Empirical Tests of Joint Solvency-Liquidity Transmission
What Does Emergency Borrowing During A Crisis Reveal About Bank Runs?
Mohua Ferdousi
April 22, 2026
Rpub Links: http://rpubs.com/mohua_ferdousi/1424690
1. Setup
1.1 Libraries
1.2 Helpers
# ── Basic utilities ────────────────────────────────────────────────────
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])
}
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
}
fmt <- function(x, d = 0) formatC(x, format = "f", digits = d, big.mark = ",")
fmt2 <- function(x) formatC(x, format = "f", digits = 2, big.mark = ",")
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 ~ ""
)
fmt_est <- function(est, p) if (is.na(est)) "" else sprintf("%.3f%s", est, stars_pval(p))
fmt_se <- function(se) if (is.na(se)) "" else sprintf("(%.3f)", se)
# ── Winsorize + z-standardize a set of columns in one step ─────────────
wz_cols <- function(data, vars) {
vars <- vars[vars %in% names(data)]
data %>%
mutate(across(all_of(vars), ~ winsorize(.x), .names = "{.col}_w")) %>%
mutate(across(all_of(paste0(vars, "_w")), ~ z_std(.x), .names = "{.col}_z"))
}1.3 Paths and file-saving helpers
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_02")
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()
}1.4 Calibration, periods, and plotting theme
# ── Theory constants ───────────────────────────────────────────────────
y_10yr <- 0.0392
delta_decay <- 0.10
cap_factor <- 1 / (y_10yr + delta_decay)
phi_star_baseline <- 1.0
phi_star_struct <- 0.5
# ── Period dates ───────────────────────────────────────────────────────
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")
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"
)
period_order <- c("P0: Pre-Crisis", "P1: SVB Week",
"P2: SVB to FRC", "P3: FRC Week")
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")
)
# ── Plotting ───────────────────────────────────────────────────────────
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")1.5 Flexible model wrapper (LPM / logit / probit switchable)
# ── GLOBAL MODEL FAMILY ────────────────────────────────────────────────
# Change this single value to switch all extensive-margin regressions
# between: "lpm", "logit", "probit"
# ────────────────────────────────────────────────────────────────────────
MODEL_FAMILY <- "lpm"
#' Fit model with family dispatch
#' @param formula A formula
#' @param data A data frame
#' @param family One of "lpm", "logit", "probit"
fit_model <- function(formula, data, family = MODEL_FAMILY) {
switch(
family,
"lpm" = lm(formula, data = data),
"logit" = glm(formula, data = data, family = binomial(link = "logit")),
"probit" = glm(formula, data = data, family = binomial(link = "probit")),
stop(sprintf("Unknown model family: '%s'", family))
)
}
#' Robust coefficient tidy (works for lm and glm)
#' Uses HC1 for lm, HC0 (sandwich) for glm.
get_robust_tidy <- function(model, vcov_type = "HC1") {
V <- if (inherits(model, "glm") && !inherits(model, "lm")) {
sandwich::vcovHC(model, type = "HC0")
} else {
sandwich::vcovHC(model, type = vcov_type)
}
ct <- lmtest::coeftest(model, vcov. = V)
tibble::tibble(
term = rownames(ct),
estimate = ct[, 1],
std.error = ct[, 2],
p.value = ct[, 4]
)
}
#' Extract model fit stats (works for lm and glm)
get_fit_stats <- function(model) {
n <- nobs(model)
if (inherits(model, "glm") && !inherits(model, "lm")) {
# Pseudo-R² (McFadden)
ll0 <- logLik(update(model, . ~ 1))
pr2 <- 1 - as.numeric(logLik(model) / ll0)
list(n = n, fit_label = "Pseudo R²", fit_value = pr2)
} else {
list(n = n, fit_label = "R²", fit_value = summary(model)$r.squared)
}
}
#' Joint equality test across two subsamples (Chow test)
chow_test <- function(rhs, dv, data, split_var) {
rest_f <- as.formula(paste(dv, "~", split_var, "+", rhs))
full_f <- as.formula(paste(dv, "~", split_var, "*(", rhs, ")"))
m_rest <- fit_model(rest_f, data)
m_full <- fit_model(full_f, data)
V <- if (inherits(m_full, "glm") && !inherits(m_full, "lm"))
sandwich::vcovHC(m_full, type = "HC0")
else sandwich::vcovHC(m_full, type = "HC1")
w <- lmtest::waldtest(m_rest, m_full, vcov = V)
tibble(chi2 = w$F[2], p_value = w$`Pr(>F)`[2])
}
cat(sprintf("Model family in use: %s\n", toupper(MODEL_FAMILY)))## Model family in use: LPM2. Data Loading and Variable Construction
2.1 Load raw datasets
call_raw <- read_csv(file.path(DATA_DIR, "final_call_gsib.csv"),
show_col_types = FALSE) %>%
mutate(idrssd = as.character(idrssd))
btfp_raw <- read_csv(file.path(DATA_DIR, "btfp_loan_bank_only.csv"),
show_col_types = FALSE) %>%
mutate(rssd_id = as.character(rssd_id),
btfp_loan_date = mdy(btfp_loan_date),
btfp_repayment_date = mdy(btfp_repayment_date),
btfp_maturity_date = mdy(btfp_maturity_date))
dw_raw <- read_csv(file.path(DATA_DIR, "dw_loan_bank_2023.csv"),
show_col_types = FALSE) %>%
mutate(rssd_id = as.character(rssd_id),
dw_loan_date = ymd(dw_loan_date),
dw_repayment_date = ymd(dw_repayment_date),
dw_maturity_date = ymd(dw_maturity_date),
dw_credit_type_clean = str_squish(as.character(dw_credit_type))) %>%
filter(str_detect(dw_credit_type_clean, "^Primary Credit"))
dssw_raw <- read_csv(file.path(DATA_DIR, "dssw_deposit_betas.csv"),
show_col_types = FALSE) %>%
mutate(idrssd = as.character(idrssd))
dssw_costs_file <- file.path(DATA_DIR, "dssw_deposit_costs.csv")
HAS_DEPOSIT_COSTS <- file.exists(dssw_costs_file)
if (HAS_DEPOSIT_COSTS) {
dssw_costs_raw <- read_csv(dssw_costs_file, show_col_types = FALSE) %>%
mutate(idrssd = as.character(idrssd))
}
cat(sprintf("Call panel : %s bank-quarters, %s banks\n",
fmt(nrow(call_raw)), fmt(n_distinct(call_raw$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 DSSW merge + franchise variables
dssw_for_quarter <- function(q) {
dssw_raw %>%
filter(estimation_date == q) %>%
select(idrssd, beta_overall, beta_uninsured, beta_insured,
beta_uninsured_w, beta_insured_w)
}
dssw_costs_for_quarter <- function(q) {
if (!HAS_DEPOSIT_COSTS)
return(tibble(idrssd = character(),
deposit_cost_insured = numeric(),
deposit_cost_uninsured = numeric(),
deposit_cost_weighted = numeric()))
dssw_costs_raw %>%
filter(period == q) %>%
select(idrssd, deposit_cost_insured,
deposit_cost_uninsured, deposit_cost_weighted)
}
add_franchise_vars <- function(data) {
data %>%
mutate(
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)),
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),
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),
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
)
}2.3 Build 2022Q4 cross-section with all derived variables
df <- call_raw %>%
filter(period == "2022Q4", gsib == 0, failed_bank == 0) %>%
left_join(dssw_for_quarter("2022Q4"), by = "idrssd") %>%
left_join(dssw_costs_for_quarter("2022Q4"), by = "idrssd") %>%
add_franchise_vars() %>%
mutate(
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),
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,
# ── Solvency measures: three views ──────────────────────────────
# (1) With full franchise (DSSW view)
E_MV = total_equity - all_asset_loss,
E_MV_F = E_MV + F_total,
emv_f_ta = 100 * safe_div(E_MV_F, total_asset),
# (2) Post-uninsured-run (key measure in the paper)
E_MV_F_insured = E_MV + F_insured,
v_postrun = E_MV_F_insured,
v_postrun_ta = 100 * safe_div(v_postrun, total_asset),
# (3) Without franchise (naive mark-to-market)
emv_ta = 100 * safe_div(E_MV, total_asset),
# Liquidity & coverage
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),
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),
ell_x_uninsured = ell * du_ta,
# Negative solvency flags
emv_neg = as.integer(E_MV < 0),
emv_f_neg = as.integer(E_MV_F < 0),
v_postrun_neg = as.integer(v_postrun < 0),
# Liabilities
fhlb_ta = fhlb_to_total_asset,
wholesale_ta = fed_fund_purchase_to_total_asset + repo_to_total_asset +
fhlb_to_total_asset + other_borr_to_total_asset,
# Convenience
ta_billion = total_asset / 1e6,
mu_pct = 100 * mu,
loan_to_dep = 100 * safe_div(total_loan, total_deposit),
di_ta = 100 * safe_div(insured_deposit, total_asset, 0)
)
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$beta_overall))))## DSSW merge: 4,602 matched (98.0%)2.4 Period-tagged loan tables
btfp_clean <- btfp_raw %>% filter(failed_bank == 0) %>%
mutate(sub_period = assign_period(btfp_loan_date))
dw_clean <- dw_raw %>% filter(failed_bank == 0) %>%
mutate(sub_period = assign_period(dw_loan_date))
dw_pf <- dw_clean %>%
filter(dw_loan_date >= P0_start, dw_loan_date <= P3_end) %>%
mutate(period = assign_period(dw_loan_date),
rssd_id = as.character(rssd_id))
btfp_pf <- btfp_clean %>%
filter(btfp_loan_date >= P2_start, btfp_loan_date <= P3_end) %>%
mutate(period = assign_period(btfp_loan_date),
rssd_id = as.character(rssd_id))
all_borrow <- bind_rows(
dw_pf %>% select(rssd_id, period),
btfp_pf %>% select(rssd_id, period)
)
prior_set <- function(p) {
i <- match(p, period_order)
if (i == 1) return(character(0))
unique(all_borrow$rssd_id[all_borrow$period %in% period_order[seq_len(i - 1)]])
}
banks_in_cell <- function(p, f) {
data <- if (f == "DW") dw_pf else btfp_pf
unique(data$rssd_id[data$period == p])
}2.5 Classify borrowers and merge loan aggregates
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)
btfp_bank <- btfp_crisis %>%
group_by(rssd_id) %>%
summarise(
btfp_amount = sum(btfp_loan_amount, na.rm = TRUE) / 1000,
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)
dw_bank <- dw_crisis %>%
group_by(rssd_id) %>%
summarise(
dw_amount = sum(dw_loan_amount, na.rm = TRUE) / 1000,
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),
log_borrow = ifelse(total_borrow > 0, log(total_borrow), NA_real_)
)
cat(sprintf("\nBorrower counts (crisis %s to %s):\n", CRISIS_START, CRISIS_END))##
## Borrower counts (crisis 2023-03-08 to 2023-05-04):for (t in c("Non-Borrower", "DW Only", "BTFP Only", "Both"))
cat(sprintf(" %-13s: %s\n", t, fmt(sum(df$borrower_type == t))))## Non-Borrower : 3,836
## DW Only : 341
## BTFP Only : 412
## Both : 107## Total sample : 4,6962.6 Regression-ready variables
reg_vars <- c(
"f_ta", "fu_ta", "fi_ta", "emv_ta", "v_postrun_ta", "emv_f_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", "di_ta", "mu", "wholesale_ta",
"log_ta", "loan_to_dep", "roa", "borrow_ta"
)
df <- wz_cols(df, reg_vars)
cat(sprintf("Regression transforms: %s winsorized+standardized vars\n",
fmt(sum(paste0(reg_vars, "_w_z") %in% names(df)))))## Regression transforms: 30 winsorized+standardized vars2.7 Arbitrage-window sample
btfp_arb_bank <- btfp_clean %>%
filter(btfp_loan_date >= ARB_START, btfp_loan_date <= ARB_END) %>%
group_by(rssd_id) %>%
summarise(btfp_arb_amount = sum(btfp_loan_amount, na.rm = TRUE) / 1000,
.groups = "drop") %>%
rename(idrssd = rssd_id)
df_arb <- call_raw %>%
filter(period == "2023Q3", gsib == 0, failed_bank == 0) %>%
left_join(dssw_for_quarter("2022Q4"), by = "idrssd") %>%
left_join(dssw_costs_for_quarter("2022Q4"), by = "idrssd") %>%
add_franchise_vars() %>%
mutate(
idrssd = as.character(idrssd),
# ── 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,
E_MV = total_equity - all_asset_loss,
v_postrun = E_MV + F_insured,
v_postrun_ta = 100 * safe_div(v_postrun, total_asset),
eq_ta = book_equity_to_total_asset,
cash_ta = cash_to_total_asset,
du_ta = uninsured_leverage,
log_ta = log(total_asset),
loan_to_dep = 100 * safe_div(total_loan, total_deposit),
wholesale_ta = fed_fund_purchase_to_total_asset + repo_to_total_asset +
fhlb_to_total_asset + other_borr_to_total_asset,
roa = roa
) %>%
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)
)
df_arb <- wz_cols(df_arb, c("ell", "du_ta", "log_ta", "cash_ta",
"loan_to_dep", "eq_ta", "wholesale_ta", "roa"))
cat(sprintf("Arbitrage sample: %s banks, %s borrowers\n",
fmt(nrow(df_arb)), fmt(sum(df_arb$borrowed_arb))))## Arbitrage sample: 4,604 banks, 766 borrowers3. Descriptive Tables
3.1 Table 1 — Emergency Borrowing by Sub-Period × Facility
The refined Table 1 adds three maturity-band rows that tell the DW-liquidity vs BTFP-solvency story in one glance:
- <5 days: emergency overnight liquidity — routine DW use, liquid-but-stressed banks
- 5–90 days: within the DW contractual maximum — banks wanting term funding for weeks
- >90 days: beyond the DW maximum — BTFP’s unique role as a term solvency tool
# ── Per-loan helper columns (maturity bands, early repayment) ──────────
add_loan_fields <- function(data, amt, coll, term, repay, mat,
held, rate, facility_name, date_col) {
data %>%
mutate(
amt_b = !!sym(amt) / 1e9, # loan principal, $B
coll_b = !!sym(coll) / 1e9,
loan_to_coll = safe_div(!!sym(amt), !!sym(coll)),
term_days = !!sym(term),
held_days = !!sym(held),
rate_pct = !!sym(rate),
mat_band = dplyr::case_when(
term_days < 5 ~ "<5 days",
term_days >= 5 & term_days <= 90 ~ "5-90 days",
term_days > 90 ~ ">90 days",
TRUE ~ NA_character_
),
early_repay = as.integer(!is.na(!!sym(repay)) & !is.na(!!sym(mat)) &
!!sym(repay) < !!sym(mat)),
facility = facility_name,
loan_date = !!sym(date_col)
)
}
dw_L <- add_loan_fields(dw_pf, "dw_loan_amount", "dw_total_collateral",
"dw_term", "dw_repayment_date", "dw_maturity_date",
"dw_effective_maturity_days", "dw_interest_rate",
"DW", "dw_loan_date")
btfp_L <- add_loan_fields(btfp_pf, "btfp_loan_amount", "btfp_total_collateral",
"btfp_term", "btfp_repayment_date", "btfp_maturity_date",
"btfp_effective_maturity_days", "btfp_interest_rate",
"BTFP", "btfp_loan_date")
loans_all <- bind_rows(
dw_L %>% select(period, facility, rssd_id, amt_b, coll_b, loan_to_coll,
term_days, held_days, rate_pct, mat_band, early_repay),
btfp_L %>% select(period, facility, rssd_id, amt_b, coll_b, loan_to_coll,
term_days, held_days, rate_pct, mat_band, early_repay)
)
# ── Build each cell's stats ────────────────────────────────────────────
build_cell_stats <- function(p, f) {
loans <- loans_all %>% filter(period == p, facility == f)
if (nrow(loans) == 0)
return(tibble(col_id = paste(p, f, sep = " | ")))
banks_cell <- unique(loans$rssd_id)
n_banks <- length(banks_cell)
prior <- prior_set(p)
n_new <- sum(!(banks_cell %in% prior))
n_return <- sum(banks_cell %in% prior)
per_bank <- loans %>%
group_by(rssd_id) %>%
summarise(bank_total = sum(amt_b, na.rm = TRUE), .groups = "drop")
total_b <- sum(per_bank$bank_total, na.rm = TRUE)
mean_m <- mean(per_bank$bank_total, na.rm = TRUE) * 1000
median_m <- median(per_bank$bank_total, na.rm = TRUE) * 1000
tibble(
col_id = paste(p, f, sep = " | "),
`N (Loans)` = nrow(loans),
`N (Banks)` = n_banks,
`New banks` = n_new,
`Returning banks` = n_return,
`Total borrow ($B)` = total_b,
`Mean borrow ($M)` = mean_m,
`Median borrow ($M)` = median_m,
`Loan/Coll (aggregate)` = sum(loans$amt_b, na.rm = TRUE) /
pmax(sum(loans$coll_b, na.rm = TRUE), 1e-12),
`Term — mean (days)` = mean(loans$term_days, na.rm = TRUE),
`Term — median (days)` = median(loans$term_days, na.rm = TRUE),
# ── Maturity bands (NEW) ──
`% Term <5 days` = 100 * mean(loans$mat_band == "<5 days", na.rm = TRUE),
`% Term 5-90 days` = 100 * mean(loans$mat_band == "5-90 days", na.rm = TRUE),
`% Term >90 days` = 100 * mean(loans$mat_band == ">90 days", na.rm = TRUE),
`% Early repayment` = 100 * mean(loans$early_repay, na.rm = TRUE),
`Held days — mean` = mean(loans$held_days, na.rm = TRUE),
`Held days — median` = median(loans$held_days, na.rm = TRUE),
`Rate (%)` = mean(loans$rate_pct, na.rm = TRUE)
)
}
cell_stats <- col_specs %>%
rowwise() %>%
mutate(stats = list(build_cell_stats(period, facility))) %>%
pull(stats) %>% bind_rows()
# Pivot: stats × (period × facility)
table1 <- cell_stats %>%
pivot_longer(-col_id, names_to = "Statistic", values_to = "value") %>%
pivot_wider(names_from = col_id, values_from = value) %>%
mutate(Statistic = factor(Statistic, levels = c(
"N (Loans)", "N (Banks)", "New banks", "Returning banks",
"Total borrow ($B)", "Mean borrow ($M)", "Median borrow ($M)",
"Loan/Coll (aggregate)",
"Term — mean (days)", "Term — median (days)",
"% Term <5 days", "% Term 5-90 days", "% Term >90 days",
"% Early repayment",
"Held days — mean", "Held days — median",
"Rate (%)"
))) %>% arrange(Statistic)
print(table1, n = Inf)## # A tibble: 17 × 7
## Statistic `P0: Pre-Crisis | DW` `P1: SVB Week | DW` `P2: SVB to FRC | DW`
## <fct> <dbl> <dbl> <dbl>
## 1 N (Loans) 171 124 1492
## 2 N (Banks) 72 68 406
## 3 New banks 72 33 340
## 4 Returning ba… 0 35 66
## 5 Total borrow… 9.46 10.1 518.
## 6 Mean borrow … 131. 149. 1277.
## 7 Median borro… 9.75 8.98 0.5
## 8 Loan/Coll (a… 0.172 0.176 0.329
## 9 Term — mean … 5.25 3.84 4.41
## 10 Term — media… 1 1 1
## 11 % Term <5 da… 86.5 87.1 88.0
## 12 % Term 5-90 … 13.5 12.9 11.9
## 13 % Term >90 d… 0 0 0.134
## 14 % Early repa… 6.43 5.65 4.83
## 15 Held days — … 4.08 3.02 3.01
## 16 Held days — … 1 1 1
## 17 Rate (%) 4.75 4.75 4.92
## # ℹ 3 more variables: `P2: SVB to FRC | BTFP` <dbl>, `P3: FRC Week | DW` <dbl>,
## # `P3: FRC Week | BTFP` <dbl>save_kbl_latex(table1, "table1_emergency_borrowing",
caption = "Emergency borrowing by sub-period × facility, with maturity-band decomposition.")
kbl(table1, digits = 3, align = c("l", rep("r", 6)),
caption = "Table 1: Emergency Borrowing by Sub-Period × Facility") %>%
kable_styling(bootstrap_options = c("striped", "hover", "condensed"),
full_width = FALSE, font_size = 11) %>%
pack_rows("Counts", 1, 4) %>%
pack_rows("Dollar volumes", 5, 7) %>%
pack_rows("Collateral", 8, 8) %>%
pack_rows("Term structure", 9, 13) %>%
pack_rows("Repayment", 14, 16) %>%
pack_rows("Pricing", 17, 17) %>%
footnote(general = paste(
"Maturity bands are defined at origination. <5 days captures",
"overnight/emergency liquidity. 5-90 days captures term funding within the",
"Discount Window's contractual maximum. >90 days captures funding beyond",
"the DW maximum — a range where only BTFP operates. BTFP became operational",
"on March 13, 2023 (start of P2)."),
general_title = "Notes:", footnote_as_chunk = TRUE)| 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 |
|---|---|---|---|---|---|---|
| Counts | ||||||
| N (Loans) | 171.000 | 124.000 | 1492.000 | 1032.000 | 213.000 | 279.000 |
| N (Banks) | 72.000 | 68.000 | 406.000 | 472.000 | 101.000 | 184.000 |
| New banks | 72.000 | 33.000 | 340.000 | 442.000 | 34.000 | 54.000 |
| Returning banks | 0.000 | 35.000 | 66.000 | 30.000 | 67.000 | 130.000 |
| Dollar volumes | ||||||
| Total borrow (\(B) </td> <td style="text-align:right;"> 9.455 </td> <td style="text-align:right;"> 10.102 </td> <td style="text-align:right;"> 518.485 </td> <td style="text-align:right;"> 122.358 </td> <td style="text-align:right;"> 9.613 </td> <td style="text-align:right;"> 11.326 </td> </tr> <tr> <td style="text-align:left;padding-left: 2em;" indentlevel="1"> Mean borrow (\)M) | 131.324 | 148.565 | 1277.056 | 259.232 | 95.175 | 61.553 |
| Median borrow ($M) | 9.750 | 8.977 | 0.500 | 20.000 | 4.000 | 12.850 |
| Collateral | ||||||
| Loan/Coll (aggregate) | 0.172 | 0.176 | 0.329 | 0.406 | 0.146 | 0.294 |
| Term structure | ||||||
| Term — mean (days) | 5.251 | 3.839 | 4.405 | 313.568 | 3.831 | 322.305 |
| Term — median (days) | 1.000 | 1.000 | 1.000 | 365.000 | 1.000 | 365.000 |
| % Term <5 days | 86.550 | 87.097 | 88.003 | 10.659 | 90.610 | 7.527 |
| % Term 5-90 days | 13.450 | 12.903 | 11.863 | 2.907 | 9.390 | 3.584 |
| % Term >90 days | 0.000 | 0.000 | 0.134 | 86.434 | 0.000 | 88.889 |
| Repayment | ||||||
| % Early repayment | 6.433 | 5.645 | 4.826 | 64.922 | 2.817 | 60.932 |
| Held days — mean | 4.076 | 3.016 | 3.005 | 151.043 | 2.784 | 177.219 |
| Held days — median | 1.000 | 1.000 | 1.000 | 14.500 | 1.000 | 222.000 |
| Pricing | ||||||
| Rate (%) | 4.750 | 4.750 | 4.920 | 4.678 | 5.050 | 4.788 |
| Notes: Maturity bands are defined at origination. <5 days captures overnight/emergency liquidity. 5-90 days captures term funding within the Discount Window’s contractual maximum. >90 days captures funding beyond the DW maximum — a range where only BTFP operates. BTFP became operational on March 13, 2023 (start of P2). | ||||||
3.2 Table 2 — Borrower Characteristics vs Non-Borrowers
Redesigned structure: - Panel A — Theory-relevant variables (what the DSSW/ours prediction depends on) - Panel B — Standard bank controls (regression covariates) - New “Diff vs Never” column with t-test stars
# Safe t-test wrapper
t_diff_star <- function(x, y) {
x <- x[is.finite(x)]; y <- y[is.finite(y)]
if (length(x) < 3 || length(y) < 3) return(list(diff = NA_real_, p = NA_real_))
t <- suppressWarnings(t.test(x, y))
list(diff = mean(x, na.rm = TRUE) - mean(y, na.rm = TRUE), p = t$p.value)
}
nonborr <- df %>% filter(borrower_type == "Non-Borrower")
# Cell bank set (all rssd_ids that appear in the cell's loan set)
cell_bank_df <- function(p, f) {
ids <- banks_in_cell(p, f)
df %>% filter(idrssd %in% ids)
}
# Variables to show, in order, labels and source columns
vars_panelA <- tribble(
~label, ~col,
"Uninsured leverage (%)", "du_ta",
"MTM loss / TA (%)", "ell",
"OMO-Sec MTM loss / TA (%)", "ell_omo",
"Liquidity buffer ρ (C+θS)/Du", "rho",
"Franchise / TA (%)", "f_ta",
"v (post-run) / TA (%)", "v_postrun_ta"
)
vars_panelB <- tribble(
~label, ~col,
"Total assets ($B)", "ta_billion",
"Book equity / TA (%)", "eq_ta",
"Cash / TA (%)", "cash_ta",
"Loan / Deposit (%)", "loan_to_dep",
"Wholesale funding / TA (%)", "wholesale_ta",
"ROA (%)", "roa"
)
build_char_row <- function(var_col, label) {
out <- tibble(Statistic = label)
for (i in seq_len(nrow(col_specs))) {
p <- col_specs$period[i]; f <- col_specs$facility[i]
cid <- col_specs$col_id[i]
cell <- cell_bank_df(p, f)
m_val <- mean(cell[[var_col]], na.rm = TRUE)
diff <- t_diff_star(cell[[var_col]], nonborr[[var_col]])
out[[cid]] <- sprintf("%.2f%s", m_val, stars_pval(diff$p))
}
out[["Non-Borrower (N=3,815)"]] <- sprintf("%.2f", mean(nonborr[[var_col]], na.rm = TRUE))
out
}
panelA <- map2_dfr(vars_panelA$col, vars_panelA$label, build_char_row)
panelB <- map2_dfr(vars_panelB$col, vars_panelB$label, build_char_row)
# Add bank counts at top
bank_counts <- tibble(Statistic = "N (banks)")
for (i in seq_len(nrow(col_specs))) {
bank_counts[[col_specs$col_id[i]]] <- fmt(
nrow(cell_bank_df(col_specs$period[i], col_specs$facility[i])))
}
bank_counts[["Non-Borrower (N=3,815)"]] <- fmt(nrow(nonborr))
table2 <- bind_rows(bank_counts, panelA, panelB)
print(table2, n = Inf)## # A tibble: 13 × 8
## Statistic `P0: Pre-Crisis | DW` `P1: SVB Week | DW` `P2: SVB to FRC | DW`
## <chr> <chr> <chr> <chr>
## 1 N (banks) 72 67 397
## 2 Uninsured le… 26.87*** 29.52*** 28.45***
## 3 MTM loss / T… 9.33* 8.92 9.03***
## 4 OMO-Sec MTM … 1.39** 1.68*** 1.65***
## 5 Liquidity bu… 0.62*** 0.57*** 1.09**
## 6 Franchise / … 12.42*** 11.94*** 12.54***
## 7 v (post-run)… 9.28*** 8.51*** 9.43***
## 8 Total assets… 4.40* 7.59*** 6.51***
## 9 Book equity … 9.05*** 8.41*** 8.89***
## 10 Cash / TA (%) 4.38*** 3.77*** 6.08***
## 11 Loan / Depos… 76.00 78.28*** 75.73***
## 12 Wholesale fu… 5.65*** 6.72*** 5.04***
## 13 ROA (%) 1.03* 1.04* 1.16
## # ℹ 4 more variables: `P2: SVB to FRC | BTFP` <chr>, `P3: FRC Week | DW` <chr>,
## # `P3: FRC Week | BTFP` <chr>, `Non-Borrower (N=3,815)` <chr>save_kbl_latex(table2, "table2_borrower_characteristics",
caption = "Borrower vs non-borrower characteristics at 2022Q4. Stars from t-tests vs non-borrower mean.")
n_panelA <- nrow(panelA); n_panelB <- nrow(panelB)
kbl(table2, align = c("l", rep("r", 7)),
caption = "Table 2: Borrower Characteristics by Cell vs Non-Borrowers (2022Q4)") %>%
kable_styling(bootstrap_options = c("striped", "hover", "condensed"),
full_width = FALSE, font_size = 11) %>%
pack_rows("Panel A. Theory-relevant variables", 2, 1 + n_panelA) %>%
pack_rows("Panel B. Standard bank controls",
2 + n_panelA, 1 + n_panelA + n_panelB) %>%
footnote(general = paste(
"Significance stars compare cell mean vs non-borrower mean via two-sided",
"t-test. Liquidity buffer ρ = (Cash + MV of OMO-eligible securities) /",
"Uninsured deposits. Franchise f/TA and v/TA are Option A (DSSW) measures",
"using estimated uninsured deposit betas. * p<0.10, ** p<0.05, *** p<0.01."),
general_title = "Notes:", footnote_as_chunk = TRUE)| 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 (N=3,815) |
|---|---|---|---|---|---|---|---|
| N (banks) | 72 | 67 | 397 | 460 | 101 | 182 | 3,836 |
| Panel A. Theory-relevant variables | |||||||
| Uninsured leverage (%) | 26.87*** | 29.52*** | 28.45*** | 27.42*** | 25.96*** | 26.89*** | 22.40 |
| MTM loss / TA (%) | 9.33* | 8.92 | 9.03*** | 9.61*** | 8.78 | 9.90*** | 8.40 |
| OMO-Sec MTM loss / TA (%) | 1.39** | 1.68*** | 1.65*** | 1.78*** | 1.51** | 1.76*** | 1.05 |
| Liquidity buffer ρ (C+θS)/Du | 0.62*** | 0.57*** | 1.09** | 0.78*** | 0.75*** | 0.73*** | 2.90 |
| Franchise / TA (%) | 12.42*** | 11.94*** | 12.54*** | 12.78*** | 12.53*** | 13.23 | 13.25 |
| v (post-run) / TA (%) | 9.28*** | 8.51*** | 9.43*** | 8.43*** | 10.12*** | 8.35*** | 12.64 |
| Panel B. Standard bank controls | |||||||
| Total assets ($B) | 4.40* | 7.59*** | 6.51*** | 6.35*** | 2.76 | 5.12 | 1.70 |
| Book equity / TA (%) | 9.05*** | 8.41*** | 8.89*** | 8.16*** | 8.99*** | 8.10*** | 11.38 |
| Cash / TA (%) | 4.38*** | 3.77*** | 6.08*** | 4.68*** | 5.34*** | 4.19*** | 9.55 |
| Loan / Deposit (%) | 76.00 | 78.28*** | 75.73*** | 72.96 | 76.20** | 70.95 | 71.94 |
| Wholesale funding / TA (%) | 5.65*** | 6.72*** | 5.04*** | 5.48*** | 5.33*** | 5.09*** | 3.33 |
| ROA (%) | 1.03* | 1.04* | 1.16 | 1.07* | 1.15 | 1.01* | 1.42 |
| Notes: Significance stars compare cell mean vs non-borrower mean via two-sided t-test. Liquidity buffer ρ = (Cash + MV of OMO-eligible securities) / Uninsured deposits. Franchise f/TA and v/TA are Option A (DSSW) measures using estimated uninsured deposit betas. * p<0.10, ** p<0.05, *** p<0.01. | |||||||
3.3 Table 3 — Solvency Three Views
Three solvency panels to reveal how solvency depends on the franchise assumption: - Panel A (with full franchise): E^{MV} + F_total — DSSW’s view. Almost all banks solvent. - Panel B (post-uninsured run): v = E^{MV} + F_insured — paper’s v measure. - Panel C (without franchise): E^{MV} = equity − MTM loss — naive mark-to-market.
solvency_stats <- function(col_var, neg_flag, data) {
tibble(
mean_pct = mean(data[[col_var]], na.rm = TRUE),
median_pct = median(data[[col_var]], na.rm = TRUE),
share_neg = 100 * mean(data[[neg_flag]], na.rm = TRUE)
)
}
build_solvency_panel <- function(measure_col, neg_col, panel_label) {
out <- tibble(
Statistic = c(sprintf("%s mean (%%)", panel_label),
sprintf("%s median (%%)", panel_label),
sprintf("%% with %s < 0", panel_label))
)
for (i in seq_len(nrow(col_specs))) {
p <- col_specs$period[i]; f <- col_specs$facility[i]
cell <- cell_bank_df(p, f)
s <- solvency_stats(measure_col, neg_col, cell)
out[[col_specs$col_id[i]]] <- c(
sprintf("%.2f", s$mean_pct),
sprintf("%.2f", s$median_pct),
sprintf("%.2f", s$share_neg)
)
}
s_nb <- solvency_stats(measure_col, neg_col, nonborr)
out[["Non-Borrower"]] <- c(
sprintf("%.2f", s_nb$mean_pct),
sprintf("%.2f", s_nb$median_pct),
sprintf("%.2f", s_nb$share_neg)
)
out
}
solv_A <- build_solvency_panel("emv_f_ta", "emv_f_neg", "E^MV + F_total / TA")
solv_B <- build_solvency_panel("v_postrun_ta", "v_postrun_neg", "v = E^MV + F_insured / TA")
solv_C <- build_solvency_panel("emv_ta", "emv_neg", "E^MV / TA")
# N row
n_row <- tibble(Statistic = "N (banks)")
for (i in seq_len(nrow(col_specs))) {
n_row[[col_specs$col_id[i]]] <- fmt(
nrow(cell_bank_df(col_specs$period[i], col_specs$facility[i])))
}
n_row[["Non-Borrower"]] <- fmt(nrow(nonborr))
table3 <- bind_rows(n_row, solv_A, solv_B, solv_C)
print(table3, n = Inf)## # A tibble: 10 × 8
## Statistic `P0: Pre-Crisis | DW` `P1: SVB Week | DW` `P2: SVB to FRC | DW`
## <chr> <chr> <chr> <chr>
## 1 N (banks) 72 67 397
## 2 E^MV + F_tot… 12.14 11.42 12.52
## 3 E^MV + F_tot… 11.66 11.45 12.49
## 4 % with E^MV … 0.00 0.00 1.02
## 5 v = E^MV + F… 9.28 8.51 9.43
## 6 v = E^MV + F… 8.58 8.42 9.43
## 7 % with v = E… 1.39 1.49 3.81
## 8 E^MV / TA me… -0.27 -0.52 -0.13
## 9 E^MV / TA me… -0.84 -1.18 -0.23
## 10 % with E^MV … 59.72 58.21 51.89
## # ℹ 4 more variables: `P2: SVB to FRC | BTFP` <chr>, `P3: FRC Week | DW` <chr>,
## # `P3: FRC Week | BTFP` <chr>, `Non-Borrower` <chr>save_kbl_latex(table3, "table3_solvency_three_views",
caption = "Solvency under three franchise views: with full franchise, post-uninsured run, and without franchise.")
kbl(table3, align = c("l", rep("r", 7)),
caption = "Table 3: Solvency by Franchise Assumption") %>%
kable_styling(bootstrap_options = c("striped", "hover", "condensed"),
full_width = FALSE, font_size = 11) %>%
pack_rows("Panel A. With full franchise (E^MV + F_total)", 2, 4) %>%
pack_rows("Panel B. Post uninsured run (v = E^MV + F_ins)", 5, 7) %>%
pack_rows("Panel C. Without franchise (E^MV = E - MTM)", 8, 10) %>%
footnote(general = paste(
"Panel A is DSSW's solvency measure where the full deposit franchise is",
"preserved. Panel B measures fundamental value after an uninsured run",
"destroys the uninsured franchise, retaining only insured franchise value.",
"Panel C is the naive mark-to-market equity without any franchise benefit.",
"The % with value < 0 row reveals how many banks become technically",
"insolvent under each view."),
general_title = "Notes:", footnote_as_chunk = TRUE)| 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 |
|---|---|---|---|---|---|---|---|
| N (banks) | 72 | 67 | 397 | 460 | 101 | 182 | 3,836 |
| Panel A. With full franchise (E^MV + F_total) | |||||||
| E^MV + F_total / TA mean (%) | 12.14 | 11.42 | 12.52 | 11.43 | 12.87 | 11.42 | 15.18 |
| E^MV + F_total / TA median (%) | 11.66 | 11.45 | 12.49 | 11.58 | 12.82 | 11.63 | 14.61 |
| % with E^MV + F_total / TA < 0 | 0.00 | 0.00 | 1.02 | 0.66 | 1.00 | 0.55 | 0.51 |
| Panel B. Post uninsured run (v = E^MV + F_ins) | |||||||
| v = E^MV + F_insured / TA mean (%) | 9.28 | 8.51 | 9.43 | 8.43 | 10.12 | 8.35 | 12.64 |
| v = E^MV + F_insured / TA median (%) | 8.58 | 8.42 | 9.43 | 8.63 | 9.59 | 8.71 | 11.99 |
| % with v = E^MV + F_insured / TA < 0 | 1.39 | 1.49 | 3.81 | 4.40 | 2.00 | 5.49 | 1.41 |
| Panel C. Without franchise (E^MV = E - MTM) | |||||||
| E^MV / TA mean (%) | -0.27 | -0.52 | -0.13 | -1.45 | 0.22 | -1.81 | 2.77 |
| E^MV / TA median (%) | -0.84 | -1.18 | -0.23 | -1.08 | 0.04 | -1.39 | 1.52 |
| % with E^MV / TA < 0 | 59.72 | 58.21 | 51.89 | 58.91 | 48.51 | 59.89 | 40.34 |
| Notes: Panel A is DSSW’s solvency measure where the full deposit franchise is preserved. Panel B measures fundamental value after an uninsured run destroys the uninsured franchise, retaining only insured franchise value. Panel C is the naive mark-to-market equity without any franchise benefit. The % with value < 0 row reveals how many banks become technically insolvent under each view. | |||||||
3.4 Table 4 — Concentration of Borrowing
New table making the concentration finding the headline empirical fact:
build_concentration <- function() {
out <- tibble(Statistic = c(
"N banks in cell",
"Top 3 banks' share of $ (%)",
"Top 10 banks' share of $ (%)",
"Top decile share of $ (%)",
"HHI",
"Median borrow ($M)",
"Mean borrow ($M)",
"Mean/Median ratio"
))
for (i in seq_len(nrow(col_specs))) {
p <- col_specs$period[i]; f <- col_specs$facility[i]
cid <- col_specs$col_id[i]
loans <- loans_all %>% filter(period == p, facility == f)
if (nrow(loans) == 0) {
out[[cid]] <- rep(NA_character_, 8); next
}
per_bank <- loans %>%
group_by(rssd_id) %>%
summarise(b = sum(amt_b, na.rm = TRUE), .groups = "drop")
total <- sum(per_bank$b)
shares <- per_bank$b / total
sorted <- sort(per_bank$b, decreasing = TRUE)
n <- nrow(per_bank)
decile_n <- max(ceiling(n * 0.10), 1)
top3 <- sum(head(sorted, 3)) / total * 100
top10 <- sum(head(sorted, 10)) / total * 100
top_dec <- sum(head(sorted, decile_n)) / total * 100
hhi <- sum(shares^2)
med <- median(per_bank$b) * 1000
mean_val <- mean(per_bank$b) * 1000
out[[cid]] <- c(
fmt(n),
sprintf("%.1f", top3),
sprintf("%.1f", top10),
sprintf("%.1f", top_dec),
sprintf("%.3f", hhi),
sprintf("%.2f", med),
sprintf("%.2f", mean_val),
sprintf("%.1f×", mean_val / pmax(med, 1e-9))
)
}
out
}
table4 <- build_concentration()
print(table4, n = Inf)## # A tibble: 8 × 7
## Statistic `P0: Pre-Crisis | DW` `P1: SVB Week | DW` `P2: SVB to FRC | DW`
## <chr> <chr> <chr> <chr>
## 1 N banks in ce… 72 68 406
## 2 Top 3 banks' … 48.8 42.6 81.4
## 3 Top 10 banks'… 83.8 84.2 94.3
## 4 Top decile sh… 77.5 73.6 99.1
## 5 HHI 0.102 0.096 0.338
## 6 Median borrow… 9.75 8.98 0.50
## 7 Mean borrow (… 131.32 148.56 1277.06
## 8 Mean/Median r… 13.5× 16.5× 2554.1×
## # ℹ 3 more variables: `P2: SVB to FRC | BTFP` <chr>, `P3: FRC Week | DW` <chr>,
## # `P3: FRC Week | BTFP` <chr>save_kbl_latex(table4, "table4_concentration",
caption = "Concentration of emergency borrowing within each cell.")
kbl(table4, align = c("l", rep("r", 6)),
caption = "Table 4: Borrowing Concentration by Cell") %>%
kable_styling(bootstrap_options = c("striped", "hover", "condensed"),
full_width = FALSE, font_size = 11) %>%
footnote(general = paste(
"Top-3, Top-10, and top-decile shares show cumulative dollar-borrowing",
"concentration within each cell. HHI is the Herfindahl-Hirschman Index",
"of within-cell borrowing shares; values above 0.25 indicate high",
"concentration. A large mean/median ratio indicates extreme right-skew",
"in borrowing volumes."),
general_title = "Notes:", footnote_as_chunk = TRUE)| 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 |
|---|---|---|---|---|---|---|
| N banks in cell | 72 | 68 | 406 | 472 | 101 | 184 |
| Top 3 banks’ share of $ (%) | 48.8 | 42.6 | 81.4 | 46.4 | 52.1 | 23.8 |
| Top 10 banks’ share of $ (%) | 83.8 | 84.2 | 94.3 | 65.0 | 82.3 | 57.3 |
| Top decile share of $ (%) | 77.5 | 73.6 | 99.1 | 87.7 | 84.2 | 71.0 |
| HHI | 0.102 | 0.096 | 0.338 | 0.120 | 0.135 | 0.039 |
| Median borrow (\(M) </td> <td style="text-align:right;"> 9.75 </td> <td style="text-align:right;"> 8.98 </td> <td style="text-align:right;"> 0.50 </td> <td style="text-align:right;"> 20.00 </td> <td style="text-align:right;"> 4.00 </td> <td style="text-align:right;"> 12.85 </td> </tr> <tr> <td style="text-align:left;"> Mean borrow (\)M) | 131.32 | 148.56 | 1277.06 | 259.23 | 95.17 | 61.55 |
| Mean/Median ratio | 13.5× | 16.5× | 2554.1× | 13.0× | 23.8× | 4.8× |
| Notes: Top-3, Top-10, and top-decile shares show cumulative dollar-borrowing concentration within each cell. HHI is the Herfindahl-Hirschman Index of within-cell borrowing shares; values above 0.25 indicate high concentration. A large mean/median ratio indicates extreme right-skew in borrowing volumes. |
3.5 Table 5 — Test-Borrower Classification (BTFP)
TEST_THRESHOLD <- 1e6
btfp_bank_summary <- btfp_clean %>%
filter(btfp_loan_date >= P2_start, btfp_loan_date <= P3_end) %>%
mutate(rssd_id = as.character(rssd_id)) %>%
group_by(rssd_id) %>%
summarise(
n_loans_total = n(),
n_test_loans = sum(btfp_loan_amount < TEST_THRESHOLD),
smallest_m = min(btfp_loan_amount, na.rm = TRUE) / 1e6,
largest_m = max(btfp_loan_amount, na.rm = TRUE) / 1e6,
total_all_m = sum(btfp_loan_amount, na.rm = TRUE) / 1e6,
.groups = "drop"
) %>%
mutate(tester_type = dplyr::case_when(
largest_m < TEST_THRESHOLD / 1e6 ~ "Pure tester",
smallest_m < TEST_THRESHOLD / 1e6 ~ "Tested then borrowed",
TRUE ~ "No tiny loans"
),
tester_type = factor(tester_type,
levels = c("Pure tester", "Tested then borrowed", "No tiny loans"))) %>%
left_join(df %>% select(idrssd, total_asset, cash_ta, du_ta, ell,
eq_ta, wholesale_ta),
by = c("rssd_id" = "idrssd"))
table5 <- btfp_bank_summary %>%
group_by(tester_type) %>%
summarise(
`N (banks)` = n(),
`Mean TA ($B)` = round(mean(total_asset / 1e6, na.rm = TRUE), 2),
`Mean # BTFP loans` = round(mean(n_loans_total), 1),
`Mean smallest ($M)` = round(mean(smallest_m, na.rm = TRUE), 2),
`Mean largest ($M)` = round(mean(largest_m, na.rm = TRUE), 1),
`Mean total ($M)` = round(mean(total_all_m, na.rm = TRUE), 1),
`Cash/TA (%)` = round(mean(cash_ta, na.rm = TRUE), 2),
`Uninsured lev (%)` = round(mean(du_ta, na.rm = TRUE), 2),
`MTM loss/TA (%)` = round(mean(ell, na.rm = TRUE), 2),
`Equity/TA (%)` = round(mean(eq_ta, na.rm = TRUE), 2),
`Wholesale/TA (%)` = round(mean(wholesale_ta, na.rm = TRUE), 2),
.groups = "drop"
)
print(table5, n = Inf)## # A tibble: 3 × 12
## tester_type `N (banks)` `Mean TA ($B)` `Mean # BTFP loans`
## <fct> <int> <dbl> <dbl>
## 1 Pure tester 46 24.9 1
## 2 Tested then borrowed 13 1.69 7.5
## 3 No tiny loans 473 5.31 2.5
## # ℹ 8 more variables: `Mean smallest ($M)` <dbl>, `Mean largest ($M)` <dbl>,
## # `Mean total ($M)` <dbl>, `Cash/TA (%)` <dbl>, `Uninsured lev (%)` <dbl>,
## # `MTM loss/TA (%)` <dbl>, `Equity/TA (%)` <dbl>, `Wholesale/TA (%)` <dbl>save_kbl_latex(table5, "table5_test_borrowers",
caption = "BTFP test-borrower classification with balance-sheet characteristics.")
kbl(table5, align = c("l", rep("r", 11)),
caption = "Table 5: BTFP Test-Borrower Analysis") %>%
kable_styling(bootstrap_options = c("striped", "hover", "condensed"),
full_width = FALSE, font_size = 10) %>%
footnote(general = paste(
"Pure testers borrowed only tiny loans (under $1M) and never borrowed",
"substantively. Tested-then-borrowed banks started with a test loan before",
"taking real BTFP funds. No-tiny-loans banks never borrowed below $1M."),
general_title = "Notes:", footnote_as_chunk = TRUE)| tester_type | N (banks) | Mean TA (\(B) </th> <th style="text-align:right;"> Mean # BTFP loans </th> <th style="text-align:right;"> Mean smallest (\)M) | Mean largest (\(M) </th> <th style="text-align:right;"> Mean total (\)M) | Cash/TA (%) | Uninsured lev (%) | MTM loss/TA (%) | Equity/TA (%) | Wholesale/TA (%) | |||
|---|---|---|---|---|---|---|---|---|---|---|---|
| Pure tester | 46 | 24.94 | 1.0 | 0.06 | 0.1 | 0.1 | 7.56 | 31.49 | 8.31 | 9.17 | 2.96 |
| Tested then borrowed | 13 | 1.69 | 7.5 | 0.39 | 55.2 | 146.3 | 5.05 | 25.80 | 9.82 | 8.53 | 4.34 |
| No tiny loans | 473 | 5.31 | 2.5 | 53.47 | 109.1 | 278.6 | 4.40 | 26.91 | 9.70 | 8.08 | 5.55 |
| Notes: Pure testers borrowed only tiny loans (under $1M) and never borrowed substantively. Tested-then-borrowed banks started with a test loan before taking real BTFP funds. No-tiny-loans banks never borrowed below $1M. |
4. Plots
4.1 Figure 1 — Daily crisis borrowing (DW and BTFP)
daily_dw <- dw_clean %>%
filter(dw_loan_date >= P0_start, dw_loan_date <= P3_end) %>%
group_by(date = dw_loan_date) %>%
summarise(DW = sum(dw_loan_amount, na.rm = TRUE) / 1e9, .groups = "drop")
daily_btfp <- btfp_clean %>%
filter(btfp_loan_date >= P0_start, btfp_loan_date <= P3_end) %>%
group_by(date = btfp_loan_date) %>%
summarise(BTFP = sum(btfp_loan_amount, na.rm = TRUE) / 1e9, .groups = "drop")
daily <- full_join(daily_dw, daily_btfp, by = "date") %>%
mutate(DW = replace_na(DW, 0), BTFP = replace_na(BTFP, 0)) %>%
pivot_longer(c(DW, BTFP), names_to = "Facility", values_to = "amount")
key_events <- tibble(
date = as.Date(c("2023-03-10", "2023-03-12", "2023-03-13", "2023-05-01")),
label = c("SVB failed", "Signature failed", "BTFP live + DW no-haircut",
"FRC failed")
)
fig1 <- ggplot(daily, aes(x = date, y = amount, color = Facility)) +
geom_line(linewidth = 0.8) +
geom_vline(data = key_events, aes(xintercept = date),
linetype = "dashed", color = "grey40", linewidth = 0.3) +
geom_text(data = key_events, aes(x = date, y = Inf, label = label),
inherit.aes = FALSE, size = 3, angle = 90, hjust = 1.1,
vjust = 1.1, color = "grey30") +
scale_color_manual(values = c(DW = "#E53935", BTFP = "#1565C0")) +
scale_y_continuous(labels = label_dollar(suffix = "B")) +
scale_x_date(date_breaks = "1 week", date_labels = "%b %d") +
labs(title = "Daily emergency borrowing, crisis window",
subtitle = "Mar 1 – May 4, 2023",
x = NULL, y = "Daily principal originated",
color = NULL) +
theme_gp
print(fig1)
4.2 Figure 2 — Distribution of borrowing (by-facility)
borrow_plot_df <- df %>%
filter(borrower_type != "Non-Borrower") %>%
mutate(borrow_m = total_borrow * 1000, # thousands → $ / 1e3 → $M (total_borrow is in thousands $)
ta_b = total_asset / 1e6)
# Panel A: cumulative borrowing, log x
figA <- ggplot(borrow_plot_df, aes(x = borrow_m, fill = borrower_type,
color = borrower_type)) +
geom_density(alpha = 0.35, linewidth = 0.6) +
geom_rug(sides = "b", alpha = 0.3, length = unit(0.03, "npc")) +
scale_x_log10(labels = label_dollar(suffix = "M", accuracy = 1),
breaks = c(1, 10, 100, 1000, 10000)) +
scale_fill_manual (values = fac_colors) +
scale_color_manual(values = fac_colors) +
facet_wrap(~ borrower_type, nrow = 1) +
labs(title = "A. Cumulative crisis-window borrowing by facility",
x = "Cumulative borrowing (log scale)", y = "Density") +
theme_gp + theme(legend.position = "none")
# Panel B: borrower TA
figB <- ggplot(borrow_plot_df, aes(x = ta_b, fill = borrower_type,
color = borrower_type)) +
geom_density(alpha = 0.35, linewidth = 0.6) +
geom_rug(sides = "b", alpha = 0.3, length = unit(0.03, "npc")) +
scale_x_log10(labels = label_dollar(suffix = "B", accuracy = 0.1),
breaks = c(0.1, 1, 10, 100, 1000)) +
scale_fill_manual (values = fac_colors) +
scale_color_manual(values = fac_colors) +
facet_wrap(~ borrower_type, nrow = 1) +
labs(title = "B. Borrower total assets (2022Q4) by facility",
x = "Total assets (log scale)", y = "Density") +
theme_gp + theme(legend.position = "none")
# Panel C: borrow/TA, capped
cap_C <- quantile(borrow_plot_df$borrow_ta, 0.95, na.rm = TRUE)
figC <- ggplot(borrow_plot_df %>% filter(borrow_ta <= cap_C),
aes(x = borrow_ta, fill = borrower_type, color = borrower_type)) +
geom_density(alpha = 0.35, linewidth = 0.6) +
geom_rug(sides = "b", alpha = 0.3, length = unit(0.03, "npc")) +
scale_x_continuous(labels = label_percent(scale = 1, accuracy = 1)) +
scale_fill_manual (values = fac_colors) +
scale_color_manual(values = fac_colors) +
facet_wrap(~ borrower_type, nrow = 1) +
labs(title = "C. Borrow / TA by facility",
subtitle = sprintf("Capped at 95th pct (%.1f%%)", cap_C),
x = "Cumulative borrowing / Total assets", y = "Density") +
theme_gp + theme(legend.position = "none")
fig2 <- (figA / figB / figC)
print(fig2)
4.3 Figure 3 — Cumulative vs peak (rollover visual)
# Reconstruct daily outstanding for peak
dw_daily <- dw_clean %>%
filter(!is.na(dw_repayment_date), dw_repayment_date > dw_loan_date,
dw_loan_date >= P0_start, dw_loan_date <= P3_end) %>%
mutate(rssd_id = as.character(rssd_id)) %>%
transmute(rssd_id,
active = map2(dw_loan_date, dw_repayment_date - 1,
~ seq(.x, .y, by = "1 day")),
amt = dw_loan_amount) %>%
unnest(active) %>%
group_by(rssd_id, date = active) %>%
summarise(dw_out = sum(amt, na.rm = TRUE), .groups = "drop")
btfp_daily <- btfp_clean %>%
filter(!is.na(btfp_repayment_date), btfp_repayment_date > btfp_loan_date,
btfp_loan_date >= P2_start, btfp_loan_date <= P3_end) %>%
mutate(rssd_id = as.character(rssd_id)) %>%
transmute(rssd_id,
active = map2(btfp_loan_date, btfp_repayment_date - 1,
~ seq(.x, .y, by = "1 day")),
amt = btfp_loan_amount) %>%
unnest(active) %>%
group_by(rssd_id, date = active) %>%
summarise(btfp_out = sum(amt, na.rm = TRUE), .groups = "drop")
daily_combined <- full_join(dw_daily, btfp_daily, by = c("rssd_id", "date")) %>%
mutate(dw_out = replace_na(dw_out, 0), btfp_out = replace_na(btfp_out, 0),
total_out = dw_out + btfp_out)
peak_bank <- daily_combined %>%
group_by(rssd_id) %>%
summarise(peak_m = max(total_out, na.rm = TRUE) / 1e6, .groups = "drop")
scatter_df <- df %>%
filter(borrower_type != "Non-Borrower") %>%
mutate(rssd_id = idrssd, cum_m = total_borrow * 1000) %>% # thousands → $M
select(rssd_id, cum_m, borrower_type) %>%
left_join(peak_bank, by = "rssd_id") %>%
filter(cum_m > 0, peak_m > 0, is.finite(peak_m))
fig3 <- ggplot(scatter_df, aes(x = peak_m, y = cum_m, color = borrower_type)) +
geom_abline(slope = 1, intercept = 0, linetype = "dashed",
color = "grey40", linewidth = 0.4) +
geom_point(alpha = 0.45, size = 1.3) +
scale_x_log10(labels = label_dollar(suffix = "M", accuracy = 1)) +
scale_y_log10(labels = label_dollar(suffix = "M", accuracy = 1)) +
scale_color_manual(values = fac_colors, name = NULL) +
labs(title = "Cumulative borrowing vs peak outstanding balance",
subtitle = "Distance above 45° line = rollover intensity",
x = "Peak daily outstanding balance (log)",
y = "Cumulative borrowing, whole crisis (log)") +
theme_gp
print(fig3)
Table 6 — New vs Returning borrowers
# ══════════════════════════════════════════════════════════════════════
# Helper: build two-panel table (Panel A type1, Panel B type2)
# Used for New/Returning and One-time/Repeat decompositions
# ══════════════════════════════════════════════════════════════════════
# Variables to show in each two-panel table (same list for both)
two_panel_vars <- tribble(
~label, ~col,
"N (banks)", "N", # special-cased
"Total assets ($B)", "ta_billion",
"Cash / TA (%)", "cash_ta",
"Securities / TA (%)", "sec_ta",
"Loans / TA (%)", "loan_ta",
"Book equity / TA (%)", "eq_ta",
"Uninsured / Deposits (%)", "mu_pct",
"Uninsured leverage (%)", "du_ta",
"Wholesale funding / TA (%)", "wholesale_ta",
"FHLB / TA (%)", "fhlb_ta",
"ROA (%)", "roa",
"MTM loss / TA (%)", "ell",
"E^MV / TA (%)", "emv_ta",
"v / TA (post-run, %)", "v_postrun_ta",
"% with E^MV < 0", "emv_neg", # treated as %
"% with v < 0 (post-run)", "v_postrun_neg"
)
build_two_panel_table <- function(get_ids_fn, type_label_1, type_label_2) {
# Returns: list(table = data_frame, n_stat = number_of_variable_rows)
build_panel <- function(type_label) {
out <- tibble(Statistic = two_panel_vars$label)
for (i in seq_len(nrow(col_specs))) {
p <- col_specs$period[i]; f <- col_specs$facility[i]
cid <- col_specs$col_id[i]
ids <- get_ids_fn(p, f, type_label)
cell <- df %>% filter(idrssd %in% ids)
vals <- map_dbl(seq_len(nrow(two_panel_vars)), function(j) {
col <- two_panel_vars$col[j]
if (col == "N") return(nrow(cell))
if (grepl("^%", two_panel_vars$label[j])) {
return(100 * mean(cell[[col]], na.rm = TRUE))
}
mean(cell[[col]], na.rm = TRUE)
})
out[[cid]] <- vals
}
out
}
panelA <- build_panel(type_label_1)
panelB <- build_panel(type_label_2)
tbl <- bind_rows(panelA, panelB)
list(table = tbl, n_stat = nrow(two_panel_vars))
}# ══════════════════════════════════════════════════════════════════════
# Table A1 — New vs Returning borrowers
# Returning in period p = borrowed from DW or BTFP in any earlier period
# New in p = first-time appearance in DW or BTFP
# ══════════════════════════════════════════════════════════════════════
get_ids_new_ret <- function(p, f, t) {
banks <- banks_in_cell(p, f)
prior <- prior_set(p)
if (t == "Returning") banks[banks %in% prior] else banks[!(banks %in% prior)]
}
out_newret <- build_two_panel_table(get_ids_new_ret, "New", "Returning")
tableA1 <- out_newret$table
n_stat_A1 <- out_newret$n_stat
cat(sprintf("Table A1 shape: %d x %d\n", nrow(tableA1), ncol(tableA1)))## Table A1 shape: 32 x 7## # A tibble: 32 × 7
## Statistic `P0: Pre-Crisis | DW` `P1: SVB Week | DW` `P2: SVB to FRC | DW`
## <chr> <dbl> <dbl> <dbl>
## 1 N (banks) 72 32 332
## 2 Total assets… 4.40 12.4 6.77
## 3 Cash / TA (%) 4.38 3.31 6.46
## 4 Securities /… 26.7 21.1 24.1
## 5 Loans / TA (… 63.6 69.0 63.4
## 6 Book equity … 9.05 8.70 9.01
## 7 Uninsured / … 32.0 36.2 33.2
## 8 Uninsured le… 26.9 29.8 28.2
## 9 Wholesale fu… 5.65 6.22 4.73
## 10 FHLB / TA (%) 3.53 4.69 3.45
## 11 ROA (%) 1.03 1.18 1.18
## 12 MTM loss / T… 9.33 9.07 9.07
## 13 E^MV / TA (%) -0.274 -0.372 -0.0590
## 14 v / TA (post… 9.28 8.63 9.62
## 15 % with E^MV … 59.7 53.1 50.6
## 16 % with v < 0… 1.39 0 4.26
## 17 N (banks) 0 35 65
## 18 Total assets… NaN 3.20 5.19
## 19 Cash / TA (%) NaN 4.20 4.13
## 20 Securities /… NaN 28.5 26.3
## 21 Loans / TA (… NaN 62.0 64.0
## 22 Book equity … NaN 8.14 8.32
## 23 Uninsured / … NaN 35.0 35.3
## 24 Uninsured le… NaN 29.3 29.6
## 25 Wholesale fu… NaN 7.18 6.62
## 26 FHLB / TA (%) NaN 4.45 4.44
## 27 ROA (%) NaN 0.915 1.03
## 28 MTM loss / T… NaN 8.79 8.83
## 29 E^MV / TA (%) NaN -0.653 -0.509
## 30 v / TA (post… NaN 8.40 8.47
## 31 % with E^MV … NaN 62.9 58.5
## 32 % with v < 0… NaN 2.86 1.54
## # ℹ 3 more variables: `P2: SVB to FRC | BTFP` <dbl>, `P3: FRC Week | DW` <dbl>,
## # `P3: FRC Week | BTFP` <dbl># Print bank counts per cell (sanity vs Table 1's New/Returning rows)
cat("\nBank counts per cell (should reconcile to Table 1):\n")##
## Bank counts per cell (should reconcile to Table 1):walk(seq_len(nrow(col_specs)), function(i) {
p <- col_specs$period[i]; f <- col_specs$facility[i]
n_new <- length(get_ids_new_ret(p, f, "New"))
n_ret <- length(get_ids_new_ret(p, f, "Returning"))
cat(sprintf(" %-22s New = %3d Returning = %3d Total = %3d\n",
col_specs$col_id[i], n_new, n_ret, n_new + n_ret))
})## P0: Pre-Crisis | DW New = 72 Returning = 0 Total = 72
## P1: SVB Week | DW New = 33 Returning = 35 Total = 68
## P2: SVB to FRC | DW New = 340 Returning = 66 Total = 406
## P2: SVB to FRC | BTFP New = 442 Returning = 30 Total = 472
## P3: FRC Week | DW New = 34 Returning = 67 Total = 101
## P3: FRC Week | BTFP New = 54 Returning = 130 Total = 184tableA1_k <- tableA1 %>%
kbl(digits = 2, align = c("l", rep("r", 6)),
caption = "Table A1: New vs Returning Borrowers by Period × Facility (2022Q4)") %>%
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", 1, n_stat_A1) %>%
pack_rows("Panel B. Returning borrowers", n_stat_A1+1, 2*n_stat_A1) %>%
footnote(general = paste(
"A bank is Returning in period p if it borrowed from either DW or BTFP",
"in any earlier period; New otherwise. P0 has no prior period, so all P0",
"borrowers are by construction New (Panel B for P0 is empty).",
"Characteristics are 2022Q4 means (excluding GSIBs and failed banks).",
"v = E_MV + F_insured (post uninsured-run fundamental value)."),
general_title = "Notes:", footnote_as_chunk = TRUE)
tableA1_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 | ||||||
| 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</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: A bank is Returning in period p if it borrowed from either DW or BTFP in any earlier period; New otherwise. P0 has no prior period, so all P0 borrowers are by construction New (Panel B for P0 is empty). Characteristics are 2022Q4 means (excluding GSIBs and failed banks). v = E_MV + F_insured (post uninsured-run fundamental value). | ||||||
Table 6B — One-time vs Repeat borrowers
# ══════════════════════════════════════════════════════════════════════
# Table A2 — One-time vs Repeat borrowers
# One-time: 1 distinct loan date in the cell
# Repeat : ≥2 distinct loan dates in the 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_onetime_rep <- function(p, f, t) {
cell_types %>%
filter(period == p, facility == f, type == t) %>%
pull(rssd_id)
}
out_otrep <- build_two_panel_table(get_ids_onetime_rep, "One-time", "Repeat")
tableA2 <- out_otrep$table
n_stat_A2 <- out_otrep$n_stat
cat(sprintf("Table A2 shape: %d x %d\n", nrow(tableA2), ncol(tableA2)))## Table A2 shape: 32 x 7## # A tibble: 32 × 7
## Statistic `P0: Pre-Crisis | DW` `P1: SVB Week | DW` `P2: SVB to FRC | DW`
## <chr> <dbl> <dbl> <dbl>
## 1 N (banks) 40 37 284
## 2 Total assets… 5.27 11.0 7.57
## 3 Cash / TA (%) 4.74 4.52 6.84
## 4 Securities /… 23.5 22.1 23.2
## 5 Loans / TA (… 66.2 67.2 64.1
## 6 Book equity … 9.81 8.75 9.20
## 7 Uninsured / … 28.5 36.7 32.4
## 8 Uninsured le… 23.8 30.5 27.7
## 9 Wholesale fu… 5.22 5.74 4.41
## 10 FHLB / TA (%) 3.49 4.01 3.32
## 11 ROA (%) 1.06 1.10 1.19
## 12 MTM loss / T… 9.16 8.66 8.87
## 13 E^MV / TA (%) 0.657 0.0895 0.329
## 14 v / TA (post… 10.5 8.98 9.99
## 15 % with E^MV … 50 48.6 47.9
## 16 % with v < 0… 0 0 3.18
## 17 N (banks) 32 30 113
## 18 Total assets… 3.31 3.39 3.87
## 19 Cash / TA (%) 3.92 2.85 4.16
## 20 Securities /… 30.6 28.5 27.7
## 21 Loans / TA (… 60.4 63.0 62.1
## 22 Book equity … 8.10 7.98 8.13
## 23 Uninsured / … 36.4 34.2 36.2
## 24 Uninsured le… 30.7 28.3 30.3
## 25 Wholesale fu… 6.18 7.94 6.61
## 26 FHLB / TA (%) 3.57 5.25 4.35
## 27 ROA (%) 0.989 0.964 1.08
## 28 MTM loss / T… 9.54 9.25 9.42
## 29 E^MV / TA (%) -1.44 -1.27 -1.29
## 30 v / TA (post… 7.73 7.93 8.01
## 31 % with E^MV … 71.9 70 61.9
## 32 % with v < 0… 3.12 3.33 5.41
## # ℹ 3 more variables: `P2: SVB to FRC | BTFP` <dbl>, `P3: FRC Week | DW` <dbl>,
## # `P3: FRC Week | BTFP` <dbl>##
## Bank counts per cell (one-time | repeat):walk(seq_len(nrow(col_specs)), function(i) {
p <- col_specs$period[i]; f <- col_specs$facility[i]
n_ot <- length(get_ids_onetime_rep(p, f, "One-time"))
n_rp <- length(get_ids_onetime_rep(p, f, "Repeat"))
cat(sprintf(" %-22s One-time = %3d Repeat = %3d Total = %3d\n",
col_specs$col_id[i], n_ot, n_rp, n_ot + n_rp))
})## P0: Pre-Crisis | DW One-time = 40 Repeat = 32 Total = 72
## P1: SVB Week | DW One-time = 37 Repeat = 31 Total = 68
## P2: SVB to FRC | DW One-time = 292 Repeat = 114 Total = 406
## P2: SVB to FRC | BTFP One-time = 235 Repeat = 237 Total = 472
## P3: FRC Week | DW One-time = 56 Repeat = 45 Total = 101
## P3: FRC Week | BTFP One-time = 126 Repeat = 58 Total = 184tableA2_k <- tableA2 %>%
kbl(digits = 2, align = c("l", rep("r", 6)),
caption = "Table A2: One-time vs Repeat Borrowers by Period × Facility (2022Q4)") %>%
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)",
1, n_stat_A2) %>%
pack_rows("Panel B. Repeat borrowers (≥2 distinct loan dates)",
n_stat_A2+1, 2*n_stat_A2) %>%
footnote(general = paste(
"One-time vs Repeat is defined within each period × facility cell by the",
"number of distinct loan dates during that cell's date range. A bank can",
"appear as One-time in one cell and Repeat in another. Characteristics are",
"2022Q4 means (excluding GSIBs and failed banks)."),
general_title = "Notes:", footnote_as_chunk = TRUE)
tableA2_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) | ||||||
| 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)</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 during that cell’s date range. A bank can appear as One-time in one cell and Repeat in another. Characteristics are 2022Q4 means (excluding GSIBs and failed banks). | ||||||
5. Regressions
All regressions use the fit_model() wrapper. To switch
from LPM to logit or probit for the extensive-margin regressions, change
MODEL_FAMILY at the top of the document from
"lpm" to "logit" or "probit". All
extensive-margin results will re-estimate.
5.2 Table 6 — Main LPM (extensive margin, all cells)
# Build DVs: one for each (period, facility) cell on the full cross-section
build_dep <- function(df, cell_spec) {
ids <- banks_in_cell(cell_spec$period, cell_spec$facility)
as.integer(df$idrssd %in% ids)
}
df_reg <- df %>% filter(!is.na(du_ta_w_z), !is.na(ell_w_z))
dep_vars <- list()
for (i in seq_len(nrow(col_specs))) {
cs <- col_specs[i, ]
dep_name <- paste0("dep_",
gsub("[^a-z0-9]", "_", tolower(cs$col_id)))
df_reg[[dep_name]] <- build_dep(df_reg, cs)
dep_vars[[cs$col_id]] <- dep_name
}
# Fit one regression per cell
models_T6 <- list()
for (nm in names(dep_vars)) {
f <- as.formula(paste(dep_vars[[nm]], "~", rhs_base))
models_T6[[nm]] <- fit_model(f, df_reg)
}
table6 <- build_coef_table(models_T6, var_order, var_labels)
table6 %>% as_tibble() %>% print(n = Inf)## # A tibble: 24 × 7
## Variable `P0: Pre-Crisis | DW` `P1: SVB Week | DW` `P2: SVB to FRC | DW`
## <chr> <chr> <chr> <chr>
## 1 "MTM loss (t… "0.001" "-0.002" "0.012**"
## 2 "" "(0.002)" "(0.002)" "(0.005)"
## 3 "Uninsured l… "0.000" "0.002" "0.012**"
## 4 "" "(0.003)" "(0.002)" "(0.005)"
## 5 "MTM × Unins… "0.002" "0.001" "0.013***"
## 6 "" "(0.002)" "(0.002)" "(0.004)"
## 7 "Ln(assets)" "0.013***" "0.014***" "0.066***"
## 8 "" "(0.003)" "(0.003)" "(0.006)"
## 9 "Cash / TA" "-0.004*" "-0.003**" "0.003"
## 10 "" "(0.002)" "(0.001)" "(0.004)"
## 11 "Loan / Depo… "-0.005*" "-0.005**" "-0.007"
## 12 "" "(0.003)" "(0.002)" "(0.005)"
## 13 "Book equity… "0.002" "-0.000" "0.001"
## 14 "" "(0.002)" "(0.001)" "(0.004)"
## 15 "Wholesale f… "0.006**" "0.008***" "0.015***"
## 16 "" "(0.003)" "(0.003)" "(0.005)"
## 17 "ROA" "-0.002" "-0.002" "0.001"
## 18 "" "(0.002)" "(0.002)" "(0.004)"
## 19 "Constant" "0.016***" "0.014***" "0.086***"
## 20 "" "(0.002)" "(0.002)" "(0.004)"
## 21 "" "" "" ""
## 22 "N" "4,632" "4,632" "4,632"
## 23 "R²" "0.015" "0.023" "0.069"
## 24 "Mean of DV" "0.0155" "0.0145" "0.0857"
## # ℹ 3 more variables: `P2: SVB to FRC | BTFP` <chr>, `P3: FRC Week | DW` <chr>,
## # `P3: FRC Week | BTFP` <chr>5.3 Table 7 — Robustness: drop top-10 borrowers by $
Re-run Table 6 excluding the top 10 of borrowers by cumulative $ to check whether the interaction mechanism survives the removal of volume drivers.
# ══════════════════════════════════════════════════════════════════════
# Table 7 — Robustness: drop the TOP 10 BANKS by cumulative crisis $
# ══════════════════════════════════════════════════════════════════════
# ── Option 2 (primary): 10 largest crisis-wide borrowers ───────────
top10_ids <- df_reg %>%
filter(borrowed == 1) %>%
arrange(desc(total_borrow)) %>%
slice_head(n = 10) %>%
pull(idrssd)
df_reg_trim <- df_reg %>% filter(!(idrssd %in% top10_ids))
cat(sprintf("Dropping %d banks (the 10 largest crisis-wide borrowers):\n",
length(top10_ids)))## Dropping 10 banks (the 10 largest crisis-wide borrowers):df_reg %>%
filter(idrssd %in% top10_ids) %>%
arrange(desc(total_borrow)) %>%
transmute(Rank = row_number(),
RSSD = idrssd,
`Cum $ (M)` = round(total_borrow * 1000, 0),
`TA ($B)` = round(total_asset / 1e6, 2)) %>%
print()## # A tibble: 10 × 4
## Rank RSSD `Cum $ (M)` `TA ($B)`
## <int> <chr> <dbl> <dbl>
## 1 1 3138146 269300000000 67.7
## 2 2 494261 144715000000 41.2
## 3 3 3284397 39050000000 26.0
## 4 4 671464 27163000000 19.2
## 5 5 936855 22525000000 38.3
## 6 6 936462 18263000000 18.1
## 7 7 450856 10919500000 7.61
## 8 8 197478 10000100000 64.1
## 9 9 200378 8760000000 9.19
## 10 10 739560 7080000000 5.45# ── Fit regressions on trimmed sample ──────────────────────────────
models_T7 <- list()
for (nm in names(dep_vars)) {
f <- as.formula(paste(dep_vars[[nm]], "~", rhs_base))
models_T7[[nm]] <- fit_model(f, df_reg_trim)
}
table7 <- build_coef_table(models_T7, var_order, var_labels)
table7 %>% as_tibble() %>% print(n = Inf)## # A tibble: 24 × 7
## Variable `P0: Pre-Crisis | DW` `P1: SVB Week | DW` `P2: SVB to FRC | DW`
## <chr> <chr> <chr> <chr>
## 1 "MTM loss (t… "0.000" "-0.003" "0.011**"
## 2 "" "(0.002)" "(0.002)" "(0.005)"
## 3 "Uninsured l… "-0.000" "0.000" "0.010*"
## 4 "" "(0.002)" "(0.002)" "(0.005)"
## 5 "MTM × Unins… "0.001" "-0.001" "0.011***"
## 6 "" "(0.002)" "(0.002)" "(0.004)"
## 7 "Ln(assets)" "0.012***" "0.012***" "0.063***"
## 8 "" "(0.003)" "(0.003)" "(0.006)"
## 9 "Cash / TA" "-0.004*" "-0.004**" "0.003"
## 10 "" "(0.002)" "(0.001)" "(0.004)"
## 11 "Loan / Depo… "-0.005*" "-0.005**" "-0.007"
## 12 "" "(0.003)" "(0.002)" "(0.005)"
## 13 "Book equity… "0.002" "-0.001" "-0.000"
## 14 "" "(0.002)" "(0.001)" "(0.004)"
## 15 "Wholesale f… "0.006**" "0.008***" "0.015***"
## 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***" "0.013***" "0.085***"
## 20 "" "(0.002)" "(0.002)" "(0.004)"
## 21 "" "" "" ""
## 22 "N" "4,622" "4,622" "4,622"
## 23 "R²" "0.012" "0.018" "0.063"
## 24 "Mean of DV" "0.0147" "0.0132" "0.0839"
## # ℹ 3 more variables: `P2: SVB to FRC | BTFP` <chr>, `P3: FRC Week | DW` <chr>,
## # `P3: FRC Week | BTFP` <chr>5.4 Table 8 — Robustness: drop BTFP pure testers
tester_ids <- btfp_bank_summary %>%
filter(tester_type == "Pure tester") %>% pull(rssd_id)
df_reg_notest <- df_reg %>% filter(!(idrssd %in% tester_ids))
cat(sprintf("Excluding %d BTFP pure testers from the sample.\n",
length(tester_ids)))## Excluding 46 BTFP pure testers from the sample.models_T8 <- list()
for (nm in names(dep_vars)) {
f <- as.formula(paste(dep_vars[[nm]], "~", rhs_base))
models_T8[[nm]] <- fit_model(f, df_reg_notest)
}
table8 <- build_coef_table(models_T8, var_order, var_labels)
table8 %>% as_tibble() %>% print(n = Inf)## # A tibble: 24 × 7
## Variable `P0: Pre-Crisis | DW` `P1: SVB Week | DW` `P2: SVB to FRC | DW`
## <chr> <chr> <chr> <chr>
## 1 "MTM loss (t… "0.001" "-0.001" "0.012**"
## 2 "" "(0.003)" "(0.002)" "(0.005)"
## 3 "Uninsured l… "0.000" "0.001" "0.010*"
## 4 "" "(0.003)" "(0.002)" "(0.005)"
## 5 "MTM × Unins… "0.002" "0.001" "0.012***"
## 6 "" "(0.002)" "(0.002)" "(0.004)"
## 7 "Ln(assets)" "0.014***" "0.014***" "0.063***"
## 8 "" "(0.003)" "(0.003)" "(0.006)"
## 9 "Cash / TA" "-0.004*" "-0.003**" "0.002"
## 10 "" "(0.002)" "(0.001)" "(0.004)"
## 11 "Loan / Depo… "-0.005*" "-0.005**" "-0.006"
## 12 "" "(0.003)" "(0.002)" "(0.005)"
## 13 "Book equity… "0.002" "-0.000" "0.001"
## 14 "" "(0.002)" "(0.001)" "(0.004)"
## 15 "Wholesale f… "0.006**" "0.008***" "0.015***"
## 16 "" "(0.003)" "(0.003)" "(0.005)"
## 17 "ROA" "-0.002" "-0.002" "0.002"
## 18 "" "(0.002)" "(0.002)" "(0.004)"
## 19 "Constant" "0.016***" "0.014***" "0.083***"
## 20 "" "(0.002)" "(0.002)" "(0.004)"
## 21 "" "" "" ""
## 22 "N" "4,589" "4,589" "4,589"
## 23 "R²" "0.015" "0.021" "0.066"
## 24 "Mean of DV" "0.0157" "0.0142" "0.0822"
## # ℹ 3 more variables: `P2: SVB to FRC | BTFP` <chr>, `P3: FRC Week | DW` <chr>,
## # `P3: FRC Week | BTFP` <chr>5.5 Table 9 — Two-regime analysis (ordinary vs extreme borrowers)
Conditional on borrowing, compare ordinary (bottom 90%) vs extreme
(top 10%) borrowers. Uses log(total_borrow + 1) as DV
because this is intensive-margin. The two-regime table always uses
lm() regardless of MODEL_FAMILY, since the DV
is continuous.
borrowers <- df_reg %>% filter(borrowed == 1) %>%
mutate(cum_m = total_borrow * 1000) # thousands → $M
ext_cutoff <- quantile(borrowers$cum_m, 0.90, na.rm = TRUE)
borrowers <- borrowers %>%
mutate(extreme = as.integer(cum_m >= ext_cutoff))
ord_df <- borrowers %>% filter(extreme == 0)
ext_df <- borrowers %>% filter(extreme == 1)
m_full <- lm(as.formula(paste("log(cum_m) ~", rhs_base)), data = borrowers)
m_ord <- lm(as.formula(paste("log(cum_m) ~", rhs_base)), data = ord_df)
m_ext <- lm(as.formula(paste("log(cum_m) ~", rhs_base)), data = ext_df)
chow <- chow_test(rhs_base, "log(cum_m)", borrowers, "extreme")
cat(sprintf("Chow test: H0 all slopes equal across ordinary vs extreme.\n"))## Chow test: H0 all slopes equal across ordinary vs extreme.## F(9,840) = 16.304, p = 0.0000models_T9 <- list(Full = m_full, Ordinary = m_ord, Extreme = m_ext)
table9 <- build_coef_table(models_T9, var_order, var_labels)
table9 %>% as_tibble() %>% print(n = Inf)## # A tibble: 24 × 4
## Variable Full Ordinary Extreme
## <chr> <chr> <chr> <chr>
## 1 "MTM loss (total)" "-0.248" "-0.229" "-0.127"
## 2 "" "(0.186)" "(0.185)" "(0.168)"
## 3 "Uninsured leverage" "0.661***" "0.758***" "0.111"
## 4 "" "(0.178)" "(0.163)" "(0.124)"
## 5 "MTM × Uninsured Lev" "-0.046" "-0.276**" "0.273**"
## 6 "" "(0.146)" "(0.139)" "(0.113)"
## 7 "Ln(assets)" "0.332*" "-0.727***" "0.845***"
## 8 "" "(0.191)" "(0.179)" "(0.169)"
## 9 "Cash / TA" "-1.909***" "-2.149***" "0.169"
## 10 "" "(0.271)" "(0.236)" "(0.173)"
## 11 "Loan / Deposit" "-0.932***" "-0.615***" "0.038"
## 12 "" "(0.240)" "(0.230)" "(0.246)"
## 13 "Book equity / TA" "-0.157" "-0.248" "0.044"
## 14 "" "(0.257)" "(0.252)" "(0.250)"
## 15 "Wholesale funding" "0.912***" "0.640***" "0.029"
## 16 "" "(0.150)" "(0.144)" "(0.114)"
## 17 "ROA" "0.043" "0.037" "0.178"
## 18 "" "(0.180)" "(0.176)" "(0.160)"
## 19 "Constant" "13.500***" "13.375***" "19.260***"
## 20 "" "(0.185)" "(0.179)" "(0.351)"
## 21 "" "" "" ""
## 22 "N" "860" "774" "86"
## 23 "R²" "0.152" "0.143" "0.323"
## 24 "Mean of DV" "14.7768" "14.0938" "20.9237"5.6 Table 10 — Extreme-borrower analysis by facility
run_facility_regime <- function(fac_grp_data, label) {
n <- nrow(fac_grp_data)
if (n < 50) {
cat(sprintf("%s: sample too small (N=%d); skipping.\n", label, n))
return(NULL)
}
cutoff <- quantile(fac_grp_data$cum_m, 0.90, na.rm = TRUE)
fac_grp_data <- fac_grp_data %>% mutate(extreme = as.integer(cum_m >= cutoff))
ord <- fac_grp_data %>% filter(extreme == 0)
ext <- fac_grp_data %>% filter(extreme == 1)
if (nrow(ext) < 15) {
cat(sprintf("%s: fewer than 15 extreme banks (N_ext=%d); unstable.\n",
label, nrow(ext)))
}
list(
full = lm(as.formula(paste("log(cum_m) ~", rhs_base)), data = fac_grp_data),
ord = lm(as.formula(paste("log(cum_m) ~", rhs_base)), data = ord),
ext = lm(as.formula(paste("log(cum_m) ~", rhs_base)), data = ext),
chow = tryCatch(chow_test(rhs_base, "log(cum_m)", fac_grp_data, "extreme"),
error = function(e) tibble(chi2 = NA, p_value = NA))
)
}
dw_only <- borrowers %>% filter(used_dw == 1, used_btfp == 0)
btfp_only <- borrowers %>% filter(used_btfp == 1, used_dw == 0)
both <- borrowers %>% filter(used_dw == 1, used_btfp == 1)
r_dw <- run_facility_regime(dw_only, "DW Only")
r_btfp <- run_facility_regime(btfp_only, "BTFP Only")
r_both <- run_facility_regime(both, "Both")## Both: fewer than 15 extreme banks (N_ext=11); unstable.##
## Chow test p-values by facility:## DW Only : p = 0.0000## BTFP Only: p = 0.0335## Both : p = 0.0000# Build compact cross-facility summary
summarise_facility <- function(r, lbl) {
get_coef <- function(m, v) {
if (is.null(m)) return("")
tm <- get_robust_tidy(m)
i <- which(tm$term == v)
if (length(i) == 0) "" else fmt_est(tm$estimate[i], tm$p.value[i])
}
tibble(
Facility = lbl,
`Chow p` = sprintf("%.4f", r$chow$p_value),
`MTM×U (ord)` = get_coef(r$ord, "ell_w_z:du_ta_w_z"),
`MTM×U (ext)` = get_coef(r$ext, "ell_w_z:du_ta_w_z"),
`Ln(TA) (ord)` = get_coef(r$ord, "log_ta_w_z"),
`Ln(TA) (ext)` = get_coef(r$ext, "log_ta_w_z"),
`Cash/TA (ord)` = get_coef(r$ord, "cash_ta_w_z"),
`Cash/TA (ext)` = get_coef(r$ext, "cash_ta_w_z"),
`N (ord)` = if (is.null(r$ord)) "" else fmt(nobs(r$ord)),
`N (ext)` = if (is.null(r$ext)) "" else fmt(nobs(r$ext))
)
}
table10 <- bind_rows(
summarise_facility(r_dw, "DW Only"),
summarise_facility(r_btfp, "BTFP Only"),
summarise_facility(r_both, "Both")
)
table10 %>% as_tibble() %>% print(n = Inf)## # A tibble: 3 × 10
## Facility `Chow p` `MTM×U (ord)` `MTM×U (ext)` `Ln(TA) (ord)` `Ln(TA) (ext)`
## <chr> <chr> <chr> <chr> <chr> <chr>
## 1 DW Only 0.0000 0.089 -0.083 -0.495* 0.480
## 2 BTFP Only 0.0335 -0.107 0.265*** 0.221 1.126***
## 3 Both 0.0000 0.104 -0.503 -0.059 4.036
## # ℹ 4 more variables: `Cash/TA (ord)` <chr>, `Cash/TA (ext)` <chr>,
## # `N (ord)` <chr>, `N (ext)` <chr>5.7 Table 11 — Crisis vs Arbitrage (falsification test)
In the arbitrage window the run equilibrium is dead (BTFP rate < IORB, so banks borrow for arbitrage, not stress). Theory predicts c3 ≈ 0 there, and c3 > 0 in the crisis window.
f_crisis <- as.formula(paste("borrowed ~", rhs_base))
f_arb <- as.formula(paste("borrowed_arb ~", rhs_base))
m_crisis <- fit_model(f_crisis, df_reg)
m_arb <- fit_model(f_arb, df_arb)
models_T11 <- list(Crisis = m_crisis, Arbitrage = m_arb)
table11 <- build_coef_table(models_T11, var_order, var_labels)
table11 %>% as_tibble() %>% print(n = Inf)## # A tibble: 24 × 3
## Variable Crisis Arbitrage
## <chr> <chr> <chr>
## 1 "MTM loss (total)" "0.023***" "0.013**"
## 2 "" "(0.006)" "(0.006)"
## 3 "Uninsured leverage" "0.021***" "0.016**"
## 4 "" "(0.007)" "(0.006)"
## 5 "MTM × Uninsured Lev" "0.019***" "0.009*"
## 6 "" "(0.005)" "(0.005)"
## 7 "Ln(assets)" "0.099***" "0.057***"
## 8 "" "(0.007)" "(0.007)"
## 9 "Cash / TA" "-0.022***" "-0.043***"
## 10 "" "(0.006)" "(0.005)"
## 11 "Loan / Deposit" "-0.027***" "-0.038***"
## 12 "" "(0.006)" "(0.006)"
## 13 "Book equity / TA" "-0.012**" "-0.008"
## 14 "" "(0.005)" "(0.006)"
## 15 "Wholesale funding" "0.040***" "0.060***"
## 16 "" "(0.007)" "(0.007)"
## 17 "ROA" "0.003" "-0.022***"
## 18 "" "(0.006)" "(0.005)"
## 19 "Constant" "0.185***" "0.166***"
## 20 "" "(0.005)" "(0.005)"
## 21 "" "" ""
## 22 "N" "4,632" "4,531"
## 23 "R²" "0.113" "0.093"
## 24 "Mean of DV" "0.1857" "0.1691"5.8 Table 12 — Crisis vs Arbitrage (DW only, btfp only, both)
# ══════════════════════════════════════════════════════════════════════
# Table 11b — Crisis vs Arbitrage by borrower type (DW Only / BTFP Only / Both)
# Six-column structure matching Table 3's borrower classification
# ══════════════════════════════════════════════════════════════════════
# ── Build three crisis DVs from the 2022Q4 sample ──────────────────
df_reg <- df_reg %>%
mutate(
dv_crisis_dw = as.integer(used_dw == 1 & used_btfp == 0),
dv_crisis_btfp = as.integer(used_btfp == 1 & used_dw == 0),
dv_crisis_both = as.integer(used_dw == 1 & used_btfp == 1)
)
cat(sprintf("Crisis window (N = %s):\n", fmt(nrow(df_reg))))## Crisis window (N = 4,678):## DW Only : 341## BTFP Only : 412## Both : 107# ── Build three arbitrage DVs from the 2023Q3 sample ───────────────
# Requires DW arbitrage-window loan data as well; construct it here
dw_arb_bank <- dw_clean %>%
filter(dw_loan_date >= ARB_START, dw_loan_date <= ARB_END) %>%
group_by(rssd_id) %>%
summarise(dw_arb_amount = sum(dw_loan_amount, na.rm = TRUE) / 1000,
.groups = "drop") %>%
rename(idrssd = rssd_id)
df_arb <- df_arb %>%
left_join(dw_arb_bank, by = "idrssd") %>%
mutate(
dw_arb_amount = replace_na(dw_arb_amount, 0),
used_dw_arb = as.integer(dw_arb_amount > 0),
used_btfp_arb = as.integer(btfp_arb_amount > 0),
dv_arb_dw = as.integer(used_dw_arb == 1 & used_btfp_arb == 0),
dv_arb_btfp = as.integer(used_btfp_arb == 1 & used_dw_arb == 0),
dv_arb_both = as.integer(used_dw_arb == 1 & used_btfp_arb == 1)
)
cat(sprintf("\nArbitrage window (N = %s):\n", fmt(nrow(df_arb))))##
## Arbitrage window (N = 4,604):## DW Only : 257## BTFP Only : 655## Both : 111# ── Fit six regressions ────────────────────────────────────────────
f_cr_dw <- as.formula(paste("dv_crisis_dw ~", rhs_base))
f_cr_btfp <- as.formula(paste("dv_crisis_btfp ~", rhs_base))
f_cr_both <- as.formula(paste("dv_crisis_both ~", rhs_base))
f_arb_dw <- as.formula(paste("dv_arb_dw ~", rhs_base))
f_arb_btfp <- as.formula(paste("dv_arb_btfp ~", rhs_base))
f_arb_both <- as.formula(paste("dv_arb_both ~", rhs_base))
models_T11b <- list(
`Crisis — DW Only` = fit_model(f_cr_dw, df_reg),
`Crisis — BTFP Only` = fit_model(f_cr_btfp, df_reg),
`Crisis — Both` = fit_model(f_cr_both, df_reg),
`Arbitrage — DW Only` = fit_model(f_arb_dw, df_arb),
`Arbitrage — BTFP Only` = fit_model(f_arb_btfp, df_arb),
`Arbitrage — Both` = fit_model(f_arb_both, df_arb)
)
table11b <- build_coef_table(models_T11b, var_order, var_labels)
table11b %>% as_tibble() %>% print(n = Inf)## # A tibble: 24 × 7
## Variable `Crisis — DW Only` `Crisis — BTFP Only` `Crisis — Both`
## <chr> <chr> <chr> <chr>
## 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"
## # ℹ 3 more variables: `Arbitrage — DW Only` <chr>,
## # `Arbitrage — BTFP Only` <chr>, `Arbitrage — Both` <chr>INSURED leverage
# ══════════════════════════════════════════════════════════════════════
# Table 6b — Main extensive-margin regression with INSURED leverage
# Specification check: the DSSW mechanism should operate through UNINSURED
# leverage, not insured. The MTM × Insured Lev coefficient should be
# substantially weaker (or null) compared to the MTM × Uninsured Lev
# coefficient in Table 6.
# ══════════════════════════════════════════════════════════════════════
# Build insured leverage variable if not present
if (!"di_ta_w_z" %in% names(df_reg)) {
df_reg <- df_reg %>%
mutate(di_ta = 100 * safe_div(insured_deposit, total_asset, 0)) %>%
wz_cols("di_ta")
}
# Swap du_ta_w_z → di_ta_w_z in the RHS
rhs_insured <- "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_T6b <- list()
for (nm in names(dep_vars)) {
f <- as.formula(paste(dep_vars[[nm]], "~", rhs_insured))
models_T6b[[nm]] <- fit_model(f, df_reg)
}
var_order_ins <- 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_ins <- 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"
)
table6b <- build_coef_table(models_T6b, var_order_ins, var_labels_ins)
table6b %>% as_tibble() %>% print(n = Inf)## # A tibble: 24 × 7
## Variable `P0: Pre-Crisis | DW` `P1: SVB Week | DW` `P2: SVB to FRC | DW`
## <chr> <chr> <chr> <chr>
## 1 "MTM loss (t… "0.000" "-0.002" "0.010**"
## 2 "" "(0.002)" "(0.002)" "(0.005)"
## 3 "Insured lev… "0.001" "-0.001" "-0.012**"
## 4 "" "(0.003)" "(0.002)" "(0.006)"
## 5 "MTM × Insur… "-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 / Depo… "-0.005*" "-0.005**" "-0.008"
## 12 "" "(0.003)" "(0.002)" "(0.005)"
## 13 "Book equity… "0.002" "-0.001" "-0.005"
## 14 "" "(0.002)" "(0.001)" "(0.004)"
## 15 "Wholesale f… "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"
## # ℹ 3 more variables: `P2: SVB to FRC | BTFP` <chr>, `P3: FRC Week | DW` <chr>,
## # `P3: FRC Week | BTFP` <chr>save_kbl_latex(table6b, sprintf("table6b_insured_leverage_%s", MODEL_FAMILY),
caption = sprintf(
"Specification check (%s): main regression with INSURED leverage (di_ta) replacing uninsured leverage. Theory predicts MTM × Insured Lev weaker than MTM × Uninsured Lev in Table 6.",
toupper(MODEL_FAMILY)))
# ── Side-by-side comparison of the two interactions ────────────────
cat("\nInteraction coefficient comparison (Table 6 vs Table 6b):\n")##
## Interaction coefficient comparison (Table 6 vs Table 6b):tibble(
Cell = names(models_T6),
`MTM × Uninsured (T6)` = map_chr(models_T6, function(m) {
tm <- get_robust_tidy(m); i <- which(tm$term == "ell_w_z:du_ta_w_z")
if (length(i) == 0) "" else fmt_est(tm$estimate[i], tm$p.value[i])
}),
`MTM × Insured (T6b)` = map_chr(models_T6b, function(m) {
tm <- get_robust_tidy(m); i <- which(tm$term == "ell_w_z:di_ta_w_z")
if (length(i) == 0) "" else fmt_est(tm$estimate[i], tm$p.value[i])
})
) %>% as_tibble() %>% print(n = Inf)## # A tibble: 6 × 3
## Cell `MTM × Uninsured (T6)` `MTM × Insured (T6b)`
## <chr> <chr> <chr>
## 1 P0: Pre-Crisis | DW 0.002 -0.001
## 2 P1: SVB Week | DW 0.001 0.001
## 3 P2: SVB to FRC | DW 0.013*** -0.010**
## 4 P2: SVB to FRC | BTFP 0.012*** -0.006
## 5 P3: FRC Week | DW 0.005** -0.004*
## 6 P3: FRC Week | BTFP 0.005* -0.003# ══════════════════════════════════════════════════════════════════════
# Table A3 — Returning-borrower LPM (regression counterpart of Table A1)
# Among borrowers in cell (p, f), what predicts being a RETURNING borrower?
# Sample: only banks that borrowed in cell (p, f). P0 dropped because
# all P0 borrowers are new by construction.
# ══════════════════════════════════════════════════════════════════════
# Build DV for each cell: 1 if returning, 0 if new; NA if not in cell
df_returning <- df_reg # Start with df_reg, then add per-cell DVs
for (i in seq_len(nrow(col_specs))) {
cs <- col_specs[i, ]
dep_name <- paste0("ret_",
gsub("[^a-z0-9]", "_", tolower(cs$col_id)))
ids_cell <- banks_in_cell(cs$period, cs$facility)
prior <- prior_set(cs$period)
df_returning[[dep_name]] <- dplyr::case_when(
!(df_returning$idrssd %in% ids_cell) ~ NA_integer_,
df_returning$idrssd %in% prior ~ 1L,
TRUE ~ 0L
)
}
# Fit only cells with variation in the DV (drops P0-DW, where all are new)
models_T_ret <- list()
for (i in seq_len(nrow(col_specs))) {
cs <- col_specs[i, ]
cid <- cs$col_id
dep_name <- paste0("ret_",
gsub("[^a-z0-9]", "_", tolower(cid)))
sub <- df_returning %>% filter(!is.na(.data[[dep_name]]))
if (var(sub[[dep_name]], na.rm = TRUE) == 0) {
cat(sprintf("Skipping %s: no variation (all %s).\n",
cid,
if (mean(sub[[dep_name]]) == 0) "new" else "returning"))
next
}
f <- as.formula(paste(dep_name, "~", rhs_base))
models_T_ret[[cid]] <- fit_model(f, sub)
}## Skipping P0: Pre-Crisis | DW: no variation (all new).tableA3 <- build_coef_table(models_T_ret, var_order, var_labels)
tableA3 %>% as_tibble() %>% print(n = Inf)## # A tibble: 24 × 6
## Variable `P1: SVB Week | DW` `P2: SVB to FRC | DW` P2: SVB to FRC | BTF…¹
## <chr> <chr> <chr> <chr>
## 1 "MTM loss (… "-0.091" "-0.052**" "-0.024"
## 2 "" "(0.067)" "(0.025)" "(0.016)"
## 3 "Uninsured … "0.081" "0.013" "0.010"
## 4 "" "(0.090)" "(0.019)" "(0.015)"
## 5 "MTM × Unin… "0.053" "-0.010" "-0.003"
## 6 "" "(0.082)" "(0.016)" "(0.011)"
## 7 "Ln(assets)" "-0.107" "0.024" "0.042***"
## 8 "" "(0.081)" "(0.021)" "(0.015)"
## 9 "Cash / TA" "-0.084" "-0.061**" "-0.024"
## 10 "" "(0.119)" "(0.025)" "(0.028)"
## 11 "Loan / Dep… "-0.210***" "-0.046" "-0.027"
## 12 "" "(0.079)" "(0.031)" "(0.019)"
## 13 "Book equit… "0.174" "-0.031" "0.011"
## 14 "" "(0.165)" "(0.032)" "(0.023)"
## 15 "Wholesale … "0.066" "0.059***" "0.020"
## 16 "" "(0.064)" "(0.021)" "(0.014)"
## 17 "ROA" "-0.215***" "-0.022" "-0.010"
## 18 "" "(0.074)" "(0.022)" "(0.015)"
## 19 "Constant" "0.649***" "0.115***" "0.028*"
## 20 "" "(0.107)" "(0.023)" "(0.016)"
## 21 "" "" "" ""
## 22 "N" "67" "397" "460"
## 23 "R²" "0.217" "0.060" "0.049"
## 24 "Mean of DV" "0.5224" "0.1637" "0.0630"
## # ℹ abbreviated name: ¹`P2: SVB to FRC | BTFP`
## # ℹ 2 more variables: `P3: FRC Week | DW` <chr>, `P3: FRC Week | BTFP` <chr>save_kbl_latex(tableA3, sprintf("tableA3_returning_lpm_%s", MODEL_FAMILY),
caption = sprintf(
"Returning-borrower regression (%s): conditional on borrowing in cell, LPM for returning status.",
toupper(MODEL_FAMILY)))# ══════════════════════════════════════════════════════════════════════
# Table A4 — Repeat-borrower LPM (regression counterpart of Table A2)
# Among borrowers in cell (p, f), what predicts being a REPEAT borrower?
# Sample: only banks that borrowed in cell (p, f).
# ══════════════════════════════════════════════════════════════════════
# Attach cell_types (built in Table A2) for the repeat/one-time flag
# NOTE: cell_types must exist in scope; if running this chunk standalone,
# re-run Table A2 construction first.
df_repeat <- df_reg
for (i in seq_len(nrow(col_specs))) {
cs <- col_specs[i, ]
dep_name <- paste0("rep_",
gsub("[^a-z0-9]", "_", tolower(cs$col_id)))
cell_flags <- cell_types %>%
filter(period == cs$period, facility == cs$facility) %>%
transmute(idrssd = rssd_id,
repeat_flag = as.integer(type == "Repeat"))
# Left-join so non-borrowers get NA
df_repeat[[dep_name]] <- cell_flags$repeat_flag[match(df_repeat$idrssd,
cell_flags$idrssd)]
}
# Fit only cells with variation
models_T_rep <- list()
for (i in seq_len(nrow(col_specs))) {
cs <- col_specs[i, ]
cid <- cs$col_id
dep_name <- paste0("rep_",
gsub("[^a-z0-9]", "_", tolower(cid)))
sub <- df_repeat %>% filter(!is.na(.data[[dep_name]]))
if (var(sub[[dep_name]], na.rm = TRUE) == 0) {
cat(sprintf("Skipping %s: no variation.\n", cid))
next
}
f <- as.formula(paste(dep_name, "~", rhs_base))
models_T_rep[[cid]] <- fit_model(f, sub)
}
tableA4 <- build_coef_table(models_T_rep, var_order, var_labels)
tableA4 %>% as_tibble() %>% print(n = Inf)## # A tibble: 24 × 7
## Variable `P0: Pre-Crisis | DW` `P1: SVB Week | DW` `P2: SVB to FRC | DW`
## <chr> <chr> <chr> <chr>
## 1 "MTM loss (t… "-0.033" "-0.021" "-0.036"
## 2 "" "(0.062)" "(0.072)" "(0.029)"
## 3 "Uninsured l… "0.152***" "0.097" "0.065***"
## 4 "" "(0.056)" "(0.090)" "(0.025)"
## 5 "MTM × Unins… "0.010" "-0.014" "0.026"
## 6 "" "(0.062)" "(0.076)" "(0.019)"
## 7 "Ln(assets)" "0.055" "-0.122" "-0.023"
## 8 "" "(0.067)" "(0.085)" "(0.026)"
## 9 "Cash / TA" "-0.104" "-0.330**" "-0.103***"
## 10 "" "(0.100)" "(0.131)" "(0.030)"
## 11 "Loan / Depo… "-0.157**" "-0.113" "-0.077**"
## 12 "" "(0.063)" "(0.098)" "(0.036)"
## 13 "Book equity… "-0.128**" "0.111" "-0.031"
## 14 "" "(0.062)" "(0.186)" "(0.041)"
## 15 "Wholesale f… "0.053" "0.080" "0.102***"
## 16 "" "(0.053)" "(0.063)" "(0.024)"
## 17 "ROA" "-0.075" "-0.103" "-0.001"
## 18 "" "(0.076)" "(0.091)" "(0.029)"
## 19 "Constant" "0.290***" "0.372**" "0.231***"
## 20 "" "(0.087)" "(0.141)" "(0.029)"
## 21 "" "" "" ""
## 22 "N" "72" "67" "397"
## 23 "R²" "0.223" "0.142" "0.106"
## 24 "Mean of DV" "0.4444" "0.4478" "0.2846"
## # ℹ 3 more variables: `P2: SVB to FRC | BTFP` <chr>, `P3: FRC Week | DW` <chr>,
## # `P3: FRC Week | BTFP` <chr>5.9 Summary: how to switch model family
# To regenerate all LPM tables as logit:
# 1. At the top of the Rmd, set:
# MODEL_FAMILY <- "logit"
# 2. Re-knit. All extensive-margin tables (6, 7, 8, 11) will regenerate.
# Tables 9, 10, 12 remain lm() because their DV is continuous.
#
# Saved files use family suffix: e.g., table6_main_lpm.tex, table6_main_logit.tex
# so you can compare specifications side-by-side.