No controls. Cols 1--5 match DSSW Table A.10. Robust SEs. z-standardized.",
extra_lines = list(c("Spec", "C1", "C2", "C3", "C4", "C5")))
etable(models_nc_dw[!sapply(models_nc_dw, is.null)],
fitstat = ~ n + r2, se.below = TRUE)## (1) (2) (3) (4)
## Dependent Var.: dw_crisis dw_crisis dw_crisis dw_crisis
##
## Constant 0.1199*** 0.1206*** 0.1195*** 0.1195***
## (0.0054) (0.0054) (0.0054) (0.0054)
## Uninsured Leverage (z) 0.0459*** 0.0470***
## (0.0057) (0.0057)
## Uninsured $\beta$ (z) 0.0219***
## (0.0058)
## Uninsured $\times$ Unins. $\beta$ 0.0014
## (0.0054)
## $(1 - \beta^U) \times$ Uninsured 0.0349***
## (0.0057)
## Uninsured Deposit Franchise 0.0349***
## (0.0057)
## Insured Deposit Franchise
##
## _________________________________ __________ __________ __________ __________
## S.E. type Hete.-rob. Hete.-rob. Hete.-rob. Hete.-rob.
## Observations 3,599 3,599 3,599 3,599
## R2 0.01998 0.02463 0.01159 0.01159
##
## (5)
## Dependent Var.: dw_crisis
##
## Constant 0.1195***
## (0.0053)
## Uninsured Leverage (z)
##
## Uninsured $\beta$ (z)
##
## Uninsured $\times$ Unins. $\beta$
##
## $(1 - \beta^U) \times$ Uninsured
##
## Uninsured Deposit Franchise 0.0120
## (0.0066)
## Insured Deposit Franchise -0.0449***
## (0.0068)
## _________________________________ __________
## S.E. type Hete.-rob.
## Observations 3,599
## R2 0.02577
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1# --- FHLB Falsification (Cols 1–5, no controls) ---
cat("\n=== Panel D: FHLB Falsification (No Controls) ===\n")##
## === Panel D: FHLB Falsification (No Controls) ===nc_fhlb_c1 <- safe_run_nc(df_a10_fhlb, "fhlb_user", "uninsured_lev")
nc_fhlb_c2 <- safe_run_nc(df_a10_fhlb, "fhlb_user", "uninsured_lev + uninsured_beta + unins_x_unins_beta")
nc_fhlb_c3 <- safe_run_nc(df_a10_fhlb, "fhlb_user", "one_minus_betaU_x_unins")
nc_fhlb_c4 <- safe_run_nc(df_a10_fhlb, "fhlb_user", "unins_franchise")
nc_fhlb_c5 <- safe_run_nc(df_a10_fhlb, "fhlb_user", "unins_franchise + ins_franchise")
models_nc_fhlb <- list(
"(1)" = nc_fhlb_c1, "(2)" = nc_fhlb_c2, "(3)" = nc_fhlb_c3,
"(4)" = nc_fhlb_c4, "(5)" = nc_fhlb_c5)
save_etable(models_nc_fhlb, "DSSW_A10_FHLB_nocontrols",
title_text = "DSSW Table A.10 Analog — FHLB Falsification, No Controls",
notes_text = "LPM. No controls. Falsification test. Cols 1--5 match DSSW Table A.10. Robust SEs. z-standardized.",
extra_lines = list(c("Spec", "C1", "C2", "C3", "C4", "C5")))
etable(models_nc_fhlb[!sapply(models_nc_fhlb, is.null)],
fitstat = ~ n + r2, se.below = TRUE)## (1) (2) (3) (4)
## Dependent Var.: fhlb_user fhlb_user fhlb_user fhlb_user
##
## Constant 0.0868*** 0.0877*** 0.0862*** 0.0862***
## (0.0048) (0.0048) (0.0048) (0.0048)
## Uninsured Leverage (z) 0.0130** 0.0142**
## (0.0048) (0.0048)
## Uninsured $\beta$ (z) 0.0300***
## (0.0053)
## Uninsured $\times$ Unins. $\beta$ 0.0069
## (0.0045)
## $(1 - \beta^U) \times$ Uninsured 0.0016
## (0.0044)
## Uninsured Deposit Franchise 0.0016
## (0.0044)
## Insured Deposit Franchise
##
## _________________________________ __________ __________ __________ __________
## S.E. type Hete.-rob. Hete.-rob. Hete.-rob. Hete.-rob.
## Observations 3,468 3,468 3,468 3,468
## R2 0.00206 0.01506 3.08e-5 3.08e-5
##
## (5)
## Dependent Var.: fhlb_user
##
## Constant 0.0862***
## (0.0047)
## Uninsured Leverage (z)
##
## Uninsured $\beta$ (z)
##
## Uninsured $\times$ Unins. $\beta$
##
## $(1 - \beta^U) \times$ Uninsured
##
## Uninsured Deposit Franchise -0.0172**
## (0.0053)
## Insured Deposit Franchise -0.0368***
## (0.0057)
## _________________________________ __________
## S.E. type Hete.-rob.
## Observations 3,468
## R2 0.01275
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1# ==============================================================================
# DSSW TABLE A.10 — EXACT REPLICATION WITH SVB BETA AS DV
#
# DSSW's DV is "SVB beta" = a bank's cumulative stock return during the
# SVB crisis window (March 6 to March 13, 2023). This is only available
# for publicly traded banks.
#
# We load daily CRSP returns, compute SVB beta as the cumulative return
# over this window, merge into our cross-section, and run Cols 1–5
# with NO controls (exact DSSW specification).
#
# Panel A: Public banks (have stock returns)
# Panel B: Non-public banks → cannot compute SVB beta (no stock data)
# Instead, we use our borrowing DV for non-public banks as a
# comparison to show the deposit fragility channel operates
# even without equity market signaling.
# ==============================================================================
cat("=== DSSW TABLE A.10 — SVB BETA AS DV ===\n\n")## === DSSW TABLE A.10 — SVB BETA AS DV ===# --- Load daily stock returns ---
df_stock <- read_csv(file.path(DATA_PROC, "df_public_bank.csv"), show_col_types = FALSE) %>%
mutate(idrssd = as.character(rssd_bank),
DlyCalDt = as.Date(DlyCalDt),
ret = as.numeric(ret))
# --- Compute SVB beta = cumulative return (product of 1+r) from Mar 6–13, 2023 ---
svb_window <- df_stock %>%
filter(DlyCalDt >= as.Date("2023-03-06") & DlyCalDt <= as.Date("2023-03-13")) %>%
group_by(idrssd) %>%
summarise(
n_days = n(),
svb_beta_raw = prod(1 + ret, na.rm = TRUE) - 1,
.groups = "drop"
) %>%
filter(n_days >= 4) # require at least 4 of 6 trading days
cat(sprintf(" SVB beta computed for %d public banks\n", nrow(svb_window)))## SVB beta computed for 1235 public bankscat(sprintf(" Mean SVB beta: %.4f (%.2f%%)\n", mean(svb_window$svb_beta_raw), mean(svb_window$svb_beta_raw) * 100))## Mean SVB beta: -0.1781 (-17.81%)cat(sprintf(" SD: %.4f | Min: %.4f | Max: %.4f\n",
sd(svb_window$svb_beta_raw), min(svb_window$svb_beta_raw), max(svb_window$svb_beta_raw)))## SD: 0.1081 | Min: -0.8616 | Max: -0.0122# --- Merge SVB beta into crisis cross-section ---
df_crisis_svb <- df_crisis %>%
inner_join(svb_window %>% select(idrssd, svb_beta_raw), by = "idrssd") %>%
filter(!is.na(uninsured_beta_w) & !is.na(beta_insured))
# Add DSSW A.10 variables (already added to df_*_s but df_crisis may not have them)
df_crisis_svb <- df_crisis_svb %>% mutate(
one_minus_betaU_x_unins_raw = (1 - uninsured_beta_raw) * uninsured_lev_raw,
one_minus_betaU_x_unins_w = winsorize(one_minus_betaU_x_unins_raw),
one_minus_betaU_x_unins = standardize_z(one_minus_betaU_x_unins_w),
unins_franchise_raw = (1 - uninsured_beta_raw) * uninsured_lev_raw,
unins_franchise_w = winsorize(unins_franchise_raw),
unins_franchise = standardize_z(unins_franchise_w),
ins_franchise_raw = (1 - beta_insured) * insured_lev_raw,
ins_franchise_w = winsorize(ins_franchise_raw),
ins_franchise = standardize_z(ins_franchise_w)
)
cat(sprintf(" Merged sample: %d public banks with SVB beta + deposit betas\n", nrow(df_crisis_svb)))## Merged sample: 265 public banks with SVB beta + deposit betas# =========================================================================
# Panel A: SVB Beta as DV — Public Banks (Exact DSSW Replication)
# =========================================================================
cat("\n=== Panel A: SVB Beta (Public Banks, No Controls) ===\n")##
## === Panel A: SVB Beta (Public Banks, No Controls) ===# SVB beta is continuous — use run_nc directly (safe_run_nc checks DV==1 count)
svb_c1 <- tryCatch(run_nc(df_crisis_svb, "svb_beta_raw", "uninsured_lev"), error = function(e) NULL)
svb_c2 <- tryCatch(run_nc(df_crisis_svb, "svb_beta_raw", "uninsured_lev + uninsured_beta + unins_x_unins_beta"), error = function(e) NULL)
svb_c3 <- tryCatch(run_nc(df_crisis_svb, "svb_beta_raw", "one_minus_betaU_x_unins"), error = function(e) NULL)
svb_c4 <- tryCatch(run_nc(df_crisis_svb, "svb_beta_raw", "unins_franchise"), error = function(e) NULL)
svb_c5 <- tryCatch(run_nc(df_crisis_svb, "svb_beta_raw", "unins_franchise + ins_franchise"), error = function(e) NULL)
models_svb_beta <- list(
"(1)" = svb_c1, "(2)" = svb_c2, "(3)" = svb_c3,
"(4)" = svb_c4, "(5)" = svb_c5)
save_etable(models_svb_beta, "DSSW_A10_SVBbeta_public",
title_text = "DSSW Table A.10 Replication: SVB Beta as DV (Public Banks, No Controls)",
notes_text = paste0(
"OLS. DV = SVB beta (cumulative stock return, March 6--13, 2023). ",
"Public banks only. No controls (exact DSSW specification). ",
"Col~1: uninsured leverage. Col~2: + $\\beta^U$ + $\\beta^U \\times$ uninsured. ",
"Col~3: $(1-\\beta^U) \\times$ uninsured. ",
"Col~4: uninsured franchise$/TA$. Col~5: + insured franchise$/TA$. ",
"Robust SEs. z-standardized."),
extra_lines = list(c("Spec", "C1", "C2", "C3", "C4", "C5")))
models_svb_beta_ok <- models_svb_beta[!sapply(models_svb_beta, is.null)]
if (length(models_svb_beta_ok) > 0) etable(models_svb_beta_ok, fitstat = ~ n + r2, se.below = TRUE)## (1) (2) (3)
## Dependent Var.: svb_beta_raw svb_beta_raw svb_beta_raw
##
## Constant -0.1394*** -0.1285*** -0.1644***
## (0.0054) (0.0057) (0.0051)
## Uninsured Leverage (z) -0.0314*** -0.0364***
## (0.0067) (0.0071)
## Uninsured $\beta$ (z) -0.0233***
## (0.0046)
## Uninsured $\times$ Unins. $\beta$ 0.0075
## (0.0041)
## $(1 - \beta^U) \times$ Uninsured -0.0175**
## (0.0066)
## Uninsured Deposit Franchise
##
## Insured Deposit Franchise
##
## _________________________________ ____________ ____________ ____________
## S.E. type Hetero.-rob. Hetero.-rob. Hetero.-rob.
## Observations 265 265 265
## R2 0.11414 0.18345 0.04370
##
## (4) (5)
## Dependent Var.: svb_beta_raw svb_beta_raw
##
## Constant -0.1644*** -0.1644***
## (0.0051) (0.0045)
## Uninsured Leverage (z)
##
## Uninsured $\beta$ (z)
##
## Uninsured $\times$ Unins. $\beta$
##
## $(1 - \beta^U) \times$ Uninsured
##
## Uninsured Deposit Franchise -0.0175** -0.0067
## (0.0066) (0.0059)
## Insured Deposit Franchise 0.0379***
## (0.0062)
## _________________________________ ____________ ____________
## S.E. type Hetero.-rob. Hetero.-rob.
## Observations 265 265
## R2 0.04370 0.23105
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1# =========================================================================
# Panel A.v2: SVB Beta as DV — Deduplicated to 1 Bank per BHC
#
# Panel A assigns the SAME stock return (SVB beta) to every subsidiary
# under a BHC (rssd_top). E.g., Wintrust (WTFC) has 15 subs sharing
# identical SVB beta. This inflates N and biases inference.
#
# Fix: keep only the LARGEST subsidiary (by total_asset) per BHC.
# This gives one independent stock return per publicly traded entity.
# =========================================================================
cat("\n=== Panel A.v2: SVB Beta — Deduplicated (1 Bank per BHC) ===\n")##
## === Panel A.v2: SVB Beta — Deduplicated (1 Bank per BHC) ===# Bring rssd_top into the merged data from the stock file
rssd_top_map <- df_stock %>%
distinct(idrssd, rssd_top = as.character(rssd_top))
df_crisis_svb_dedup <- df_crisis_svb %>%
left_join(rssd_top_map, by = "idrssd") %>%
group_by(rssd_top) %>%
slice_max(order_by = total_asset, n = 1, with_ties = FALSE) %>%
ungroup()
cat(sprintf(" Before dedup: %d banks (%d unique BHCs)\n",
nrow(df_crisis_svb), n_distinct(df_crisis_svb %>% left_join(rssd_top_map, by = "idrssd") %>% pull(rssd_top))))## Before dedup: 265 banks (234 unique BHCs)cat(sprintf(" After dedup: %d banks (1 per BHC)\n", nrow(df_crisis_svb_dedup)))## After dedup: 234 banks (1 per BHC)svb2_c1 <- tryCatch(run_nc(df_crisis_svb_dedup, "svb_beta_raw", "uninsured_lev"), error = function(e) NULL)
svb2_c2 <- tryCatch(run_nc(df_crisis_svb_dedup, "svb_beta_raw", "uninsured_lev + uninsured_beta + unins_x_unins_beta"), error = function(e) NULL)
svb2_c3 <- tryCatch(run_nc(df_crisis_svb_dedup, "svb_beta_raw", "one_minus_betaU_x_unins"), error = function(e) NULL)
svb2_c4 <- tryCatch(run_nc(df_crisis_svb_dedup, "svb_beta_raw", "unins_franchise"), error = function(e) NULL)
svb2_c5 <- tryCatch(run_nc(df_crisis_svb_dedup, "svb_beta_raw", "unins_franchise + ins_franchise"), error = function(e) NULL)
models_svb_dedup <- list(
"(1)" = svb2_c1, "(2)" = svb2_c2, "(3)" = svb2_c3,
"(4)" = svb2_c4, "(5)" = svb2_c5)
save_etable(models_svb_dedup, "DSSW_A10_SVBbeta_public_dedup",
title_text = "DSSW Table A.10 Replication: SVB Beta — Deduplicated (1 Bank per BHC)",
notes_text = paste0(
"OLS. DV = SVB beta (cumulative stock return, March 6--13, 2023). ",
"Public banks only, largest subsidiary per BHC (rssd\\_top). ",
"Eliminates duplicate stock returns from multi-charter BHCs. ",
"No controls (exact DSSW specification). Robust SEs. z-standardized."),
extra_lines = list(c("Spec", "C1", "C2", "C3", "C4", "C5")))
models_svb_dedup_ok <- models_svb_dedup[!sapply(models_svb_dedup, is.null)]
if (length(models_svb_dedup_ok) > 0) etable(models_svb_dedup_ok, fitstat = ~ n + r2, se.below = TRUE)## (1) (2) (3)
## Dependent Var.: svb_beta_raw svb_beta_raw svb_beta_raw
##
## Constant -0.1318*** -0.1213*** -0.1616***
## (0.0062) (0.0061) (0.0055)
## Uninsured Leverage (z) -0.0369*** -0.0423***
## (0.0077) (0.0077)
## Uninsured $\beta$ (z) -0.0237***
## (0.0050)
## Uninsured $\times$ Unins. $\beta$ 0.0091*
## (0.0044)
## $(1 - \beta^U) \times$ Uninsured -0.0211**
## (0.0075)
## Uninsured Deposit Franchise
##
## Insured Deposit Franchise
##
## _________________________________ ____________ ____________ ____________
## S.E. type Hetero.-rob. Hetero.-rob. Hetero.-rob.
## Observations 234 234 234
## R2 0.13742 0.20097 0.05631
##
## (4) (5)
## Dependent Var.: svb_beta_raw svb_beta_raw
##
## Constant -0.1616*** -0.1626***
## (0.0055) (0.0050)
## Uninsured Leverage (z)
##
## Uninsured $\beta$ (z)
##
## Uninsured $\times$ Unins. $\beta$
##
## $(1 - \beta^U) \times$ Uninsured
##
## Uninsured Deposit Franchise -0.0211** -0.0096
## (0.0075) (0.0065)
## Insured Deposit Franchise 0.0404***
## (0.0069)
## _________________________________ ____________ ____________
## S.E. type Hetero.-rob. Hetero.-rob.
## Observations 234 234
## R2 0.05631 0.25443
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1# =========================================================================
# Panel B: Borrowing DV — Public Banks Only (No Controls)
# For comparison: same public-bank sample but with borrowing as DV
# =========================================================================
cat("\n=== Panel B: Borrowing DV — Public Banks Only (No Controls) ===\n")##
## === Panel B: Borrowing DV — Public Banks Only (No Controls) ===pub_c1 <- safe_run_nc(df_crisis_svb, "any_fed", "uninsured_lev")
pub_c2 <- safe_run_nc(df_crisis_svb, "any_fed", "uninsured_lev + uninsured_beta + unins_x_unins_beta")
pub_c3 <- safe_run_nc(df_crisis_svb, "any_fed", "one_minus_betaU_x_unins")
pub_c4 <- safe_run_nc(df_crisis_svb, "any_fed", "unins_franchise")
pub_c5 <- safe_run_nc(df_crisis_svb, "any_fed", "unins_franchise + ins_franchise")
models_pub_borrow <- list(
"(1)" = pub_c1, "(2)" = pub_c2, "(3)" = pub_c3,
"(4)" = pub_c4, "(5)" = pub_c5)
save_etable(models_pub_borrow, "DSSW_A10_borrow_public",
title_text = "DSSW A.10 Analog: Borrowing DV — Public Banks Only (No Controls)",
notes_text = paste0(
"LPM. DV = 1 if borrowed from any Fed facility. Public banks with SVB beta coverage only. ",
"Same sample as SVB beta panel for direct comparison. No controls. Robust SEs. z-standardized."),
extra_lines = list(c("Spec", "C1", "C2", "C3", "C4", "C5")))
models_pub_borrow_ok <- models_pub_borrow[!sapply(models_pub_borrow, is.null)]
if (length(models_pub_borrow_ok) > 0) etable(models_pub_borrow_ok, fitstat = ~ n + r2, se.below = TRUE)## (1) (2) (3) (4)
## Dependent Var.: any_fed any_fed any_fed any_fed
##
## Constant 0.2652*** 0.2556*** 0.3623*** 0.3623***
## (0.0343) (0.0358) (0.0290) (0.0290)
## Uninsured Leverage (z) 0.1219*** 0.1348***
## (0.0304) (0.0315)
## Uninsured $\beta$ (z) 0.0145
## (0.0275)
## Uninsured $\times$ Unins. $\beta$ -0.0230
## (0.0220)
## $(1 - \beta^U) \times$ Uninsured 0.0955**
## (0.0291)
## Uninsured Deposit Franchise 0.0955**
## (0.0291)
## Insured Deposit Franchise
##
## _________________________________ __________ __________ __________ __________
## S.E. type Hete.-rob. Hete.-rob. Hete.-rob. Hete.-rob.
## Observations 265 265 265 265
## R2 0.05228 0.05550 0.03934 0.03934
##
## (5)
## Dependent Var.: any_fed
##
## Constant 0.3623***
## (0.0291)
## Uninsured Leverage (z)
##
## Uninsured $\beta$ (z)
##
## Uninsured $\times$ Unins. $\beta$
##
## $(1 - \beta^U) \times$ Uninsured
##
## Uninsured Deposit Franchise 0.0886**
## (0.0308)
## Insured Deposit Franchise -0.0242
## (0.0304)
## _________________________________ __________
## S.E. type Hete.-rob.
## Observations 265
## R2 0.04166
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1# =========================================================================
# Panel C: Borrowing DV — Non-Public Banks Only (No Controls)
# Non-public banks have no stock returns, so SVB beta is unavailable.
# We show the deposit fragility channel operates without equity signaling.
# =========================================================================
cat("\n=== Panel C: Borrowing DV — Non-Public Banks Only (No Controls) ===\n")##
## === Panel C: Borrowing DV — Non-Public Banks Only (No Controls) ===df_nonpub <- df_a10_any %>% filter(is_public == 0)
cat(sprintf(" Non-public banks with beta coverage: %d\n", nrow(df_nonpub)))## Non-public banks with beta coverage: 3709np_c1 <- safe_run_nc(df_nonpub, "any_fed", "uninsured_lev")
np_c2 <- safe_run_nc(df_nonpub, "any_fed", "uninsured_lev + uninsured_beta + unins_x_unins_beta")
np_c3 <- safe_run_nc(df_nonpub, "any_fed", "one_minus_betaU_x_unins")
np_c4 <- safe_run_nc(df_nonpub, "any_fed", "unins_franchise")
np_c5 <- safe_run_nc(df_nonpub, "any_fed", "unins_franchise + ins_franchise")
models_np_borrow <- list(
"(1)" = np_c1, "(2)" = np_c2, "(3)" = np_c3,
"(4)" = np_c4, "(5)" = np_c5)
save_etable(models_np_borrow, "DSSW_A10_borrow_nonpublic",
title_text = "DSSW A.10 Analog: Borrowing DV — Non-Public Banks (No Controls)",
notes_text = paste0(
"LPM. DV = 1 if borrowed from any Fed facility. Non-public banks only (no stock return data). ",
"Tests whether deposit fragility channel operates without equity market signaling. ",
"No controls. Robust SEs. z-standardized."),
extra_lines = list(c("Spec", "C1", "C2", "C3", "C4", "C5")))
models_np_borrow_ok <- models_np_borrow[!sapply(models_np_borrow, is.null)]
if (length(models_np_borrow_ok) > 0) etable(models_np_borrow_ok, fitstat = ~ n + r2, se.below = TRUE)## (1) (2) (3) (4)
## Dependent Var.: any_fed any_fed any_fed any_fed
##
## Constant 0.1949*** 0.1960*** 0.1944*** 0.1944***
## (0.0065) (0.0065) (0.0065) (0.0065)
## Uninsured Leverage (z) 0.0464*** 0.0485***
## (0.0066) (0.0066)
## Uninsured $\beta$ (z) 0.0290***
## (0.0070)
## Uninsured $\times$ Unins. $\beta$ -0.0059
## (0.0062)
## $(1 - \beta^U) \times$ Uninsured 0.0353***
## (0.0065)
## Uninsured Deposit Franchise 0.0353***
## (0.0065)
## Insured Deposit Franchise
##
## _________________________________ __________ __________ __________ __________
## S.E. type Hete.-rob. Hete.-rob. Hete.-rob. Hete.-rob.
## Observations 3,709 3,709 3,709 3,709
## R2 0.01319 0.01809 0.00781 0.00781
##
## (5)
## Dependent Var.: any_fed
##
## Constant 0.1969***
## (0.0065)
## Uninsured Leverage (z)
##
## Uninsured $\beta$ (z)
##
## Uninsured $\times$ Unins. $\beta$
##
## $(1 - \beta^U) \times$ Uninsured
##
## Uninsured Deposit Franchise 0.0101
## (0.0078)
## Insured Deposit Franchise -0.0507***
## (0.0080)
## _________________________________ __________
## S.E. type Hete.-rob.
## Observations 3,709
## R2 0.01939
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1# --- Summary ---
cat("\n=== DSSW A.10 SVB BETA SUMMARY ===\n")##
## === DSSW A.10 SVB BETA SUMMARY ===cat(" Panel A: SVB beta (stock return) as DV — public banks — EXACT DSSW replication\n")## Panel A: SVB beta (stock return) as DV — public banks — EXACT DSSW replicationcat(" Panel B: Borrowing as DV — SAME public bank sample — for comparison\n")## Panel B: Borrowing as DV — SAME public bank sample — for comparisoncat(" Panel C: Borrowing as DV — non-public banks — equity signal not required\n")## Panel C: Borrowing as DV — non-public banks — equity signal not requiredcat("======================================================================\n")## ======================================================================cat(" COMPREHENSIVE ANALYSIS — COMPLETE\n")## COMPREHENSIVE ANALYSIS — COMPLETEcat("======================================================================\n\n")## ======================================================================cat("MAIN RESULTS (Crisis, Extensive Margin):\n")## MAIN RESULTS (Crisis, Extensive Margin):cat(" A. Full Sample: 4 regressions (AnyFed, BTFP, DW, FHLB)\n")## A. Full Sample: 4 regressions (AnyFed, BTFP, DW, FHLB)cat(" B. Jiang MTM Sol/Ins: 8 regressions (4 × 2)\n")## B. Jiang MTM Sol/Ins: 8 regressions (4 × 2)cat(" C. IDCR-100% Sol/Ins: 8 regressions (4 × 2)\n")## C. IDCR-100% Sol/Ins: 8 regressions (4 × 2)cat(" D. DSSW Diagnostic: 0 insolvent → supports coordination story\n\n")## D. DSSW Diagnostic: 0 insolvent → supports coordination storycat("TEMPORAL ROBUSTNESS:\n")## TEMPORAL ROBUSTNESS:cat(" Full sample: 4 regressions (BTFP/DW × Crisis/Arb)\n")## Full sample: 4 regressions (BTFP/DW × Crisis/Arb)cat(" Jiang MTM Sol/Ins: 8 regressions (BTFP/DW × Crisis/Arb × Sol/Ins)\n")## Jiang MTM Sol/Ins: 8 regressions (BTFP/DW × Crisis/Arb × Sol/Ins)cat(" IDCR-100% Sol/Ins: 8 regressions (BTFP/DW × Crisis/Arb × Sol/Ins)\n")## IDCR-100% Sol/Ins: 8 regressions (BTFP/DW × Crisis/Arb × Sol/Ins)cat(" → Solvency × Period DID: interaction only among solvent banks in crisis\n\n")## → Solvency × Period DID: interaction only among solvent banks in crisiscat("DEPOSIT BETA CHANNEL:\n")## DEPOSIT BETA CHANNEL:cat(" Full sample: 7 regressions (nested/full × 3 facilities + FHLB)\n")## Full sample: 7 regressions (nested/full × 3 facilities + FHLB)cat(" Jiang MTM Sol/Ins: 6 regressions (3 facilities × Sol/Ins)\n")## Jiang MTM Sol/Ins: 6 regressions (3 facilities × Sol/Ins)cat(" IDCR-100% Sol/Ins: 6 regressions (3 facilities × Sol/Ins)\n")## IDCR-100% Sol/Ins: 6 regressions (3 facilities × Sol/Ins)cat(" → β^U triple should work only among solvent (panic-region) banks\n\n")## → β^U triple should work only among solvent (panic-region) bankscat("FACILITY COMPLEMENTARITY:\n")## FACILITY COMPLEMENTARITY:cat(" 4a. Multinomial: facility choice {BTFP, DW, Both}\n")## 4a. Multinomial: facility choice {BTFP, DW, Both}cat(" 4b. Complementarity: DW borrowers → also BTFP?\n")## 4b. Complementarity: DW borrowers → also BTFP?cat(" 4c. Substitution: BTFP-only vs DW-only\n")## 4c. Substitution: BTFP-only vs DW-onlycat(" 4d. Descriptive t-tests\n\n")## 4d. Descriptive t-testscat("BTFP PAR RECAPITALIZATION & DW COMPLEMENTARITY:\n")## BTFP PAR RECAPITALIZATION & DW COMPLEMENTARITY:cat(" Par Recap → DW: 4 regressions (Base, +Recap, +Recap×UI, Full)\n")## Par Recap → DW: 4 regressions (Base, +Recap, +Recap×UI, Full)cat(" BTFP Borrowers → Also DW: 4 regressions (within-BTFP complementarity)\n")## BTFP Borrowers → Also DW: 4 regressions (within-BTFP complementarity)cat(" Joint Usage (Both Fed): 5 regressions (clean sample + AnyFed sample)\n")## Joint Usage (Both Fed): 5 regressions (clean sample + AnyFed sample)cat(" Intensive (Total Fed): 5 regressions (%TA + log($) × 3 specs)\n")## Intensive (Total Fed): 5 regressions (%TA + log($) × 3 specs)cat(" Descriptive + figures: Boxplots, loess curves, t-tests\n")## Descriptive + figures: Boxplots, loess curves, t-testscat(" → BTFP par valuation = implicit recapitalization; does it crowd IN DW usage?\n\n")## → BTFP par valuation = implicit recapitalization; does it crowd IN DW usage?cat("COLLATERAL UTILIZATION & LIQUIDITY HIERARCHY:\n")## COLLATERAL UTILIZATION & LIQUIDITY HIERARCHY:cat(" Run Severity: 6 regressions (Util %TA × 4 specs + log(trips) × 2)\n")## Run Severity: 6 regressions (Util %TA × 4 specs + log(trips) × 2)cat(" BTFP Exhaustion → DW: 4 regressions (complementarity via collateral channel)\n")## BTFP Exhaustion → DW: 4 regressions (complementarity via collateral channel)cat(" DW Collateral Composition: 5 regressions (OMO share × 3 + Loan share × 2)\n")## DW Collateral Composition: 5 regressions (OMO share × 3 + Loan share × 2)cat(" Advance Rate Gap: 2 regressions + paired t-test (par vs. market)\n")## Advance Rate Gap: 2 regressions + paired t-test (par vs. market)cat(" Repeat Borrowing: 2 regressions (log trips ~ run pressure)\n")## Repeat Borrowing: 2 regressions (log trips ~ run pressure)cat(" Figures: Utilization dist, DW composition boxplot, MTM scatter, advance rate,\n")## Figures: Utilization dist, DW composition boxplot, MTM scatter, advance rate,cat(" collateral type composition (BTFP vs DW)\n")## collateral type composition (BTFP vs DW)cat(" → Collateral pecking order: BTFP (par, OMO) → exhaustion → DW (loans, haircuts)\n\n")## → Collateral pecking order: BTFP (par, OMO) → exhaustion → DW (loans, haircuts)cat("SIZE-SPLIT REGRESSIONS:\n")## SIZE-SPLIT REGRESSIONS:cat(" Small (≤$10B): 4 regressions (AnyFed, BTFP, DW, FHLB)\n")## Small (≤$10B): 4 regressions (AnyFed, BTFP, DW, FHLB)cat(" Large (>$10B): 4 regressions (AnyFed, BTFP, DW, FHLB)\n")## Large (>$10B): 4 regressions (AnyFed, BTFP, DW, FHLB)cat(" → Test whether MTM × Uninsured effect differs by bank size\n\n")## → Test whether MTM × Uninsured effect differs by bank sizecat("THRESHOLD GRADIENT (UNINSURED TERCILES):\n")## THRESHOLD GRADIENT (UNINSURED TERCILES):cat(" Any Fed: 3 regressions (Low, Medium, High UI)\n")## Any Fed: 3 regressions (Low, Medium, High UI)cat(" BTFP: 3 regressions (Low, Medium, High UI)\n")## BTFP: 3 regressions (Low, Medium, High UI)cat(" DW: 3 regressions (Low, Medium, High UI)\n")## DW: 3 regressions (Low, Medium, High UI)cat(" → Prediction: β^(H) >> β^(M) > β^(L) — MTM matters most for high-UI banks\n\n")## → Prediction: β^(H) >> β^(M) > β^(L) — MTM matters most for high-UI bankscat("LOW β^U INTERACTION:\n")## LOW β^U INTERACTION:cat(" Full sample: 4 regressions (AnyFed, BTFP, DW, FHLB)\n")## Full sample: 4 regressions (AnyFed, BTFP, DW, FHLB)cat(" Small (≤$10B): 4 regressions\n")## Small (≤$10B): 4 regressionscat(" Large (>$10B): 4 regressions\n")## Large (>$10B): 4 regressionscat(" → Tests whether sticky-deposit (low β^U) banks show stronger panic borrowing\n\n")## → Tests whether sticky-deposit (low β^U) banks show stronger panic borrowingcat("PUBLIC vs. NON-PUBLIC BANKS:\n")## PUBLIC vs. NON-PUBLIC BANKS:cat(" Public banks: 4 regressions (AnyFed, BTFP, DW, FHLB)\n")## Public banks: 4 regressions (AnyFed, BTFP, DW, FHLB)cat(" Non-public banks: 4 regressions (AnyFed, BTFP, DW, FHLB)\n")## Non-public banks: 4 regressions (AnyFed, BTFP, DW, FHLB)cat(" Combined table: 8 columns (Pub/NP × 4 facilities)\n")## Combined table: 8 columns (Pub/NP × 4 facilities)cat(" Descriptive comparison & borrowing rate differences\n")## Descriptive comparison & borrowing rate differencescat(" → If MTM × Uninsured significant among non-public: coordination ≠ equity signal\n\n")## → If MTM × Uninsured significant among non-public: coordination ≠ equity signalcat("SVB CASE STUDY:\n")## SVB CASE STUDY:cat(" Percentile profile: 12 variables ranked vs. cross-section\n")## Percentile profile: 12 variables ranked vs. cross-sectioncat(" Solvency classification: Jiang / IDCR-100% / DSSW\n")## Solvency classification: Jiang / IDCR-100% / DSSWcat(" Beta decomposition: β_overall = s_U × β^U + (1-s_U) × β^I\n")## Beta decomposition: β_overall = s_U × β^U + (1-s_U) × β^Icat(" MTM × Uninsured scatter + β^U distribution (with SVB highlighted)\n")## MTM × Uninsured scatter + β^U distribution (with SVB highlighted)cat(" SVB-like regressions: 8 regressions (Like/Unlike × 4 facilities)\n")## SVB-like regressions: 8 regressions (Like/Unlike × 4 facilities)cat(" → SVB-like = above-median β^U AND above-median uninsured share\n")## → SVB-like = above-median β^U AND above-median uninsured sharecat(" → If MTM × UI significant among SVB-unlike: coordination failure is pervasive\n\n")## → If MTM × UI significant among SVB-unlike: coordination failure is pervasivecat("INTENSIVE MARGIN (BORROWING AMOUNTS):\n")## INTENSIVE MARGIN (BORROWING AMOUNTS):cat(" BTFP: 6 models (4 specs × %TA + 2 log($) robustness)\n")## BTFP: 6 models (4 specs × %TA + 2 log($) robustness)cat(" DW: 6 models (4 specs × %TA + 2 log($) robustness)\n")## DW: 6 models (4 specs × %TA + 2 log($) robustness)cat(" Combined BTFP vs DW: 4 models (M1/M4 side-by-side)\n")## Combined BTFP vs DW: 4 models (M1/M4 side-by-side)cat(" Model progression:\n")## Model progression:cat(" M1: Run pressure (MTM × Uninsured)\n")## M1: Run pressure (MTM × Uninsured)cat(" M2: + Deposit beta channel (β^U triple interaction)\n")## M2: + Deposit beta channel (β^U triple interaction)cat(" M3: + Collateral/par supply (par benefit for BTFP; capacity for both)\n")## M3: + Collateral/par supply (par benefit for BTFP; capacity for both)cat(" M4: Full specification (all channels)\n")## M4: Full specification (all channels)cat(" Descriptive distributions + correlations + scatter plots\n")## Descriptive distributions + correlations + scatter plotscat(" → Tests what determines HOW MUCH a bank borrows, conditional on borrowing\n\n")## → Tests what determines HOW MUCH a bank borrows, conditional on borrowingcat("KEY INSIGHT FROM DSSW:\n")## KEY INSIGHT FROM DSSW:cat(" Every bank is DSSW-solvent. DFV ≈ 68%/TA >> MTM ≈ 5.5%/TA.\n")## Every bank is DSSW-solvent. DFV ≈ 68%/TA >> MTM ≈ 5.5%/TA.cat(" But franchise exists ONLY if depositors stay.\n")## But franchise exists ONLY if depositors stay.cat(" 828 banks borrowed despite being DSSW-solvent\n")## 828 banks borrowed despite being DSSW-solventcat(" → Coordination failure, not insolvency, drove borrowing.\n")## → Coordination failure, not insolvency, drove borrowing.cat(" → The triple interaction (β^U) directly tests the DSSW mechanism.\n\n")## → The triple interaction (β^U) directly tests the DSSW mechanism.cat("Tables:", TABLE_PATH, "\n")## Tables: C:/Users/mohua/OneDrive - Louisiana State University/Finance_PhD/DW_Stigma_paper/Liquidity_project_2025/03_documentation/Comprehensive_Analysis/tablescat("Figures:", FIG_PATH, "\n")## Figures: C:/Users/mohua/OneDrive - Louisiana State University/Finance_PhD/DW_Stigma_paper/Liquidity_project_2025/03_documentation/Comprehensive_Analysis/figurescat("======================================================================\n")## ======================================================================# ==============================================================================
# PARTICIPATION PUZZLE BY SOLVENCY STATUS
#
# Key question: Among banks classified as solvent (insolvent) as of 2022Q4,
# what percentage borrowed from each facility during the crisis and
# arbitrage periods?
#
# Solvency classified at BASELINE (2022Q4) for crisis, (2023Q3) for arb.
# ==============================================================================
cat("================================================================\n")## ================================================================cat(" PANEL A: JIANG MTM SOLVENCY — BORROWING BY FACILITY & PERIOD\n")## PANEL A: JIANG MTM SOLVENCY — BORROWING BY FACILITY & PERIODcat("================================================================\n\n")## ================================================================# --- Crisis Period ---
cat("--- CRISIS PERIOD (Mar 8 – May 4, 2023) ---\n")## --- CRISIS PERIOD (Mar 8 – May 4, 2023) ---cat("Solvency measured at 2022Q4 baseline\n\n")## Solvency measured at 2022Q4 baselinecrisis_mtm <- df_crisis %>%
mutate(Solvency = ifelse(mtm_solvent == 1, "Solvent", "Insolvent")) %>%
group_by(Solvency) %>%
summarise(
N = n(),
AnyFed_N = sum(any_fed, na.rm = TRUE),
AnyFed_pct = round(100 * mean(any_fed, na.rm = TRUE), 2),
BTFP_N = sum(btfp_crisis, na.rm = TRUE),
BTFP_pct = round(100 * mean(btfp_crisis, na.rm = TRUE), 2),
DW_N = sum(dw_crisis, na.rm = TRUE),
DW_pct = round(100 * mean(dw_crisis, na.rm = TRUE), 2),
FHLB_N = sum(fhlb_user, na.rm = TRUE),
FHLB_pct = round(100 * mean(fhlb_user, na.rm = TRUE), 2),
.groups = "drop"
)
print(crisis_mtm, width = Inf)## # A tibble: 3 × 10
## Solvency N AnyFed_N AnyFed_pct BTFP_N BTFP_pct DW_N DW_pct FHLB_N
## <chr> <int> <int> <dbl> <int> <dbl> <int> <dbl> <int>
## 1 Insolvent 825 205 24.8 144 17.4 85 10.3 45
## 2 Solvent 3457 623 18.0 357 10.3 348 10.1 257
## 3 <NA> 10 0 0 0 0 0 0 0
## FHLB_pct
## <dbl>
## 1 5.45
## 2 7.43
## 3 0# Nicely formatted
cat("\nCrisis Borrowing Rates (Jiang MTM):\n")##
## Crisis Borrowing Rates (Jiang MTM):for (i in 1:nrow(crisis_mtm)) {
cat(sprintf(" %s (N=%d):\n", crisis_mtm$Solvency[i], crisis_mtm$N[i]))
cat(sprintf(" Any Fed: %d (%.2f%%)\n", crisis_mtm$AnyFed_N[i], crisis_mtm$AnyFed_pct[i]))
cat(sprintf(" BTFP: %d (%.2f%%)\n", crisis_mtm$BTFP_N[i], crisis_mtm$BTFP_pct[i]))
cat(sprintf(" DW: %d (%.2f%%)\n", crisis_mtm$DW_N[i], crisis_mtm$DW_pct[i]))
cat(sprintf(" FHLB: %d (%.2f%%)\n", crisis_mtm$FHLB_N[i], crisis_mtm$FHLB_pct[i]))
}## Insolvent (N=825):
## Any Fed: 205 (24.85%)
## BTFP: 144 (17.45%)
## DW: 85 (10.30%)
## FHLB: 45 (5.45%)
## Solvent (N=3457):
## Any Fed: 623 (18.02%)
## BTFP: 357 (10.33%)
## DW: 348 (10.07%)
## FHLB: 257 (7.43%)
## NA (N=10):
## Any Fed: 0 (0.00%)
## BTFP: 0 (0.00%)
## DW: 0 (0.00%)
## FHLB: 0 (0.00%)# Chi-squared tests for participation differences
cat("\n--- Chi-squared Tests: Solvent vs. Insolvent (Crisis) ---\n")##
## --- Chi-squared Tests: Solvent vs. Insolvent (Crisis) ---for (fac in c("any_fed", "btfp_crisis", "dw_crisis", "fhlb_user")) {
tbl <- table(df_crisis$mtm_solvent, df_crisis[[fac]])
chi <- tryCatch(chisq.test(tbl, correct = FALSE), error = function(e) NULL)
if (!is.null(chi)) {
stars <- case_when(chi$p.value < 0.01 ~ "***", chi$p.value < 0.05 ~ "**",
chi$p.value < 0.10 ~ "*", TRUE ~ "")
cat(sprintf(" %-15s χ²=%.2f p=%.4f %s\n", fac, chi$statistic, chi$p.value, stars))
}
}## any_fed χ²=19.90 p=0.0000 ***
## btfp_crisis χ²=32.75 p=0.0000 ***
## dw_crisis χ²=0.04 p=0.8396
## fhlb_user χ²=3.98 p=0.0460 **# --- Arbitrage Period ---
cat("\n\n--- ARBITRAGE PERIOD (Nov 15, 2023 – Jan 24, 2024) ---\n")##
##
## --- ARBITRAGE PERIOD (Nov 15, 2023 – Jan 24, 2024) ---cat("Solvency measured at 2023Q3 baseline\n\n")## Solvency measured at 2023Q3 baselinearb_mtm <- df_arb %>%
mutate(Solvency = ifelse(mtm_solvent == 1, "Solvent", "Insolvent")) %>%
group_by(Solvency) %>%
summarise(
N = n(),
AnyFed_N = sum(any_fed, na.rm = TRUE),
AnyFed_pct = round(100 * mean(any_fed, na.rm = TRUE), 2),
BTFP_N = sum(btfp_arb, na.rm = TRUE),
BTFP_pct = round(100 * mean(btfp_arb, na.rm = TRUE), 2),
DW_N = sum(dw_arb, na.rm = TRUE),
DW_pct = round(100 * mean(dw_arb, na.rm = TRUE), 2),
FHLB_N = sum(fhlb_user, na.rm = TRUE),
FHLB_pct = round(100 * mean(fhlb_user, na.rm = TRUE), 2),
.groups = "drop"
)
print(arb_mtm, width = Inf)## # A tibble: 3 × 10
## Solvency N AnyFed_N AnyFed_pct BTFP_N BTFP_pct DW_N DW_pct FHLB_N
## <chr> <int> <int> <dbl> <int> <dbl> <int> <dbl> <int>
## 1 Insolvent 801 244 30.5 208 26.0 70 8.74 31
## 2 Solvent 3396 757 22.3 541 15.9 292 8.6 165
## 3 <NA> 17 0 0 0 0 0 0 0
## FHLB_pct
## <dbl>
## 1 3.87
## 2 4.86
## 3 0cat("\nArbitrage Borrowing Rates (Jiang MTM):\n")##
## Arbitrage Borrowing Rates (Jiang MTM):for (i in 1:nrow(arb_mtm)) {
cat(sprintf(" %s (N=%d):\n", arb_mtm$Solvency[i], arb_mtm$N[i]))
cat(sprintf(" Any Fed: %d (%.2f%%)\n", arb_mtm$AnyFed_N[i], arb_mtm$AnyFed_pct[i]))
cat(sprintf(" BTFP: %d (%.2f%%)\n", arb_mtm$BTFP_N[i], arb_mtm$BTFP_pct[i]))
cat(sprintf(" DW: %d (%.2f%%)\n", arb_mtm$DW_N[i], arb_mtm$DW_pct[i]))
cat(sprintf(" FHLB: %d (%.2f%%)\n", arb_mtm$FHLB_N[i], arb_mtm$FHLB_pct[i]))
}## Insolvent (N=801):
## Any Fed: 244 (30.46%)
## BTFP: 208 (25.97%)
## DW: 70 (8.74%)
## FHLB: 31 (3.87%)
## Solvent (N=3396):
## Any Fed: 757 (22.29%)
## BTFP: 541 (15.93%)
## DW: 292 (8.60%)
## FHLB: 165 (4.86%)
## NA (N=17):
## Any Fed: 0 (0.00%)
## BTFP: 0 (0.00%)
## DW: 0 (0.00%)
## FHLB: 0 (0.00%)# Combined table for LaTeX
crisis_mtm_long <- crisis_mtm %>% mutate(Period = "Crisis")
arb_mtm_long <- arb_mtm %>% mutate(Period = "Arbitrage")
combined_mtm <- bind_rows(crisis_mtm_long, arb_mtm_long)
cat("\n--- Combined Borrowing Table (Jiang MTM) ---\n")##
## --- Combined Borrowing Table (Jiang MTM) ---print(combined_mtm, width = Inf)## # A tibble: 6 × 11
## Solvency N AnyFed_N AnyFed_pct BTFP_N BTFP_pct DW_N DW_pct FHLB_N
## <chr> <int> <int> <dbl> <int> <dbl> <int> <dbl> <int>
## 1 Insolvent 825 205 24.8 144 17.4 85 10.3 45
## 2 Solvent 3457 623 18.0 357 10.3 348 10.1 257
## 3 <NA> 10 0 0 0 0 0 0 0
## 4 Insolvent 801 244 30.5 208 26.0 70 8.74 31
## 5 Solvent 3396 757 22.3 541 15.9 292 8.6 165
## 6 <NA> 17 0 0 0 0 0 0 0
## FHLB_pct Period
## <dbl> <chr>
## 1 5.45 Crisis
## 2 7.43 Crisis
## 3 0 Crisis
## 4 3.87 Arbitrage
## 5 4.86 Arbitrage
## 6 0 Arbitrage# --- Display table ---
disp_mtm <- combined_mtm %>%
mutate(
`Any Fed` = sprintf("%d (%.1f%%)", AnyFed_N, AnyFed_pct),
BTFP = sprintf("%d (%.1f%%)", BTFP_N, BTFP_pct),
DW = sprintf("%d (%.1f%%)", DW_N, DW_pct),
FHLB = sprintf("%d (%.1f%%)", FHLB_N, FHLB_pct)
) %>%
select(Period, Solvency, N, `Any Fed`, BTFP, DW, FHLB)
kbl(disp_mtm, format = "html", escape = FALSE,
caption = "Borrowing Rates by Jiang MTM Solvency Status and Period") %>%
kable_styling(bootstrap_options = c("striped", "hover", "condensed"),
full_width = FALSE, position = "left") %>%
collapse_rows(columns = 1, valign = "middle")| Period | Solvency | N | Any Fed | BTFP | DW | FHLB |
|---|---|---|---|---|---|---|
| Crisis | Insolvent | 825 | 205 (24.9%) | 144 (17.4%) | 85 (10.3%) | 45 (5.4%) |
| Solvent | 3457 | 623 (18.0%) | 357 (10.3%) | 348 (10.1%) | 257 (7.4%) | |
| NA | 10 | 0 (0.0%) | 0 (0.0%) | 0 (0.0%) | 0 (0.0%) | |
| Arbitrage | Insolvent | 801 | 244 (30.5%) | 208 (26.0%) | 70 (8.7%) | 31 (3.9%) |
| Solvent | 3396 | 757 (22.3%) | 541 (15.9%) | 292 (8.6%) | 165 (4.9%) | |
| NA | 17 | 0 (0.0%) | 0 (0.0%) | 0 (0.0%) | 0 (0.0%) |
# --- Save LaTeX version ---
tex_mtm <- combined_mtm %>%
mutate(
AnyFed = sprintf("%d (%.1f\\%%)", AnyFed_N, AnyFed_pct),
BTFP = sprintf("%d (%.1f\\%%)", BTFP_N, BTFP_pct),
DW = sprintf("%d (%.1f\\%%)", DW_N, DW_pct),
FHLB = sprintf("%d (%.1f\\%%)", FHLB_N, FHLB_pct)
) %>%
select(Period, Solvency, N, AnyFed, BTFP, DW, FHLB)
kbl_mtm_tex <- kbl(tex_mtm, format = "latex", booktabs = TRUE, escape = FALSE,
caption = "Borrowing Rates by Jiang MTM Solvency Status and Period") %>%
kable_styling(latex_options = c("hold_position")) %>%
collapse_rows(columns = 1, valign = "middle")
tex_file_mtm <- file.path(TABLE_PATH, "Table_Participation_ByFacility_MTM.tex")
writeLines(kbl_mtm_tex, tex_file_mtm)
cat(sprintf("Saved: %s\n", tex_file_mtm))## Saved: C:/Users/mohua/OneDrive - Louisiana State University/Finance_PhD/DW_Stigma_paper/Liquidity_project_2025/03_documentation/Comprehensive_Analysis/tables/Table_Participation_ByFacility_MTM.texcat("================================================================\n")## ================================================================cat(" PANEL B: IDCR-100%% SOLVENCY — BORROWING BY FACILITY & PERIOD\n")## PANEL B: IDCR-100%% SOLVENCY — BORROWING BY FACILITY & PERIODcat("================================================================\n\n")## ================================================================# --- Crisis Period ---
cat("--- CRISIS PERIOD (Mar 8 – May 4, 2023) ---\n")## --- CRISIS PERIOD (Mar 8 – May 4, 2023) ---cat("Solvency: IDCR = (MV Assets - Uninsured - Insured) / Insured\n\n")## Solvency: IDCR = (MV Assets - Uninsured - Insured) / Insuredcrisis_idcr <- df_crisis %>%
mutate(Solvency = ifelse(solvent_idcr_100 == 1, "Solvent", "Insolvent")) %>%
group_by(Solvency) %>%
summarise(
N = n(),
AnyFed_N = sum(any_fed, na.rm = TRUE),
AnyFed_pct = round(100 * mean(any_fed, na.rm = TRUE), 2),
BTFP_N = sum(btfp_crisis, na.rm = TRUE),
BTFP_pct = round(100 * mean(btfp_crisis, na.rm = TRUE), 2),
DW_N = sum(dw_crisis, na.rm = TRUE),
DW_pct = round(100 * mean(dw_crisis, na.rm = TRUE), 2),
FHLB_N = sum(fhlb_user, na.rm = TRUE),
FHLB_pct = round(100 * mean(fhlb_user, na.rm = TRUE), 2),
.groups = "drop"
)
print(crisis_idcr, width = Inf)## # A tibble: 3 × 10
## Solvency N AnyFed_N AnyFed_pct BTFP_N BTFP_pct DW_N DW_pct FHLB_N
## <chr> <int> <int> <dbl> <int> <dbl> <int> <dbl> <int>
## 1 Insolvent 364 78 21.4 57 15.7 30 8.24 13
## 2 Solvent 3887 750 19.3 444 11.4 403 10.4 289
## 3 <NA> 41 0 0 0 0 0 0 0
## FHLB_pct
## <dbl>
## 1 3.57
## 2 7.44
## 3 0cat("\nCrisis Borrowing Rates (IDCR-100%):\n")##
## Crisis Borrowing Rates (IDCR-100%):for (i in 1:nrow(crisis_idcr)) {
cat(sprintf(" %s (N=%d):\n", crisis_idcr$Solvency[i], crisis_idcr$N[i]))
cat(sprintf(" Any Fed: %d (%.2f%%)\n", crisis_idcr$AnyFed_N[i], crisis_idcr$AnyFed_pct[i]))
cat(sprintf(" BTFP: %d (%.2f%%)\n", crisis_idcr$BTFP_N[i], crisis_idcr$BTFP_pct[i]))
cat(sprintf(" DW: %d (%.2f%%)\n", crisis_idcr$DW_N[i], crisis_idcr$DW_pct[i]))
cat(sprintf(" FHLB: %d (%.2f%%)\n", crisis_idcr$FHLB_N[i], crisis_idcr$FHLB_pct[i]))
}## Insolvent (N=364):
## Any Fed: 78 (21.43%)
## BTFP: 57 (15.66%)
## DW: 30 (8.24%)
## FHLB: 13 (3.57%)
## Solvent (N=3887):
## Any Fed: 750 (19.30%)
## BTFP: 444 (11.42%)
## DW: 403 (10.37%)
## FHLB: 289 (7.44%)
## NA (N=41):
## Any Fed: 0 (0.00%)
## BTFP: 0 (0.00%)
## DW: 0 (0.00%)
## FHLB: 0 (0.00%)# Chi-squared tests
cat("\n--- Chi-squared Tests: Solvent vs. Insolvent (Crisis, IDCR) ---\n")##
## --- Chi-squared Tests: Solvent vs. Insolvent (Crisis, IDCR) ---for (fac in c("any_fed", "btfp_crisis", "dw_crisis", "fhlb_user")) {
tbl <- table(df_crisis$solvent_idcr_100, df_crisis[[fac]])
chi <- tryCatch(chisq.test(tbl, correct = FALSE), error = function(e) NULL)
if (!is.null(chi)) {
stars <- case_when(chi$p.value < 0.01 ~ "***", chi$p.value < 0.05 ~ "**",
chi$p.value < 0.10 ~ "*", TRUE ~ "")
cat(sprintf(" %-15s χ²=%.2f p=%.4f %s\n", fac, chi$statistic, chi$p.value, stars))
}
}## any_fed χ²=0.97 p=0.3257
## btfp_crisis χ²=5.75 p=0.0165 **
## dw_crisis χ²=1.64 p=0.1997
## fhlb_user χ²=7.53 p=0.0061 ***# --- Arbitrage Period ---
cat("\n\n--- ARBITRAGE PERIOD (Nov 15, 2023 – Jan 24, 2024) ---\n\n")##
##
## --- ARBITRAGE PERIOD (Nov 15, 2023 – Jan 24, 2024) ---arb_idcr <- df_arb %>%
mutate(Solvency = ifelse(solvent_idcr_100 == 1, "Solvent", "Insolvent")) %>%
group_by(Solvency) %>%
summarise(
N = n(),
AnyFed_N = sum(any_fed, na.rm = TRUE),
AnyFed_pct = round(100 * mean(any_fed, na.rm = TRUE), 2),
BTFP_N = sum(btfp_arb, na.rm = TRUE),
BTFP_pct = round(100 * mean(btfp_arb, na.rm = TRUE), 2),
DW_N = sum(dw_arb, na.rm = TRUE),
DW_pct = round(100 * mean(dw_arb, na.rm = TRUE), 2),
FHLB_N = sum(fhlb_user, na.rm = TRUE),
FHLB_pct = round(100 * mean(fhlb_user, na.rm = TRUE), 2),
.groups = "drop"
)
print(arb_idcr, width = Inf)## # A tibble: 3 × 10
## Solvency N AnyFed_N AnyFed_pct BTFP_N BTFP_pct DW_N DW_pct FHLB_N
## <chr> <int> <int> <dbl> <int> <dbl> <int> <dbl> <int>
## 1 Insolvent 268 50 18.7 40 14.9 15 5.6 7
## 2 Solvent 3900 951 24.4 709 18.2 347 8.9 189
## 3 <NA> 46 0 0 0 0 0 0 0
## FHLB_pct
## <dbl>
## 1 2.61
## 2 4.85
## 3 0cat("\nArbitrage Borrowing Rates (IDCR-100%):\n")##
## Arbitrage Borrowing Rates (IDCR-100%):for (i in 1:nrow(arb_idcr)) {
cat(sprintf(" %s (N=%d):\n", arb_idcr$Solvency[i], arb_idcr$N[i]))
cat(sprintf(" Any Fed: %d (%.2f%%)\n", arb_idcr$AnyFed_N[i], arb_idcr$AnyFed_pct[i]))
cat(sprintf(" BTFP: %d (%.2f%%)\n", arb_idcr$BTFP_N[i], arb_idcr$BTFP_pct[i]))
cat(sprintf(" DW: %d (%.2f%%)\n", arb_idcr$DW_N[i], arb_idcr$DW_pct[i]))
cat(sprintf(" FHLB: %d (%.2f%%)\n", arb_idcr$FHLB_N[i], arb_idcr$FHLB_pct[i]))
}## Insolvent (N=268):
## Any Fed: 50 (18.66%)
## BTFP: 40 (14.93%)
## DW: 15 (5.60%)
## FHLB: 7 (2.61%)
## Solvent (N=3900):
## Any Fed: 951 (24.38%)
## BTFP: 709 (18.18%)
## DW: 347 (8.90%)
## FHLB: 189 (4.85%)
## NA (N=46):
## Any Fed: 0 (0.00%)
## BTFP: 0 (0.00%)
## DW: 0 (0.00%)
## FHLB: 0 (0.00%)# Combined + LaTeX
crisis_idcr_long <- crisis_idcr %>% mutate(Period = "Crisis")
arb_idcr_long <- arb_idcr %>% mutate(Period = "Arbitrage")
combined_idcr <- bind_rows(crisis_idcr_long, arb_idcr_long)
cat("\n--- Combined Borrowing Table (IDCR-100%) ---\n")##
## --- Combined Borrowing Table (IDCR-100%) ---print(combined_idcr, width = Inf)## # A tibble: 6 × 11
## Solvency N AnyFed_N AnyFed_pct BTFP_N BTFP_pct DW_N DW_pct FHLB_N
## <chr> <int> <int> <dbl> <int> <dbl> <int> <dbl> <int>
## 1 Insolvent 364 78 21.4 57 15.7 30 8.24 13
## 2 Solvent 3887 750 19.3 444 11.4 403 10.4 289
## 3 <NA> 41 0 0 0 0 0 0 0
## 4 Insolvent 268 50 18.7 40 14.9 15 5.6 7
## 5 Solvent 3900 951 24.4 709 18.2 347 8.9 189
## 6 <NA> 46 0 0 0 0 0 0 0
## FHLB_pct Period
## <dbl> <chr>
## 1 3.57 Crisis
## 2 7.44 Crisis
## 3 0 Crisis
## 4 2.61 Arbitrage
## 5 4.85 Arbitrage
## 6 0 Arbitragetex_idcr <- combined_idcr %>%
mutate(
AnyFed = sprintf("%d (%.1f\\%%)", AnyFed_N, AnyFed_pct),
BTFP = sprintf("%d (%.1f\\%%)", BTFP_N, BTFP_pct),
DW = sprintf("%d (%.1f\\%%)", DW_N, DW_pct),
FHLB = sprintf("%d (%.1f\\%%)", FHLB_N, FHLB_pct)
) %>%
select(Period, Solvency, N, AnyFed, BTFP, DW, FHLB)
# --- Display table ---
disp_idcr <- combined_idcr %>%
mutate(
`Any Fed` = sprintf("%d (%.1f%%)", AnyFed_N, AnyFed_pct),
BTFP = sprintf("%d (%.1f%%)", BTFP_N, BTFP_pct),
DW = sprintf("%d (%.1f%%)", DW_N, DW_pct),
FHLB = sprintf("%d (%.1f%%)", FHLB_N, FHLB_pct)
) %>%
select(Period, Solvency, N, `Any Fed`, BTFP, DW, FHLB)
kbl(disp_idcr, format = "html", escape = FALSE,
caption = "Borrowing Rates by IDCR-100% Solvency Status and Period") %>%
kable_styling(bootstrap_options = c("striped", "hover", "condensed"),
full_width = FALSE, position = "left") %>%
collapse_rows(columns = 1, valign = "middle")| Period | Solvency | N | Any Fed | BTFP | DW | FHLB |
|---|---|---|---|---|---|---|
| Crisis | Insolvent | 364 | 78 (21.4%) | 57 (15.7%) | 30 (8.2%) | 13 (3.6%) |
| Solvent | 3887 | 750 (19.3%) | 444 (11.4%) | 403 (10.4%) | 289 (7.4%) | |
| NA | 41 | 0 (0.0%) | 0 (0.0%) | 0 (0.0%) | 0 (0.0%) | |
| Arbitrage | Insolvent | 268 | 50 (18.7%) | 40 (14.9%) | 15 (5.6%) | 7 (2.6%) |
| Solvent | 3900 | 951 (24.4%) | 709 (18.2%) | 347 (8.9%) | 189 (4.8%) | |
| NA | 46 | 0 (0.0%) | 0 (0.0%) | 0 (0.0%) | 0 (0.0%) |
# --- Save LaTeX version ---
tex_idcr <- combined_idcr %>%
mutate(
AnyFed = sprintf("%d (%.1f\\%%)", AnyFed_N, AnyFed_pct),
BTFP = sprintf("%d (%.1f\\%%)", BTFP_N, BTFP_pct),
DW = sprintf("%d (%.1f\\%%)", DW_N, DW_pct),
FHLB = sprintf("%d (%.1f\\%%)", FHLB_N, FHLB_pct)
) %>%
select(Period, Solvency, N, AnyFed, BTFP, DW, FHLB)
kbl_idcr_tex <- kbl(tex_idcr, format = "latex", booktabs = TRUE, escape = FALSE,
caption = "Borrowing Rates by IDCR-100\\% Solvency Status and Period") %>%
kable_styling(latex_options = c("hold_position")) %>%
collapse_rows(columns = 1, valign = "middle")
tex_file_idcr <- file.path(TABLE_PATH, "Table_Participation_ByFacility_IDCR.tex")
writeLines(kbl_idcr_tex, tex_file_idcr)
cat(sprintf("Saved: %s\n", tex_file_idcr))## Saved: C:/Users/mohua/OneDrive - Louisiana State University/Finance_PhD/DW_Stigma_paper/Liquidity_project_2025/03_documentation/Comprehensive_Analysis/tables/Table_Participation_ByFacility_IDCR.texcat("================================================================\n")## ================================================================cat(" PANEL C: DESCRIPTIVE STATISTICS BY JIANG MTM SOLVENCY (2022Q4)\n")## PANEL C: DESCRIPTIVE STATISTICS BY JIANG MTM SOLVENCY (2022Q4)cat("================================================================\n\n")## ================================================================# Variables to summarize
desc_vars <- c("ln_assets_raw", "cash_ratio_raw", "securities_ratio_raw",
"loan_ratio_raw", "book_equity_ratio_raw", "roa_raw", "fhlb_ratio_raw",
"loan_to_deposit_raw", "wholesale_raw", "mtm_total_raw", "uninsured_lev_raw",
"adjusted_equity_raw", "idcr_100")
desc_labels <- c("Log(Assets)", "Cash / TA", "Securities / TA",
"Loans / TA", "Book Equity / TA", "ROA", "FHLB / TA",
"Loan-to-Deposit", "Wholesale Funding", "MTM Loss / TA",
"Uninsured Dep. / TA", "Adj. Equity (MTM)", "IDCR-100%")
# --- Solvent (MTM) ---
df_sol_mtm <- df_2022q4 %>% filter(mtm_solvent == 1)
df_ins_mtm <- df_2022q4 %>% filter(mtm_insolvent == 1)
cat(sprintf("MTM Solvent: N = %d (%.1f%%)\n", nrow(df_sol_mtm),
100 * nrow(df_sol_mtm) / nrow(df_2022q4)))## MTM Solvent: N = 3457 (80.5%)cat(sprintf("MTM Insolvent: N = %d (%.1f%%)\n\n", nrow(df_ins_mtm),
100 * nrow(df_ins_mtm) / nrow(df_2022q4)))## MTM Insolvent: N = 825 (19.2%)# Build summary table
build_desc_table <- function(df_a, df_b, label_a, label_b, vars, labels) {
results <- data.frame(
Variable = labels,
stringsAsFactors = FALSE
)
results[[paste0("Mean_", label_a)]] <- sapply(vars, function(v) round(mean(df_a[[v]], na.rm = TRUE), 3))
results[[paste0("SD_", label_a)]] <- sapply(vars, function(v) round(sd(df_a[[v]], na.rm = TRUE), 3))
results[[paste0("Median_", label_a)]] <- sapply(vars, function(v) round(median(df_a[[v]], na.rm = TRUE), 3))
results[[paste0("Mean_", label_b)]] <- sapply(vars, function(v) round(mean(df_b[[v]], na.rm = TRUE), 3))
results[[paste0("SD_", label_b)]] <- sapply(vars, function(v) round(sd(df_b[[v]], na.rm = TRUE), 3))
results[[paste0("Median_", label_b)]] <- sapply(vars, function(v) round(median(df_b[[v]], na.rm = TRUE), 3))
# T-test for difference in means
results$Diff <- results[[paste0("Mean_", label_a)]] - results[[paste0("Mean_", label_b)]]
results$t_stat <- sapply(vars, function(v) {
tt <- tryCatch(t.test(df_a[[v]], df_b[[v]]), error = function(e) NULL)
if (!is.null(tt)) round(tt$statistic, 2) else NA_real_
})
results$p_val <- sapply(vars, function(v) {
tt <- tryCatch(t.test(df_a[[v]], df_b[[v]]), error = function(e) NULL)
if (!is.null(tt)) round(tt$p.value, 4) else NA_real_
})
results$Stars <- sapply(results$p_val, function(p) {
if (is.na(p)) "" else if (p < 0.01) "***" else if (p < 0.05) "**" else if (p < 0.10) "*" else ""
})
return(results)
}
desc_mtm <- build_desc_table(df_sol_mtm, df_ins_mtm, "Solvent", "Insolvent",
desc_vars, desc_labels)
# --- Display table (HTML for RPubs) ---
desc_mtm_disp <- desc_mtm %>%
mutate(
`Solvent Mean (SD)` = sprintf("%.3f (%.3f)", Mean_Solvent, SD_Solvent),
`Insolvent Mean (SD)` = sprintf("%.3f (%.3f)", Mean_Insolvent, SD_Insolvent),
Difference = sprintf("%.3f%s", Diff, Stars),
`t-stat` = round(t_stat, 2)
) %>%
select(Variable, `Solvent Mean (SD)`, `Insolvent Mean (SD)`, Difference, `t-stat`)
kbl(desc_mtm_disp, format = "html", escape = FALSE,
caption = sprintf("Descriptive Statistics: Jiang MTM Solvent (N=%d) vs. Insolvent (N=%d)",
nrow(df_sol_mtm), nrow(df_ins_mtm))) %>%
kable_styling(bootstrap_options = c("striped", "hover", "condensed"),
full_width = FALSE, position = "left") %>%
footnote(general = "Solvency: Adj. Equity = Book Equity/TA - MTM Loss/TA. Solvent: AE >= 0. Stars: *** p<0.01, ** p<0.05, * p<0.10.",
general_title = "")| Variable | Solvent Mean (SD) | Insolvent Mean (SD) | Difference | t-stat |
|---|---|---|---|---|
| Log(Assets) | 12.906 (1.540) | 12.804 (1.204) | 0.102** | 2.07 |
| Cash / TA | 8.790 (9.798) | 5.274 (4.629) | 3.516*** | 15.17 |
| Securities / TA | 22.914 (14.581) | 37.185 (15.293) | -14.271*** | -24.30 |
| Loans / TA | 61.965 (17.386) | 52.103 (16.108) | 9.862*** | 15.56 |
| Book Equity / TA | 11.254 (9.192) | 5.468 (1.871) | 5.786*** | 34.16 |
| ROA | 1.244 (2.818) | 0.901 (0.485) | 0.343*** | 6.76 |
| FHLB / TA | 2.657 (4.274) | 2.631 (3.979) | 0.026 | 0.17 |
| Loan-to-Deposit | 73.649 (24.475) | 58.367 (19.636) | 15.282*** | 19.09 |
| Wholesale Funding | 0.967 (3.221) | 1.101 (2.581) | -0.134 | -1.27 |
| MTM Loss / TA | 4.905 (1.991) | 7.822 (1.472) | -2.917*** | -47.50 |
| Uninsured Dep. / TA | 23.432 (12.375) | 24.307 (11.126) | -0.875** | -1.99 |
| Adj. Equity (MTM) | 6.348 (9.697) | -2.354 (1.945) | 8.702*** | 48.82 |
| IDCR-100% | 1.067 (19.228) | 0.038 (0.303) | 1.029*** | 3.13 |
| Solvency: Adj. Equity = Book Equity/TA - MTM Loss/TA. Solvent: AE >= 0. Stars: *** p<0.01, ** p<0.05, * p<0.10. |
# --- Save LaTeX version ---
desc_mtm_tex <- desc_mtm %>%
mutate(
Solvent_col = sprintf("%.3f (%.3f)", Mean_Solvent, SD_Solvent),
Insolvent_col = sprintf("%.3f (%.3f)", Mean_Insolvent, SD_Insolvent),
Diff_col = sprintf("%.3f%s", Diff, Stars)
) %>%
select(Variable, Solvent_col, Insolvent_col, Diff_col, t_stat)
names(desc_mtm_tex) <- c("Variable", "Solvent Mean (SD)", "Insolvent Mean (SD)",
"Difference", "t-stat")
kbl_desc_mtm_tex <- kbl(desc_mtm_tex, format = "latex", booktabs = TRUE, escape = FALSE,
caption = sprintf("Descriptive Statistics: Jiang MTM Solvent (N=%d) vs. Insolvent (N=%d)",
nrow(df_sol_mtm), nrow(df_ins_mtm))) %>%
kable_styling(latex_options = c("hold_position", "scale_down")) %>%
footnote(general = "Solvency: Adj. Equity = Book Equity/TA $-$ MTM Loss/TA. Solvent: AE $\\\\geq$ 0. Stars: *** p<0.01, ** p<0.05, * p<0.10.",
escape = FALSE, general_title = "")
tex_desc_mtm <- file.path(TABLE_PATH, "Table_DescStats_MTM_Solvency.tex")
writeLines(kbl_desc_mtm_tex, tex_desc_mtm)
cat(sprintf("Saved: %s\n", tex_desc_mtm))## Saved: C:/Users/mohua/OneDrive - Louisiana State University/Finance_PhD/DW_Stigma_paper/Liquidity_project_2025/03_documentation/Comprehensive_Analysis/tables/Table_DescStats_MTM_Solvency.tex# Also include uninsured beta if available
if ("uninsured_beta_raw" %in% names(df_2022q4)) {
cat("\n--- Deposit Beta by MTM Solvency ---\n")
cat(sprintf(" Solvent: β^U mean = %.4f, median = %.4f (N=%d)\n",
mean(df_sol_mtm$uninsured_beta_raw, na.rm = TRUE),
median(df_sol_mtm$uninsured_beta_raw, na.rm = TRUE),
sum(!is.na(df_sol_mtm$uninsured_beta_raw))))
cat(sprintf(" Insolvent: β^U mean = %.4f, median = %.4f (N=%d)\n",
mean(df_ins_mtm$uninsured_beta_raw, na.rm = TRUE),
median(df_ins_mtm$uninsured_beta_raw, na.rm = TRUE),
sum(!is.na(df_ins_mtm$uninsured_beta_raw))))
}##
## --- Deposit Beta by MTM Solvency ---
## Solvent: β^U mean = 0.3367, median = 0.3139 (N=3413)
## Insolvent: β^U mean = 0.3087, median = 0.2961 (N=813)cat("================================================================\n")## ================================================================cat(" PANEL D: DESCRIPTIVE STATISTICS BY IDCR-100%% SOLVENCY (2022Q4)\n")## PANEL D: DESCRIPTIVE STATISTICS BY IDCR-100%% SOLVENCY (2022Q4)cat("================================================================\n\n")## ================================================================df_sol_idcr <- df_2022q4 %>% filter(solvent_idcr_100 == 1)
df_ins_idcr <- df_2022q4 %>% filter(insolvent_idcr_100 == 1)
cat(sprintf("IDCR-100%% Solvent: N = %d (%.1f%%)\n", nrow(df_sol_idcr),
100 * nrow(df_sol_idcr) / nrow(df_2022q4)))## IDCR-100% Solvent: N = 3887 (90.6%)cat(sprintf("IDCR-100%% Insolvent: N = %d (%.1f%%)\n\n", nrow(df_ins_idcr),
100 * nrow(df_ins_idcr) / nrow(df_2022q4)))## IDCR-100% Insolvent: N = 364 (8.5%)desc_idcr <- build_desc_table(df_sol_idcr, df_ins_idcr, "Solvent", "Insolvent",
desc_vars, desc_labels)
# --- Display table (HTML for RPubs) ---
desc_idcr_disp <- desc_idcr %>%
mutate(
`Solvent Mean (SD)` = sprintf("%.3f (%.3f)", Mean_Solvent, SD_Solvent),
`Insolvent Mean (SD)` = sprintf("%.3f (%.3f)", Mean_Insolvent, SD_Insolvent),
Difference = sprintf("%.3f%s", Diff, Stars),
`t-stat` = round(t_stat, 2)
) %>%
select(Variable, `Solvent Mean (SD)`, `Insolvent Mean (SD)`, Difference, `t-stat`)
kbl(desc_idcr_disp, format = "html", escape = FALSE,
caption = sprintf("Descriptive Statistics: IDCR-100%% Solvent (N=%d) vs. Insolvent (N=%d)",
nrow(df_sol_idcr), nrow(df_ins_idcr))) %>%
kable_styling(bootstrap_options = c("striped", "hover", "condensed"),
full_width = FALSE, position = "left") %>%
footnote(general = "Solvency: IDCR = (MV Assets - Uninsured - Insured) / Insured. Solvent: IDCR >= 0. Stars: *** p<0.01, ** p<0.05, * p<0.10.",
general_title = "")| Variable | Solvent Mean (SD) | Insolvent Mean (SD) | Difference | t-stat |
|---|---|---|---|---|
| Log(Assets) | 12.934 (1.477) | 12.594 (1.283) | 0.340*** | 4.76 |
| Cash / TA | 8.098 (8.896) | 6.571 (5.535) | 1.527*** | 4.72 |
| Securities / TA | 24.100 (14.620) | 40.405 (16.126) | -16.305*** | -18.59 |
| Loans / TA | 61.723 (16.379) | 47.473 (16.636) | 14.250*** | 15.65 |
| Book Equity / TA | 10.040 (5.739) | 4.881 (1.949) | 5.159*** | 37.52 |
| ROA | 1.077 (1.811) | 0.936 (0.493) | 0.141*** | 3.63 |
| FHLB / TA | 2.879 (4.348) | 0.456 (1.217) | 2.423*** | 25.63 |
| Loan-to-Deposit | 73.135 (23.228) | 50.775 (18.511) | 22.360*** | 21.51 |
| Wholesale Funding | 1.076 (3.246) | 0.193 (0.589) | 0.883*** | 14.58 |
| MTM Loss / TA | 5.280 (2.125) | 7.809 (1.490) | -2.529*** | -29.67 |
| Uninsured Dep. / TA | 23.574 (12.003) | 25.891 (12.052) | -2.317*** | -3.51 |
| Adj. Equity (MTM) | 4.760 (6.381) | -2.928 (2.287) | 7.688*** | 48.78 |
| IDCR-100% | 0.953 (18.055) | -0.048 (0.183) | 1.001*** | 3.45 |
| Solvency: IDCR = (MV Assets - Uninsured - Insured) / Insured. Solvent: IDCR >= 0. Stars: *** p<0.01, ** p<0.05, * p<0.10. |
# --- Save LaTeX version ---
desc_idcr_tex <- desc_idcr %>%
mutate(
Solvent_col = sprintf("%.3f (%.3f)", Mean_Solvent, SD_Solvent),
Insolvent_col = sprintf("%.3f (%.3f)", Mean_Insolvent, SD_Insolvent),
Diff_col = sprintf("%.3f%s", Diff, Stars)
) %>%
select(Variable, Solvent_col, Insolvent_col, Diff_col, t_stat)
names(desc_idcr_tex) <- c("Variable", "Solvent Mean (SD)", "Insolvent Mean (SD)",
"Difference", "t-stat")
kbl_desc_idcr_tex <- kbl(desc_idcr_tex, format = "latex", booktabs = TRUE, escape = FALSE,
caption = sprintf("Descriptive Statistics: IDCR-100\\%% Solvent (N=%d) vs. Insolvent (N=%d)",
nrow(df_sol_idcr), nrow(df_ins_idcr))) %>%
kable_styling(latex_options = c("hold_position", "scale_down")) %>%
footnote(general = "Solvency: IDCR = (MV Assets $-$ Uninsured $-$ Insured) / Insured. Solvent: IDCR $\\\\geq$ 0. Stars: *** p<0.01, ** p<0.05, * p<0.10.",
escape = FALSE, general_title = "")
tex_desc_idcr <- file.path(TABLE_PATH, "Table_DescStats_IDCR_Solvency.tex")
writeLines(kbl_desc_idcr_tex, tex_desc_idcr)
cat(sprintf("Saved: %s\n", tex_desc_idcr))## Saved: C:/Users/mohua/OneDrive - Louisiana State University/Finance_PhD/DW_Stigma_paper/Liquidity_project_2025/03_documentation/Comprehensive_Analysis/tables/Table_DescStats_IDCR_Solvency.tex# Beta comparison
if ("uninsured_beta_raw" %in% names(df_2022q4)) {
cat("\n--- Deposit Beta by IDCR-100% Solvency ---\n")
cat(sprintf(" Solvent: β^U mean = %.4f, median = %.4f (N=%d)\n",
mean(df_sol_idcr$uninsured_beta_raw, na.rm = TRUE),
median(df_sol_idcr$uninsured_beta_raw, na.rm = TRUE),
sum(!is.na(df_sol_idcr$uninsured_beta_raw))))
cat(sprintf(" Insolvent: β^U mean = %.4f, median = %.4f (N=%d)\n",
mean(df_ins_idcr$uninsured_beta_raw, na.rm = TRUE),
median(df_ins_idcr$uninsured_beta_raw, na.rm = TRUE),
sum(!is.na(df_ins_idcr$uninsured_beta_raw))))
}##
## --- Deposit Beta by IDCR-100% Solvency ---
## Solvent: β^U mean = 0.3343, median = 0.3132 (N=3871)
## Insolvent: β^U mean = 0.2978, median = 0.2866 (N=355)cat("================================================================\n")================================================================
cat(" PANEL F: BORROWER DESCRIPTIVE STATS — MTM SOLVENCY (CRISIS)\n")PANEL F: BORROWER DESCRIPTIVE STATS — MTM SOLVENCY (CRISIS)
cat("================================================================\n\n")================================================================
# For each facility: compare solvent borrowers vs insolvent borrowers
facility_list <- list(
list(name = "Any Fed", var = "any_fed"),
list(name = "BTFP", var = "btfp_crisis"),
list(name = "DW", var = "dw_crisis")
)
for (fac in facility_list) {
df_sol_b <- df_crisis %>% filter(mtm_solvent == 1, !!sym(fac$var) == 1)
df_ins_b <- df_crisis %>% filter(mtm_insolvent == 1, !!sym(fac$var) == 1)
cat(sprintf("\n--- %s Borrowers: MTM Solvent (N=%d) vs. Insolvent (N=%d) ---\n",
fac$name, nrow(df_sol_b), nrow(df_ins_b)))
if (nrow(df_sol_b) < 2 || nrow(df_ins_b) < 2) {
cat(" Insufficient observations for comparison.\n")
next
}
desc_fac <- build_desc_table(df_sol_b, df_ins_b, "Solvent", "Insolvent",
desc_vars, desc_labels)
# HTML display
desc_fac_disp <- desc_fac %>%
mutate(
`Solvent Mean (SD)` = sprintf("%.3f (%.3f)", Mean_Solvent, SD_Solvent),
`Insolvent Mean (SD)` = sprintf("%.3f (%.3f)", Mean_Insolvent, SD_Insolvent),
Difference = sprintf("%.3f%s", Diff, Stars),
`t-stat` = round(t_stat, 2)
) %>%
select(Variable, `Solvent Mean (SD)`, `Insolvent Mean (SD)`, Difference, `t-stat`)
tbl_html <- kbl(desc_fac_disp, format = "html", escape = FALSE,
caption = sprintf("%s Borrowers (Crisis): MTM Solvent (N=%d) vs. Insolvent (N=%d)",
fac$name, nrow(df_sol_b), nrow(df_ins_b))) %>%
kable_styling(bootstrap_options = c("striped", "hover", "condensed"),
full_width = FALSE, position = "left") %>%
footnote(general = "Sample: borrowers only (DV=1). MTM Solvency at 2022Q4 baseline. *** p<0.01, ** p<0.05, * p<0.10.",
general_title = "")
cat(tbl_html)
cat("\n\n")
# LaTeX save
desc_fac_tex <- desc_fac %>%
mutate(
Solvent_col = sprintf("%.3f (%.3f)", Mean_Solvent, SD_Solvent),
Insolvent_col = sprintf("%.3f (%.3f)", Mean_Insolvent, SD_Insolvent),
Diff_col = sprintf("%.3f%s", Diff, Stars)
) %>%
select(Variable, Solvent_col, Insolvent_col, Diff_col, t_stat)
names(desc_fac_tex) <- c("Variable", "Solvent Mean (SD)", "Insolvent Mean (SD)",
"Difference", "t-stat")
kbl_tex <- kbl(desc_fac_tex, format = "latex", booktabs = TRUE, escape = FALSE,
caption = sprintf("%s Borrowers (Crisis): MTM Solvent (N=%d) vs. Insolvent (N=%d)",
fac$name, nrow(df_sol_b), nrow(df_ins_b))) %>%
kable_styling(latex_options = c("hold_position", "scale_down"))
fname <- paste0("Table_DescStats_Borrowers_MTM_", gsub(" ", "", fac$name), ".tex")
writeLines(kbl_tex, file.path(TABLE_PATH, fname))
cat(sprintf("Saved: %s\n", fname))
}| Variable | Solvent Mean (SD) | Insolvent Mean (SD) | Difference | t-stat |
|---|---|---|---|---|
| Log(Assets) | 13.892 (1.580) | 13.369 (1.266) | 0.523*** | 4.82 |
| Cash / TA | 5.647 (5.966) | 4.068 (3.576) | 1.579*** | 4.57 |
| Securities / TA | 22.806 (12.329) | 37.614 (13.995) | -14.808*** | -13.52 |
| Loans / TA | 65.556 (13.319) | 53.092 (15.019) | 12.464*** | 10.59 |
| Book Equity / TA | 9.637 (2.690) | 5.207 (1.878) | 4.430*** | 26.09 |
| ROA | 1.146 (0.633) | 0.928 (0.360) | 0.218*** | 6.11 |
| FHLB / TA | 3.794 (4.937) | 3.109 (3.774) | 0.685** | 2.08 |
| Loan-to-Deposit | 78.508 (18.232) | 60.140 (18.884) | 18.368*** | 12.18 |
| Wholesale Funding | 1.495 (3.487) | 1.635 (3.435) | -0.140 | -0.50 |
| MTM Loss / TA | 5.321 (1.746) | 7.863 (1.334) | -2.542*** | -21.81 |
| Uninsured Dep. / TA | 27.504 (12.461) | 26.068 (10.602) | 1.436 | 1.61 |
| Adj. Equity (MTM) | 4.316 (3.207) | -2.656 (1.959) | 6.972*** | 37.15 |
| IDCR-100% | 0.203 (0.196) | 0.049 (0.101) | 0.154*** | 14.59 |
| Sample: borrowers only (DV=1). MTM Solvency at 2022Q4 baseline. *** p<0.01, ** p<0.05, * p<0.10. |
Saved: Table_DescStats_Borrowers_MTM_AnyFed.tex
— BTFP Borrowers: MTM Solvent (N=357) vs. Insolvent (N=144) —| Variable | Solvent Mean (SD) | Insolvent Mean (SD) | Difference | t-stat |
|---|---|---|---|---|
| Log(Assets) | 13.899 (1.668) | 13.265 (1.155) | 0.634*** | 4.86 |
| Cash / TA | 4.956 (5.045) | 3.965 (3.407) | 0.991** | 2.54 |
| Securities / TA | 24.349 (11.952) | 38.178 (14.138) | -13.829*** | -10.34 |
| Loans / TA | 64.747 (12.692) | 52.760 (14.737) | 11.987*** | 8.56 |
| Book Equity / TA | 9.420 (2.551) | 5.095 (1.919) | 4.325*** | 20.67 |
| ROA | 1.126 (0.593) | 0.917 (0.327) | 0.209*** | 5.04 |
| FHLB / TA | 4.144 (5.182) | 3.206 (3.947) | 0.938** | 2.19 |
| Loan-to-Deposit | 77.619 (17.122) | 59.746 (18.903) | 17.873*** | 9.83 |
| Wholesale Funding | 1.572 (3.393) | 1.490 (2.769) | 0.082 | 0.28 |
| MTM Loss / TA | 5.393 (1.692) | 7.863 (1.340) | -2.470*** | -17.26 |
| Uninsured Dep. / TA | 28.047 (12.837) | 25.771 (10.429) | 2.276** | 2.06 |
| Adj. Equity (MTM) | 4.027 (2.993) | -2.768 (2.049) | 6.795*** | 29.17 |
| IDCR-100% | 0.209 (0.194) | 0.045 (0.102) | 0.164*** | 12.29 |
| Sample: borrowers only (DV=1). MTM Solvency at 2022Q4 baseline. *** p<0.01, ** p<0.05, * p<0.10. |
Saved: Table_DescStats_Borrowers_MTM_BTFP.tex
— DW Borrowers: MTM Solvent (N=348) vs. Insolvent (N=85) —| Variable | Solvent Mean (SD) | Insolvent Mean (SD) | Difference | t-stat |
|---|---|---|---|---|
| Log(Assets) | 14.111 (1.612) | 13.622 (1.372) | 0.489*** | 2.84 |
| Cash / TA | 6.193 (6.650) | 4.064 (3.675) | 2.129*** | 3.98 |
| Securities / TA | 21.563 (12.495) | 37.407 (14.938) | -15.844*** | -9.04 |
| Loans / TA | 66.229 (13.699) | 53.070 (16.754) | 13.159*** | 6.71 |
| Book Equity / TA | 9.749 (2.672) | 5.231 (1.960) | 4.518*** | 17.62 |
| ROA | 1.170 (0.654) | 0.928 (0.422) | 0.242*** | 4.20 |
| FHLB / TA | 3.520 (4.994) | 3.087 (3.664) | 0.433 | 0.90 |
| Loan-to-Deposit | 79.292 (18.776) | 60.545 (21.266) | 18.747*** | 7.45 |
| Wholesale Funding | 1.486 (3.452) | 1.859 (4.204) | -0.373 | -0.76 |
| MTM Loss / TA | 5.217 (1.742) | 7.908 (1.351) | -2.691*** | -15.49 |
| Uninsured Dep. / TA | 28.312 (12.834) | 27.009 (10.766) | 1.303 | 0.96 |
| Adj. Equity (MTM) | 4.532 (3.262) | -2.677 (2.039) | 7.209*** | 25.56 |
| IDCR-100% | 0.211 (0.216) | 0.057 (0.112) | 0.154*** | 9.16 |
| Sample: borrowers only (DV=1). MTM Solvency at 2022Q4 baseline. *** p<0.01, ** p<0.05, * p<0.10. |
Saved: Table_DescStats_Borrowers_MTM_DW.tex
cat("================================================================\n")================================================================
cat(" PANEL G: BORROWER DESCRIPTIVE STATS — IDCR SOLVENCY (CRISIS)\n")PANEL G: BORROWER DESCRIPTIVE STATS — IDCR SOLVENCY (CRISIS)
cat("================================================================\n\n")================================================================
for (fac in facility_list) {
df_sol_b <- df_crisis %>% filter(solvent_idcr_100 == 1, !!sym(fac$var) == 1)
df_ins_b <- df_crisis %>% filter(insolvent_idcr_100 == 1, !!sym(fac$var) == 1)
cat(sprintf("\n--- %s Borrowers: IDCR Solvent (N=%d) vs. Insolvent (N=%d) ---\n",
fac$name, nrow(df_sol_b), nrow(df_ins_b)))
if (nrow(df_sol_b) < 2 || nrow(df_ins_b) < 2) {
cat(" Insufficient observations for comparison.\n")
next
}
desc_fac <- build_desc_table(df_sol_b, df_ins_b, "Solvent", "Insolvent",
desc_vars, desc_labels)
# HTML display
desc_fac_disp <- desc_fac %>%
mutate(
`Solvent Mean (SD)` = sprintf("%.3f (%.3f)", Mean_Solvent, SD_Solvent),
`Insolvent Mean (SD)` = sprintf("%.3f (%.3f)", Mean_Insolvent, SD_Insolvent),
Difference = sprintf("%.3f%s", Diff, Stars),
`t-stat` = round(t_stat, 2)
) %>%
select(Variable, `Solvent Mean (SD)`, `Insolvent Mean (SD)`, Difference, `t-stat`)
tbl_html <- kbl(desc_fac_disp, format = "html", escape = FALSE,
caption = sprintf("%s Borrowers (Crisis): IDCR Solvent (N=%d) vs. Insolvent (N=%d)",
fac$name, nrow(df_sol_b), nrow(df_ins_b))) %>%
kable_styling(bootstrap_options = c("striped", "hover", "condensed"),
full_width = FALSE, position = "left") %>%
footnote(general = "Sample: borrowers only (DV=1). IDCR-100% Solvency at 2022Q4 baseline. *** p<0.01, ** p<0.05, * p<0.10.",
general_title = "")
cat(tbl_html)
cat("\n\n")
# LaTeX save
desc_fac_tex <- desc_fac %>%
mutate(
Solvent_col = sprintf("%.3f (%.3f)", Mean_Solvent, SD_Solvent),
Insolvent_col = sprintf("%.3f (%.3f)", Mean_Insolvent, SD_Insolvent),
Diff_col = sprintf("%.3f%s", Diff, Stars)
) %>%
select(Variable, Solvent_col, Insolvent_col, Diff_col, t_stat)
names(desc_fac_tex) <- c("Variable", "Solvent Mean (SD)", "Insolvent Mean (SD)",
"Difference", "t-stat")
kbl_tex <- kbl(desc_fac_tex, format = "latex", booktabs = TRUE, escape = FALSE,
caption = sprintf("%s Borrowers (Crisis): IDCR Solvent (N=%d) vs. Insolvent (N=%d)",
fac$name, nrow(df_sol_b), nrow(df_ins_b))) %>%
kable_styling(latex_options = c("hold_position", "scale_down"))
fname <- paste0("Table_DescStats_Borrowers_IDCR_", gsub(" ", "", fac$name), ".tex")
writeLines(kbl_tex, file.path(TABLE_PATH, fname))
cat(sprintf("Saved: %s\n", fname))
}| Variable | Solvent Mean (SD) | Insolvent Mean (SD) | Difference | t-stat |
|---|---|---|---|---|
| Log(Assets) | 13.812 (1.512) | 13.290 (1.568) | 0.522*** | 2.81 |
| Cash / TA | 5.266 (5.635) | 5.159 (4.191) | 0.107 | 0.21 |
| Securities / TA | 24.865 (13.031) | 41.929 (16.345) | -17.064*** | -8.93 |
| Loans / TA | 64.000 (13.578) | 47.754 (17.501) | 16.246*** | 7.95 |
| Book Equity / TA | 8.933 (2.984) | 4.769 (2.152) | 4.164*** | 15.60 |
| ROA | 1.103 (0.598) | 0.985 (0.420) | 0.118** | 2.26 |
| FHLB / TA | 3.928 (4.785) | 0.699 (1.813) | 3.229*** | 11.98 |
| Loan-to-Deposit | 76.295 (18.501) | 51.512 (20.308) | 24.783*** | 10.34 |
| Wholesale Funding | 1.665 (3.615) | 0.233 (0.716) | 1.432*** | 9.24 |
| MTM Loss / TA | 5.736 (1.907) | 8.018 (1.466) | -2.282*** | -12.68 |
| Uninsured Dep. / TA | 27.051 (12.143) | 28.087 (10.992) | -1.036 | -0.78 |
| Adj. Equity (MTM) | 3.197 (3.873) | -3.250 (2.567) | 6.447*** | 19.94 |
| IDCR-100% | 0.187 (0.184) | -0.050 (0.061) | 0.237*** | 24.52 |
| Sample: borrowers only (DV=1). IDCR-100% Solvency at 2022Q4 baseline. *** p<0.01, ** p<0.05, * p<0.10. |
Saved: Table_DescStats_Borrowers_IDCR_AnyFed.tex
— BTFP Borrowers: IDCR Solvent (N=444) vs. Insolvent (N=57) —| Variable | Solvent Mean (SD) | Insolvent Mean (SD) | Difference | t-stat |
|---|---|---|---|---|
| Log(Assets) | 13.821 (1.585) | 12.908 (1.097) | 0.913*** | 5.58 |
| Cash / TA | 4.634 (4.739) | 4.968 (3.936) | -0.334 | -0.59 |
| Securities / TA | 26.362 (12.429) | 43.607 (16.699) | -17.245*** | -7.53 |
| Loans / TA | 63.196 (12.853) | 46.543 (16.879) | 16.653*** | 7.19 |
| Book Equity / TA | 8.652 (2.860) | 4.475 (2.147) | 4.177*** | 13.26 |
| ROA | 1.079 (0.559) | 0.962 (0.328) | 0.117** | 2.30 |
| FHLB / TA | 4.300 (4.994) | 0.561 (1.489) | 3.739*** | 12.12 |
| Loan-to-Deposit | 75.386 (17.391) | 49.863 (19.522) | 25.523*** | 9.40 |
| Wholesale Funding | 1.714 (3.378) | 0.257 (0.777) | 1.457*** | 7.65 |
| MTM Loss / TA | 5.848 (1.854) | 8.087 (1.497) | -2.239*** | -10.32 |
| Uninsured Dep. / TA | 27.318 (12.490) | 27.973 (10.022) | -0.655 | -0.45 |
| Adj. Equity (MTM) | 2.804 (3.703) | -3.612 (2.584) | 6.416*** | 16.68 |
| IDCR-100% | 0.189 (0.181) | -0.049 (0.057) | 0.238*** | 20.84 |
| Sample: borrowers only (DV=1). IDCR-100% Solvency at 2022Q4 baseline. *** p<0.01, ** p<0.05, * p<0.10. |
Saved: Table_DescStats_Borrowers_IDCR_BTFP.tex
— DW Borrowers: IDCR Solvent (N=403) vs. Insolvent (N=30) —| Variable | Solvent Mean (SD) | Insolvent Mean (SD) | Difference | t-stat |
|---|---|---|---|---|
| Log(Assets) | 14.017 (1.554) | 13.986 (1.906) | 0.031 | 0.09 |
| Cash / TA | 5.801 (6.351) | 5.432 (4.426) | 0.369 | 0.43 |
| Securities / TA | 23.423 (13.452) | 41.481 (16.833) | -18.058*** | -5.74 |
| Loans / TA | 64.860 (14.161) | 47.339 (19.771) | 17.521*** | 4.76 |
| Book Equity / TA | 9.163 (2.953) | 4.818 (2.362) | 4.345*** | 9.54 |
| ROA | 1.129 (0.627) | 1.024 (0.563) | 0.105 | 0.98 |
| FHLB / TA | 3.630 (4.847) | 0.816 (2.120) | 2.814*** | 6.17 |
| Loan-to-Deposit | 77.412 (19.350) | 51.434 (22.720) | 25.978*** | 6.10 |
| Wholesale Funding | 1.660 (3.719) | 0.209 (0.621) | 1.451*** | 6.68 |
| MTM Loss / TA | 5.573 (1.910) | 8.059 (1.446) | -2.486*** | -8.86 |
| Uninsured Dep. / TA | 27.907 (12.495) | 30.064 (11.905) | -2.157 | -0.95 |
| Adj. Equity (MTM) | 3.590 (3.886) | -3.241 (2.741) | 6.831*** | 12.73 |
| IDCR-100% | 0.198 (0.205) | -0.056 (0.066) | 0.254*** | 16.07 |
| Sample: borrowers only (DV=1). IDCR-100% Solvency at 2022Q4 baseline. *** p<0.01, ** p<0.05, * p<0.10. |
Saved: Table_DescStats_Borrowers_IDCR_DW.tex
cat("================================================================\n")## ================================================================cat(" PANEL E: CROSS-TABULATION — MTM vs IDCR SOLVENCY & BORROWING\n")## PANEL E: CROSS-TABULATION — MTM vs IDCR SOLVENCY & BORROWINGcat("================================================================\n\n")## ================================================================# Cross-tab: MTM × IDCR solvency × borrowing
cat("--- Cross-Tab: MTM × IDCR Solvency Classification ---\n")## --- Cross-Tab: MTM × IDCR Solvency Classification ---xtab_solv <- df_crisis %>%
count(
MTM = ifelse(mtm_solvent == 1, "MTM-Sol", "MTM-Ins"),
IDCR = ifelse(solvent_idcr_100 == 1, "IDCR-Sol", "IDCR-Ins")
) %>%
arrange(MTM, IDCR)
print(xtab_solv)## # A tibble: 6 × 3
## MTM IDCR n
## <chr> <chr> <int>
## 1 MTM-Ins IDCR-Ins 355
## 2 MTM-Ins IDCR-Sol 470
## 3 MTM-Sol IDCR-Ins 9
## 4 MTM-Sol IDCR-Sol 3417
## 5 MTM-Sol <NA> 31
## 6 <NA> <NA> 10# Borrowing rates within each cross-cell
cat("\n--- Borrowing Rates by Joint Solvency Status (Crisis) ---\n")##
## --- Borrowing Rates by Joint Solvency Status (Crisis) ---joint_borrow <- df_crisis %>%
mutate(
Joint = case_when(
mtm_solvent == 1 & solvent_idcr_100 == 1 ~ "Both Solvent",
mtm_solvent == 1 & insolvent_idcr_100 == 1 ~ "MTM-Sol / IDCR-Ins",
mtm_insolvent == 1 & solvent_idcr_100 == 1 ~ "MTM-Ins / IDCR-Sol",
mtm_insolvent == 1 & insolvent_idcr_100 == 1 ~ "Both Insolvent"
)
) %>%
group_by(Joint) %>%
summarise(
N = n(),
AnyFed_pct = round(100 * mean(any_fed, na.rm = TRUE), 2),
BTFP_pct = round(100 * mean(btfp_crisis, na.rm = TRUE), 2),
DW_pct = round(100 * mean(dw_crisis, na.rm = TRUE), 2),
FHLB_pct = round(100 * mean(fhlb_user, na.rm = TRUE), 2),
.groups = "drop"
)
print(joint_borrow, width = Inf)## # A tibble: 5 × 6
## Joint N AnyFed_pct BTFP_pct DW_pct FHLB_pct
## <chr> <int> <dbl> <dbl> <dbl> <dbl>
## 1 Both Insolvent 355 21.1 15.8 7.89 3.66
## 2 Both Solvent 3417 18.1 10.4 10.1 7.52
## 3 MTM-Ins / IDCR-Sol 470 27.7 18.7 12.1 6.81
## 4 MTM-Sol / IDCR-Ins 9 33.3 11.1 22.2 0
## 5 <NA> 41 0 0 0 0cat("\n--- Key Insight ---\n")##
## --- Key Insight ---n_sol_borrowers <- df_crisis %>%
filter(mtm_solvent == 1, any_fed == 1) %>% nrow()
n_sol_total <- df_crisis %>% filter(mtm_solvent == 1) %>% nrow()
cat(sprintf(" %d out of %d MTM-solvent banks (%.1f%%) borrowed from Fed facilities\n",
n_sol_borrowers, n_sol_total, 100 * n_sol_borrowers / n_sol_total))## 623 out of 3457 MTM-solvent banks (18.0%) borrowed from Fed facilitiesn_sol_idcr_borrowers <- df_crisis %>%
filter(solvent_idcr_100 == 1, any_fed == 1) %>% nrow()
n_sol_idcr_total <- df_crisis %>% filter(solvent_idcr_100 == 1) %>% nrow()
cat(sprintf(" %d out of %d IDCR-solvent banks (%.1f%%) borrowed from Fed facilities\n",
n_sol_idcr_borrowers, n_sol_idcr_total,
100 * n_sol_idcr_borrowers / n_sol_idcr_total))## 750 out of 3887 IDCR-solvent banks (19.3%) borrowed from Fed facilitiescat(" → Solvent banks borrowing = participation puzzle (coordination failure, not insolvency)\n")## → Solvent banks borrowing = participation puzzle (coordination failure, not insolvency)