Empirical Tests of Joint Solvency-Liquidity Transmission
What Does Emergency Borrowing During A Crisis Reveal About Bank Runs?
Mohua Ferdousi
April 21, 2026
1. Setup
# ── Data wrangling ──
library(data.table); library(dplyr); library(tidyr); library(stringr)
library(lubridate); library(purrr); library(tibble); library(readr)
# ── Display ──
library(knitr); library(kableExtra)
# ── Plotting ──
library(ggplot2); library(scales); library(patchwork)
# ── Inference ──
library(sandwich) # HC-robust variance
library(lmtest) # coeftest with robust SE# ══════════════════════════════════════════════════════════════════════
# HELPERS
# ══════════════════════════════════════════════════════════════════════
safe_div <- function(num, denom, default = NA_real_) {
ifelse(is.na(denom) | denom == 0, default, num / denom)
}
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])
}
fmt <- function(x, d = 0) formatC(x, format = "f", digits = d, big.mark = ",")
fmt2 <- function(x) fmt(x, 2)
fmt3 <- function(x) fmt(x, 3)
fmt4 <- function(x) fmt(x, 4)
z_std <- function(x) {
mu <- mean(x, na.rm = TRUE); s <- sd(x, na.rm = TRUE)
if (is.na(s) || s == 0) return(rep(0, length(x)))
(x - mu) / s
}
pct <- function(x) sprintf("%.1f%%", 100 * mean(x, na.rm = TRUE))
stars_pval <- function(p) {
dplyr::case_when(
is.na(p) ~ "",
p < 0.01 ~ "***",
p < 0.05 ~ "**",
p < 0.10 ~ "*",
TRUE ~ ""
)
}
robust_summary <- function(model, vcov_type = "HC1") {
ct <- coeftest(model, vcov. = vcovHC(model, type = vcov_type))
data.frame(
term = rownames(ct),
estimate = ct[, 1],
std.error = ct[, 2],
t.value = ct[, 3],
p.value = ct[, 4],
stars = stars_pval(ct[, 4]),
stringsAsFactors = FALSE
)
}# ══════════════════════════════════════════════════════════════════════
# PATHS
# ══════════════════════════════════════════════════════════════════════
BASE_PATH <- "C:/Users/mferdo2/OneDrive - Louisiana State University/Finance_PhD/Research 2026"
DATA_DIR <- file.path(BASE_PATH, "01_data/Final dataset")
OUT_PATH <- file.path(BASE_PATH, "03_documentation/results")
TABLE_PATH <- file.path(OUT_PATH, "tables")
FIG_PATH <- file.path(OUT_PATH, "figures")
for (p in c(TABLE_PATH, FIG_PATH))
if (!dir.exists(p)) dir.create(p, recursive = TRUE)
save_kbl_latex <- function(df, filename, col.names = NULL, caption = "",
align = NULL, ...) {
tex <- kbl(df, format = "latex", booktabs = TRUE, escape = FALSE,
col.names = col.names, caption = caption, align = align, ...) %>%
kable_styling(latex_options = c("hold_position"))
writeLines(tex, file.path(TABLE_PATH, paste0(filename, ".tex")))
invisible()
}
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")
invisible()
}# ══════════════════════════════════════════════════════════════════════
# CALIBRATION
# ══════════════════════════════════════════════════════════════════════
y_10yr <- 0.0392 # 10-year Treasury yield (DSSW benchmark rate)
r_market <- y_10yr # alias for theory notation
delta_decay <- 0.10 # deposit decay rate
cap_factor <- 1 / (y_10yr + delta_decay) # DSSW capitalization factor
phi_star_baseline <- 1.0
phi_star_struct <- 0.5
# ── Periods ──
P0_start <- as.Date("2023-03-01"); P0_end <- as.Date("2023-03-07")
P1_start <- as.Date("2023-03-08"); P1_end <- as.Date("2023-03-12")
P2_start <- as.Date("2023-03-13"); P2_end <- as.Date("2023-04-27")
P3_start <- as.Date("2023-04-28"); P3_end <- as.Date("2023-05-04")
CRISIS_START <- P1_start
CRISIS_END <- P3_end
ARB_START <- as.Date("2023-11-15")
ARB_END <- as.Date("2024-01-24")
BTFP_LAUNCH <- as.Date("2023-03-13")
BTFP_CLOSE <- as.Date("2024-03-11")
# ── DW primary credit contractual maximum (days) ──
DW_CONTRACT_MAX <- 90
assign_period <- function(d) {
dplyr::case_when(
d >= P0_start & d <= P0_end ~ "P0: Pre-Crisis",
d >= P1_start & d <= P1_end ~ "P1: SVB Week",
d >= P2_start & d <= P2_end ~ "P2: SVB to FRC",
d >= P3_start & d <= P3_end ~ "P3: FRC Week",
d >= ARB_START & d <= ARB_END ~ "Arbitrage",
d > CRISIS_END & d < ARB_START ~ "Inter-Period",
d > ARB_END & d <= BTFP_CLOSE ~ "Post-Arbitrage",
TRUE ~ "Other"
)
}
theme_gp <- theme_minimal(base_size = 13) +
theme(plot.title = element_text(face = "bold", size = 14),
plot.subtitle = element_text(color = "grey40", size = 11),
legend.position = "bottom",
panel.grid.minor = element_blank())
fac_colors <- c("BTFP Only" = "#1565C0", "DW Only" = "#E53935",
"Both" = "#7B1FA2", "Non-Borrower" = "grey60")2. Data Loading and Variable Construction
2.1 Load four raw datasets
call_raw <- read_csv(file.path(DATA_DIR, "final_call_gsib.csv"),
show_col_types = FALSE) %>%
mutate(idrssd = as.character(idrssd))
btfp_raw <- read_csv(file.path(DATA_DIR, "btfp_loan_bank_only.csv"),
show_col_types = FALSE) %>%
mutate(rssd_id = as.character(rssd_id),
btfp_loan_date = mdy(btfp_loan_date),
btfp_repayment_date = mdy(btfp_repayment_date),
btfp_maturity_date = mdy(btfp_maturity_date))
# FIX: parse dw_maturity_date so Table 1 early-repay logic works
dw_raw <- read_csv(file.path(DATA_DIR, "dw_loan_bank_2023.csv"),
show_col_types = FALSE) %>%
mutate(rssd_id = as.character(rssd_id),
dw_loan_date = ymd(dw_loan_date),
dw_repayment_date = ymd(dw_repayment_date),
dw_maturity_date = ymd(dw_maturity_date),
dw_credit_type_clean = str_squish(as.character(dw_credit_type))) %>%
filter(str_detect(dw_credit_type_clean, "^Primary Credit"))
dssw_raw <- read_csv(file.path(DATA_DIR, "dssw_deposit_betas.csv"),
show_col_types = FALSE) %>%
mutate(idrssd = as.character(idrssd))
# ── DSSW deposit costs ──
dssw_costs_file <- file.path(DATA_DIR, "dssw_deposit_costs.csv")
if (file.exists(dssw_costs_file)) {
dssw_costs_raw <- read_csv(dssw_costs_file, show_col_types = FALSE) %>%
mutate(idrssd = as.character(idrssd))
HAS_DEPOSIT_COSTS <- TRUE
} else {
HAS_DEPOSIT_COSTS <- FALSE
}
cat(sprintf("Call panel : %s bank-quarters, %s banks\n",
fmt(nrow(call_raw)), fmt(n_distinct(call_raw$idrssd))))## Call panel : 75,989 bank-quarters, 5,074 bankscat(sprintf("BTFP loans : %s transactions, %s banks\n",
fmt(nrow(btfp_raw)), fmt(n_distinct(btfp_raw$rssd_id))))## BTFP loans : 6,734 transactions, 1,327 bankscat(sprintf("DW loans : %s transactions, %s banks\n",
fmt(nrow(dw_raw)), fmt(n_distinct(dw_raw$rssd_id))))## DW loans : 9,673 transactions, 1,468 bankscat(sprintf("DSSW betas : %s bank-quarters, %s banks\n",
fmt(nrow(dssw_raw)), fmt(n_distinct(dssw_raw$idrssd))))## DSSW betas : 13,588 bank-quarters, 4,660 banks2.2 Build the 2022Q4 cross-section
df <- call_raw %>%
filter(period == "2022Q4") %>%
filter(gsib == 0, failed_bank == 0)
# FIX: pull beta_insured_w (was missing)
dssw_2022q4 <- dssw_raw %>%
filter(estimation_date == "2022Q4") %>%
select(idrssd,
beta_overall,
beta_uninsured, beta_insured,
beta_uninsured_w, beta_insured_w)
# ── Deposit costs (DSSW) ──
if (HAS_DEPOSIT_COSTS) {
dssw_costs_2022q4 <- dssw_costs_raw %>%
filter(period == "2022Q4") %>%
select(idrssd,
deposit_cost_insured,
deposit_cost_uninsured,
deposit_cost_weighted)
} else {
dssw_costs_2022q4 <- tibble(idrssd = character(),
deposit_cost_insured = numeric(),
deposit_cost_uninsured = numeric(),
deposit_cost_weighted = numeric())
}
# FIX: the previous version did the left_join TWICE, creating .x/.y suffix
# columns and breaking downstream references to beta_overall, etc.
# Single join only.
df <- df %>%
left_join(dssw_2022q4, by = "idrssd") %>%
left_join(dssw_costs_2022q4, by = "idrssd") %>%
mutate(
# Clip betas to [0, 1]
beta_clipped = pmax(0, pmin(1, beta_overall)),
beta_u_clipped = pmax(0, pmin(1, beta_uninsured_w)),
beta_i_clipped = pmax(0, pmin(1, beta_insured_w)),
# Costs: substitute 0 when missing; track availability
cost_u_raw = ifelse(HAS_DEPOSIT_COSTS & !is.na(deposit_cost_uninsured),
deposit_cost_uninsured, 0),
cost_i_raw = ifelse(HAS_DEPOSIT_COSTS & !is.na(deposit_cost_insured),
deposit_cost_insured, 0),
has_cost_data = as.integer(HAS_DEPOSIT_COSTS &
!is.na(deposit_cost_uninsured))
)
cat(sprintf("2022Q4 cross-section: %s banks (excl. GSIBs, failed)\n",
fmt(nrow(df))))## 2022Q4 cross-section: 4,696 banks (excl. GSIBs, failed)cat(sprintf("DSSW merge: %s matched (%.1f%%)\n",
fmt(sum(!is.na(df$beta_overall))),
100 * mean(!is.na(df$beta_overall))))## DSSW merge: 4,602 matched (98.0%)cat(sprintf("beta_insured_w matched: %s (%.1f%%)\n",
fmt(sum(!is.na(df$beta_insured_w))),
100 * mean(!is.na(df$beta_insured_w))))## beta_insured_w matched: 4,602 (98.0%)2.3 Construct theory variables
df <- df %>%
mutate(
# ── Size and ratios (pp) ──
log_ta = log(total_asset),
eq_ta = book_equity_to_total_asset,
cash_ta = cash_to_total_asset,
sec_ta = security_to_total_asset,
omo_ta = omo_eligible_to_total_asset,
loan_ta = total_loan_to_total_asset,
dep_ta = total_deposit_to_total_asset,
du_ta = uninsured_leverage,
mu = safe_div(uninsured_deposit, total_deposit, 0),
# ── MTM losses / assets (pp) ──
ell = mtm_loss_to_total_asset,
ell_sec = loss_total_sec_to_ta,
ell_omo = loss_omo_sec_to_ta,
ell_nonomo = loss_nonomo_sec_to_ta,
ell_loan = loss_total_loan_to_ta,
# ── Deposit franchise (DSSW methodology, Option A: separate legs) ──
# F^U/A = max[(1-β^U)·r - c^U, 0] · (1/(r+δ)) · (D^U/A)
# F^I/A = max[(1-β^I)·r - c^I, 0] · (1/(r+δ)) · (D^I/A)
# F/A = F^U/A + F^I/A
d_u_over_ta = safe_div(uninsured_deposit, total_asset, 0),
d_i_over_ta = safe_div(pmax(total_deposit - uninsured_deposit, 0),
total_asset, 0),
d_over_ta = safe_div(total_deposit, total_asset, 0),
uninsured_share_d = safe_div(uninsured_deposit, total_deposit, 0),
insured_share_d = pmax(1 - uninsured_share_d, 0),
# Per-dollar rents (as fractions, not pp)
rent_u = pmax((1 - beta_u_clipped) * y_10yr - cost_u_raw, 0),
rent_i = pmax((1 - beta_i_clipped) * y_10yr - cost_i_raw, 0),
# Franchise as % of total assets (pp)
fu_ta = ifelse(!is.na(beta_u_clipped),
rent_u * cap_factor * d_u_over_ta * 100, NA_real_),
fi_ta = ifelse(!is.na(beta_i_clipped),
rent_i * cap_factor * d_i_over_ta * 100, NA_real_),
# f_ta = sum of legs; NA if EITHER leg missing (conservative)
f_ta = rowSums(cbind(fu_ta, fi_ta), na.rm = FALSE),
# Dollar-value franchise
F_total = f_ta / 100 * total_asset,
F_uninsured = fu_ta / 100 * total_asset,
F_insured = fi_ta / 100 * total_asset,
# ── Market-value equity and post-run value ──
E_MV = total_equity - all_asset_loss, # Without franchise
E_MV_F = E_MV + F_total, # With total franchise
E_MV_F_insured = E_MV + F_insured,
E_MV_F_uninsured = E_MV + F_uninsured,
# Post-run value: uninsured flee (lose share μ of franchise)
v = E_MV + (1 - mu) * F_total,
emv_ta = 100 * safe_div(E_MV, total_asset),
v_ta = 100 * safe_div(v, total_asset),
# ── Coverage ratio and decomposition ──
omo_mv = pmax(omo_eligible - loss_omo_sec, 0),
rho = safe_div(cash + omo_mv, uninsured_deposit),
rho_0 = safe_div(cash + omo_eligible, uninsured_deposit),
rho_C = safe_div(cash, uninsured_deposit),
rho_S = safe_div(omo_mv, uninsured_deposit),
# ── Liquidity gap ──
liq_gap = pmax(phi_star_baseline * uninsured_deposit
- (cash + omo_mv), 0),
liq_gap_ta = 100 * safe_div(liq_gap, total_asset),
has_gap = as.integer(liq_gap > 0),
liq_gap_struct = pmax(phi_star_struct * uninsured_deposit
- (cash + omo_mv), 0),
has_gap_struct = as.integer(liq_gap_struct > 0),
# ── Descriptive interaction ──
ell_x_uninsured = ell * du_ta,
# ── other Liabilities ──
roa = roa,
fhlb_ta = fhlb_to_total_asset,
loan_to_deposit =loan_to_deposit,
wholesale_ta = fed_fund_purchase_to_total_asset + repo_to_total_asset +
fhlb_to_total_asset + other_borr_to_total_asset
)Franchise sanity check
# Option A produces insured_share_F > insured_share_D because insured β
# is lower and the insured leg is worth more per dollar of deposit.
# The old code made them equal by construction.
df %>%
filter(!is.na(f_ta)) %>%
summarise(
n_banks = n(),
mean_f_ta = mean(f_ta, na.rm = TRUE),
median_f_ta = median(f_ta, na.rm = TRUE),
mean_fu_ta = mean(fu_ta, na.rm = TRUE),
mean_fi_ta = mean(fi_ta, na.rm = TRUE),
insured_share_F = mean(fi_ta / f_ta, na.rm = TRUE),
insured_share_D = mean(insured_share_d, na.rm = TRUE)
) %>%
kbl(digits = 3,
caption = "Franchise sanity check (insured_share_F should exceed insured_share_D)") %>%
kable_styling(full_width = FALSE)| n_banks | mean_f_ta | median_f_ta | mean_fu_ta | mean_fi_ta | insured_share_F | insured_share_D |
|---|---|---|---|---|---|---|
| 4602 | 13.17 | 13.804 | 2.617 | 10.553 | 0.796 | 0.724 |
2.4 Classify borrowers and merge loan-level aggregates
btfp_clean <- btfp_raw %>% filter(failed_bank == 0) %>%
mutate(sub_period = assign_period(btfp_loan_date))
dw_clean <- dw_raw %>% filter(failed_bank == 0) %>%
mutate(sub_period = assign_period(dw_loan_date))
btfp_crisis <- btfp_clean %>%
filter(btfp_loan_date >= CRISIS_START & btfp_loan_date <= CRISIS_END)
dw_crisis <- dw_clean %>%
filter(dw_loan_date >= CRISIS_START & dw_loan_date <= CRISIS_END)
# ── Aggregate BTFP loans and COLLATERAL by bank (crisis) ──
btfp_bank <- btfp_crisis %>%
group_by(rssd_id) %>%
summarise(
btfp_amount = sum(btfp_loan_amount, na.rm = TRUE) / 1000, # $000
btfp_n_loans = n(),
btfp_mean_term = mean(btfp_term, na.rm = TRUE),
btfp_mean_effmat = mean(btfp_effective_maturity_days, na.rm = TRUE),
btfp_mean_rate = mean(btfp_interest_rate, na.rm = TRUE),
btfp_total_collateral = sum(btfp_total_collateral, na.rm = TRUE) / 1000,
.groups = "drop"
) %>% rename(idrssd = rssd_id)
# ── Aggregate DW loans and COLLATERAL by bank (crisis) ──
dw_bank <- dw_crisis %>%
group_by(rssd_id) %>%
summarise(
dw_amount = sum(dw_loan_amount, na.rm = TRUE) / 1000, # $000
dw_n_loans = n(),
dw_mean_term = mean(dw_term, na.rm = TRUE),
dw_mean_effmat = mean(dw_effective_maturity_days, na.rm = TRUE),
dw_mean_rate = mean(dw_interest_rate, na.rm = TRUE),
dw_total_collateral = sum(dw_total_collateral, na.rm = TRUE) / 1000,
dw_omo_collateral = sum(dw_omo_eligible, na.rm = TRUE) / 1000,
dw_nonomo_collateral = sum(dw_non_omo_eligible, na.rm = TRUE) / 1000,
.groups = "drop"
) %>% rename(idrssd = rssd_id)
df <- df %>%
left_join(btfp_bank, by = "idrssd") %>%
left_join(dw_bank, by = "idrssd") %>%
mutate(
btfp_amount = replace_na(btfp_amount, 0),
dw_amount = replace_na(dw_amount, 0),
btfp_n_loans = replace_na(btfp_n_loans, 0L),
dw_n_loans = replace_na(dw_n_loans, 0L),
used_btfp = as.integer(btfp_amount > 0),
used_dw = as.integer(dw_amount > 0),
borrowed = as.integer(used_btfp == 1 | used_dw == 1),
borrower_type = dplyr::case_when(
used_btfp == 1 & used_dw == 1 ~ "Both",
used_btfp == 1 ~ "BTFP Only",
used_dw == 1 ~ "DW Only",
TRUE ~ "Non-Borrower"
),
total_borrow = btfp_amount + dw_amount,
borrow_ta = 100 * safe_div(total_borrow, total_asset),
borrow_du = safe_div(total_borrow, uninsured_deposit),
log_borrow = ifelse(total_borrow > 0, log(total_borrow), NA_real_),
gap_fill_ratio = safe_div(total_borrow, liq_gap),
# ── CAPACITY-UTILIZATION RATIOS (Prediction 3, key diagnostic) ──
btfp_loan_to_coll = safe_div(btfp_amount, btfp_total_collateral),
dw_loan_to_coll = safe_div(dw_amount, dw_total_collateral)
)
cat(sprintf("\nBorrower counts (crisis window %s to %s):\n",
CRISIS_START, CRISIS_END))##
## Borrower counts (crisis window 2023-03-08 to 2023-05-04):## Non-Borrowers: 3,836## DW Only : 341## BTFP Only : 412## Both : 107## Total sample : 4,6962.5 Create regression-ready variables
reg_vars <- c(
"f_ta", "fu_ta", "fi_ta", "emv_ta", "v_ta",
"ell", "ell_sec", "ell_omo", "ell_nonomo", "ell_loan",
"rho", "rho_0", "rho_C", "rho_S", "liq_gap_ta",
"eq_ta", "cash_ta", "sec_ta", "omo_ta", "loan_ta", "dep_ta",
"du_ta", "mu", "wholesale_ta",
"borrow_ta", "borrow_du", "gap_fill_ratio",
"btfp_loan_to_coll", "dw_loan_to_coll"
)
reg_vars <- reg_vars[reg_vars %in% names(df)]
df <- df %>%
mutate(across(all_of(reg_vars), ~ winsorize(.x), .names = "{.col}_w")) %>%
mutate(across(all_of(paste0(reg_vars, "_w")), ~ z_std(.x), .names = "{.col}_z"))
cat(sprintf("Regression transforms created: %s winsorized + %s standardized vars\n",
fmt(length(reg_vars)), fmt(length(reg_vars))))## Regression transforms created: 29 winsorized + 29 standardized vars2.6 Arbitrage-window sample (Prediction 5)
btfp_arb <- btfp_clean %>%
filter(btfp_loan_date >= ARB_START & btfp_loan_date <= ARB_END)
btfp_arb_bank <- btfp_arb %>%
group_by(rssd_id) %>%
summarise(btfp_arb_amount = sum(btfp_loan_amount, na.rm = TRUE) / 1000,
.groups = "drop") %>%
rename(idrssd = rssd_id)
# FIX: pull beta_insured_w + deposit_cost_insured; apply Option A franchise
df_arb <- call_raw %>%
filter(period == "2023Q3", gsib == 0, failed_bank == 0) %>%
left_join(dssw_raw %>% filter(estimation_date == "2022Q4") %>%
select(idrssd, beta_overall,
beta_uninsured_w, beta_insured_w),
by = "idrssd") %>%
left_join(if (HAS_DEPOSIT_COSTS) dssw_costs_2022q4 else
tibble(idrssd = character(),
deposit_cost_insured = numeric(),
deposit_cost_uninsured = numeric(),
deposit_cost_weighted = numeric()),
by = "idrssd") %>%
mutate(
idrssd = as.character(idrssd),
# Clip betas
beta_clipped = pmax(0, pmin(1, beta_overall)),
beta_u_clipped = pmax(0, pmin(1, beta_uninsured_w)),
beta_i_clipped = pmax(0, pmin(1, beta_insured_w)),
# Costs
cost_u_raw = ifelse(HAS_DEPOSIT_COSTS & !is.na(deposit_cost_uninsured),
deposit_cost_uninsured, 0),
cost_i_raw = ifelse(HAS_DEPOSIT_COSTS & !is.na(deposit_cost_insured),
deposit_cost_insured, 0),
mu = safe_div(uninsured_deposit, total_asset, 0),
ell = all_asset_loss_pct,
ell_sec = loss_total_sec_to_ta,
ell_omo = loss_omo_sec_to_ta,
ell_loan = loss_total_loan_to_ta,
# Deposit shares
d_u_over_ta = safe_div(uninsured_deposit, total_asset, 0),
d_i_over_ta = safe_div(pmax(total_deposit - uninsured_deposit, 0),
total_asset, 0),
d_over_ta = safe_div(total_deposit, total_asset, 0),
uninsured_share_d = safe_div(uninsured_deposit, total_deposit, 0),
insured_share_d = pmax(1 - uninsured_share_d, 0),
# Option A franchise
rent_u = pmax((1 - beta_u_clipped) * y_10yr - cost_u_raw, 0),
rent_i = pmax((1 - beta_i_clipped) * y_10yr - cost_i_raw, 0),
fu_ta = ifelse(!is.na(beta_u_clipped),
rent_u * cap_factor * d_u_over_ta * 100, NA_real_),
fi_ta = ifelse(!is.na(beta_i_clipped),
rent_i * cap_factor * d_i_over_ta * 100, NA_real_),
f_ta = rowSums(cbind(fu_ta, fi_ta), na.rm = FALSE),
F_total = f_ta / 100 * total_asset,
F_uninsured = fu_ta / 100 * total_asset,
F_insured = fi_ta / 100 * total_asset,
E_MV = total_equity - all_asset_loss,
# Post-uninsured-run fundamental value (uninsured lose full F^U, insured keep F^I)
v = E_MV + F_insured, # not E_MV + (1-mu)*F_total
v_ta = 100 * safe_div(v, total_asset),
omo_mv = pmax(omo_eligible - loss_omo_sec, 0),
rho = safe_div(cash + omo_mv, uninsured_deposit),
eq_ta = book_equity_to_total_asset,
cash_ta = cash_to_total_asset,
log_ta = log(total_asset),
wholesale_ta = fed_fund_purchase_to_total_asset + repo_to_total_asset +
fhlb_to_total_asset + other_borr_to_total_asset,
ell_x_mu = ell * mu
) %>%
left_join(btfp_arb_bank, by = "idrssd") %>%
mutate(
btfp_arb_amount = replace_na(btfp_arb_amount, 0),
borrowed_arb = as.integer(btfp_arb_amount > 0)
)
cat(sprintf("Arbitrage-window sample: %s banks, %s borrowers\n",
fmt(nrow(df_arb)), fmt(sum(df_arb$borrowed_arb))))## Arbitrage-window sample: 4,604 banks, 766 borrowers3. Descriptive Tables
Table 3: Emergency Borrowing During Crisis (Mar 1 – May 4, 2023)
# ══════════════════════════════════════════════════════════════════════
# TABLE 1: EMERGENCY BORROWING DURING CRISIS (Mar 1 – May 4, 2023)
# Columns: P0|DW, P1|DW, P2|DW, P2|BTFP, P3|DW, P3|BTFP
# ══════════════════════════════════════════════════════════════════════
period_order <- c("P0: Pre-Crisis", "P1: SVB Week",
"P2: SVB to FRC", "P3: FRC Week")
# ── A. Loan-level tables with derived fields ─────────────────────────
dw_tab <- dw_clean %>%
filter(dw_loan_date >= P0_start, dw_loan_date <= P3_end) %>%
mutate(
period = assign_period(dw_loan_date),
amount = dw_loan_amount,
collateral = dw_total_collateral,
term = dw_term,
held_days = dw_effective_maturity_days, # = repayment - loan
rate = dw_interest_rate,
loan_to_coll = safe_div(dw_loan_amount, dw_total_collateral),
term_below_5 = as.integer(dw_term < 5),
term_atleast5 = as.integer(dw_term >= 5),
early_repay = ifelse(is.na(dw_repayment_date) | is.na(dw_maturity_date),
NA_integer_,
as.integer(dw_repayment_date < dw_maturity_date)),
facility = "DW"
)
btfp_tab <- btfp_clean %>%
filter(btfp_loan_date >= P2_start, btfp_loan_date <= P3_end) %>% # BTFP starts P2
mutate(
period = assign_period(btfp_loan_date),
amount = btfp_loan_amount,
collateral = btfp_total_collateral,
term = btfp_term,
held_days = btfp_effective_maturity_days,
rate = btfp_interest_rate,
loan_to_coll = safe_div(btfp_loan_amount, btfp_total_collateral),
term_below_5 = as.integer(btfp_term < 5),
term_atleast5 = as.integer(btfp_term >= 5),
early_repay = ifelse(is.na(btfp_repayment_date) | is.na(btfp_maturity_date),
NA_integer_,
as.integer(btfp_repayment_date < btfp_maturity_date)),
facility = "BTFP"
)
# ── B. Prior-borrower set per period (across BOTH facilities) ────────
all_borrow <- bind_rows(
dw_tab %>% select(rssd_id, period),
btfp_tab %>% select(rssd_id, period)
)
prior_set <- function(p) {
i <- match(p, period_order)
if (i == 1) return(character(0))
unique(all_borrow$rssd_id[all_borrow$period %in% period_order[seq_len(i - 1)]])
}
# ── C. Per-cell summariser ───────────────────────────────────────────
summarise_cell <- function(data, period_label, facility_label) {
x <- data %>% filter(period == period_label, facility == facility_label)
prior <- prior_set(period_label)
banks <- unique(x$rssd_id)
tibble(
col_id = paste(period_label, facility_label, sep = " | "),
`N (Loans)` = nrow(x),
`N (Banks)` = length(banks),
` New banks` = sum(!banks %in% prior),
` Returning banks` = sum(banks %in% prior),
`Total borrow ($B)` = sum(x$amount, na.rm = TRUE) / 1e9,
`Mean borrow ($M)` = mean(x$amount, na.rm = TRUE) / 1e6,
`Median borrow ($M)` = median(x$amount, na.rm = TRUE) / 1e6,
`Loan/Coll (aggregate)`= safe_div(sum(x$amount, na.rm = TRUE),
sum(x$collateral, na.rm = TRUE)),
`Term — mean (days)` = mean(x$term, na.rm = TRUE),
`Term — median (days)` = median(x$term, na.rm = TRUE),
`% Term < 5 days` = 100 * mean(x$term_below_5, na.rm = TRUE),
`% Term ≥ 5 days` = 100 * mean(x$term_atleast5, na.rm = TRUE),
`% Early repayment` = 100 * mean(x$early_repay, na.rm = TRUE),
`Held days — mean` = mean(x$held_days, na.rm = TRUE),
`Held days — median` = median(x$held_days, na.rm = TRUE),
`Rate (%)` = mean(x$rate, na.rm = TRUE)
)
}
# ── D. Build all six cells ───────────────────────────────────────────
cells <- bind_rows(
summarise_cell(dw_tab, "P0: Pre-Crisis", "DW"),
summarise_cell(dw_tab, "P1: SVB Week", "DW"),
summarise_cell(dw_tab, "P2: SVB to FRC", "DW"),
summarise_cell(btfp_tab, "P2: SVB to FRC", "BTFP"),
summarise_cell(dw_tab, "P3: FRC Week", "DW"),
summarise_cell(btfp_tab, "P3: FRC Week", "BTFP")
)
# ── E. Pivot to final layout (rows = stats, cols = period|facility) ──
col_order <- c("P0: Pre-Crisis | DW",
"P1: SVB Week | DW",
"P2: SVB to FRC | DW", "P2: SVB to FRC | BTFP",
"P3: FRC Week | DW", "P3: FRC Week | BTFP")
stat_levels <- setdiff(names(cells), "col_id")
table1 <- cells %>%
pivot_longer(-col_id, names_to = "Statistic", values_to = "value") %>%
mutate(Statistic = factor(Statistic, levels = stat_levels),
col_id = factor(col_id, levels = col_order)) %>%
pivot_wider(names_from = col_id, values_from = value) %>%
arrange(Statistic) %>%
select(Statistic, all_of(col_order)) # force column order
# Quick sanity print so you can SEE the data regardless of HTML issues
cat("Table 1 shape:", nrow(table1), "rows x", ncol(table1), "cols\n")## Table 1 shape: 16 rows x 7 cols## Statistic P0: Pre-Crisis | DW P1: SVB Week | DW
## N (Loans) 171.000 124.000
## N (Banks) 72.000 68.000
## New banks 72.000 33.000
## Returning banks 0.000 35.000
## Total borrow ($B) 9.455 10.102
## Mean borrow ($M) 55.294 81.471
## Median borrow ($M) 10.000 10.475
## Loan/Coll (aggregate) 0.172 0.176
## Term — mean (days) 5.251 3.839
## Term — median (days) 1.000 1.000
## % Term < 5 days 86.550 87.097
## % Term ≥ 5 days 13.450 12.903
## % Early repayment 6.433 5.645
## Held days — mean 4.076 3.016
## Held days — median 1.000 1.000
## Rate (%) 4.750 4.750
## P2: SVB to FRC | DW P2: SVB to FRC | BTFP P3: FRC Week | DW
## 1492.000 1032.000 213.000
## 406.000 472.000 101.000
## 340.000 442.000 34.000
## 66.000 30.000 67.000
## 518.485 122.358 9.613
## 347.510 118.564 45.130
## 10.000 15.000 8.000
## 0.329 0.406 0.146
## 4.405 313.568 3.831
## 1.000 365.000 1.000
## 88.003 10.659 90.610
## 11.997 89.341 9.390
## 4.826 64.922 2.817
## 3.005 151.043 2.784
## 1.000 14.500 1.000
## 4.920 4.678 5.050
## P3: FRC Week | BTFP
## 279.000
## 184.000
## 54.000
## 130.000
## 11.326
## 40.594
## 10.000
## 0.294
## 322.305
## 365.000
## 7.527
## 92.473
## 60.932
## 177.219
## 222.000
## 4.788# ── F. Render HTML (appears in Viewer pane when run interactively) ───
tbl_k <- table1 %>%
kbl(digits = 2, align = c("l", rep("r", 6)),
caption = "Table 1: Emergency Borrowing During Crisis (March 1 – May 4, 2023)") %>%
kable_styling(bootstrap_options = c("striped", "hover", "condensed"),
full_width = FALSE, position = "left") %>%
add_header_above(c(" " = 1, "Pre-Crisis" = 1, "SVB Week" = 1,
"SVB → FRC" = 2, "FRC Week" = 2)) %>%
pack_rows("Participation", 1, 4) %>%
pack_rows("Amounts", 5, 7) %>%
pack_rows("Collateral use", 8, 8) %>%
pack_rows("Maturity terms", 9, 13) %>%
pack_rows("Realized life", 14, 15) %>%
pack_rows("Price", 16, 16)
tbl_k # explicit print| Statistic | P0: Pre-Crisis | DW | P1: SVB Week | DW | P2: SVB to FRC | DW | P2: SVB to FRC | BTFP | P3: FRC Week | DW | P3: FRC Week | BTFP |
|---|---|---|---|---|---|---|
| Participation | ||||||
| N (Loans) | 171.00 | 124.00 | 1492.00 | 1032.00 | 213.00 | 279.00 |
| N (Banks) | 72.00 | 68.00 | 406.00 | 472.00 | 101.00 | 184.00 |
| New banks | 72.00 | 33.00 | 340.00 | 442.00 | 34.00 | 54.00 |
| Returning banks | 0.00 | 35.00 | 66.00 | 30.00 | 67.00 | 130.00 |
| Amounts | ||||||
| Total borrow (\(B) </td> <td style="text-align:right;"> 9.46 </td> <td style="text-align:right;"> 10.10 </td> <td style="text-align:right;"> 518.48 </td> <td style="text-align:right;"> 122.36 </td> <td style="text-align:right;"> 9.61 </td> <td style="text-align:right;"> 11.33 </td> </tr> <tr> <td style="text-align:left;padding-left: 2em;" indentlevel="1"> Mean borrow (\)M) | 55.29 | 81.47 | 347.51 | 118.56 | 45.13 | 40.59 |
| Median borrow ($M) | 10.00 | 10.47 | 10.00 | 15.00 | 8.00 | 10.00 |
| Collateral use | ||||||
| Loan/Coll (aggregate) | 0.17 | 0.18 | 0.33 | 0.41 | 0.15 | 0.29 |
| Maturity terms | ||||||
| Term — mean (days) | 5.25 | 3.84 | 4.41 | 313.57 | 3.83 | 322.30 |
| Term — median (days) | 1.00 | 1.00 | 1.00 | 365.00 | 1.00 | 365.00 |
| % Term < 5 days | 86.55 | 87.10 | 88.00 | 10.66 | 90.61 | 7.53 |
| % Term ≥ 5 days | 13.45 | 12.90 | 12.00 | 89.34 | 9.39 | 92.47 |
| % Early repayment | 6.43 | 5.65 | 4.83 | 64.92 | 2.82 | 60.93 |
| Realized life | ||||||
| Held days — mean | 4.08 | 3.02 | 3.01 | 151.04 | 2.78 | 177.22 |
| Held days — median | 1.00 | 1.00 | 1.00 | 14.50 | 1.00 | 222.00 |
| Price | ||||||
| Rate (%) | 4.75 | 4.75 | 4.92 | 4.68 | 5.05 | 4.79 |
Figure 1: Crisis Period Borrowing
# ══════════════════════════════════════════════════════════════════════
# FIGURE 1: DAILY EMERGENCY BORROWING DURING CRISIS (Mar 1 – May 4, 2023)
# Line version — two panels: volume ($B) and unique banks/day
# Sample: excludes failed banks (already in *_clean) and GSIBs
# ══════════════════════════════════════════════════════════════════════
# ── A. GSIB list from 2022Q4 call panel ──────────────────────────────
gsib_ids <- call_raw %>%
filter(period == "2022Q4", gsib == 1) %>%
pull(idrssd) %>% unique() %>% as.character()
cat("Excluding", length(gsib_ids), "GSIBs from loan data.\n")## Excluding 33 GSIBs from loan data.# ── B. Daily aggregation by facility ─────────────────────────────────
plot_start <- P0_start # 2023-03-01
plot_end <- P3_end # 2023-05-04
dw_daily <- dw_clean %>%
filter(!rssd_id %in% gsib_ids,
dw_loan_date >= plot_start, dw_loan_date <= plot_end) %>%
group_by(date = dw_loan_date) %>%
summarise(volume_b = sum(dw_loan_amount, na.rm = TRUE) / 1e9,
n_banks = n_distinct(rssd_id),
.groups = "drop") %>%
mutate(facility = "DW")
btfp_daily <- btfp_clean %>%
filter(!rssd_id %in% gsib_ids,
btfp_loan_date >= plot_start, btfp_loan_date <= plot_end) %>%
group_by(date = btfp_loan_date) %>%
summarise(volume_b = sum(btfp_loan_amount, na.rm = TRUE) / 1e9,
n_banks = n_distinct(rssd_id),
.groups = "drop") %>%
mutate(facility = "BTFP")
# Full grid: missing days → zero (so the line touches the x-axis on quiet days)
daily_df <- expand.grid(
date = seq(plot_start, plot_end, by = "1 day"),
facility = c("DW", "BTFP"),
stringsAsFactors = FALSE
) %>%
left_join(bind_rows(dw_daily, btfp_daily), by = c("date", "facility")) %>%
mutate(volume_b = replace_na(volume_b, 0),
n_banks = replace_na(n_banks, 0),
facility = factor(facility, levels = c("DW", "BTFP")))
# BTFP didn't exist pre Mar 13 → drop those rows so the BTFP line starts at launch
daily_df <- daily_df %>%
filter(!(facility == "BTFP" & date < BTFP_LAUNCH))
# ── C. Key events ────────────────────────────────────────────────────
events <- tribble(
~date, ~label,
as.Date("2023-03-10"), "SVB failed",
as.Date("2023-03-12"), "Signature failed",
as.Date("2023-03-13"), "BTFP launched",
as.Date("2023-05-01"), "First Republic failed"
)
fac_cols <- c("DW" = "#E53935", "BTFP" = "#1565C0")
# ── D. Panel A: Daily volume ─────────────────────────────────────────
y_max_A <- max(daily_df$volume_b, na.rm = TRUE)
pA <- ggplot(daily_df, aes(x = date, y = volume_b,
color = facility, group = facility)) +
geom_line(linewidth = 0.9) +
geom_point(size = 1.3, alpha = 0.85) +
geom_vline(data = events, aes(xintercept = date),
linetype = "dashed", color = "grey30", linewidth = 0.35) +
geom_text(data = events,
aes(x = date, y = y_max_A * 1.03, label = label),
angle = 90, hjust = 0, vjust = -0.2, size = 2.9,
color = "grey20", inherit.aes = FALSE) +
scale_color_manual(values = fac_cols, name = NULL) +
scale_x_date(date_breaks = "1 week", date_labels = "%b %d",
limits = c(plot_start, plot_end),
expand = expansion(mult = c(0.01, 0.01))) +
scale_y_continuous(expand = expansion(mult = c(0.02, 0.45))) +
labs(title = "A. Daily emergency-borrowing volume",
subtitle = sprintf(
"DW vs BTFP; excludes failed banks and GSIBs",
length(gsib_ids)),
x = NULL, y = "Daily volume ($B)") +
theme_gp
# ── E. Panel B: Number of unique banks per day ───────────────────────
pB <- ggplot(daily_df, aes(x = date, y = n_banks,
color = facility, group = facility)) +
geom_line(linewidth = 0.9) +
geom_point(size = 1.3, alpha = 0.85) +
geom_vline(data = events, aes(xintercept = date),
linetype = "dashed", color = "grey30", linewidth = 0.35) +
scale_color_manual(values = fac_cols, name = NULL) +
scale_x_date(date_breaks = "1 week", date_labels = "%b %d",
limits = c(plot_start, plot_end),
expand = expansion(mult = c(0.01, 0.01))) +
scale_y_continuous(expand = expansion(mult = c(0.02, 0.12))) +
labs(title = "B. Number of unique banks borrowing per day",
x = "Date", y = "Number of banks") +
theme_gp
# ── F. Combine, print, save PDF ─────────────────────────────────────
fig1_crisis <- (pA / pB) +
plot_layout(heights = c(1.25, 1), guides = "collect") &
theme(legend.position = "bottom")
print(fig1_crisis)
Table 4: Mean Characteristics of Borrowers vs Non-Borrowers (2022Q4)
# ══════════════════════════════════════════════════════════════════════
# TABLE 2: Mean Characteristics of Borrowers vs Non-Borrowers (2022Q4)
# Columns mirror Table 1: 6 period|facility cells + 1 Non-Borrower column
# Sample: 2022Q4 cross-section, excl. GSIBs and failed banks (already in df)
# ══════════════════════════════════════════════════════════════════════
# ── A. Assemble borrower sets per period|facility ────────────────────
dw_with_period <- dw_clean %>%
filter(dw_loan_date >= P0_start, dw_loan_date <= P3_end) %>%
mutate(period = assign_period(dw_loan_date))
btfp_with_period <- btfp_clean %>%
filter(btfp_loan_date >= P2_start, btfp_loan_date <= P3_end) %>%
mutate(period = assign_period(btfp_loan_date))
get_banks <- function(data, period_label)
unique(as.character(data$rssd_id[data$period == period_label]))
borrower_sets <- list(
"P0: Pre-Crisis | DW" = get_banks(dw_with_period, "P0: Pre-Crisis"),
"P1: SVB Week | DW" = get_banks(dw_with_period, "P1: SVB Week"),
"P2: SVB to FRC | DW" = get_banks(dw_with_period, "P2: SVB to FRC"),
"P2: SVB to FRC | BTFP" = get_banks(btfp_with_period, "P2: SVB to FRC"),
"P3: FRC Week | DW" = get_banks(dw_with_period, "P3: FRC Week"),
"P3: FRC Week | BTFP" = get_banks(btfp_with_period, "P3: FRC Week")
)
# Non-borrower = banks in df that never borrowed in ANY period (P0-P3)
all_period_borrowers <- unique(unlist(borrower_sets, use.names = FALSE))
non_borrower_ids <- setdiff(as.character(df$idrssd), all_period_borrowers)
# ── B. Prepare derived variables on df ───────────────────────────────
df <- df %>%
mutate(
total_asset_b = total_asset / 1e6, # thousands → $B
mu_pct = 100 * mu,
)
# ── C. Variables to show, with display labels (in desired row order) ─
tbl2_vars <- c(
"total_asset_b" = "Total assets ($B)",
"cash_ta" = "Cash / TA (%)",
"sec_ta" = "Securities / TA (%)",
"loan_ta" = "Loans / TA (%)",
"ell" = "MTM loss — total / TA (%)",
"ell_omo" = " OMO-eligible sec. loss / TA (%)",
"ell_nonomo" = " Non-OMO sec. loss / TA (%)",
"ell_loan" = " Loan MTM loss / TA (%)",
"eq_ta" = "Book equity / TA (%)",
"dep_ta" = "Total deposits / TA (%)",
"mu_pct" = "Uninsured / Deposits (%)",
"du_ta" = "Uninsured leverage (%)",
"loan_to_deposit" = "Loan / Total deposits",
"wholesale_ta" = "Wholesale funding / TA (%)",
"fhlb_ta" = "FHLB advances / TA (%)",
"roa" = "ROA (%)"
)
# Drop any variables that aren't in df (keeps code robust if roa is missing)
tbl2_vars <- tbl2_vars[names(tbl2_vars) %in% names(df)]
# ── D. Per-group summariser ──────────────────────────────────────────
summarise_group <- function(ids, group_label) {
sub <- df %>% filter(idrssd %in% ids)
out <- tibble(group = group_label, `N (banks)` = nrow(sub))
for (v in names(tbl2_vars)) {
out[[ tbl2_vars[[v]] ]] <- mean(sub[[v]], na.rm = TRUE)
}
out
}
# ── E. Build all seven group rows ────────────────────────────────────
groups <- bind_rows(
summarise_group(borrower_sets[["P0: Pre-Crisis | DW"]], "P0: Pre-Crisis | DW"),
summarise_group(borrower_sets[["P1: SVB Week | DW"]], "P1: SVB Week | DW"),
summarise_group(borrower_sets[["P2: SVB to FRC | DW"]], "P2: SVB to FRC | DW"),
summarise_group(borrower_sets[["P2: SVB to FRC | BTFP"]], "P2: SVB to FRC | BTFP"),
summarise_group(borrower_sets[["P3: FRC Week | DW"]], "P3: FRC Week | DW"),
summarise_group(borrower_sets[["P3: FRC Week | BTFP"]], "P3: FRC Week | BTFP"),
summarise_group(non_borrower_ids, "Non-Borrower")
)
# ── F. Pivot to final layout (rows = stats, cols = groups) ───────────
col_order <- c(
"P0: Pre-Crisis | DW", "P1: SVB Week | DW",
"P2: SVB to FRC | DW", "P2: SVB to FRC | BTFP",
"P3: FRC Week | DW", "P3: FRC Week | BTFP",
"Non-Borrower"
)
stat_order <- c("N (banks)", unname(tbl2_vars))
table2 <- groups %>%
pivot_longer(-group, names_to = "Statistic", values_to = "value") %>%
mutate(
Statistic = factor(Statistic, levels = stat_order),
group = factor(group, levels = col_order)
) %>%
arrange(Statistic, group) %>%
pivot_wider(names_from = group, values_from = value) %>%
select(Statistic, all_of(col_order))
# ── G. Quick console view + kable render ─────────────────────────────
cat("Table 2 shape:", nrow(table2), "rows x", ncol(table2), "cols\n")## Table 2 shape: 17 rows x 8 cols## Bank counts per group:## # A tibble: 7 × 2
## group `N (banks)`
## <chr> <int>
## 1 P0: Pre-Crisis | DW 72
## 2 P1: SVB Week | DW 67
## 3 P2: SVB to FRC | DW 397
## 4 P2: SVB to FRC | BTFP 460
## 5 P3: FRC Week | DW 101
## 6 P3: FRC Week | BTFP 182
## 7 Non-Borrower 3815tbl2_k <- table2 %>%
kbl(digits = 2, align = c("l", rep("r", 7)),
caption = "Table 2: Mean Characteristics of Borrowers vs Non-Borrowers (2022Q4 baseline)") %>%
kable_styling(bootstrap_options = c("striped", "hover", "condensed"),
full_width = FALSE, position = "left", font_size = 12) %>%
add_header_above(c(" " = 1,
"Pre-Crisis" = 1, "SVB Week" = 1,
"SVB → FRC" = 2, "FRC Week" = 2,
"Never Borrowed" = 1)) %>%
pack_rows("Sample size", 1, 1) %>%
pack_rows("Size & composition", 2, 5) %>%
pack_rows("MTM losses", 6, 9) %>%
pack_rows("Capital & funding", 10, 14) %>%
pack_rows("Profitability", 15, nrow(table2))
tbl2_k| Statistic | P0: Pre-Crisis | DW | P1: SVB Week | DW | P2: SVB to FRC | DW | P2: SVB to FRC | BTFP | P3: FRC Week | DW | P3: FRC Week | BTFP | Non-Borrower |
|---|---|---|---|---|---|---|---|
| Sample size | |||||||
| N (banks) | 72.00 | 67.00 | 397.00 | 460.00 | 101.00 | 182.00 | 3815.00 |
| Size & composition | |||||||
| Total assets ($B) | 4.40 | 7.59 | 6.51 | 6.35 | 2.76 | 5.12 | 1.67 |
| Cash / TA (%) | 4.38 | 3.77 | 6.08 | 4.68 | 5.34 | 4.19 | 9.58 |
| Securities / TA (%) | 26.66 | 24.97 | 24.46 | 28.03 | 25.02 | 29.81 | 24.18 |
| Loans / TA (%) | 63.64 | 65.33 | 63.53 | 61.61 | 64.15 | 60.35 | 59.76 |
| MTM losses | |||||||
| MTM loss — total / TA (%) | 9.33 | 8.92 | 9.03 | 9.61 | 8.78 | 9.90 | 8.39 |
| OMO-eligible sec. loss / TA (%) | 1.39 | 1.68 | 1.65 | 1.78 | 1.51 | 1.76 | 1.05 |
| Non-OMO sec. loss / TA (%) | 2.92 | 2.48 | 2.45 | 2.95 | 2.58 | 3.15 | 2.50 |
| Loan MTM loss / TA (%) | 5.39 | 5.20 | 5.40 | 5.28 | 5.04 | 5.31 | 5.00 |
| Capital & funding | |||||||
| Book equity / TA (%) | 9.05 | 8.41 | 8.89 | 8.16 | 8.99 | 8.10 | 11.38 |
| Total deposits / TA (%) | 84.42 | 83.97 | 85.05 | 85.47 | 84.84 | 86.07 | 84.22 |
| Uninsured / Deposits (%) | 31.99 | 35.55 | 33.51 | 32.10 | 30.75 | 31.13 | 26.46 |
| Uninsured leverage (%) | 26.87 | 29.52 | 28.45 | 27.42 | 25.96 | 26.89 | 22.41 |
| Loan / Total deposits | 76.00 | 78.28 | 75.73 | 72.96 | 76.20 | 70.95 | 70.98 |
| Profitability | |||||||
| Wholesale funding / TA (%) | 5.65 | 6.72 | 5.04 | 5.48 | 5.33 | 5.09 | 3.32 |
| FHLB advances / TA (%) | 3.53 | 4.56 | 3.61 | 4.04 | 3.72 | 3.58 | 2.51 |
| ROA (%) | 1.03 | 1.04 | 1.16 | 1.07 | 1.15 | 1.01 | 1.42 |
Table 5
# ══════════════════════════════════════════════════════════════════════
# TABLE 3: Solvency Measures, Size, and Borrowing Concentration
# Columns mirror Table 1: 6 period|facility + Non-Borrower
# Post-run value v = E_MV + F_insured (correct under Option A franchise)
# ══════════════════════════════════════════════════════════════════════
# ── A. Borrower identities AND borrowing amounts by period|facility ──
dw_pf <- dw_clean %>%
filter(dw_loan_date >= P0_start, dw_loan_date <= P3_end) %>%
mutate(period = assign_period(dw_loan_date))
btfp_pf <- btfp_clean %>%
filter(btfp_loan_date >= P2_start, btfp_loan_date <= P3_end) %>%
mutate(period = assign_period(btfp_loan_date))
# Per-bank amounts within each cell (needed for concentration stats)
amt_by_cell <- bind_rows(
dw_pf %>% group_by(period, rssd_id) %>%
summarise(amt = sum(dw_loan_amount, na.rm = TRUE), .groups = "drop") %>%
mutate(facility = "DW"),
btfp_pf %>% group_by(period, rssd_id) %>%
summarise(amt = sum(btfp_loan_amount, na.rm = TRUE), .groups = "drop") %>%
mutate(facility = "BTFP")
) %>% mutate(rssd_id = as.character(rssd_id))
get_banks <- function(p, f) amt_by_cell %>%
filter(period == p, facility == f) %>% pull(rssd_id) %>% unique()
borrower_sets <- list(
"P0: Pre-Crisis | DW" = get_banks("P0: Pre-Crisis", "DW"),
"P1: SVB Week | DW" = get_banks("P1: SVB Week", "DW"),
"P2: SVB to FRC | DW" = get_banks("P2: SVB to FRC", "DW"),
"P2: SVB to FRC | BTFP" = get_banks("P2: SVB to FRC", "BTFP"),
"P3: FRC Week | DW" = get_banks("P3: FRC Week", "DW"),
"P3: FRC Week | BTFP" = get_banks("P3: FRC Week", "BTFP")
)
# Never-borrowed = banks in df that didn't appear in any cell
non_borrower_ids <- setdiff(as.character(df$idrssd),
unique(unlist(borrower_sets, use.names = FALSE)))
# Prior-period borrower set for new/repeat split (same logic as Table 1)
period_order <- c("P0: Pre-Crisis", "P1: SVB Week",
"P2: SVB to FRC", "P3: FRC Week")
flat_borrowers <- amt_by_cell %>% select(rssd_id, period) %>% distinct()
prior_banks <- function(p) {
i <- match(p, period_order)
if (i == 1) return(character(0))
flat_borrowers %>% filter(period %in% period_order[seq_len(i - 1)]) %>%
pull(rssd_id) %>% unique()
}
# ── B. Derive solvency variables on df ───────────────────────────────
df <- df %>%
mutate(
emv_f_ta = 100 * safe_div(E_MV_F, total_asset),
v_postrun = E_MV_F_insured, # correct under Option A
v_postrun_ta = 100 * safe_div(v_postrun, total_asset),
emv_neg = as.integer(E_MV < 0),
emv_f_neg = as.integer(E_MV_F < 0),
v_postrun_neg = as.integer(v_postrun < 0),
ta_billion = total_asset / 1e6 # thousands → $B
)
ta_p90 <- quantile(df$total_asset, 0.9, na.rm = TRUE) # top-decile TA cut
# ── C. Per-group summariser ──────────────────────────────────────────
summarise_solvency <- function(ids, period_label = NA, facility_label = NA) {
sub <- df %>% filter(idrssd %in% ids)
prior <- if (is.na(period_label)) character(0) else prior_banks(period_label)
# New/repeat counts
n_new <- sum(!ids %in% prior)
n_repeat <- sum( ids %in% prior)
if (is.na(period_label)) { n_new <- NA_integer_; n_repeat <- NA_integer_ }
# Concentration metrics (only for period|facility cells, not non-borrowers)
if (!is.na(period_label) && !is.na(facility_label)) {
cell <- amt_by_cell %>%
filter(period == period_label, facility == facility_label) %>%
left_join(df %>% select(idrssd, total_asset, v_postrun_neg, emv_neg),
by = c("rssd_id" = "idrssd"))
total_amt <- sum(cell$amt, na.rm = TRUE)
shares <- cell$amt / total_amt
top10_share <- sum(sort(shares, decreasing = TRUE)[seq_len(min(10, length(shares)))])
hhi <- sum(shares^2)
sh_v_neg <- sum(cell$amt[cell$v_postrun_neg == 1], na.rm = TRUE) / total_amt
sh_emv_neg <- sum(cell$amt[cell$emv_neg == 1], na.rm = TRUE) / total_amt
sh_top_decile <- sum(cell$amt[cell$total_asset >= ta_p90], na.rm = TRUE) / total_amt
} else {
top10_share <- NA_real_; hhi <- NA_real_
sh_v_neg <- NA_real_; sh_emv_neg <- NA_real_; sh_top_decile <- NA_real_
}
tibble(
`N (banks)` = nrow(sub),
` of which new` = n_new,
` of which repeat` = n_repeat,
# Solvency — no franchise (asset-side book/market equity)
`E_MV / TA mean (%)` = mean(sub$emv_ta, na.rm = TRUE),
`E_MV / TA median (%)` = median(sub$emv_ta, na.rm = TRUE),
`% with E_MV < 0` = 100 * mean(sub$emv_neg, na.rm = TRUE),
# Solvency — with full franchise (no-run fundamental)
`E_MV_F / TA mean (%)` = mean(sub$emv_f_ta, na.rm = TRUE),
`E_MV_F / TA median (%)` = median(sub$emv_f_ta, na.rm = TRUE),
`% with E_MV_F < 0` = 100 * mean(sub$emv_f_neg, na.rm = TRUE),
# Post uninsured-run: v = E_MV + F_insured
`v / TA mean (%)` = mean(sub$v_postrun_ta, na.rm = TRUE),
`v / TA median (%)` = median(sub$v_postrun_ta, na.rm = TRUE),
`% with v < 0 (post-run)` = 100 * mean(sub$v_postrun_neg, na.rm = TRUE),
# Size
`Total assets mean ($B)` = mean(sub$ta_billion, na.rm = TRUE),
`Total assets median ($B)` = median(sub$ta_billion, na.rm = TRUE),
`log(TA) mean` = mean(sub$log_ta, na.rm = TRUE),
# Concentration of borrowing
`Top-10 banks' share of borrow (%)`= 100 * top10_share,
`HHI of borrow shares` = hhi,
`% of borrow by v<0 (post-run) banks` = 100 * sh_v_neg,
`% of borrow by E_MV<0 banks` = 100 * sh_emv_neg,
`% of borrow by top-decile TA` = 100 * sh_top_decile
)
}
# ── D. Build and assemble all group rows ─────────────────────────────
group_spec <- tibble(
col_id = c("P0: Pre-Crisis | DW", "P1: SVB Week | DW",
"P2: SVB to FRC | DW", "P2: SVB to FRC | BTFP",
"P3: FRC Week | DW", "P3: FRC Week | BTFP"),
period = c("P0: Pre-Crisis", "P1: SVB Week",
"P2: SVB to FRC", "P2: SVB to FRC",
"P3: FRC Week", "P3: FRC Week"),
facility = c("DW", "DW", "DW", "BTFP", "DW", "BTFP")
)
rows_list <- lapply(seq_len(nrow(group_spec)), function(i) {
r <- summarise_solvency(borrower_sets[[group_spec$col_id[i]]],
period_label = group_spec$period[i],
facility_label = group_spec$facility[i])
r$col_id <- group_spec$col_id[i]; r
})
nb_row <- summarise_solvency(non_borrower_ids)
nb_row$col_id <- "Non-Borrower"
cells <- bind_rows(rows_list) %>% bind_rows(nb_row)
# ── E. Pivot to final layout ─────────────────────────────────────────
col_order <- c(group_spec$col_id, "Non-Borrower")
stat_order <- setdiff(names(cells), "col_id")
table3 <- cells %>%
pivot_longer(-col_id, names_to = "Statistic", values_to = "value") %>%
mutate(Statistic = factor(Statistic, levels = stat_order),
col_id = factor(col_id, levels = col_order)) %>%
arrange(Statistic, col_id) %>%
pivot_wider(names_from = col_id, values_from = value) %>%
select(Statistic, all_of(col_order))
cat("Table 3 shape:", nrow(table3), "rows x", ncol(table3), "cols\n")## Table 3 shape: 20 rows x 8 cols## Statistic P0: Pre-Crisis | DW P1: SVB Week | DW
## N (banks) 72.0000 67.0000
## of which new 72.0000 33.0000
## of which repeat 0.0000 35.0000
## E_MV / TA mean (%) -0.2741 -0.5191
## E_MV / TA median (%) -0.8408 -1.1788
## % with E_MV < 0 59.7222 58.2090
## E_MV_F / TA mean (%) 12.1415 11.4190
## E_MV_F / TA median (%) 11.6592 11.4464
## % with E_MV_F < 0 0.0000 0.0000
## v / TA mean (%) 9.2846 8.5093
## v / TA median (%) 8.5761 8.4155
## % with v < 0 (post-run) 1.3889 1.4925
## Total assets mean ($B) 4.4025 7.5907
## Total assets median ($B) 0.9680 1.3270
## log(TA) mean 14.0283 14.4322
## Top-10 banks' share of borrow (%) 83.7907 84.2176
## HHI of borrow shares 0.1020 0.0963
## % of borrow by v<0 (post-run) banks 0.0542 0.0517
## % of borrow by E_MV<0 banks 48.8703 38.2778
## % of borrow by top-decile TA 78.3040 88.9797
## P2: SVB to FRC | DW P2: SVB to FRC | BTFP P3: FRC Week | DW
## 397.000 460.000 101.0000
## 340.000 442.000 34.0000
## 66.000 30.000 67.0000
## -0.133 -1.446 0.2153
## -0.229 -1.080 0.0369
## 51.889 58.913 48.5149
## 12.516 11.432 12.8744
## 12.485 11.576 12.8153
## 1.015 0.659 1.0000
## 9.430 8.425 10.1197
## 9.435 8.635 9.5864
## 3.807 4.396 2.0000
## 6.514 6.350 2.7638
## 0.948 0.673 0.8237
## 14.012 13.729 13.7549
## 94.312 64.957 82.2555
## 0.338 0.120 0.1353
## 0.947 3.698 0.2234
## 63.935 29.687 46.4463
## 97.828 87.133 82.0336
## P3: FRC Week | BTFP Non-Borrower
## 182.0000 3815.000
## 54.0000 NA
## 130.0000 NA
## -1.8072 2.790
## -1.3880 1.525
## 59.8901 40.269
## 11.4197 15.194
## 11.6306 14.614
## 0.5495 0.510
## 8.3489 12.656
## 8.7105 11.992
## 5.4945 1.422
## 5.1194 1.668
## 0.6529 0.263
## 13.5647 12.597
## 57.2853 NA
## 0.0394 NA
## 5.9766 NA
## 65.1593 NA
## 72.0261 NA# ── F. Render ────────────────────────────────────────────────────────
tbl3_k <- table3 %>%
kbl(digits = 2, align = c("l", rep("r", 7)),
caption = "Table 3: Solvency Measures, Size, and Borrowing Concentration (2022Q4 baseline)") %>%
kable_styling(bootstrap_options = c("striped", "hover", "condensed"),
full_width = FALSE, position = "left", font_size = 11) %>%
add_header_above(c(" " = 1,
"Pre-Crisis" = 1, "SVB Week" = 1,
"SVB → FRC" = 2, "FRC Week" = 2,
"Never" = 1)) %>%
pack_rows("Participation", 1, 3) %>%
pack_rows("Solvency: no franchise", 4, 6) %>%
pack_rows("Solvency: with franchise", 7, 9) %>%
pack_rows("Solvency: post uninsured run", 10, 12) %>%
pack_rows("Size distribution", 13, 15) %>%
pack_rows("Concentration of borrowing", 16, 20)
tbl3_k| Statistic | P0: Pre-Crisis | DW | P1: SVB Week | DW | P2: SVB to FRC | DW | P2: SVB to FRC | BTFP | P3: FRC Week | DW | P3: FRC Week | BTFP | Non-Borrower |
|---|---|---|---|---|---|---|---|
| Participation | |||||||
| N (banks) | 72.00 | 67.00 | 397.00 | 460.00 | 101.00 | 182.00 | 3815.00 |
| of which new | 72.00 | 33.00 | 340.00 | 442.00 | 34.00 | 54.00 | NA |
| of which repeat | 0.00 | 35.00 | 66.00 | 30.00 | 67.00 | 130.00 | NA |
| Solvency: no franchise | |||||||
| E_MV / TA mean (%) | -0.27 | -0.52 | -0.13 | -1.45 | 0.22 | -1.81 | 2.79 |
| E_MV / TA median (%) | -0.84 | -1.18 | -0.23 | -1.08 | 0.04 | -1.39 | 1.52 |
| % with E_MV < 0 | 59.72 | 58.21 | 51.89 | 58.91 | 48.51 | 59.89 | 40.27 |
| Solvency: with franchise | |||||||
| E_MV_F / TA mean (%) | 12.14 | 11.42 | 12.52 | 11.43 | 12.87 | 11.42 | 15.19 |
| E_MV_F / TA median (%) | 11.66 | 11.45 | 12.49 | 11.58 | 12.82 | 11.63 | 14.61 |
| % with E_MV_F < 0 | 0.00 | 0.00 | 1.02 | 0.66 | 1.00 | 0.55 | 0.51 |
| Solvency: post uninsured run | |||||||
| v / TA mean (%) | 9.28 | 8.51 | 9.43 | 8.43 | 10.12 | 8.35 | 12.66 |
| v / TA median (%) | 8.58 | 8.42 | 9.43 | 8.63 | 9.59 | 8.71 | 11.99 |
| % with v < 0 (post-run) | 1.39 | 1.49 | 3.81 | 4.40 | 2.00 | 5.49 | 1.42 |
| Size distribution | |||||||
| Total assets mean (\(B) </td> <td style="text-align:right;"> 4.40 </td> <td style="text-align:right;"> 7.59 </td> <td style="text-align:right;"> 6.51 </td> <td style="text-align:right;"> 6.35 </td> <td style="text-align:right;"> 2.76 </td> <td style="text-align:right;"> 5.12 </td> <td style="text-align:right;"> 1.67 </td> </tr> <tr> <td style="text-align:left;padding-left: 2em;" indentlevel="1"> Total assets median (\)B) | 0.97 | 1.33 | 0.95 | 0.67 | 0.82 | 0.65 | 0.26 |
| log(TA) mean | 14.03 | 14.43 | 14.01 | 13.73 | 13.75 | 13.56 | 12.60 |
| Concentration of borrowing | |||||||
| Top-10 banks’ share of borrow (%) | 83.79 | 84.22 | 94.31 | 64.96 | 82.26 | 57.29 | NA |
| HHI of borrow shares | 0.10 | 0.10 | 0.34 | 0.12 | 0.14 | 0.04 | NA |
| % of borrow by v<0 (post-run) banks | 0.05 | 0.05 | 0.95 | 3.70 | 0.22 | 5.98 | NA |
| % of borrow by E_MV<0 banks | 48.87 | 38.28 | 63.94 | 29.69 | 46.45 | 65.16 | NA |
| % of borrow by top-decile TA | 78.30 | 88.98 | 97.83 | 87.13 | 82.03 | 72.03 | NA |
Table 6
# ══════════════════════════════════════════════════════════════════════
# TABLE 3C: New vs Returning Borrowers — By Period | Facility
# Uses Table 1's definition (matches Table 1 counts exactly):
# New = did NOT borrow (DW or BTFP) in any prior period
# Returning = borrowed (DW or BTFP) in at least one prior period
# Sample: 2022Q4 cross-section (excl. GSIBs and failed banks)
# ══════════════════════════════════════════════════════════════════════
# ── A. Period-assigned loan tables (self-contained) ──────────────────
dw_pf <- dw_clean %>%
filter(dw_loan_date >= P0_start, dw_loan_date <= P3_end) %>%
mutate(period = assign_period(dw_loan_date),
rssd_id = as.character(rssd_id))
btfp_pf <- btfp_clean %>%
filter(btfp_loan_date >= P2_start, btfp_loan_date <= P3_end) %>%
mutate(period = assign_period(btfp_loan_date),
rssd_id = as.character(rssd_id))
# ── B. Prior-borrower set per period (same logic as Table 1) ─────────
period_order <- c("P0: Pre-Crisis", "P1: SVB Week",
"P2: SVB to FRC", "P3: FRC Week")
all_borrow <- bind_rows(
dw_pf %>% select(rssd_id, period),
btfp_pf %>% select(rssd_id, period)
)
prior_set <- function(p) {
i <- match(p, period_order)
if (i == 1) return(character(0))
unique(all_borrow$rssd_id[all_borrow$period %in% period_order[seq_len(i - 1)]])
}
# ── C. Classify borrowers as New/Returning WITHIN each cell ──────────
# (matches Table 1's new_banks / returning_banks counts exactly)
classify_cell <- function(period_label, facility_label) {
data <- if (facility_label == "DW") dw_pf else btfp_pf
banks <- unique(data$rssd_id[data$period == period_label])
prior <- prior_set(period_label)
tibble(
rssd_id = banks,
period = period_label,
facility = facility_label,
type = if_else(banks %in% prior, "Returning", "New")
)
}
col_specs <- tibble(
col_id = c("P0: Pre-Crisis | DW", "P1: SVB Week | DW",
"P2: SVB to FRC | DW", "P2: SVB to FRC | BTFP",
"P3: FRC Week | DW", "P3: FRC Week | BTFP"),
period = c("P0: Pre-Crisis", "P1: SVB Week",
"P2: SVB to FRC", "P2: SVB to FRC",
"P3: FRC Week", "P3: FRC Week"),
facility = c("DW", "DW", "DW", "BTFP", "DW", "BTFP")
)
cell_classification <- bind_rows(
lapply(seq_len(nrow(col_specs)), function(i)
classify_cell(col_specs$period[i], col_specs$facility[i]))
)
get_ids_3c <- function(p, f, t) {
cell_classification %>%
filter(period == p, facility == f, type == t) %>%
pull(rssd_id)
}
# ── D. Ensure derived variables exist on df (safe if already present) ─
df <- df %>%
mutate(
ta_billion = total_asset / 1e6, # thousands → $B
mu_pct = 100 * mu,
fhlb_ta = fhlb_to_total_asset,
v_postrun = E_MV_F_insured, # correct under Option A
v_postrun_ta = 100 * safe_div(v_postrun, total_asset),
emv_neg = as.integer(E_MV < 0),
v_postrun_neg = as.integer(v_postrun < 0),
roa = if ("roa" %in% names(.)) roa
else if ("net_income_to_total_asset" %in% names(.)) net_income_to_total_asset
else NA_real_
)
# ── E. Per-cell summariser ───────────────────────────────────────────
summarise_cell_3c <- function(ids, col_id) {
sub <- df %>% filter(idrssd %in% ids)
tibble(
col_id = col_id,
`N (banks)` = nrow(sub),
`Total assets ($B)` = mean(sub$ta_billion, na.rm = TRUE),
`Cash / TA (%)` = mean(sub$cash_ta, na.rm = TRUE),
`Securities / TA (%)` = mean(sub$sec_ta, na.rm = TRUE),
`Loans / TA (%)` = mean(sub$loan_ta, na.rm = TRUE),
`Book equity / TA (%)` = mean(sub$eq_ta, na.rm = TRUE),
`Uninsured / Deposits (%)` = mean(sub$mu_pct, na.rm = TRUE),
`Uninsured leverage (%)` = mean(sub$du_ta, na.rm = TRUE),
`Wholesale funding / TA (%)` = mean(sub$wholesale_ta, na.rm = TRUE),
`FHLB / TA (%)` = mean(sub$fhlb_ta, na.rm = TRUE),
`ROA (%)` = mean(sub$roa, na.rm = TRUE),
`MTM loss / TA (%)` = mean(sub$ell, na.rm = TRUE),
`E_MV / TA (%)` = mean(sub$emv_ta, na.rm = TRUE),
`v / TA (post-run, %)` = mean(sub$v_postrun_ta, na.rm = TRUE),
`% with E_MV < 0` = 100 * mean(sub$emv_neg, na.rm = TRUE),
`% with v < 0 (post-run)` = 100 * mean(sub$v_postrun_neg, na.rm = TRUE)
)
}
# ── F. Build both panels ─────────────────────────────────────────────
build_panel_3c <- function(type_label) {
rows <- lapply(seq_len(nrow(col_specs)), function(i) {
ids <- get_ids_3c(col_specs$period[i], col_specs$facility[i], type_label)
summarise_cell_3c(ids, col_specs$col_id[i])
})
bind_rows(rows)
}
new_cells <- build_panel_3c("New")
returning_cells <- build_panel_3c("Returning")
# ── G. Pivot each panel ──────────────────────────────────────────────
stat_order <- setdiff(names(new_cells), "col_id")
col_order <- col_specs$col_id
pivot_panel_3c <- function(cells) {
cells %>%
pivot_longer(-col_id, names_to = "Statistic", values_to = "value") %>%
mutate(Statistic = factor(Statistic, levels = stat_order),
col_id = factor(col_id, levels = col_order)) %>%
arrange(Statistic, col_id) %>%
pivot_wider(names_from = col_id, values_from = value) %>%
select(Statistic, all_of(col_order))
}
new_panel <- pivot_panel_3c(new_cells)
returning_panel <- pivot_panel_3c(returning_cells)
# ── H. Stack vertically ──────────────────────────────────────────────
table3c <- bind_rows(new_panel, returning_panel)
# ── I. Diagnostics — verify match with Table 1 ───────────────────────
cat("Table 3C shape:", nrow(table3c), "rows x", ncol(table3c), "cols\n\n")## Table 3C shape: 32 rows x 7 cols## Bank counts by cell and type (should match Table 1's New/Returning rows):cell_counts <- cell_classification %>%
count(period, facility, type) %>%
pivot_wider(names_from = type, values_from = n, values_fill = 0L) %>%
mutate(Total = New + Returning,
col_id = paste(period, facility, sep = " | ")) %>%
select(col_id, New, Returning, Total)
print(as.data.frame(cell_counts), row.names = FALSE)## col_id New Returning Total
## P0: Pre-Crisis | DW 72 0 72
## P1: SVB Week | DW 33 35 68
## P2: SVB to FRC | BTFP 442 30 472
## P2: SVB to FRC | DW 340 66 406
## P3: FRC Week | BTFP 54 130 184
## P3: FRC Week | DW 34 67 101##
## Row-by-row comparison with Table 1 (if `table1` object is in memory):if (exists("table1")) {
t1_counts <- table1 %>%
filter(Statistic %in% c("N (Banks)", " New banks", " Returning banks")) %>%
as.data.frame()
print(t1_counts, row.names = FALSE)
cat("→ Table 3C 'New' column totals above should equal Table 1's",
"'New banks' row.\n")
cat("→ Table 3C 'Returning' column totals above should equal Table 1's",
"'Returning banks' row.\n")
} else {
cat("(Run Table 1 first to auto-verify.)\n")
}## Statistic P0: Pre-Crisis | DW P1: SVB Week | DW P2: SVB to FRC | DW
## N (Banks) 72 68 406
## New banks 72 33 340
## Returning banks 0 35 66
## P2: SVB to FRC | BTFP P3: FRC Week | DW P3: FRC Week | BTFP
## 472 101 184
## 442 34 54
## 30 67 130
## → Table 3C 'New' column totals above should equal Table 1's 'New banks' row.
## → Table 3C 'Returning' column totals above should equal Table 1's 'Returning banks' row.## Statistic P0: Pre-Crisis | DW P1: SVB Week | DW
## N (banks) 72.000 32.000
## Total assets ($B) 4.403 12.392
## Cash / TA (%) 4.378 3.307
## Securities / TA (%) 26.656 21.146
## Loans / TA (%) 63.642 68.956
## Book equity / TA (%) 9.053 8.699
## Uninsured / Deposits (%) 31.992 36.154
## Uninsured leverage (%) 26.871 29.799
## Wholesale funding / TA (%) 5.648 6.220
## FHLB / TA (%) 3.527 4.692
## ROA (%) 1.028 1.179
## MTM loss / TA (%) 9.327 9.072
## E_MV / TA (%) -0.274 -0.372
## v / TA (post-run, %) 9.285 8.629
## % with E_MV < 0 59.722 53.125
## % with v < 0 (post-run) 1.389 0.000
## N (banks) 0.000 35.000
## Total assets ($B) NaN 3.201
## Cash / TA (%) NaN 4.197
## Securities / TA (%) NaN 28.461
## Loans / TA (%) NaN 62.017
## Book equity / TA (%) NaN 8.137
## Uninsured / Deposits (%) NaN 35.002
## Uninsured leverage (%) NaN 29.274
## Wholesale funding / TA (%) NaN 7.180
## FHLB / TA (%) NaN 4.448
## ROA (%) NaN 0.915
## MTM loss / TA (%) NaN 8.790
## E_MV / TA (%) NaN -0.653
## v / TA (post-run, %) NaN 8.400
## % with E_MV < 0 NaN 62.857
## % with v < 0 (post-run) NaN 2.857
## P2: SVB to FRC | DW P2: SVB to FRC | BTFP P3: FRC Week | DW
## 332.000 431.0000 34.000
## 6.773 6.0548 2.975
## 6.459 4.7394 6.805
## 24.092 28.0427 21.447
## 63.433 61.5511 66.155
## 9.007 8.1333 9.680
## 33.158 31.6623 26.580
## 28.232 27.1223 22.859
## 4.727 5.3776 3.277
## 3.447 4.0134 2.252
## 1.182 1.0665 1.120
## 9.066 9.6739 8.061
## -0.059 -1.5407 1.619
## 9.620 8.4291 12.141
## 50.602 59.1647 35.294
## 4.255 4.4601 0.000
## 65.000 29.0000 67.000
## 5.191 10.7393 2.657
## 4.132 3.8688 4.603
## 26.319 27.7836 26.834
## 64.000 62.5457 63.129
## 8.320 8.5775 8.643
## 35.330 38.5895 32.869
## 29.576 31.8581 27.531
## 6.620 6.9576 6.370
## 4.441 4.4418 4.466
## 1.032 1.0939 1.159
## 8.829 8.6178 9.140
## -0.509 -0.0403 -0.497
## 8.473 8.3706 9.078
## 58.462 55.1724 55.224
## 1.538 3.4483 3.030
## P3: FRC Week | BTFP
## 53.00
## 1.40
## 4.61
## 30.70
## 58.89
## 8.31
## 29.21
## 25.54
## 3.61
## 2.38
## 1.05
## 9.35
## -1.05
## 9.62
## 52.83
## 1.89
## 129.00
## 6.65
## 4.02
## 29.44
## 60.96
## 8.01
## 31.92
## 27.44
## 5.70
## 4.08
## 1.00
## 10.13
## -2.12
## 7.83
## 62.79
## 6.98# ── J. Render ────────────────────────────────────────────────────────
n_stat <- length(stat_order)
tbl3c_k <- table3c %>%
kbl(digits = 2, align = c("l", rep("r", 6)),
caption = paste("Table 3C: New vs Returning Borrowers by Period | Facility",
"(2022Q4 baseline)")) %>%
kable_styling(bootstrap_options = c("striped", "hover", "condensed"),
full_width = FALSE, position = "left", font_size = 11) %>%
add_header_above(c(" " = 1,
"Pre-Crisis" = 1, "SVB Week" = 1,
"SVB → FRC" = 2, "FRC Week" = 2)) %>%
pack_rows("Panel A: New borrowers (no prior borrowing in earlier periods)",
1, n_stat) %>%
pack_rows("Panel B: Returning borrowers (borrowed in at least one prior period)",
n_stat + 1, 2 * n_stat) %>%
footnote(general = paste(
"New vs Returning classification matches Table 1. A bank is Returning in",
"period p if it borrowed from DW or BTFP in any earlier period (P0, ...,",
"p-1); otherwise New. Cross-facility: prior BTFP borrowing makes a bank",
"Returning in a later DW cell, and vice versa. P0 has no prior period, so",
"all P0 borrowers are New by construction. Characteristics are 2022Q4",
"balance-sheet means (sample excl. GSIBs and failed banks).",
"v = E_MV + F_insured, the fundamental value after full uninsured-depositor",
"exit."),
general_title = "Notes:", footnote_as_chunk = TRUE)
tbl3c_k| Statistic | P0: Pre-Crisis | DW | P1: SVB Week | DW | P2: SVB to FRC | DW | P2: SVB to FRC | BTFP | P3: FRC Week | DW | P3: FRC Week | BTFP |
|---|---|---|---|---|---|---|
| Panel A: New borrowers (no prior borrowing in earlier periods) | ||||||
| N (banks) | 72.00 | 32.00 | 332.00 | 431.00 | 34.00 | 53.00 |
| Total assets (\(B) </td> <td style="text-align:right;"> 4.40 </td> <td style="text-align:right;"> 12.39 </td> <td style="text-align:right;"> 6.77 </td> <td style="text-align:right;"> 6.05 </td> <td style="text-align:right;"> 2.97 </td> <td style="text-align:right;"> 1.40 </td> </tr> <tr> <td style="text-align:left;padding-left: 2em;" indentlevel="1"> Cash / TA (%) </td> <td style="text-align:right;"> 4.38 </td> <td style="text-align:right;"> 3.31 </td> <td style="text-align:right;"> 6.46 </td> <td style="text-align:right;"> 4.74 </td> <td style="text-align:right;"> 6.81 </td> <td style="text-align:right;"> 4.61 </td> </tr> <tr> <td style="text-align:left;padding-left: 2em;" indentlevel="1"> Securities / TA (%) </td> <td style="text-align:right;"> 26.66 </td> <td style="text-align:right;"> 21.15 </td> <td style="text-align:right;"> 24.09 </td> <td style="text-align:right;"> 28.04 </td> <td style="text-align:right;"> 21.45 </td> <td style="text-align:right;"> 30.70 </td> </tr> <tr> <td style="text-align:left;padding-left: 2em;" indentlevel="1"> Loans / TA (%) </td> <td style="text-align:right;"> 63.64 </td> <td style="text-align:right;"> 68.96 </td> <td style="text-align:right;"> 63.43 </td> <td style="text-align:right;"> 61.55 </td> <td style="text-align:right;"> 66.16 </td> <td style="text-align:right;"> 58.89 </td> </tr> <tr> <td style="text-align:left;padding-left: 2em;" indentlevel="1"> Book equity / TA (%) </td> <td style="text-align:right;"> 9.05 </td> <td style="text-align:right;"> 8.70 </td> <td style="text-align:right;"> 9.01 </td> <td style="text-align:right;"> 8.13 </td> <td style="text-align:right;"> 9.68 </td> <td style="text-align:right;"> 8.31 </td> </tr> <tr> <td style="text-align:left;padding-left: 2em;" indentlevel="1"> Uninsured / Deposits (%) </td> <td style="text-align:right;"> 31.99 </td> <td style="text-align:right;"> 36.15 </td> <td style="text-align:right;"> 33.16 </td> <td style="text-align:right;"> 31.66 </td> <td style="text-align:right;"> 26.58 </td> <td style="text-align:right;"> 29.21 </td> </tr> <tr> <td style="text-align:left;padding-left: 2em;" indentlevel="1"> Uninsured leverage (%) </td> <td style="text-align:right;"> 26.87 </td> <td style="text-align:right;"> 29.80 </td> <td style="text-align:right;"> 28.23 </td> <td style="text-align:right;"> 27.12 </td> <td style="text-align:right;"> 22.86 </td> <td style="text-align:right;"> 25.54 </td> </tr> <tr> <td style="text-align:left;padding-left: 2em;" indentlevel="1"> Wholesale funding / TA (%) </td> <td style="text-align:right;"> 5.65 </td> <td style="text-align:right;"> 6.22 </td> <td style="text-align:right;"> 4.73 </td> <td style="text-align:right;"> 5.38 </td> <td style="text-align:right;"> 3.28 </td> <td style="text-align:right;"> 3.61 </td> </tr> <tr> <td style="text-align:left;padding-left: 2em;" indentlevel="1"> FHLB / TA (%) </td> <td style="text-align:right;"> 3.53 </td> <td style="text-align:right;"> 4.69 </td> <td style="text-align:right;"> 3.45 </td> <td style="text-align:right;"> 4.01 </td> <td style="text-align:right;"> 2.25 </td> <td style="text-align:right;"> 2.38 </td> </tr> <tr> <td style="text-align:left;padding-left: 2em;" indentlevel="1"> ROA (%) </td> <td style="text-align:right;"> 1.03 </td> <td style="text-align:right;"> 1.18 </td> <td style="text-align:right;"> 1.18 </td> <td style="text-align:right;"> 1.07 </td> <td style="text-align:right;"> 1.12 </td> <td style="text-align:right;"> 1.05 </td> </tr> <tr> <td style="text-align:left;padding-left: 2em;" indentlevel="1"> MTM loss / TA (%) </td> <td style="text-align:right;"> 9.33 </td> <td style="text-align:right;"> 9.07 </td> <td style="text-align:right;"> 9.07 </td> <td style="text-align:right;"> 9.67 </td> <td style="text-align:right;"> 8.06 </td> <td style="text-align:right;"> 9.35 </td> </tr> <tr> <td style="text-align:left;padding-left: 2em;" indentlevel="1"> E_MV / TA (%) </td> <td style="text-align:right;"> -0.27 </td> <td style="text-align:right;"> -0.37 </td> <td style="text-align:right;"> -0.06 </td> <td style="text-align:right;"> -1.54 </td> <td style="text-align:right;"> 1.62 </td> <td style="text-align:right;"> -1.05 </td> </tr> <tr> <td style="text-align:left;padding-left: 2em;" indentlevel="1"> v / TA (post-run, %) </td> <td style="text-align:right;"> 9.28 </td> <td style="text-align:right;"> 8.63 </td> <td style="text-align:right;"> 9.62 </td> <td style="text-align:right;"> 8.43 </td> <td style="text-align:right;"> 12.14 </td> <td style="text-align:right;"> 9.62 </td> </tr> <tr> <td style="text-align:left;padding-left: 2em;" indentlevel="1"> % with E_MV < 0 </td> <td style="text-align:right;"> 59.72 </td> <td style="text-align:right;"> 53.12 </td> <td style="text-align:right;"> 50.60 </td> <td style="text-align:right;"> 59.16 </td> <td style="text-align:right;"> 35.29 </td> <td style="text-align:right;"> 52.83 </td> </tr> <tr> <td style="text-align:left;padding-left: 2em;" indentlevel="1"> % with v < 0 (post-run) </td> <td style="text-align:right;"> 1.39 </td> <td style="text-align:right;"> 0.00 </td> <td style="text-align:right;"> 4.26 </td> <td style="text-align:right;"> 4.46 </td> <td style="text-align:right;"> 0.00 </td> <td style="text-align:right;"> 1.89 </td> </tr> <tr grouplength="16"><td colspan="7" style="border-bottom: 1px solid;"><strong>Panel B: Returning borrowers (borrowed in at least one prior period)</strong></td></tr> <tr> <td style="text-align:left;padding-left: 2em;" indentlevel="1"> N (banks) </td> <td style="text-align:right;"> 0.00 </td> <td style="text-align:right;"> 35.00 </td> <td style="text-align:right;"> 65.00 </td> <td style="text-align:right;"> 29.00 </td> <td style="text-align:right;"> 67.00 </td> <td style="text-align:right;"> 129.00 </td> </tr> <tr> <td style="text-align:left;padding-left: 2em;" indentlevel="1"> Total assets (\)B) | NaN | 3.20 | 5.19 | 10.74 | 2.66 | 6.65 |
| Cash / TA (%) | NaN | 4.20 | 4.13 | 3.87 | 4.60 | 4.02 |
| Securities / TA (%) | NaN | 28.46 | 26.32 | 27.78 | 26.83 | 29.44 |
| Loans / TA (%) | NaN | 62.02 | 64.00 | 62.55 | 63.13 | 60.96 |
| Book equity / TA (%) | NaN | 8.14 | 8.32 | 8.58 | 8.64 | 8.01 |
| Uninsured / Deposits (%) | NaN | 35.00 | 35.33 | 38.59 | 32.87 | 31.92 |
| Uninsured leverage (%) | NaN | 29.27 | 29.58 | 31.86 | 27.53 | 27.44 |
| Wholesale funding / TA (%) | NaN | 7.18 | 6.62 | 6.96 | 6.37 | 5.70 |
| FHLB / TA (%) | NaN | 4.45 | 4.44 | 4.44 | 4.47 | 4.08 |
| ROA (%) | NaN | 0.92 | 1.03 | 1.09 | 1.16 | 1.00 |
| MTM loss / TA (%) | NaN | 8.79 | 8.83 | 8.62 | 9.14 | 10.13 |
| E_MV / TA (%) | NaN | -0.65 | -0.51 | -0.04 | -0.50 | -2.12 |
| v / TA (post-run, %) | NaN | 8.40 | 8.47 | 8.37 | 9.08 | 7.83 |
| % with E_MV < 0 | NaN | 62.86 | 58.46 | 55.17 | 55.22 | 62.79 |
| % with v < 0 (post-run) | NaN | 2.86 | 1.54 | 3.45 | 3.03 | 6.98 |
| Notes: New vs Returning classification matches Table 1. A bank is Returning in period p if it borrowed from DW or BTFP in any earlier period (P0, …, p-1); otherwise New. Cross-facility: prior BTFP borrowing makes a bank Returning in a later DW cell, and vice versa. P0 has no prior period, so all P0 borrowers are New by construction. Characteristics are 2022Q4 balance-sheet means (sample excl. GSIBs and failed banks). v = E_MV + F_insured, the fundamental value after full uninsured-depositor exit. | ||||||
save_kbl_latex(table3c, "table6_new_vs_returning",
caption = "New vs Returning Borrowers by Period | Facility")Table 6 (another angle)
# ══════════════════════════════════════════════════════════════════════
# TABLE 3B: One-time vs Repeat Borrowers — By Period | Facility
# Columns mirror Table 1: 6 period|facility cells
# Within each cell: One-time = 1 distinct loan date in that period
# Repeat = ≥2 distinct loan dates in that period
# Sample: 2022Q4 cross-section (excl. GSIBs and failed banks)
# ══════════════════════════════════════════════════════════════════════
# ── A. Period-assigned loan tables (self-contained) ──────────────────
dw_pf <- dw_clean %>%
filter(dw_loan_date >= P0_start, dw_loan_date <= P3_end) %>%
mutate(period = assign_period(dw_loan_date),
rssd_id = as.character(rssd_id))
btfp_pf <- btfp_clean %>%
filter(btfp_loan_date >= P2_start, btfp_loan_date <= P3_end) %>%
mutate(period = assign_period(btfp_loan_date),
rssd_id = as.character(rssd_id))
# ── B. Classify borrowers as One-time/Repeat WITHIN each cell ────────
dw_cell_types <- dw_pf %>%
distinct(period, rssd_id, dw_loan_date) %>%
count(period, rssd_id, name = "n_dates") %>%
mutate(type = if_else(n_dates > 1, "Repeat", "One-time"),
facility = "DW")
btfp_cell_types <- btfp_pf %>%
distinct(period, rssd_id, btfp_loan_date) %>%
count(period, rssd_id, name = "n_dates") %>%
mutate(type = if_else(n_dates > 1, "Repeat", "One-time"),
facility = "BTFP")
cell_types <- bind_rows(dw_cell_types, btfp_cell_types)
get_ids <- function(p, f, t) {
cell_types %>%
filter(period == p, facility == f, type == t) %>%
pull(rssd_id)
}
# ── C. Ensure derived variables exist on df (safe if already present) ─
df <- df %>%
mutate(
ta_billion = total_asset / 1e6, # thousands → $B
mu_pct = 100 * mu,
fhlb_ta = fhlb_to_total_asset,
v_postrun = E_MV_F_insured, # correct under Option A
v_postrun_ta = 100 * safe_div(v_postrun, total_asset),
emv_neg = as.integer(E_MV < 0),
v_postrun_neg = as.integer(v_postrun < 0),
roa = if ("roa" %in% names(.)) roa
else if ("net_income_to_total_asset" %in% names(.)) net_income_to_total_asset
else NA_real_
)
# ── D. Per-cell summariser ───────────────────────────────────────────
summarise_cell_3b <- function(ids, col_id) {
sub <- df %>% filter(idrssd %in% ids)
tibble(
col_id = col_id,
`N (banks)` = nrow(sub),
`Total assets ($B)` = mean(sub$ta_billion, na.rm = TRUE),
`Cash / TA (%)` = mean(sub$cash_ta, na.rm = TRUE),
`Securities / TA (%)` = mean(sub$sec_ta, na.rm = TRUE),
`Loans / TA (%)` = mean(sub$loan_ta, na.rm = TRUE),
`Book equity / TA (%)` = mean(sub$eq_ta, na.rm = TRUE),
`Uninsured / Deposits (%)` = mean(sub$mu_pct, na.rm = TRUE),
`Uninsured leverage (%)` = mean(sub$du_ta, na.rm = TRUE),
`Wholesale funding / TA (%)` = mean(sub$wholesale_ta, na.rm = TRUE),
`FHLB / TA (%)` = mean(sub$fhlb_ta, na.rm = TRUE),
`ROA (%)` = mean(sub$roa, na.rm = TRUE),
`MTM loss / TA (%)` = mean(sub$ell, na.rm = TRUE),
`E_MV / TA (%)` = mean(sub$emv_ta, na.rm = TRUE),
`v / TA (post-run, %)` = mean(sub$v_postrun_ta, na.rm = TRUE),
`% with E_MV < 0` = 100 * mean(sub$emv_neg, na.rm = TRUE),
`% with v < 0 (post-run)` = 100 * mean(sub$v_postrun_neg, na.rm = TRUE)
)
}
# ── E. Build both panels ─────────────────────────────────────────────
col_specs <- tibble(
col_id = c("P0: Pre-Crisis | DW", "P1: SVB Week | DW",
"P2: SVB to FRC | DW", "P2: SVB to FRC | BTFP",
"P3: FRC Week | DW", "P3: FRC Week | BTFP"),
period = c("P0: Pre-Crisis", "P1: SVB Week",
"P2: SVB to FRC", "P2: SVB to FRC",
"P3: FRC Week", "P3: FRC Week"),
facility = c("DW", "DW", "DW", "BTFP", "DW", "BTFP")
)
build_panel <- function(type_label) {
rows <- lapply(seq_len(nrow(col_specs)), function(i) {
ids <- get_ids(col_specs$period[i], col_specs$facility[i], type_label)
summarise_cell_3b(ids, col_specs$col_id[i])
})
bind_rows(rows)
}
onetime_cells <- build_panel("One-time")
repeat_cells <- build_panel("Repeat")
# ── F. Pivot each panel to rows = stat, cols = period|facility ───────
stat_order <- setdiff(names(onetime_cells), "col_id")
col_order <- col_specs$col_id
pivot_panel <- function(cells) {
cells %>%
pivot_longer(-col_id, names_to = "Statistic", values_to = "value") %>%
mutate(Statistic = factor(Statistic, levels = stat_order),
col_id = factor(col_id, levels = col_order)) %>%
arrange(Statistic, col_id) %>%
pivot_wider(names_from = col_id, values_from = value) %>%
select(Statistic, all_of(col_order))
}
onetime_panel <- pivot_panel(onetime_cells)
repeat_panel <- pivot_panel(repeat_cells)
# ── G. Stack vertically ──────────────────────────────────────────────
table3b <- bind_rows(onetime_panel, repeat_panel)
# Diagnostics
cat("Table 3B shape:", nrow(table3b), "rows x", ncol(table3b), "cols\n")## Table 3B shape: 32 rows x 7 cols## Panel A (One-time): rows 1 to 16## Panel B (Repeat) : rows 17 to 32##
## Bank counts by cell:cell_types %>%
count(period, facility, type) %>%
pivot_wider(names_from = type, values_from = n, values_fill = 0L) %>%
print(n = Inf)## # A tibble: 6 × 4
## period facility `One-time` Repeat
## <chr> <chr> <int> <int>
## 1 P0: Pre-Crisis DW 40 32
## 2 P1: SVB Week DW 37 31
## 3 P2: SVB to FRC BTFP 235 237
## 4 P2: SVB to FRC DW 292 114
## 5 P3: FRC Week BTFP 126 58
## 6 P3: FRC Week DW 56 45## Statistic P0: Pre-Crisis | DW P1: SVB Week | DW
## N (banks) 40.000 37.0000
## Total assets ($B) 5.274 10.9963
## Cash / TA (%) 4.745 4.5227
## Securities / TA (%) 23.529 22.0662
## Loans / TA (%) 66.217 67.2013
## Book equity / TA (%) 9.815 8.7492
## Uninsured / Deposits (%) 28.494 36.6735
## Uninsured leverage (%) 23.788 30.5039
## Wholesale funding / TA (%) 5.222 5.7371
## FHLB / TA (%) 3.495 4.0074
## ROA (%) 1.059 1.1041
## MTM loss / TA (%) 9.158 8.6597
## E_MV / TA (%) 0.657 0.0895
## v / TA (post-run, %) 10.529 8.9813
## % with E_MV < 0 50.000 48.6486
## % with v < 0 (post-run) 0.000 0.0000
## N (banks) 32.000 30.0000
## Total assets ($B) 3.314 3.3905
## Cash / TA (%) 3.919 2.8465
## Securities / TA (%) 30.564 28.5457
## Loans / TA (%) 60.423 63.0247
## Book equity / TA (%) 8.101 7.9811
## Uninsured / Deposits (%) 36.365 34.1691
## Uninsured leverage (%) 30.724 28.3172
## Wholesale funding / TA (%) 6.181 7.9354
## FHLB / TA (%) 3.568 5.2518
## ROA (%) 0.989 0.9643
## MTM loss / TA (%) 9.538 9.2509
## E_MV / TA (%) -1.438 -1.2698
## v / TA (post-run, %) 7.729 7.9273
## % with E_MV < 0 71.875 70.0000
## % with v < 0 (post-run) 3.125 3.3333
## P2: SVB to FRC | DW P2: SVB to FRC | BTFP P3: FRC Week | DW
## 284.000 229.00 56.000
## 7.567 9.25 2.560
## 6.841 5.08 6.620
## 23.171 26.45 21.930
## 64.077 62.93 65.799
## 9.199 8.11 9.411
## 32.449 32.87 28.231
## 27.698 28.24 23.921
## 4.412 4.89 4.508
## 3.317 3.71 3.253
## 1.189 1.08 1.251
## 8.871 9.28 8.540
## 0.329 -1.16 0.871
## 9.988 8.78 11.042
## 47.887 57.64 44.643
## 3.180 1.77 0.000
## 113.000 231.00 45.000
## 3.867 3.48 3.017
## 4.161 4.29 3.758
## 27.687 29.59 28.868
## 62.141 60.31 62.093
## 8.127 8.21 8.471
## 36.189 31.33 33.889
## 30.347 26.61 28.494
## 6.606 6.05 6.351
## 4.345 4.36 4.302
## 1.078 1.06 1.016
## 9.419 9.94 9.072
## -1.292 -1.73 -0.601
## 8.008 8.08 8.946
## 61.947 60.17 53.333
## 5.405 6.99 4.545
## P3: FRC Week | BTFP
## 124.00
## 6.13
## 4.09
## 29.91
## 60.23
## 7.97
## 30.02
## 26.00
## 5.06
## 3.58
## 1.00
## 9.94
## -1.97
## 8.36
## 62.10
## 6.45
## 58.00
## 2.95
## 4.41
## 29.57
## 60.63
## 8.37
## 33.50
## 28.78
## 5.16
## 3.58
## 1.04
## 9.83
## -1.46
## 8.33
## 55.17
## 3.45# ── H. Render ────────────────────────────────────────────────────────
n_stat <- length(stat_order)
tbl3b_k <- table3b %>%
kbl(digits = 2, align = c("l", rep("r", 6)),
caption = "Table 3B: One-time vs Repeat Borrowers by Period | Facility (2022Q4 baseline)") %>%
kable_styling(bootstrap_options = c("striped", "hover", "condensed"),
full_width = FALSE, position = "left", font_size = 11) %>%
add_header_above(c(" " = 1,
"Pre-Crisis" = 1, "SVB Week" = 1,
"SVB → FRC" = 2, "FRC Week" = 2)) %>%
pack_rows("Panel A: One-time borrowers (1 distinct loan date in the period)",
1, n_stat) %>%
pack_rows("Panel B: Repeat borrowers (≥2 distinct loan dates in the period)",
n_stat + 1, 2 * n_stat) %>%
footnote(general = paste(
"One-time vs Repeat is defined within each period | facility cell by the",
"number of distinct loan dates. Characteristics are 2022Q4 balance-sheet",
"means (sample excl. GSIBs and failed banks). v = E_MV + F_insured,",
"the fundamental value after full uninsured-depositor exit."),
general_title = "Notes:", footnote_as_chunk = TRUE)
tbl3b_k| Statistic | P0: Pre-Crisis | DW | P1: SVB Week | DW | P2: SVB to FRC | DW | P2: SVB to FRC | BTFP | P3: FRC Week | DW | P3: FRC Week | BTFP |
|---|---|---|---|---|---|---|
| Panel A: One-time borrowers (1 distinct loan date in the period) | ||||||
| N (banks) | 40.00 | 37.00 | 284.00 | 229.00 | 56.00 | 124.00 |
| Total assets (\(B) </td> <td style="text-align:right;"> 5.27 </td> <td style="text-align:right;"> 11.00 </td> <td style="text-align:right;"> 7.57 </td> <td style="text-align:right;"> 9.25 </td> <td style="text-align:right;"> 2.56 </td> <td style="text-align:right;"> 6.13 </td> </tr> <tr> <td style="text-align:left;padding-left: 2em;" indentlevel="1"> Cash / TA (%) </td> <td style="text-align:right;"> 4.74 </td> <td style="text-align:right;"> 4.52 </td> <td style="text-align:right;"> 6.84 </td> <td style="text-align:right;"> 5.08 </td> <td style="text-align:right;"> 6.62 </td> <td style="text-align:right;"> 4.09 </td> </tr> <tr> <td style="text-align:left;padding-left: 2em;" indentlevel="1"> Securities / TA (%) </td> <td style="text-align:right;"> 23.53 </td> <td style="text-align:right;"> 22.07 </td> <td style="text-align:right;"> 23.17 </td> <td style="text-align:right;"> 26.45 </td> <td style="text-align:right;"> 21.93 </td> <td style="text-align:right;"> 29.91 </td> </tr> <tr> <td style="text-align:left;padding-left: 2em;" indentlevel="1"> Loans / TA (%) </td> <td style="text-align:right;"> 66.22 </td> <td style="text-align:right;"> 67.20 </td> <td style="text-align:right;"> 64.08 </td> <td style="text-align:right;"> 62.93 </td> <td style="text-align:right;"> 65.80 </td> <td style="text-align:right;"> 60.23 </td> </tr> <tr> <td style="text-align:left;padding-left: 2em;" indentlevel="1"> Book equity / TA (%) </td> <td style="text-align:right;"> 9.81 </td> <td style="text-align:right;"> 8.75 </td> <td style="text-align:right;"> 9.20 </td> <td style="text-align:right;"> 8.11 </td> <td style="text-align:right;"> 9.41 </td> <td style="text-align:right;"> 7.97 </td> </tr> <tr> <td style="text-align:left;padding-left: 2em;" indentlevel="1"> Uninsured / Deposits (%) </td> <td style="text-align:right;"> 28.49 </td> <td style="text-align:right;"> 36.67 </td> <td style="text-align:right;"> 32.45 </td> <td style="text-align:right;"> 32.87 </td> <td style="text-align:right;"> 28.23 </td> <td style="text-align:right;"> 30.02 </td> </tr> <tr> <td style="text-align:left;padding-left: 2em;" indentlevel="1"> Uninsured leverage (%) </td> <td style="text-align:right;"> 23.79 </td> <td style="text-align:right;"> 30.50 </td> <td style="text-align:right;"> 27.70 </td> <td style="text-align:right;"> 28.24 </td> <td style="text-align:right;"> 23.92 </td> <td style="text-align:right;"> 26.00 </td> </tr> <tr> <td style="text-align:left;padding-left: 2em;" indentlevel="1"> Wholesale funding / TA (%) </td> <td style="text-align:right;"> 5.22 </td> <td style="text-align:right;"> 5.74 </td> <td style="text-align:right;"> 4.41 </td> <td style="text-align:right;"> 4.89 </td> <td style="text-align:right;"> 4.51 </td> <td style="text-align:right;"> 5.06 </td> </tr> <tr> <td style="text-align:left;padding-left: 2em;" indentlevel="1"> FHLB / TA (%) </td> <td style="text-align:right;"> 3.49 </td> <td style="text-align:right;"> 4.01 </td> <td style="text-align:right;"> 3.32 </td> <td style="text-align:right;"> 3.71 </td> <td style="text-align:right;"> 3.25 </td> <td style="text-align:right;"> 3.58 </td> </tr> <tr> <td style="text-align:left;padding-left: 2em;" indentlevel="1"> ROA (%) </td> <td style="text-align:right;"> 1.06 </td> <td style="text-align:right;"> 1.10 </td> <td style="text-align:right;"> 1.19 </td> <td style="text-align:right;"> 1.08 </td> <td style="text-align:right;"> 1.25 </td> <td style="text-align:right;"> 1.00 </td> </tr> <tr> <td style="text-align:left;padding-left: 2em;" indentlevel="1"> MTM loss / TA (%) </td> <td style="text-align:right;"> 9.16 </td> <td style="text-align:right;"> 8.66 </td> <td style="text-align:right;"> 8.87 </td> <td style="text-align:right;"> 9.28 </td> <td style="text-align:right;"> 8.54 </td> <td style="text-align:right;"> 9.94 </td> </tr> <tr> <td style="text-align:left;padding-left: 2em;" indentlevel="1"> E_MV / TA (%) </td> <td style="text-align:right;"> 0.66 </td> <td style="text-align:right;"> 0.09 </td> <td style="text-align:right;"> 0.33 </td> <td style="text-align:right;"> -1.16 </td> <td style="text-align:right;"> 0.87 </td> <td style="text-align:right;"> -1.97 </td> </tr> <tr> <td style="text-align:left;padding-left: 2em;" indentlevel="1"> v / TA (post-run, %) </td> <td style="text-align:right;"> 10.53 </td> <td style="text-align:right;"> 8.98 </td> <td style="text-align:right;"> 9.99 </td> <td style="text-align:right;"> 8.78 </td> <td style="text-align:right;"> 11.04 </td> <td style="text-align:right;"> 8.36 </td> </tr> <tr> <td style="text-align:left;padding-left: 2em;" indentlevel="1"> % with E_MV < 0 </td> <td style="text-align:right;"> 50.00 </td> <td style="text-align:right;"> 48.65 </td> <td style="text-align:right;"> 47.89 </td> <td style="text-align:right;"> 57.64 </td> <td style="text-align:right;"> 44.64 </td> <td style="text-align:right;"> 62.10 </td> </tr> <tr> <td style="text-align:left;padding-left: 2em;" indentlevel="1"> % with v < 0 (post-run) </td> <td style="text-align:right;"> 0.00 </td> <td style="text-align:right;"> 0.00 </td> <td style="text-align:right;"> 3.18 </td> <td style="text-align:right;"> 1.77 </td> <td style="text-align:right;"> 0.00 </td> <td style="text-align:right;"> 6.45 </td> </tr> <tr grouplength="16"><td colspan="7" style="border-bottom: 1px solid;"><strong>Panel B: Repeat borrowers (≥2 distinct loan dates in the period)</strong></td></tr> <tr> <td style="text-align:left;padding-left: 2em;" indentlevel="1"> N (banks) </td> <td style="text-align:right;"> 32.00 </td> <td style="text-align:right;"> 30.00 </td> <td style="text-align:right;"> 113.00 </td> <td style="text-align:right;"> 231.00 </td> <td style="text-align:right;"> 45.00 </td> <td style="text-align:right;"> 58.00 </td> </tr> <tr> <td style="text-align:left;padding-left: 2em;" indentlevel="1"> Total assets (\)B) | 3.31 | 3.39 | 3.87 | 3.48 | 3.02 | 2.95 |
| Cash / TA (%) | 3.92 | 2.85 | 4.16 | 4.29 | 3.76 | 4.41 |
| Securities / TA (%) | 30.56 | 28.55 | 27.69 | 29.59 | 28.87 | 29.57 |
| Loans / TA (%) | 60.42 | 63.02 | 62.14 | 60.31 | 62.09 | 60.63 |
| Book equity / TA (%) | 8.10 | 7.98 | 8.13 | 8.21 | 8.47 | 8.37 |
| Uninsured / Deposits (%) | 36.36 | 34.17 | 36.19 | 31.33 | 33.89 | 33.50 |
| Uninsured leverage (%) | 30.72 | 28.32 | 30.35 | 26.61 | 28.49 | 28.78 |
| Wholesale funding / TA (%) | 6.18 | 7.94 | 6.61 | 6.05 | 6.35 | 5.16 |
| FHLB / TA (%) | 3.57 | 5.25 | 4.35 | 4.36 | 4.30 | 3.58 |
| ROA (%) | 0.99 | 0.96 | 1.08 | 1.06 | 1.02 | 1.04 |
| MTM loss / TA (%) | 9.54 | 9.25 | 9.42 | 9.94 | 9.07 | 9.83 |
| E_MV / TA (%) | -1.44 | -1.27 | -1.29 | -1.73 | -0.60 | -1.46 |
| v / TA (post-run, %) | 7.73 | 7.93 | 8.01 | 8.08 | 8.95 | 8.33 |
| % with E_MV < 0 | 71.88 | 70.00 | 61.95 | 60.17 | 53.33 | 55.17 |
| % with v < 0 (post-run) | 3.12 | 3.33 | 5.41 | 6.99 | 4.55 | 3.45 |
| Notes: One-time vs Repeat is defined within each period | facility cell by the number of distinct loan dates. Characteristics are 2022Q4 balance-sheet means (sample excl. GSIBs and failed banks). v = E_MV + F_insured, the fundamental value after full uninsured-depositor exit. | ||||||
Regression
Base Model Crisis Period:
# ══════════════════════════════════════════════════════════════════════
# TABLE 4: LPM — Determinants of Borrower Status by Period|Facility
# Six LPMs; sample = 2022Q4 cross-section (df); HC1 robust SE
# All RHS variables winsorized (2.5/97.5) and z-standardized
# ══════════════════════════════════════════════════════════════════════
# ── A. Make sure all RHS variables exist and are z-standardized ──────
df <- df %>%
mutate(
# Variables not already in reg_vars
loan_to_dep = 100 * safe_div(total_loan, total_deposit),
roa = if ("roa" %in% names(.)) roa
else if ("net_income_to_total_asset" %in% names(.)) net_income_to_total_asset
else NA_real_
)
# Everything we need as `_w_z`
reg4_set <- c("ell", "du_ta", # main effects
"log_ta", "cash_ta", "loan_to_dep", # controls
"eq_ta", "wholesale_ta", "roa") # controls
# Only process those that don't already have a _w_z version
need_proc <- reg4_set[!paste0(reg4_set, "_w_z") %in% names(df)]
if (length(need_proc) > 0) {
cat("Winsorizing + z-standardizing:",
paste(need_proc, collapse = ", "), "\n")
df <- df %>%
mutate(across(all_of(need_proc), ~ winsorize(.x), .names = "{.col}_w")) %>%
mutate(across(all_of(paste0(need_proc, "_w")), ~ z_std(.x),
.names = "{.col}_z"))
}## Winsorizing + z-standardizing: log_ta, loan_to_dep, roa# ── B. Build binary dependent variables per period|facility ──────────
dw_cells <- dw_clean %>%
mutate(rssd_id = as.character(rssd_id),
period = assign_period(dw_loan_date))
btfp_cells <- btfp_clean %>%
mutate(rssd_id = as.character(rssd_id),
period = assign_period(btfp_loan_date))
ids_in <- function(data, p) unique(data$rssd_id[data$period == p])
df <- df %>%
mutate(
idrssd = as.character(idrssd),
dep_p0_dw = as.integer(idrssd %in% ids_in(dw_cells, "P0: Pre-Crisis")),
dep_p1_dw = as.integer(idrssd %in% ids_in(dw_cells, "P1: SVB Week")),
dep_p2_dw = as.integer(idrssd %in% ids_in(dw_cells, "P2: SVB to FRC")),
dep_p2_btfp = as.integer(idrssd %in% ids_in(btfp_cells, "P2: SVB to FRC")),
dep_p3_dw = as.integer(idrssd %in% ids_in(dw_cells, "P3: FRC Week")),
dep_p3_btfp = as.integer(idrssd %in% ids_in(btfp_cells, "P3: FRC Week"))
)
# Sanity check: base rates
cat("\nBorrower base rates (1 = borrowed in that period|facility):\n")##
## Borrower base rates (1 = borrowed in that period|facility):df %>%
summarise(across(starts_with("dep_"),
list(n_borrowers = ~sum(., na.rm = TRUE),
mean = ~mean(., na.rm = TRUE)))) %>%
pivot_longer(everything(), names_to = "var", values_to = "val") %>%
print(n = Inf)## # A tibble: 18 × 2
## var val
## <chr> <dbl>
## 1 dep_ta_n_borrowers 3.97e+ 5
## 2 dep_ta_mean 8.44e+ 1
## 3 dep_ta_w_n_borrowers 4.01e+ 5
## 4 dep_ta_w_mean 8.54e+ 1
## 5 dep_ta_w_z_n_borrowers -2.02e-12
## 6 dep_ta_w_z_mean -4.27e-16
## 7 dep_p0_dw_n_borrowers 7.2 e+ 1
## 8 dep_p0_dw_mean 1.53e- 2
## 9 dep_p1_dw_n_borrowers 6.7 e+ 1
## 10 dep_p1_dw_mean 1.43e- 2
## 11 dep_p2_dw_n_borrowers 3.97e+ 2
## 12 dep_p2_dw_mean 8.45e- 2
## 13 dep_p2_btfp_n_borrowers 4.6 e+ 2
## 14 dep_p2_btfp_mean 9.80e- 2
## 15 dep_p3_dw_n_borrowers 1.01e+ 2
## 16 dep_p3_dw_mean 2.15e- 2
## 17 dep_p3_btfp_n_borrowers 1.82e+ 2
## 18 dep_p3_btfp_mean 3.88e- 2# ── C. Estimate six LPMs with HC1 robust SE ──────────────────────────
controls <- "log_ta_w_z + cash_ta_w_z + loan_to_dep_w_z + eq_ta_w_z + wholesale_ta_w_z + roa_w_z"
rhs <- paste("ell_w_z * du_ta_w_z +", controls)
models <- list(
`P0: Pre-Crisis | DW` = lm(as.formula(paste("dep_p0_dw ~", rhs)), data = df),
`P1: SVB Week | DW` = lm(as.formula(paste("dep_p1_dw ~", rhs)), data = df),
`P2: SVB to FRC | DW` = lm(as.formula(paste("dep_p2_dw ~", rhs)), data = df),
`P2: SVB to FRC | BTFP` = lm(as.formula(paste("dep_p2_btfp ~", rhs)), data = df),
`P3: FRC Week | DW` = lm(as.formula(paste("dep_p3_dw ~", rhs)), data = df),
`P3: FRC Week | BTFP` = lm(as.formula(paste("dep_p3_btfp ~", rhs)), data = df)
)
# ── D. Extract coefficients with robust SE ───────────────────────────
get_robust_tidy <- function(model) {
ct <- coeftest(model, vcov. = vcovHC(model, type = "HC1"))
tibble(term = rownames(ct),
estimate = ct[, 1],
std.error = ct[, 2],
p.value = ct[, 4])
}
tidy_models <- lapply(models, get_robust_tidy)
# ── E. Build the regression table (2 rows per coef: estimate, SE) ────
var_order <- c("ell_w_z",
"du_ta_w_z",
"ell_w_z:du_ta_w_z",
"log_ta_w_z",
"cash_ta_w_z",
"loan_to_dep_w_z",
"eq_ta_w_z",
"wholesale_ta_w_z",
"roa_w_z",
"(Intercept)")
var_labels <- c(
"ell_w_z" = "MTM loss (total)",
"du_ta_w_z" = "Uninsured leverage",
"ell_w_z:du_ta_w_z" = "MTM × Uninsured Lev",
"log_ta_w_z" = "Ln(assets)",
"cash_ta_w_z" = "Cash / TA",
"loan_to_dep_w_z" = "Loan / Deposit",
"eq_ta_w_z" = "Book equity / TA",
"wholesale_ta_w_z" = "Wholesale funding",
"roa_w_z" = "ROA",
"(Intercept)" = "Constant"
)
fmt_est <- function(est, p) {
if (is.na(est)) return("")
sprintf("%.3f%s", est, stars_pval(p))
}
fmt_se <- function(se) if (is.na(se)) "" else sprintf("(%.3f)", se)
body <- list()
for (v in var_order) {
est_row <- c(); se_row <- c()
for (m_name in names(tidy_models)) {
tm <- tidy_models[[m_name]]
idx <- which(tm$term == v)
if (length(idx) == 0) {
est_row <- c(est_row, ""); se_row <- c(se_row, "")
} else {
est_row <- c(est_row, fmt_est(tm$estimate[idx], tm$p.value[idx]))
se_row <- c(se_row, fmt_se(tm$std.error[idx]))
}
}
body[[paste0(v, "_est")]] <- c(var_labels[[v]], est_row)
body[[paste0(v, "_se")]] <- c("", se_row)
}
# Footer: N, R², mean DV
n_row <- c("N")
r2_row <- c("R²")
mdv_row <- c("Mean of DV")
for (m_name in names(models)) {
m <- models[[m_name]]
n_row <- c(n_row, fmt(nobs(m)))
r2_row <- c(r2_row, sprintf("%.3f", summary(m)$r.squared))
mdv_row <- c(mdv_row, sprintf("%.4f", mean(m$model[[1]], na.rm = TRUE)))
}
body[["_blank"]] <- rep("", 7)
body[["_N"]] <- n_row
body[["_R2"]] <- r2_row
body[["_MDV"]] <- mdv_row
reg_table <- do.call(rbind, body) %>% as.data.frame(stringsAsFactors = FALSE)
rownames(reg_table) <- NULL
colnames(reg_table) <- c("Variable", names(models))
# ── F. Render ────────────────────────────────────────────────────────
cat("\nTable 7: LPM coefficients (robust SE in parentheses)\n")##
## Table 7: LPM coefficients (robust SE in parentheses)## Variable P0: Pre-Crisis | DW P1: SVB Week | DW
## 1 MTM loss (total) 0.001 -0.002
## 2 (0.002) (0.002)
## 3 Uninsured leverage 0.000 0.002
## 4 (0.003) (0.002)
## 5 MTM × Uninsured Lev 0.002 0.001
## 6 (0.002) (0.002)
## 7 Ln(assets) 0.013*** 0.014***
## 8 (0.003) (0.003)
## 9 Cash / TA -0.004* -0.003**
## 10 (0.002) (0.001)
## 11 Loan / Deposit -0.005* -0.005**
## 12 (0.003) (0.002)
## 13 Book equity / TA 0.002 -0.000
## 14 (0.002) (0.001)
## 15 Wholesale funding 0.006** 0.008***
## 16 (0.003) (0.003)
## 17 ROA -0.002 -0.002
## 18 (0.002) (0.002)
## 19 Constant 0.016*** 0.014***
## 20 (0.002) (0.002)
## 21
## 22 N 4,632 4,632
## 23 R² 0.015 0.023
## 24 Mean of DV 0.0155 0.0145
## P2: SVB to FRC | DW P2: SVB to FRC | BTFP P3: FRC Week | DW
## 1 0.012** 0.015*** -0.000
## 2 (0.005) (0.005) (0.003)
## 3 0.012** 0.017*** -0.000
## 4 (0.005) (0.006) (0.003)
## 5 0.013*** 0.012*** 0.005**
## 6 (0.004) (0.004) (0.002)
## 7 0.066*** 0.047*** 0.014***
## 8 (0.006) (0.006) (0.003)
## 9 0.003 -0.021*** -0.003
## 10 (0.004) (0.004) (0.002)
## 11 -0.007 -0.024*** -0.004
## 12 (0.005) (0.005) (0.003)
## 13 0.001 -0.010** 0.001
## 14 (0.004) (0.004) (0.002)
## 15 0.015*** 0.033*** 0.007**
## 16 (0.005) (0.006) (0.003)
## 17 0.001 -0.002 0.000
## 18 (0.004) (0.004) (0.002)
## 19 0.086*** 0.099*** 0.022***
## 20 (0.004) (0.004) (0.002)
## 21
## 22 4,632 4,632 4,632
## 23 0.069 0.069 0.013
## 24 0.0857 0.0993 0.0218
## P3: FRC Week | BTFP
## 1 0.007**
## 2 (0.003)
## 3 0.007**
## 4 (0.004)
## 5 0.005*
## 6 (0.003)
## 7 0.015***
## 8 (0.004)
## 9 -0.013***
## 10 (0.002)
## 11 -0.013***
## 12 (0.003)
## 13 -0.002
## 14 (0.003)
## 15 0.012***
## 16 (0.003)
## 17 -0.003
## 18 (0.002)
## 19 0.039***
## 20 (0.003)
## 21
## 22 4,632
## 23 0.026
## 24 0.0393n_coef_rows <- 2 * length(var_order) # 20 rows of coefficients
footer_start <- n_coef_rows + 2 # blank + N rows start here
tbl4_k <- reg_table %>%
kbl(align = c("l", rep("r", 6)),
caption = "Table 4: LPM — Determinants of Borrower Status by Period | Facility",
booktabs = TRUE) %>%
kable_styling(bootstrap_options = c("striped", "hover", "condensed"),
full_width = FALSE, position = "left", font_size = 11) %>%
add_header_above(c(" " = 1, "Pre-Crisis" = 1, "SVB Week" = 1,
"SVB → FRC" = 2, "FRC Week" = 2)) %>%
pack_rows("Key solvency-liquidity variables", 1, 6) %>%
pack_rows("Controls", 7, n_coef_rows - 2) %>%
pack_rows("Intercept", n_coef_rows - 1, n_coef_rows) %>%
pack_rows("Fit statistics", footer_start, footer_start + 2) %>%
footnote(general = paste("Dependent variable: 1 if bank borrowed from that",
"facility in that period, 0 otherwise.",
"All RHS variables winsorized at 2.5/97.5 and",
"z-standardized. HC1 robust SE in parentheses.",
"* p<0.10, ** p<0.05, *** p<0.01."),
general_title = "Notes:", footnote_as_chunk = TRUE)
tbl4_k| Variable | P0: Pre-Crisis | DW | P1: SVB Week | DW | P2: SVB to FRC | DW | P2: SVB to FRC | BTFP | P3: FRC Week | DW | P3: FRC Week | BTFP |
|---|---|---|---|---|---|---|
| Key solvency-liquidity variables | ||||||
| MTM loss (total) | 0.001 | -0.002 | 0.012** | 0.015*** | -0.000 | 0.007** |
| (0.002) | (0.002) | (0.005) | (0.005) | (0.003) | (0.003) | |
| Uninsured leverage | 0.000 | 0.002 | 0.012** | 0.017*** | -0.000 | 0.007** |
| (0.003) | (0.002) | (0.005) | (0.006) | (0.003) | (0.004) | |
| MTM × Uninsured Lev | 0.002 | 0.001 | 0.013*** | 0.012*** | 0.005** | 0.005* |
| (0.002) | (0.002) | (0.004) | (0.004) | (0.002) | (0.003) | |
| Controls | ||||||
| Ln(assets) | 0.013*** | 0.014*** | 0.066*** | 0.047*** | 0.014*** | 0.015*** |
| (0.003) | (0.003) | (0.006) | (0.006) | (0.003) | (0.004) | |
| Cash / TA | -0.004* | -0.003** | 0.003 | -0.021*** | -0.003 | -0.013*** |
| (0.002) | (0.001) | (0.004) | (0.004) | (0.002) | (0.002) | |
| Loan / Deposit | -0.005* | -0.005** | -0.007 | -0.024*** | -0.004 | -0.013*** |
| (0.003) | (0.002) | (0.005) | (0.005) | (0.003) | (0.003) | |
| Book equity / TA | 0.002 | -0.000 | 0.001 | -0.010** | 0.001 | -0.002 |
| (0.002) | (0.001) | (0.004) | (0.004) | (0.002) | (0.003) | |
| Wholesale funding | 0.006** | 0.008*** | 0.015*** | 0.033*** | 0.007** | 0.012*** |
| (0.003) | (0.003) | (0.005) | (0.006) | (0.003) | (0.003) | |
| ROA | -0.002 | -0.002 | 0.001 | -0.002 | 0.000 | -0.003 |
| (0.002) | (0.002) | (0.004) | (0.004) | (0.002) | (0.002) | |
| Intercept | ||||||
| Constant | 0.016*** | 0.014*** | 0.086*** | 0.099*** | 0.022*** | 0.039*** |
| (0.002) | (0.002) | (0.004) | (0.004) | (0.002) | (0.003) | |
| Fit statistics | ||||||
| N | 4,632 | 4,632 | 4,632 | 4,632 | 4,632 | 4,632 |
| R² | 0.015 | 0.023 | 0.069 | 0.069 | 0.013 | 0.026 |
| Mean of DV | 0.0155 | 0.0145 | 0.0857 | 0.0993 | 0.0218 | 0.0393 |
| Notes: Dependent variable: 1 if bank borrowed from that facility in that period, 0 otherwise. All RHS variables winsorized at 2.5/97.5 and z-standardized. HC1 robust SE in parentheses. * p<0.10, ** p<0.05, *** p<0.01. | ||||||
Insured Deposit Leverage
# ══════════════════════════════════════════════════════════════════════
# TABLE 8: LPM with INSURED leverage (mirrors Table 4)
# ══════════════════════════════════════════════════════════════════════
# Build insured leverage (pp), winsorize, z-standardize
df <- df %>%
mutate(di_ta = 100 * safe_div(insured_deposit, total_asset, 0),
di_ta_w = winsorize(di_ta),
di_ta_w_z = z_std(di_ta_w))
# Regressions: same RHS as Table 4, swap du_ta_w_z → di_ta_w_z
rhs_4b <- "ell_w_z * di_ta_w_z + log_ta_w_z + cash_ta_w_z + loan_to_dep_w_z + eq_ta_w_z + wholesale_ta_w_z + roa_w_z"
models_4b <- list(
`P0: Pre-Crisis | DW` = lm(as.formula(paste("dep_p0_dw ~", rhs_4b)), data = df),
`P1: SVB Week | DW` = lm(as.formula(paste("dep_p1_dw ~", rhs_4b)), data = df),
`P2: SVB to FRC | DW` = lm(as.formula(paste("dep_p2_dw ~", rhs_4b)), data = df),
`P2: SVB to FRC | BTFP` = lm(as.formula(paste("dep_p2_btfp ~", rhs_4b)), data = df),
`P3: FRC Week | DW` = lm(as.formula(paste("dep_p3_dw ~", rhs_4b)), data = df),
`P3: FRC Week | BTFP` = lm(as.formula(paste("dep_p3_btfp ~", rhs_4b)), data = df)
)
tidy_4b <- lapply(models_4b, get_robust_tidy)
# Build table (same format as Table 4)
var_order_4b <- c("ell_w_z", "di_ta_w_z", "ell_w_z:di_ta_w_z",
"log_ta_w_z", "cash_ta_w_z", "loan_to_dep_w_z",
"eq_ta_w_z", "wholesale_ta_w_z", "roa_w_z",
"(Intercept)")
var_labels_4b <- c(
"ell_w_z" = "MTM loss (total)",
"di_ta_w_z" = "Insured leverage",
"ell_w_z:di_ta_w_z" = "MTM × Insured Lev",
"log_ta_w_z" = "Ln(assets)",
"cash_ta_w_z" = "Cash / TA",
"loan_to_dep_w_z" = "Loan / Deposit",
"eq_ta_w_z" = "Book equity / TA",
"wholesale_ta_w_z" = "Wholesale funding",
"roa_w_z" = "ROA",
"(Intercept)" = "Constant"
)
body_4b <- list()
for (v in var_order_4b) {
est_row <- c(); se_row <- c()
for (m_name in names(tidy_4b)) {
tm <- tidy_4b[[m_name]]
idx <- which(tm$term == v)
if (length(idx) == 0) {
est_row <- c(est_row, ""); se_row <- c(se_row, "")
} else {
est_row <- c(est_row, fmt_est(tm$estimate[idx], tm$p.value[idx]))
se_row <- c(se_row, fmt_se(tm$std.error[idx]))
}
}
body_4b[[paste0(v, "_est")]] <- c(var_labels_4b[[v]], est_row)
body_4b[[paste0(v, "_se")]] <- c("", se_row)
}
n_row <- c("N")
r2_row <- c("R²")
mdv_row <- c("Mean of DV")
for (m in models_4b) {
n_row <- c(n_row, fmt(nobs(m)))
r2_row <- c(r2_row, sprintf("%.3f", summary(m)$r.squared))
mdv_row <- c(mdv_row, sprintf("%.4f", mean(m$model[[1]], na.rm = TRUE)))
}
body_4b[["_blank"]] <- rep("", 7)
body_4b[["_N"]] <- n_row
body_4b[["_R2"]] <- r2_row
body_4b[["_MDV"]] <- mdv_row
reg_table_4b <- do.call(rbind, body_4b) %>% as.data.frame(stringsAsFactors = FALSE)
rownames(reg_table_4b) <- NULL
colnames(reg_table_4b) <- c("Variable", names(models_4b))
# Render
cat("\nTable 4B: LPM with insured leverage (robust SE in parentheses)\n")##
## Table 4B: LPM with insured leverage (robust SE in parentheses)## Variable P0: Pre-Crisis | DW P1: SVB Week | DW P2: SVB to FRC | DW
## 1 MTM loss (total) 0.000 -0.002 0.010**
## 2 (0.002) (0.002) (0.005)
## 3 Insured leverage 0.001 -0.001 -0.012**
## 4 (0.003) (0.002) (0.006)
## 5 MTM × Insured Lev -0.001 0.001 -0.010**
## 6 (0.002) (0.002) (0.004)
## 7 Ln(assets) 0.014*** 0.015*** 0.066***
## 8 (0.003) (0.003) (0.006)
## 9 Cash / TA -0.004* -0.004** 0.002
## 10 (0.002) (0.001) (0.004)
## 11 Loan / Deposit -0.005* -0.005** -0.008
## 12 (0.003) (0.002) (0.005)
## 13 Book equity / TA 0.002 -0.001 -0.005
## 14 (0.002) (0.001) (0.004)
## 15 Wholesale funding 0.006** 0.008*** 0.010*
## 16 (0.003) (0.003) (0.005)
## 17 ROA -0.002 -0.002 0.002
## 18 (0.002) (0.002) (0.004)
## 19 Constant 0.015*** 0.014*** 0.087***
## 20 (0.002) (0.002) (0.004)
## 21
## 22 N 4,632 4,632 4,632
## 23 R² 0.015 0.023 0.068
## 24 Mean of DV 0.0155 0.0145 0.0857
## P2: SVB to FRC | BTFP P3: FRC Week | DW P3: FRC Week | BTFP
## 1 0.013*** -0.001 0.006*
## 2 (0.005) (0.002) (0.003)
## 3 -0.018*** 0.002 -0.007*
## 4 (0.006) (0.003) (0.004)
## 5 -0.006 -0.004* -0.003
## 6 (0.004) (0.002) (0.002)
## 7 0.047*** 0.015*** 0.016***
## 8 (0.006) (0.003) (0.004)
## 9 -0.022*** -0.003 -0.014***
## 10 (0.004) (0.002) (0.002)
## 11 -0.024*** -0.004* -0.014***
## 12 (0.005) (0.003) (0.003)
## 13 -0.019*** 0.001 -0.006*
## 14 (0.005) (0.002) (0.003)
## 15 0.027*** 0.007** 0.009**
## 16 (0.006) (0.003) (0.004)
## 17 -0.001 0.001 -0.003
## 18 (0.004) (0.002) (0.002)
## 19 0.098*** 0.022*** 0.039***
## 20 (0.004) (0.002) (0.003)
## 21
## 22 4,632 4,632 4,632
## 23 0.068 0.013 0.025
## 24 0.0993 0.0218 0.0393n_coef_rows_4b <- 2 * length(var_order_4b)
footer_start_4b <- n_coef_rows_4b + 2
tbl4b_k <- reg_table_4b %>%
kbl(align = c("l", rep("r", 6)),
caption = "Table 8: LPM — Determinants of Borrower Status (Insured leverage)",
booktabs = TRUE) %>%
kable_styling(bootstrap_options = c("striped", "hover", "condensed"),
full_width = FALSE, position = "left", font_size = 11) %>%
add_header_above(c(" " = 1, "Pre-Crisis" = 1, "SVB Week" = 1,
"SVB → FRC" = 2, "FRC Week" = 2)) %>%
pack_rows("Key solvency-liquidity variables", 1, 6) %>%
pack_rows("Controls", 7, n_coef_rows_4b - 2) %>%
pack_rows("Intercept", n_coef_rows_4b - 1, n_coef_rows_4b) %>%
pack_rows("Fit statistics", footer_start_4b, footer_start_4b + 2) %>%
footnote(general = paste(
"Dependent variable: 1 if bank borrowed from that facility in that",
"period, 0 otherwise. Insured leverage = 100 × insured_deposit /",
"total_asset. All RHS variables winsorized at 2.5/97.5 and",
"z-standardized. HC1 robust SE in parentheses.",
"* p<0.10, ** p<0.05, *** p<0.01."),
general_title = "Notes:", footnote_as_chunk = TRUE)
tbl4b_k| Variable | P0: Pre-Crisis | DW | P1: SVB Week | DW | P2: SVB to FRC | DW | P2: SVB to FRC | BTFP | P3: FRC Week | DW | P3: FRC Week | BTFP |
|---|---|---|---|---|---|---|
| Key solvency-liquidity variables | ||||||
| MTM loss (total) | 0.000 | -0.002 | 0.010** | 0.013*** | -0.001 | 0.006* |
| (0.002) | (0.002) | (0.005) | (0.005) | (0.002) | (0.003) | |
| Insured leverage | 0.001 | -0.001 | -0.012** | -0.018*** | 0.002 | -0.007* |
| (0.003) | (0.002) | (0.006) | (0.006) | (0.003) | (0.004) | |
| MTM × Insured Lev | -0.001 | 0.001 | -0.010** | -0.006 | -0.004* | -0.003 |
| (0.002) | (0.002) | (0.004) | (0.004) | (0.002) | (0.002) | |
| Controls | ||||||
| Ln(assets) | 0.014*** | 0.015*** | 0.066*** | 0.047*** | 0.015*** | 0.016*** |
| (0.003) | (0.003) | (0.006) | (0.006) | (0.003) | (0.004) | |
| Cash / TA | -0.004* | -0.004** | 0.002 | -0.022*** | -0.003 | -0.014*** |
| (0.002) | (0.001) | (0.004) | (0.004) | (0.002) | (0.002) | |
| Loan / Deposit | -0.005* | -0.005** | -0.008 | -0.024*** | -0.004* | -0.014*** |
| (0.003) | (0.002) | (0.005) | (0.005) | (0.003) | (0.003) | |
| Book equity / TA | 0.002 | -0.001 | -0.005 | -0.019*** | 0.001 | -0.006* |
| (0.002) | (0.001) | (0.004) | (0.005) | (0.002) | (0.003) | |
| Wholesale funding | 0.006** | 0.008*** | 0.010* | 0.027*** | 0.007** | 0.009** |
| (0.003) | (0.003) | (0.005) | (0.006) | (0.003) | (0.004) | |
| ROA | -0.002 | -0.002 | 0.002 | -0.001 | 0.001 | -0.003 |
| (0.002) | (0.002) | (0.004) | (0.004) | (0.002) | (0.002) | |
| Intercept | ||||||
| Constant | 0.015*** | 0.014*** | 0.087*** | 0.098*** | 0.022*** | 0.039*** |
| (0.002) | (0.002) | (0.004) | (0.004) | (0.002) | (0.003) | |
| Fit statistics | ||||||
| N | 4,632 | 4,632 | 4,632 | 4,632 | 4,632 | 4,632 |
| R² | 0.015 | 0.023 | 0.068 | 0.068 | 0.013 | 0.025 |
| Mean of DV | 0.0155 | 0.0145 | 0.0857 | 0.0993 | 0.0218 | 0.0393 |
| Notes: Dependent variable: 1 if bank borrowed from that facility in that period, 0 otherwise. Insured leverage = 100 × insured_deposit / total_asset. All RHS variables winsorized at 2.5/97.5 and z-standardized. HC1 robust SE in parentheses. * p<0.10, ** p<0.05, *** p<0.01. | ||||||
save_kbl_latex(reg_table_4b, "table8_lpm_insured_leverage",
caption = "LPM — Determinants of Borrower Status (Insured Leverage)")
saveRDS(models_4b, file.path(TABLE_PATH, "table4b_models.rds"))
# Quick side-by-side: the interaction across both specs
cat("\nMTM × deposit-type interaction — Table 4 vs Table 4B:\n")##
## MTM × deposit-type interaction — Table 4 vs Table 4B:tibble(
cell = names(models),
mtm_x_uninsured = sapply(tidy_models, function(t) {
i <- which(t$term == "ell_w_z:du_ta_w_z")
if (length(i) == 0) NA_real_ else t$estimate[i]
}),
mtm_x_insured = sapply(tidy_4b, function(t) {
i <- which(t$term == "ell_w_z:di_ta_w_z")
if (length(i) == 0) NA_real_ else t$estimate[i]
})
) %>% print(digits = 3)## # A tibble: 6 × 3
## cell mtm_x_uninsured mtm_x_insured
## <chr> <dbl> <dbl>
## 1 P0: Pre-Crisis | DW 0.00154 -0.00128
## 2 P1: SVB Week | DW 0.000793 0.000504
## 3 P2: SVB to FRC | DW 0.0125 -0.0101
## 4 P2: SVB to FRC | BTFP 0.0119 -0.00570
## 5 P3: FRC Week | DW 0.00457 -0.00409
## 6 P3: FRC Week | BTFP 0.00474 -0.00338Size
# ══════════════════════════════════════════════════════════════════════
# TABLE 9: LPM by Bank Size — Crisis Window (Mar 8 – May 4, 2023)
# 4 models: {DW, BTFP} × {Small (<$1B), Large (≥$1B)}
# Sample: df (2022Q4 baseline, excl. GSIBs and failed banks)
# ══════════════════════════════════════════════════════════════════════
# ── A. Size indicator and subsamples ─────────────────────────────────
SIZE_CUTOFF <- 1e6 # $1B
df <- df %>%
mutate(size_group = if_else(total_asset >= SIZE_CUTOFF, "Large", "Small"))
cat(sprintf("Size distribution: Small = %s banks, Large = %s banks\n",
fmt(sum(df$size_group == "Small")),
fmt(sum(df$size_group == "Large"))))## Size distribution: Small = 3,743 banks, Large = 953 banks# ── B. Crisis-window borrower indicators (used_dw, used_btfp exist in df) ─
# These were built in classify_borrowers and cover the full Mar 8 – May 4
# crisis window, which is exactly what we want here.
df_small <- df %>% filter(size_group == "Small")
df_large <- df %>% filter(size_group == "Large")
cat(sprintf("Small — DW borrowers: %s | BTFP borrowers: %s\n",
fmt(sum(df_small$used_dw)),
fmt(sum(df_small$used_btfp))))## Small — DW borrowers: 234 | BTFP borrowers: 325cat(sprintf("Large — DW borrowers: %s | BTFP borrowers: %s\n",
fmt(sum(df_large$used_dw)),
fmt(sum(df_large$used_btfp))))## Large — DW borrowers: 214 | BTFP borrowers: 194# ── C. Four LPMs ─────────────────────────────────────────────────────
rhs6 <- "ell_w_z * du_ta_w_z + log_ta_w_z + cash_ta_w_z + loan_to_dep_w_z + eq_ta_w_z + wholesale_ta_w_z + roa_w_z"
models_6 <- list(
`Small — DW` = lm(as.formula(paste("used_dw ~", rhs6)), data = df_small),
`Large — DW` = lm(as.formula(paste("used_dw ~", rhs6)), data = df_large),
`Small — BTFP` = lm(as.formula(paste("used_btfp ~", rhs6)), data = df_small),
`Large — BTFP` = lm(as.formula(paste("used_btfp ~", rhs6)), data = df_large)
)
tidy_6 <- lapply(models_6, get_robust_tidy)
# ── D. Format table (same pattern as Table 7) ────────────────────────
var_order_6 <- c("ell_w_z", "du_ta_w_z", "ell_w_z:du_ta_w_z",
"log_ta_w_z", "cash_ta_w_z", "loan_to_dep_w_z",
"eq_ta_w_z", "wholesale_ta_w_z", "roa_w_z",
"(Intercept)")
var_labels_6 <- c(
"ell_w_z" = "MTM loss (total)",
"du_ta_w_z" = "Uninsured leverage",
"ell_w_z:du_ta_w_z" = "MTM × Uninsured Lev",
"log_ta_w_z" = "Ln(assets)",
"cash_ta_w_z" = "Cash / TA",
"loan_to_dep_w_z" = "Loan / Deposit",
"eq_ta_w_z" = "Book equity / TA",
"wholesale_ta_w_z" = "Wholesale funding",
"roa_w_z" = "ROA",
"(Intercept)" = "Constant"
)
body_6 <- list()
for (v in var_order_6) {
est_row <- c(); se_row <- c()
for (m_name in names(tidy_6)) {
tm <- tidy_6[[m_name]]
idx <- which(tm$term == v)
if (length(idx) == 0) {
est_row <- c(est_row, ""); se_row <- c(se_row, "")
} else {
est_row <- c(est_row, fmt_est(tm$estimate[idx], tm$p.value[idx]))
se_row <- c(se_row, fmt_se(tm$std.error[idx]))
}
}
body_6[[paste0(v, "_est")]] <- c(var_labels_6[[v]], est_row)
body_6[[paste0(v, "_se")]] <- c("", se_row)
}
n_row <- c("N")
r2_row <- c("R²")
mdv_row <- c("Mean of DV")
for (m in models_6) {
n_row <- c(n_row, fmt(nobs(m)))
r2_row <- c(r2_row, sprintf("%.3f", summary(m)$r.squared))
mdv_row <- c(mdv_row, sprintf("%.4f", mean(m$model[[1]], na.rm = TRUE)))
}
body_6[["_blank"]] <- rep("", 5)
body_6[["_N"]] <- n_row
body_6[["_R2"]] <- r2_row
body_6[["_MDV"]] <- mdv_row
reg_table_6 <- do.call(rbind, body_6) %>% as.data.frame(stringsAsFactors = FALSE)
rownames(reg_table_6) <- NULL
colnames(reg_table_6) <- c("Variable", names(models_6))
# ── E. Render ────────────────────────────────────────────────────────
cat("\nTable 9: LPM by size — Crisis window (robust SE in parentheses)\n")##
## Table 9: LPM by size — Crisis window (robust SE in parentheses)## Variable Small — DW Large — DW Small — BTFP Large — BTFP
## 1 MTM loss (total) 0.007 0.015 0.012** 0.021
## 2 (0.005) (0.016) (0.006) (0.017)
## 3 Uninsured leverage 0.002 0.035** 0.017*** 0.024*
## 4 (0.006) (0.015) (0.006) (0.014)
## 5 MTM × Uninsured Lev 0.006 0.029** 0.010* 0.006
## 6 (0.004) (0.013) (0.005) (0.012)
## 7 Ln(assets) 0.058*** 0.088*** 0.050*** 0.047**
## 8 (0.008) (0.024) (0.008) (0.023)
## 9 Cash / TA 0.006 -0.046** -0.024*** -0.060***
## 10 (0.004) (0.023) (0.004) (0.020)
## 11 Loan / Deposit -0.005 -0.017 -0.023*** -0.054***
## 12 (0.005) (0.020) (0.005) (0.021)
## 13 Book equity / TA -0.007** 0.020 -0.008** -0.040*
## 14 (0.003) (0.023) (0.004) (0.021)
## 15 Wholesale funding 0.018*** -0.006 0.030*** 0.047***
## 16 (0.006) (0.014) (0.006) (0.015)
## 17 ROA 0.002 0.019 0.000 -0.000
## 18 (0.004) (0.017) (0.004) (0.015)
## 19 Constant 0.086*** 0.068* 0.111*** 0.102***
## 20 (0.006) (0.038) (0.006) (0.036)
## 21
## 22 N 3,685 947 3,685 947
## 23 R² 0.033 0.040 0.053 0.061
## 24 Mean of DV 0.0635 0.2260 0.0882 0.2049n_coef_6 <- 2 * length(var_order_6)
footer_6 <- n_coef_6 + 2
tbl6_k <- reg_table_6 %>%
kbl(align = c("l", rep("r", 4)),
caption = "Table 9: LPM by Bank Size — Crisis Window (Mar 8 – May 4, 2023)",
booktabs = TRUE) %>%
kable_styling(bootstrap_options = c("striped", "hover", "condensed"),
full_width = FALSE, position = "left", font_size = 11) %>%
add_header_above(c(" " = 1, "Discount Window" = 2, "BTFP" = 2)) %>%
pack_rows("Key solvency-liquidity variables", 1, 6) %>%
pack_rows("Controls", 7, n_coef_6 - 2) %>%
pack_rows("Intercept", n_coef_6 - 1, n_coef_6) %>%
pack_rows("Fit statistics", footer_6, footer_6 + 2) %>%
footnote(general = paste(
"Dependent variable: 1 if bank borrowed from the facility during the",
"crisis window (Mar 8 – May 4, 2023), 0 otherwise. Sample split by",
"total assets at $1B (Small < $1B; Large ≥ $1B). 2022Q4 baseline;",
"excludes GSIBs and failed banks. All RHS variables winsorized at",
"2.5/97.5 and z-standardized. HC1 robust SE in parentheses.",
"* p<0.10, ** p<0.05, *** p<0.01."),
general_title = "Notes:", footnote_as_chunk = TRUE)
tbl6_k| Variable | Small — DW | Large — DW | Small — BTFP | Large — BTFP |
|---|---|---|---|---|
| Key solvency-liquidity variables | ||||
| MTM loss (total) | 0.007 | 0.015 | 0.012** | 0.021 |
| (0.005) | (0.016) | (0.006) | (0.017) | |
| Uninsured leverage | 0.002 | 0.035** | 0.017*** | 0.024* |
| (0.006) | (0.015) | (0.006) | (0.014) | |
| MTM × Uninsured Lev | 0.006 | 0.029** | 0.010* | 0.006 |
| (0.004) | (0.013) | (0.005) | (0.012) | |
| Controls | ||||
| Ln(assets) | 0.058*** | 0.088*** | 0.050*** | 0.047** |
| (0.008) | (0.024) | (0.008) | (0.023) | |
| Cash / TA | 0.006 | -0.046** | -0.024*** | -0.060*** |
| (0.004) | (0.023) | (0.004) | (0.020) | |
| Loan / Deposit | -0.005 | -0.017 | -0.023*** | -0.054*** |
| (0.005) | (0.020) | (0.005) | (0.021) | |
| Book equity / TA | -0.007** | 0.020 | -0.008** | -0.040* |
| (0.003) | (0.023) | (0.004) | (0.021) | |
| Wholesale funding | 0.018*** | -0.006 | 0.030*** | 0.047*** |
| (0.006) | (0.014) | (0.006) | (0.015) | |
| ROA | 0.002 | 0.019 | 0.000 | -0.000 |
| (0.004) | (0.017) | (0.004) | (0.015) | |
| Intercept | ||||
| Constant | 0.086*** | 0.068* | 0.111*** | 0.102*** |
| (0.006) | (0.038) | (0.006) | (0.036) | |
| Fit statistics | ||||
| N | 3,685 | 947 | 3,685 | 947 |
| R² | 0.033 | 0.040 | 0.053 | 0.061 |
| Mean of DV | 0.0635 | 0.2260 | 0.0882 | 0.2049 |
| Notes: Dependent variable: 1 if bank borrowed from the facility during the crisis window (Mar 8 – May 4, 2023), 0 otherwise. Sample split by total assets at $1B (Small < $1B; Large ≥ $1B). 2022Q4 baseline; excludes GSIBs and failed banks. All RHS variables winsorized at 2.5/97.5 and z-standardized. HC1 robust SE in parentheses. * p<0.10, ** p<0.05, *** p<0.01. | ||||
save_kbl_latex(reg_table_6, "table9_lpm_by_size",
caption = "LPM by Bank Size — Crisis Window")
saveRDS(models_6, file.path(TABLE_PATH, "table6_models.rds"))
# ── F. Diagnostic: formal test of Small = Large coefficient equality ─
# For each facility, fit a pooled model with Size × all covariates and
# test whether the size-interaction coefficients are jointly zero.
# Interpretation: rejecting H0 means small and large banks respond
# differently to the same covariates (justifies the subsample split).
df <- df %>% mutate(is_large = as.integer(size_group == "Large"))
test_equality <- function(dv) {
rhs_interact <- paste0("is_large * (ell_w_z * du_ta_w_z + log_ta_w_z + ",
"cash_ta_w_z + loan_to_dep_w_z + eq_ta_w_z + ",
"wholesale_ta_w_z + roa_w_z)")
m_full <- lm(as.formula(paste(dv, "~", rhs_interact)), data = df)
m_null <- lm(as.formula(paste(dv, "~ is_large +", rhs6)), data = df) # same slopes across size
# Wald F-test with HC1
waldtest(m_null, m_full, vcov = vcovHC(m_full, type = "HC1"))
}
cat("\n── Small vs Large coefficient equality (Wald F, HC1) ──\n")##
## ── Small vs Large coefficient equality (Wald F, HC1) ──## H0: all non-intercept slopes are equal across Small and Large## DW facility:## Wald test
##
## Model 1: used_dw ~ is_large + ell_w_z * du_ta_w_z + log_ta_w_z + cash_ta_w_z +
## loan_to_dep_w_z + eq_ta_w_z + wholesale_ta_w_z + roa_w_z
## Model 2: used_dw ~ is_large * (ell_w_z * du_ta_w_z + log_ta_w_z + cash_ta_w_z +
## loan_to_dep_w_z + eq_ta_w_z + wholesale_ta_w_z + roa_w_z)
## Res.Df Df F Pr(>F)
## 1 4621
## 2 4612 9 2.2515 0.01652 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1##
## BTFP facility:## Wald test
##
## Model 1: used_btfp ~ is_large + ell_w_z * du_ta_w_z + log_ta_w_z + cash_ta_w_z +
## loan_to_dep_w_z + eq_ta_w_z + wholesale_ta_w_z + roa_w_z
## Model 2: used_btfp ~ is_large * (ell_w_z * du_ta_w_z + log_ta_w_z + cash_ta_w_z +
## loan_to_dep_w_z + eq_ta_w_z + wholesale_ta_w_z + roa_w_z)
## Res.Df Df F Pr(>F)
## 1 4621
## 2 4612 9 1.6364 0.09905 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Temporal
# ══════════════════════════════════════════════════════════════════════
# TABLE 10: LPM — Full Crisis and Arbitrage Window
# 6 models: {DW Only, BTFP Only, Both} × {Crisis, Arbitrage}
# Crisis : df (2022Q4 baseline) | loans Mar 8 – May 4, 2023
# Arbitrage: df_arb (2023Q3 baseline) | loans Nov 15, 2023 – Jan 24, 2024
# ══════════════════════════════════════════════════════════════════════
# ── A. Crisis DVs (borrower_type already built in df) ────────────────
df <- df %>%
mutate(
dep_dw_only_crisis = as.integer(borrower_type == "DW Only"),
dep_btfp_only_crisis = as.integer(borrower_type == "BTFP Only"),
dep_both_crisis = as.integer(borrower_type == "Both")
)
# ── B. Arbitrage DVs and controls in df_arb ──────────────────────────
dw_arb_banks <- dw_clean %>%
filter(dw_loan_date >= ARB_START, dw_loan_date <= ARB_END) %>%
pull(rssd_id) %>% unique() %>% as.character()
df_arb <- df_arb %>%
mutate(
idrssd = as.character(idrssd),
used_dw_arb = as.integer(idrssd %in% dw_arb_banks),
used_btfp_arb = as.integer(borrowed_arb == 1),
dep_dw_only_arb = as.integer(used_dw_arb == 1 & used_btfp_arb == 0),
dep_btfp_only_arb = as.integer(used_dw_arb == 0 & used_btfp_arb == 1),
dep_both_arb = as.integer(used_dw_arb == 1 & used_btfp_arb == 1),
# Controls that aren't already in df_arb
du_ta = uninsured_leverage,
loan_to_dep = 100 * safe_div(total_loan, total_deposit),
roa = if ("roa" %in% names(.)) roa
else if ("net_income_to_total_asset" %in% names(.)) net_income_to_total_asset
else NA_real_
)
cat("\nCrisis (n =", nrow(df), "):\n")##
## Crisis (n = 4696 ):cat(sprintf(" DW Only : %s BTFP Only : %s Both : %s\n",
fmt(sum(df$dep_dw_only_crisis)),
fmt(sum(df$dep_btfp_only_crisis)),
fmt(sum(df$dep_both_crisis))))## DW Only : 341 BTFP Only : 412 Both : 107## Arbitrage (n = 4,604):cat(sprintf(" DW Only : %s BTFP Only : %s Both : %s\n",
fmt(sum(df_arb$dep_dw_only_arb)),
fmt(sum(df_arb$dep_btfp_only_arb)),
fmt(sum(df_arb$dep_both_arb))))## DW Only : 257 BTFP Only : 655 Both : 111# ── C. Winsorize + z-standardize df_arb RHS vars ─────────────────────
arb_vars <- c("ell", "du_ta", "log_ta", "cash_ta", "loan_to_dep",
"eq_ta", "wholesale_ta", "roa")
df_arb <- df_arb %>%
mutate(across(all_of(arb_vars), ~ winsorize(.x), .names = "{.col}_w")) %>%
mutate(across(all_of(paste0(arb_vars, "_w")), ~ z_std(.x), .names = "{.col}_z"))
# ── D. Six LPMs ──────────────────────────────────────────────────────
rhs5 <- "ell_w_z * du_ta_w_z + log_ta_w_z + cash_ta_w_z + loan_to_dep_w_z + eq_ta_w_z + wholesale_ta_w_z + roa_w_z"
models_5 <- list(
`Crisis — DW Only` = lm(as.formula(paste("dep_dw_only_crisis ~", rhs5)), data = df),
`Crisis — BTFP Only` = lm(as.formula(paste("dep_btfp_only_crisis ~", rhs5)), data = df),
`Crisis — Both` = lm(as.formula(paste("dep_both_crisis ~", rhs5)), data = df),
`Arbitrage — DW Only` = lm(as.formula(paste("dep_dw_only_arb ~", rhs5)), data = df_arb),
`Arbitrage — BTFP Only` = lm(as.formula(paste("dep_btfp_only_arb ~", rhs5)), data = df_arb),
`Arbitrage — Both` = lm(as.formula(paste("dep_both_arb ~", rhs5)), data = df_arb)
)
tidy_5 <- lapply(models_5, get_robust_tidy)
# ── E. Format table (same pattern as Table 4) ────────────────────────
var_order_5 <- c("ell_w_z", "du_ta_w_z", "ell_w_z:du_ta_w_z",
"log_ta_w_z", "cash_ta_w_z", "loan_to_dep_w_z",
"eq_ta_w_z", "wholesale_ta_w_z", "roa_w_z",
"(Intercept)")
var_labels_5 <- c(
"ell_w_z" = "MTM loss (total)",
"du_ta_w_z" = "Uninsured leverage",
"ell_w_z:du_ta_w_z" = "MTM × Uninsured Lev",
"log_ta_w_z" = "Ln(assets)",
"cash_ta_w_z" = "Cash / TA",
"loan_to_dep_w_z" = "Loan / Deposit",
"eq_ta_w_z" = "Book equity / TA",
"wholesale_ta_w_z" = "Wholesale funding",
"roa_w_z" = "ROA",
"(Intercept)" = "Constant"
)
body_5 <- list()
for (v in var_order_5) {
est_row <- c(); se_row <- c()
for (m_name in names(tidy_5)) {
tm <- tidy_5[[m_name]]
idx <- which(tm$term == v)
if (length(idx) == 0) {
est_row <- c(est_row, ""); se_row <- c(se_row, "")
} else {
est_row <- c(est_row, fmt_est(tm$estimate[idx], tm$p.value[idx]))
se_row <- c(se_row, fmt_se(tm$std.error[idx]))
}
}
body_5[[paste0(v, "_est")]] <- c(var_labels_5[[v]], est_row)
body_5[[paste0(v, "_se")]] <- c("", se_row)
}
n_row <- c("N")
r2_row <- c("R²")
mdv_row <- c("Mean of DV")
for (m in models_5) {
n_row <- c(n_row, fmt(nobs(m)))
r2_row <- c(r2_row, sprintf("%.3f", summary(m)$r.squared))
mdv_row <- c(mdv_row, sprintf("%.4f", mean(m$model[[1]], na.rm = TRUE)))
}
body_5[["_blank"]] <- rep("", 7)
body_5[["_N"]] <- n_row
body_5[["_R2"]] <- r2_row
body_5[["_MDV"]] <- mdv_row
reg_table_5 <- do.call(rbind, body_5) %>% as.data.frame(stringsAsFactors = FALSE)
rownames(reg_table_5) <- NULL
colnames(reg_table_5) <- c("Variable", names(models_5))
# ── F. Render ────────────────────────────────────────────────────────
cat("\nTable 10: LPM — Crisis and Arbitrage (robust SE in parentheses)\n")##
## Table 10: LPM — Crisis and Arbitrage (robust SE in parentheses)## Variable Crisis — DW Only Crisis — BTFP Only Crisis — Both
## 1 MTM loss (total) 0.007 0.012** 0.004
## 2 (0.005) (0.005) (0.003)
## 3 Uninsured leverage 0.001 0.011** 0.008**
## 4 (0.005) (0.005) (0.003)
## 5 MTM × Uninsured Lev 0.007* 0.005 0.007**
## 6 (0.004) (0.004) (0.003)
## 7 Ln(assets) 0.051*** 0.025*** 0.024***
## 8 (0.006) (0.005) (0.004)
## 9 Cash / TA 0.004 -0.024*** -0.002
## 10 (0.004) (0.004) (0.002)
## 11 Loan / Deposit 0.001 -0.020*** -0.007***
## 12 (0.005) (0.005) (0.003)
## 13 Book equity / TA -0.001 -0.012*** 0.001
## 14 (0.004) (0.004) (0.002)
## 15 Wholesale funding 0.005 0.026*** 0.008***
## 16 (0.005) (0.005) (0.003)
## 17 ROA 0.005 0.002 -0.004*
## 18 (0.004) (0.004) (0.002)
## 19 Constant 0.074*** 0.088*** 0.024***
## 20 (0.004) (0.004) (0.002)
## 21
## 22 N 4,632 4,632 4,632
## 23 R² 0.041 0.042 0.039
## 24 Mean of DV 0.0736 0.0889 0.0231
## Arbitrage — DW Only Arbitrage — BTFP Only Arbitrage — Both
## 1 -0.008* 0.013** 0.003
## 2 (0.004) (0.006) (0.003)
## 3 -0.009** 0.014** 0.001
## 4 (0.004) (0.006) (0.003)
## 5 -0.004 0.006 0.003
## 6 (0.003) (0.004) (0.002)
## 7 0.048*** 0.039*** 0.017***
## 8 (0.005) (0.006) (0.003)
## 9 0.003 -0.037*** -0.005***
## 10 (0.004) (0.005) (0.002)
## 11 0.004 -0.034*** -0.005**
## 12 (0.004) (0.006) (0.002)
## 13 -0.005 -0.006 -0.002
## 14 (0.003) (0.005) (0.002)
## 15 -0.004 0.054*** 0.005**
## 16 (0.004) (0.006) (0.003)
## 17 -0.002 -0.016*** -0.004*
## 18 (0.004) (0.005) (0.002)
## 19 0.055*** 0.142*** 0.024***
## 20 (0.003) (0.005) (0.002)
## 21
## 22 4,531 4,531 4,531
## 23 0.037 0.072 0.020
## 24 0.0567 0.1446 0.0245n_coef_5 <- 2 * length(var_order_5)
footer_5 <- n_coef_5 + 2
tbl5_k <- reg_table_5 %>%
kbl(align = c("l", rep("r", 6)),
caption = "Table 5: LPM — Borrower Category Across Crisis and Arbitrage Windows",
booktabs = TRUE) %>%
kable_styling(bootstrap_options = c("striped", "hover", "condensed"),
full_width = FALSE, position = "left", font_size = 11) %>%
add_header_above(c(" " = 1,
"Crisis (Mar 8 – May 4, 2023; 2022Q4 baseline)" = 3,
"Arbitrage (Nov 15, 2023 – Jan 24, 2024; 2023Q3 baseline)" = 3)) %>%
pack_rows("Key solvency-liquidity variables", 1, 6) %>%
pack_rows("Controls", 7, n_coef_5 - 2) %>%
pack_rows("Intercept", n_coef_5 - 1, n_coef_5) %>%
pack_rows("Fit statistics", footer_5, footer_5 + 2) %>%
footnote(general = paste(
"Dependent variables are mutually exclusive borrower categories: DW Only,",
"BTFP Only, Both. Crisis regressions use the 2022Q4 cross-section;",
"arbitrage regressions use 2023Q3. DW loan data covers only 2023, so DW",
"usage in January 2024 is not observed — the Arbitrage DW Only and Both",
"columns effectively capture Nov 15 – Dec 31, 2023 DW activity.",
"All RHS variables winsorized at 2.5/97.5 and z-standardized. HC1 robust",
"SE in parentheses. * p<0.10, ** p<0.05, *** p<0.01."),
general_title = "Notes:", footnote_as_chunk = TRUE)
tbl5_k| Variable | Crisis — DW Only | Crisis — BTFP Only | Crisis — Both | Arbitrage — DW Only | Arbitrage — BTFP Only | Arbitrage — Both |
|---|---|---|---|---|---|---|
| Key solvency-liquidity variables | ||||||
| MTM loss (total) | 0.007 | 0.012** | 0.004 | -0.008* | 0.013** | 0.003 |
| (0.005) | (0.005) | (0.003) | (0.004) | (0.006) | (0.003) | |
| Uninsured leverage | 0.001 | 0.011** | 0.008** | -0.009** | 0.014** | 0.001 |
| (0.005) | (0.005) | (0.003) | (0.004) | (0.006) | (0.003) | |
| MTM × Uninsured Lev | 0.007* | 0.005 | 0.007** | -0.004 | 0.006 | 0.003 |
| (0.004) | (0.004) | (0.003) | (0.003) | (0.004) | (0.002) | |
| Controls | ||||||
| Ln(assets) | 0.051*** | 0.025*** | 0.024*** | 0.048*** | 0.039*** | 0.017*** |
| (0.006) | (0.005) | (0.004) | (0.005) | (0.006) | (0.003) | |
| Cash / TA | 0.004 | -0.024*** | -0.002 | 0.003 | -0.037*** | -0.005*** |
| (0.004) | (0.004) | (0.002) | (0.004) | (0.005) | (0.002) | |
| Loan / Deposit | 0.001 | -0.020*** | -0.007*** | 0.004 | -0.034*** | -0.005** |
| (0.005) | (0.005) | (0.003) | (0.004) | (0.006) | (0.002) | |
| Book equity / TA | -0.001 | -0.012*** | 0.001 | -0.005 | -0.006 | -0.002 |
| (0.004) | (0.004) | (0.002) | (0.003) | (0.005) | (0.002) | |
| Wholesale funding | 0.005 | 0.026*** | 0.008*** | -0.004 | 0.054*** | 0.005** |
| (0.005) | (0.005) | (0.003) | (0.004) | (0.006) | (0.003) | |
| ROA | 0.005 | 0.002 | -0.004* | -0.002 | -0.016*** | -0.004* |
| (0.004) | (0.004) | (0.002) | (0.004) | (0.005) | (0.002) | |
| Intercept | ||||||
| Constant | 0.074*** | 0.088*** | 0.024*** | 0.055*** | 0.142*** | 0.024*** |
| (0.004) | (0.004) | (0.002) | (0.003) | (0.005) | (0.002) | |
| Fit statistics | ||||||
| N | 4,632 | 4,632 | 4,632 | 4,531 | 4,531 | 4,531 |
| R² | 0.041 | 0.042 | 0.039 | 0.037 | 0.072 | 0.020 |
| Mean of DV | 0.0736 | 0.0889 | 0.0231 | 0.0567 | 0.1446 | 0.0245 |
| Notes: Dependent variables are mutually exclusive borrower categories: DW Only, BTFP Only, Both. Crisis regressions use the 2022Q4 cross-section; arbitrage regressions use 2023Q3. DW loan data covers only 2023, so DW usage in January 2024 is not observed — the Arbitrage DW Only and Both columns effectively capture Nov 15 – Dec 31, 2023 DW activity. All RHS variables winsorized at 2.5/97.5 and z-standardized. HC1 robust SE in parentheses. * p<0.10, ** p<0.05, *** p<0.01. | ||||||