BUILD DATASETS
df_2022q4 <- call_q %>%
filter(period == BASELINE_MAIN, !idrssd %in% excluded_banks,
!is.na(omo_eligible) & omo_eligible > 0) %>%
left_join(dssw_beta_2022q4, by = "idrssd") %>%
{ if (HAS_DEPOSIT_COSTS) left_join(., deposit_costs_2022q4, by = "idrssd") else . } %>%
left_join(public_flag %>% filter(period == "2022Q4") %>% select(idrssd, is_public), by = "idrssd") %>%
mutate(is_public = replace_na(is_public, 0L)) %>%
construct_analysis_vars()
df_2023q3 <- call_q %>%
filter(period == BASELINE_ARB, !idrssd %in% excluded_banks,
!is.na(omo_eligible) & omo_eligible > 0) %>%
left_join(dssw_beta_2022q4, by = "idrssd") %>%
{ if (HAS_DEPOSIT_COSTS) left_join(., deposit_costs_2022q4, by = "idrssd") else . } %>%
left_join(public_flag %>% filter(period == "2023Q3") %>% select(idrssd, is_public), by = "idrssd") %>%
mutate(is_public = replace_na(is_public, 0L)) %>%
construct_analysis_vars()
cat("2022Q4:", nrow(df_2022q4), "| β^U available:", sum(!is.na(df_2022q4$f_pp)), "\n")
## 2022Q4: 4292 | β^U available: 4226
join_all_borrowers <- function(df_base, btfp_df, dw_df, btfp_var, dw_var) {
df_base %>%
left_join(btfp_df %>% select(idrssd, starts_with(btfp_var)), by = "idrssd") %>%
left_join(dw_df %>% select(idrssd, starts_with(dw_var)), by = "idrssd") %>%
mutate("{btfp_var}" := replace_na(!!sym(btfp_var), 0L),
"{dw_var}" := replace_na(!!sym(dw_var), 0L),
fhlb_user = as.integer(abnormal_fhlb_borrowing_10pct == 1),
any_fed = as.integer(!!sym(btfp_var) == 1 | !!sym(dw_var) == 1),
both_fed = as.integer(!!sym(btfp_var) == 1 & !!sym(dw_var) == 1),
fed_amt = replace_na(!!sym(paste0(btfp_var, "_amt")), 0) +
replace_na(!!sym(paste0(dw_var, "_amt")), 0))
}
df_crisis <- join_all_borrowers(df_2022q4, btfp_crisis, dw_crisis, "btfp_crisis", "dw_crisis")
cat("Crisis:", nrow(df_crisis), "| Any Fed:", sum(df_crisis$any_fed), "\n")
## Crisis: 4292 | Any Fed: 828
Sample Cleaning
core_vars <- c("book_equity_to_total_asset", "total_asset", "total_liability",
"cash_to_total_asset", "security_to_total_asset",
"total_loan_to_total_asset", "loan_to_deposit", "roa",
"uninsured_deposit_to_total_asset", "wholesale_raw")
df_crisis_clean <- df_crisis %>%
filter(!is.na(mtm_loss_to_total_asset)) %>%
filter(if_all(all_of(core_vars), ~ !is.na(.))) %>%
filter(!is.na(uninsured_deposit) & !is.na(insured_deposit) & insured_deposit > 0) %>%
filter(!is.na(abnormal_fhlb_borrowing_10pct)) %>%
filter(total_asset > 0 & is.finite(ln_assets_raw))
df_model <- df_crisis_clean %>% filter(!is.na(f_u_pp))
cat(sprintf("Clean: %d | Theory model (β^U available): %d\n",
nrow(df_crisis_clean), nrow(df_model)))
## Clean: 4251 | Theory model (β^U available): 4226
cat(sprintf("Fed borrowers in model sample: %d (%.1f%%)\n",
sum(df_model$any_fed), 100 * mean(df_model$any_fed)))
## Fed borrowers in model sample: 822 (19.5%)
borr_colors <- c("Fed Borrower" = "#C62828", "Non-Borrower" = "#1565C0")
fac_colors <- c("BTFP" = "#1565C0", "DW" = "#E53935", "Both" = "#6A1B9A")
theme_gp <- theme_minimal(base_size = 13) +
theme(plot.title = element_text(face = "bold", size = 14),
plot.subtitle = element_text(color = "grey40", size = 11),
plot.caption = element_text(color = "grey50", size = 9, hjust = 0),
legend.position = "bottom", panel.grid.minor = element_blank())
BORROWING / CAPACITY: DATA CONSTRUCTION
Key design decisions (all issues from prior review
fixed):
- BTFP and DW analyzed separately — BTFP accepts
collateral at face/par value (no MV adjustment, no haircut); DW values
OMO-eligible at market value and non-OMO at market value minus haircut.
Mixing them into a single ρ confounds facility choice with run
severity.
- DW collateral:
max() not
sum() — DW uses a standing pre-pledged pool;
multiple advances draw against the same pool. sum()
double-counts. BTFP: sum() is correct because each
transaction pledges separate securities.
- Loan amounts are in actual dollars; Call Report assets in
thousands — normalizations use
total_asset × 1000.
- ρ = 0 banks diagnosed and excluded from regressions
— zero-amount draws are uninformative for revealed run
expectations.
# ==============================================================================
# BTFP aggregation: SUM amounts, SUM collateral
# Each BTFP loan pledges its own securities at FACE value.
# ρ_BTFP = total_amount / total_face_value_of_pledged_securities
#
# DW aggregation: SUM amounts, MAX collateral
# DW uses a standing pre-pledged pool (dw_total_collateral reports the
# full pool at each draw). Multiple advances tap the same pool.
# ρ_DW = total_amount / max(pool_size)
# ==============================================================================
# ── BTFP: per-loan collateral → sum both amount and collateral ──
btfp_bank <- btfp_loans %>%
filter(btfp_loan_date >= CRISIS_START, btfp_loan_date <= CRISIS_END) %>%
group_by(rssd_id) %>%
summarise(
btfp_n_loans = n(),
btfp_amt = sum(btfp_loan_amount, na.rm = TRUE),
btfp_collateral = sum(btfp_total_collateral, na.rm = TRUE),
btfp_first_date = min(btfp_loan_date),
.groups = "drop"
) %>%
rename(idrssd = rssd_id)
# ── DW: standing pool → MAX collateral, SUM amounts ──
dw_bank <- dw_loans %>%
filter(dw_loan_date >= CRISIS_START, dw_loan_date <= min(CRISIS_END, DW_DATA_END)) %>%
group_by(rssd_id) %>%
summarise(
dw_n_loans = n(),
dw_amt = sum(dw_loan_amount, na.rm = TRUE),
dw_collateral = max(dw_total_collateral, na.rm = TRUE),
dw_omo = max(dw_omo_eligible, na.rm = TRUE),
dw_non_omo = max(dw_non_omo_eligible, na.rm = TRUE),
dw_first_date = min(dw_loan_date),
.groups = "drop"
) %>%
rename(idrssd = rssd_id)
# ── Merge onto model sample ──
df_cap <- df_model %>%
left_join(btfp_bank, by = "idrssd") %>%
left_join(dw_bank, by = "idrssd") %>%
mutate(
# Explicit NA → 0 for safe math
btfp_n_loans = replace_na(btfp_n_loans, 0L),
btfp_amt = replace_na(btfp_amt, 0),
btfp_collateral = replace_na(btfp_collateral, 0),
dw_n_loans = replace_na(dw_n_loans, 0L),
dw_amt = replace_na(dw_amt, 0),
dw_collateral = replace_na(dw_collateral, 0),
dw_omo = replace_na(dw_omo, 0),
dw_non_omo = replace_na(dw_non_omo, 0),
# Identify Borrowers
btfp_crisis = as.integer(btfp_amt > 0),
dw_crisis = as.integer(dw_amt > 0),
any_fed = as.integer(btfp_crisis == 1 | dw_crisis == 1)
) %>%
filter(any_fed == 1) %>%
mutate(
# ── Facility-specific ρ ──
rho_btfp = safe_div(btfp_amt, btfp_collateral, NA_real_),
rho_dw_omo = safe_div(dw_amt, dw_omo, NA_real_),
rho_dw_non_omo = safe_div(dw_amt, dw_non_omo, NA_real_),
rho_dw = safe_div(dw_amt, dw_collateral, NA_real_),
# ── Normalize by total assets (convert TA from thousands to actual dollars) ──
btfp_amt_ta = btfp_amt / (total_asset * 1000),
btfp_collateral_ta = btfp_collateral / (total_asset * 1000),
dw_amt_ta = dw_amt / (total_asset * 1000),
dw_collateral_ta = dw_collateral / (total_asset * 1000),
dw_omo_ta = dw_omo / (total_asset * 1000),
dw_non_omo_ta = dw_non_omo / (total_asset * 1000),
# ── Multi-loan flags ──
btfp_multi = as.integer(btfp_n_loans > 1),
dw_multi = as.integer(dw_n_loans > 1),
# ── Borrower-type classification ──
borrower_type = case_when(
btfp_crisis == 1 & dw_crisis == 1 ~ "Both",
btfp_crisis == 1 & dw_crisis == 0 ~ "BTFP Only",
dw_crisis == 1 & btfp_crisis == 0 ~ "DW Only",
TRUE ~ "Other"
),
# ── Decomposition ──
one_minus_beta = 1 - beta_u_clipped
)
# ── Size quartile breakpoints from FULL model sample (not just borrowers) ──
asset_breaks <- quantile(df_model$total_asset, probs = c(0, .25, .50, .75, 1), na.rm = TRUE)
df_cap <- df_cap %>%
mutate(size_bucket = cut(total_asset, breaks = asset_breaks,
labels = c("Q1 (Small)", "Q2", "Q3", "Q4 (Large)"),
include.lowest = TRUE))
# ── Base BTFP- and DW-specific subsets ──
df_btfp <- df_cap %>% filter(btfp_n_loans > 0 & !is.na(rho_btfp))
df_dw <- df_cap %>% filter(dw_n_loans > 0 & !is.na(rho_dw))
df_cap <- df_cap %>%
mutate(
# 1. Convert balance sheet liquidity (thousands) to actual dollars
cash_dollars = cash * 1000,
# MV of Securities = (Book Ratio - MTM Loss Ratio) * Total Assets in Dollars
# This precisely handles the market value adjustment for pledgeable collateral
mv_sec_dollars = (security_to_total_asset - mtm_sec_raw) * (total_asset * 1000),
# Uninsured deposits to actual dollars
unins_dep_dollars = uninsured_deposit * 1000,
# MV of Non-OMO Securities in dollars
mv_non_omo_dollars = replace_na(mv_non_omo_securities, 0) * 1000,
# 2A. REALISTIC ASSUMPTION: Run met via Cash + Actual Fed Borrowing
w_realistic_btfp = btfp_amt + cash_dollars,
w_realistic_dw = dw_amt + cash_dollars,
# 2B. STRICT ASSUMPTION: w = g + cash + mv_sec
w_strict_btfp = btfp_amt + cash_dollars + mv_non_omo_dollars,
w_strict_dw = dw_amt + cash_dollars + mv_sec_dollars,
# 3. Calculate Revealed Expected Run Rates
run_rate_real_btfp = safe_div(w_realistic_btfp, unins_dep_dollars, NA_real_),
run_rate_real_dw = safe_div(w_realistic_dw, unins_dep_dollars, NA_real_),
run_rate_strict_btfp = safe_div(w_strict_btfp, unins_dep_dollars, NA_real_),
run_rate_strict_dw = safe_div(w_strict_dw, unins_dep_dollars, NA_real_)
)
# Propagate calculations to working subsets
df_btfp <- df_cap %>% filter(btfp_n_loans > 0 & !is.na(rho_btfp))
df_dw <- df_cap %>% filter(dw_n_loans > 0 & !is.na(rho_dw))
# ── Implied Run Rate by Size Bucket (BTFP) ──
run_size_btfp <- df_btfp %>%
group_by(size_bucket) %>%
summarise(
N = n(),
`Mean Borrowing/TA` = round(mean(btfp_amt_ta, na.rm=T), 4),
`Mean Cash/TA` = round(mean(cash_ratio_raw, na.rm=T), 4),
`Realistic Run % (Cash+Borrowing)` = round(mean(run_rate_real_btfp, na.rm=T) * 100, 2),
`Strict Run % (Cash+Borrowing+MV Sec)` = round(mean(run_rate_strict_btfp, na.rm=T) * 100, 2),
.groups = "drop"
)
kbl(run_size_btfp, format = "html", escape = FALSE,
caption = "BTFP Borrowers: Revealed Run Expectations by Size") %>%
kable_styling(bootstrap_options = c("striped", "hover", "condensed"), full_width = FALSE)
BTFP Borrowers: Revealed Run Expectations by Size
|
size_bucket
|
N
|
Mean Borrowing/TA
|
Mean Cash/TA
|
Realistic Run % (Cash+Borrowing)
|
Strict Run % (Cash+Borrowing+MV Sec)
|
|
Q1 (Small)
|
39
|
0.0752
|
7.0580
|
84.94
|
190.86
|
|
Q2
|
89
|
0.0632
|
5.9035
|
56.33
|
133.70
|
|
Q3
|
143
|
0.0587
|
4.3116
|
51.44
|
148.36
|
|
Q4 (Large)
|
225
|
0.0710
|
3.9528
|
53.05
|
100.25
|
# ── Implied Run Rate by Size Bucket (DW) ──
run_size_dw <- df_dw %>%
group_by(size_bucket) %>%
summarise(
N = n(),
`Mean Borrowing/TA` = round(mean(dw_amt_ta, na.rm=T), 4),
`Mean Cash/TA` = round(mean(cash_ratio_raw, na.rm=T), 4),
`Realistic Run % (Cash+Borrowing)` = round(mean(run_rate_real_dw, na.rm=T) * 100, 2),
`Strict Run % (Cash+Borrowing+MV Sec)` = round(mean(run_rate_strict_dw, na.rm=T) * 100, 2),
.groups = "drop"
)
kbl(run_size_dw, format = "html", escape = FALSE,
caption = "DW Borrowers: Revealed Run Expectations by Size") %>%
kable_styling(bootstrap_options = c("striped", "hover", "condensed"), full_width = FALSE)
DW Borrowers: Revealed Run Expectations by Size
|
size_bucket
|
N
|
Mean Borrowing/TA
|
Mean Cash/TA
|
Realistic Run % (Cash+Borrowing)
|
Strict Run % (Cash+Borrowing+MV Sec)
|
|
Q1 (Small)
|
25
|
0.0690
|
6.8591
|
87.53
|
17978.60
|
|
Q2
|
59
|
0.0562
|
8.2433
|
68.49
|
13064.16
|
|
Q3
|
120
|
0.0464
|
6.4866
|
51.51
|
12217.55
|
|
Q4 (Large)
|
226
|
0.1105
|
4.6321
|
109.63
|
11657.09
|
# ── Implied Run Rate: High vs Low ρ (BTFP) ──
df_btfp_valid <- df_btfp %>% filter(rho_btfp > 0 & is.finite(rho_btfp))
med_btfp <- median(df_btfp_valid$rho_btfp)
df_btfp_valid <- df_btfp_valid %>% mutate(rho_grp = ifelse(rho_btfp >= med_btfp, "High ρ", "Low ρ"))
run_rho_btfp <- df_btfp_valid %>%
group_by(rho_grp) %>%
summarise(
N = n(),
`Mean ρ` = round(mean(rho_btfp, na.rm=T), 3),
`Realistic Run % (Cash+Borrowing)` = round(mean(run_rate_real_btfp, na.rm=T) * 100, 2),
`Uninsured Dep / TA` = round(mean(uninsured_lev_raw, na.rm=T), 3),
.groups = "drop"
)
kbl(run_rho_btfp, format = "html", escape = FALSE,
caption = "BTFP: Revealed Run Rate by High/Low Borrowing Utilization (ρ)") %>%
kable_styling(bootstrap_options = c("striped", "hover", "condensed"), full_width = FALSE)
BTFP: Revealed Run Rate by High/Low Borrowing Utilization (ρ)
|
rho_grp
|
N
|
Mean ρ
|
Realistic Run % (Cash+Borrowing)
|
Uninsured Dep / TA
|
|
High ρ
|
248
|
0.856
|
54.47
|
26.792
|
|
Low ρ
|
248
|
0.289
|
56.77
|
27.994
|
cat("=== SAMPLE OVERVIEW ===\n")
## === SAMPLE OVERVIEW ===
cat(sprintf(" Total borrowers in model: %d\n", nrow(df_cap)))
## Total borrowers in model: 822
cat(sprintf(" BTFP borrowers: %d (multi-loan: %d, %.1f%%)\n",
nrow(df_btfp), sum(df_btfp$btfp_multi), 100 * mean(df_btfp$btfp_multi)))
## BTFP borrowers: 496 (multi-loan: 276, 55.6%)
cat(sprintf(" DW borrowers: %d (multi-loan: %d, %.1f%%)\n",
nrow(df_dw), sum(df_dw$dw_multi), 100 * mean(df_dw$dw_multi)))
## DW borrowers: 430 (multi-loan: 121, 28.1%)
cat(sprintf(" Both facilities: %d\n", sum(df_cap$borrower_type == "Both")))
## Both facilities: 104
cat("\n=== ρ DIAGNOSTICS (before any filtering) ===\n")
##
## === ρ DIAGNOSTICS (before any filtering) ===
cat(sprintf(" ρ_BTFP: mean=%.3f, med=%.3f, sd=%.3f, min=%.4f, max=%.4f [N=%d]\n",
mean(df_btfp$rho_btfp, na.rm = TRUE), median(df_btfp$rho_btfp, na.rm = TRUE), sd(df_btfp$rho_btfp, na.rm = TRUE),
min(df_btfp$rho_btfp, na.rm = TRUE), max(df_btfp$rho_btfp, na.rm = TRUE), sum(!is.na(df_btfp$rho_btfp))))
## ρ_BTFP: mean=0.572, med=0.570, sd=0.325, min=0.0000, max=1.0000 [N=496]
cat(sprintf(" ρ_DW (Overall): mean=%.3f, med=%.3f, sd=%.3f, min=%.4f, max=%.4f [N=%d]\n",
mean(df_dw$rho_dw, na.rm = TRUE), median(df_dw$rho_dw, na.rm = TRUE), sd(df_dw$rho_dw, na.rm = TRUE),
min(df_dw$rho_dw, na.rm = TRUE), max(df_dw$rho_dw, na.rm = TRUE), sum(!is.na(df_dw$rho_dw))))
## ρ_DW (Overall): mean=0.969, med=0.013, sd=3.134, min=0.0000, max=26.7484 [N=430]
cat(sprintf(" ρ_DW (OMO): mean=%.3f, med=%.3f, sd=%.3f, min=%.4f, max=%.4f [N=%d]\n",
mean(df_dw$rho_dw_omo, na.rm = TRUE), median(df_dw$rho_dw_omo, na.rm = TRUE), sd(df_dw$rho_dw_omo, na.rm = TRUE),
min(df_dw$rho_dw_omo, na.rm = TRUE), max(df_dw$rho_dw_omo, na.rm = TRUE), sum(!is.na(df_dw$rho_dw_omo))))
## ρ_DW (OMO): mean=886.363, med=0.130, sd=11713.504, min=0.0000, max=160585.5484 [N=188]
cat(sprintf(" ρ_DW (Non-OMO): mean=%.3f, med=%.3f, sd=%.3f, min=%.4f, max=%.4f [N=%d]\n",
mean(df_dw$rho_dw_non_omo, na.rm = TRUE), median(df_dw$rho_dw_non_omo, na.rm = TRUE), sd(df_dw$rho_dw_non_omo, na.rm = TRUE),
min(df_dw$rho_dw_non_omo, na.rm = TRUE), max(df_dw$rho_dw_non_omo, na.rm = TRUE), sum(!is.na(df_dw$rho_dw_non_omo))))
## ρ_DW (Non-OMO): mean=7.225, med=0.007, sd=69.960, min=0.0000, max=1074.3770 [N=313]
cat("\n=== EDGE-CASE DIAGNOSTICS ===\n")
##
## === EDGE-CASE DIAGNOSTICS ===
cat(sprintf(" BTFP: amt=0: %d | collateral=0: %d | ρ>1: %d\n",
sum(df_btfp$btfp_amt == 0), sum(df_btfp$btfp_collateral == 0),
sum(df_btfp$rho_btfp > 1, na.rm = TRUE)))
## BTFP: amt=0: 0 | collateral=0: 0 | ρ>1: 0
cat(sprintf(" DW: amt=0: %d | collateral=0: %d | ρ>1: %d\n",
sum(df_dw$dw_amt == 0), sum(df_dw$dw_collateral == 0),
sum(df_dw$rho_dw > 1, na.rm = TRUE)))
## DW: amt=0: 0 | collateral=0: 0 | ρ>1: 63
cat("\n=== COLLATERAL AGGREGATION CHECK (DW multi-loan) ===\n")
##
## === COLLATERAL AGGREGATION CHECK (DW multi-loan) ===
dw_multi_check <- df_dw %>% filter(dw_multi == 1)
dw_single_check <- df_dw %>% filter(dw_multi == 0)
cat(sprintf(" DW single-loan: mean collateral/TA = %.4f [N=%d]\n",
mean(dw_single_check$dw_collateral_ta), nrow(dw_single_check)))
## DW single-loan: mean collateral/TA = 0.0498 [N=309]
cat(sprintf(" DW multi-loan: mean collateral/TA = %.4f [N=%d]\n",
mean(dw_multi_check$dw_collateral_ta), nrow(dw_multi_check)))
## DW multi-loan: mean collateral/TA = 0.1001 [N=121]
cat(" (Using max() — ratio should be comparable across groups.)\n")
## (Using max() — ratio should be comparable across groups.)
DESCRIPTIVE STATISTICS
5.1 ρ Distribution by
Facility
rho_summary_fn <- function(x, label) {
tibble(Facility = label, N = sum(!is.na(x)),
Mean = mean(x, na.rm=T), Median = median(x, na.rm=T),
SD = sd(x, na.rm=T), P25 = quantile(x, .25, na.rm=T),
P75 = quantile(x, .75, na.rm=T),
Min = min(x, na.rm=T), Max = max(x, na.rm=T))
}
rho_stats <- bind_rows(
rho_summary_fn(df_btfp$rho_btfp, "BTFP (Face-Value Collateral)"),
rho_summary_fn(df_dw$rho_dw, "DW (Overall Pool)"),
rho_summary_fn(df_dw$rho_dw_omo, "DW (OMO: Market-Value Adjusted)"),
rho_summary_fn(df_dw$rho_dw_non_omo, "DW (Non-OMO: MV Minus Haircut)")
)
kbl(rho_stats %>% mutate(across(where(is.numeric) & !matches("^N$"), ~ round(., 4))),
format = "html", escape = FALSE,
caption = "Distribution of ρ by Facility") %>%
kable_styling(bootstrap_options = c("striped", "hover", "condensed"), full_width = FALSE) %>%
footnote(general = "BTFP: Collateral accepted at par/face value without MTM loss. DW: Applies MTM loss. DW OMO avoids haircut, Non-OMO applies both MTM loss and haircut.")
Distribution of ρ by Facility
|
Facility
|
N
|
Mean
|
Median
|
SD
|
P25
|
P75
|
Min
|
Max
|
|
BTFP (Face-Value Collateral)
|
496
|
0.5722
|
0.5699
|
0.3247
|
0.3098
|
0.8931
|
0
|
1.0000
|
|
DW (Overall Pool)
|
430
|
0.9691
|
0.0129
|
3.1337
|
0.0002
|
0.4124
|
0
|
26.7484
|
|
DW (OMO: Market-Value Adjusted)
|
188
|
886.3634
|
0.1302
|
11713.5038
|
0.0012
|
1.1659
|
0
|
160585.5484
|
|
DW (Non-OMO: MV Minus Haircut)
|
313
|
7.2248
|
0.0066
|
69.9605
|
0.0001
|
0.3848
|
0
|
1074.3770
|
|
Note:
|
|
BTFP: Collateral accepted at par/face value without MTM
loss. DW: Applies MTM loss. DW OMO avoids haircut, Non-OMO applies both
MTM loss and haircut.
|
save_kbl_latex(rho_stats %>% mutate(across(where(is.numeric) & !matches("^N$"), ~ round(., 4))),
"Table_Rho_Summary",
caption = "Distribution of $\\rho$ by Facility")
## Saved: Table_Rho_Summary.tex
5.2 BTFP: Above vs
Below Median ρ
# ── Filter to valid BTFP ρ > 0 ──
df_btfp_valid <- df_btfp %>% filter(rho_btfp > 0 & is.finite(rho_btfp))
med_btfp <- median(df_btfp_valid$rho_btfp)
df_btfp_valid <- df_btfp_valid %>%
mutate(rho_grp = ifelse(rho_btfp >= med_btfp, "High", "Low"))
cat(sprintf("BTFP valid: %d | Median ρ_BTFP = %.4f | High: %d | Low: %d\n",
nrow(df_btfp_valid), med_btfp,
sum(df_btfp_valid$rho_grp == "High"), sum(df_btfp_valid$rho_grp == "Low")))
## BTFP valid: 496 | Median ρ_BTFP = 0.5699 | High: 248 | Low: 248
desc_vars <- c("ln_assets_raw", "mtm_total_raw", "mtm_sec_raw", "mtm_loan_raw",
"book_equity_ratio_raw", "cash_ratio_raw", "loan_to_deposit_raw",
"wholesale_raw", "roa_raw",
"uninsured_lev_raw", "uninsured_share_raw", "uninsured_beta_raw",
"f_pp", "f_u_pp", "emv_pp", "v_pp",
"btfp_amt_ta", "btfp_collateral_ta")
desc_labels <- c("Log(Assets)", "Total MTM (ℓ)", "Securities MTM (ℓ_S)", "Loan MTM (ℓ_L)",
"Book Equity (e)", "Cash/TA", "Loan/Deposit",
"Wholesale (%)", "ROA",
"Uninsured/TA (μ)", "D^U/D", "β^U",
"Franchise (f)", "Unins. Franchise (f^U)", "MV Equity (E^MV)", "Run Value (v)",
"BTFP Amount/TA", "BTFP Collateral/TA")
btfp_split <- make_desc_comparison(df_btfp_valid, "rho_grp", "High", "Low",
desc_vars, desc_labels)
kbl(btfp_split %>% select(Variable, High, Low, Difference, p),
format = "html", escape = FALSE,
col.names = c("Variable", sprintf("High ρ_BTFP (≥%.3f)", med_btfp),
sprintf("Low ρ_BTFP (<%.3f)", med_btfp), "Difference", "p-value"),
caption = sprintf("BTFP: Above vs Below Median ρ (median = %.4f)", med_btfp)) %>%
kable_styling(bootstrap_options = c("striped", "hover", "condensed"), full_width = FALSE) %>%
footnote(general = "*** p<0.01, ** p<0.05, * p<0.10. BTFP calculates ρ as Loan Amount / Face Value.")
BTFP: Above vs Below Median ρ (median = 0.5699)
|
Variable
|
High ρ_BTFP (≥0.570)
|
Low ρ_BTFP (<0.570)
|
Difference
|
p-value
|
|
Log(Assets)
|
13.576 (1.482)
|
13.887 (1.630)
|
-0.311**
|
0.0266046
|
|
Total MTM (ℓ)
|
6.045 (1.844)
|
6.123 (2.036)
|
-0.078
|
0.6545887
|
|
Securities MTM (ℓ_S)
|
2.496 (1.565)
|
2.671 (1.739)
|
-0.175
|
0.2398733
|
|
Loan MTM (ℓ_L)
|
3.549 (1.467)
|
3.452 (1.601)
|
0.097
|
0.4833117
|
|
Book Equity (e)
|
8.095 (2.639)
|
8.366 (3.376)
|
-0.271
|
0.3205222
|
|
Cash/TA
|
4.429 (4.733)
|
4.872 (4.570)
|
-0.442
|
0.2903532
|
|
Loan/Deposit
|
74.526 (18.705)
|
71.166 (19.317)
|
3.361**
|
0.0495913
|
|
Wholesale (%)
|
1.788 (3.900)
|
1.322 (2.375)
|
0.466
|
0.1085192
|
|
ROA
|
1.053 (0.545)
|
1.083 (0.536)
|
-0.030
|
0.5367721
|
|
Uninsured/TA (μ)
|
26.792 (11.624)
|
27.994 (12.876)
|
-1.202
|
0.2755607
|
|
D^U/D
|
31.557 (13.670)
|
32.549 (15.026)
|
-0.992
|
0.4420942
|
|
β^U
|
0.358 (0.127)
|
0.328 (0.102)
|
0.030***
|
0.0044275
|
|
Franchise (f)
|
2.784 (1.519)
|
3.174 (1.839)
|
-0.390**
|
0.0103753
|
|
Unins. Franchise (f^U)
|
1.012 (0.946)
|
1.247 (1.321)
|
-0.236**
|
0.0228475
|
|
MV Equity (E^MV)
|
4.834 (3.901)
|
5.417 (4.590)
|
-0.582
|
0.1285328
|
|
Run Value (v)
|
3.823 (3.618)
|
4.169 (4.276)
|
-0.347
|
0.3302570
|
|
BTFP Amount/TA
|
0.069 (0.086)
|
0.064 (0.114)
|
0.005
|
0.5572068
|
|
BTFP Collateral/TA
|
0.087 (0.127)
|
0.210 (0.326)
|
-0.122***
|
0.0000001
|
|
Note:
|
|
*** p<0.01, ** p<0.05, * p<0.10. BTFP calculates ρ
as Loan Amount / Face Value.
|
save_kbl_latex(btfp_split %>% select(Variable, High, Low, Difference, p),
"Table_Desc_BTFP_MedianSplit",
col.names = c("Variable", "High $\\rho$", "Low $\\rho$", "Difference", "p-value"),
caption = "BTFP: Above vs Below Median $\\rho_{\\text{BTFP}}$")
## Saved: Table_Desc_BTFP_MedianSplit.tex
5.3 DW: Above vs
Below Median ρ
df_dw_valid <- df_dw %>% filter(rho_dw > 0 & is.finite(rho_dw))
med_dw <- median(df_dw_valid$rho_dw)
df_dw_valid <- df_dw_valid %>%
mutate(rho_grp = ifelse(rho_dw >= med_dw, "High", "Low"))
cat(sprintf("DW valid: %d | Median ρ_DW = %.4f | High: %d | Low: %d\n",
nrow(df_dw_valid), med_dw,
sum(df_dw_valid$rho_grp == "High"), sum(df_dw_valid$rho_grp == "Low")))
## DW valid: 430 | Median ρ_DW = 0.0129 | High: 215 | Low: 215
desc_vars_dw <- c("ln_assets_raw", "mtm_total_raw", "mtm_sec_raw", "mtm_loan_raw",
"book_equity_ratio_raw", "cash_ratio_raw", "loan_to_deposit_raw",
"wholesale_raw", "roa_raw",
"uninsured_lev_raw", "uninsured_share_raw", "uninsured_beta_raw",
"f_pp", "f_u_pp", "emv_pp", "v_pp",
"dw_amt_ta", "dw_collateral_ta")
desc_labels_dw <- c("Log(Assets)", "Total MTM (ℓ)", "Securities MTM (ℓ_S)", "Loan MTM (ℓ_L)",
"Book Equity (e)", "Cash/TA", "Loan/Deposit",
"Wholesale (%)", "ROA",
"Uninsured/TA (μ)", "D^U/D", "β^U",
"Franchise (f)", "Unins. Franchise (f^U)", "MV Equity (E^MV)", "Run Value (v)",
"DW Amount/TA", "DW Collateral/TA")
dw_split <- make_desc_comparison(df_dw_valid, "rho_grp", "High", "Low",
desc_vars_dw, desc_labels_dw)
kbl(dw_split %>% select(Variable, High, Low, Difference, p),
format = "html", escape = FALSE,
col.names = c("Variable", sprintf("High ρ_DW (≥%.3f)", med_dw),
sprintf("Low ρ_DW (<%.3f)", med_dw), "Difference", "p-value"),
caption = sprintf("DW: Above vs Below Median ρ (median = %.4f)", med_dw)) %>%
kable_styling(bootstrap_options = c("striped", "hover", "condensed"), full_width = FALSE) %>%
footnote(general = "*** p<0.01, ** p<0.05, * p<0.10. DW adjusts collateral for Market Value and Haircuts. DW multi-loans utilize max(pool) capacity.")
DW: Above vs Below Median ρ (median = 0.0129)
|
Variable
|
High ρ_DW (≥0.013)
|
Low ρ_DW (<0.013)
|
Difference
|
p-value
|
|
Log(Assets)
|
13.910 (1.463)
|
14.133 (1.685)
|
-0.224
|
0.1425810
|
|
Total MTM (ℓ)
|
5.797 (2.009)
|
5.657 (1.948)
|
0.140
|
0.4626079
|
|
Securities MTM (ℓ_S)
|
2.389 (1.657)
|
2.018 (1.457)
|
0.372**
|
0.0139135
|
|
Loan MTM (ℓ_L)
|
3.408 (1.529)
|
3.639 (1.659)
|
-0.231
|
0.1334865
|
|
Book Equity (e)
|
8.602 (3.238)
|
9.236 (2.823)
|
-0.634**
|
0.0311344
|
|
Cash/TA
|
4.920 (5.918)
|
6.629 (6.453)
|
-1.708***
|
0.0044340
|
|
Loan/Deposit
|
75.684 (20.368)
|
76.089 (20.518)
|
-0.405
|
0.8375330
|
|
Wholesale (%)
|
1.960 (4.009)
|
1.156 (3.135)
|
0.804**
|
0.0210250
|
|
ROA
|
1.146 (0.727)
|
1.104 (0.501)
|
0.042
|
0.4897857
|
|
Uninsured/TA (μ)
|
29.014 (13.066)
|
27.001 (11.808)
|
2.013*
|
0.0945391
|
|
D^U/D
|
34.407 (15.625)
|
31.555 (13.889)
|
2.853**
|
0.0460617
|
|
β^U
|
0.353 (0.130)
|
0.342 (0.116)
|
0.011
|
0.3435537
|
|
Franchise (f)
|
3.068 (1.779)
|
2.925 (1.550)
|
0.144
|
0.3725513
|
|
Unins. Franchise (f^U)
|
1.237 (1.204)
|
1.070 (0.996)
|
0.167
|
0.1177921
|
|
MV Equity (E^MV)
|
5.873 (4.362)
|
6.504 (4.169)
|
-0.630
|
0.1263336
|
|
Run Value (v)
|
4.636 (4.115)
|
5.434 (3.861)
|
-0.797**
|
0.0388968
|
|
DW Amount/TA
|
0.165 (0.480)
|
0.000 (0.000)
|
0.165***
|
0.0000009
|
|
DW Collateral/TA
|
0.073 (0.088)
|
0.055 (0.072)
|
0.019**
|
0.0170413
|
|
Note:
|
|
*** p<0.01, ** p<0.05, * p<0.10. DW adjusts
collateral for Market Value and Haircuts. DW multi-loans utilize
max(pool) capacity.
|
save_kbl_latex(dw_split %>% select(Variable, High, Low, Difference, p),
"Table_Desc_DW_MedianSplit",
col.names = c("Variable", "High $\\rho$", "Low $\\rho$", "Difference", "p-value"),
caption = "DW: Above vs Below Median $\\rho_{\\text{DW}}$")
## Saved: Table_Desc_DW_MedianSplit.tex
5.4 ρ by Size
Bucket
# ── BTFP by size ──
btfp_size <- df_btfp_valid %>%
group_by(size_bucket) %>%
summarise(
N = n(),
`ρ Mean` = round(mean(rho_btfp), 4), `ρ Median` = round(median(rho_btfp), 4),
`ρ SD` = round(sd(rho_btfp), 4),
`ℓ` = round(mean(mtm_total_raw, na.rm=T), 3), `ℓ_S` = round(mean(mtm_sec_raw, na.rm=T), 3),
`f^U` = round(mean(f_u_pp, na.rm=T), 3), `Cash/TA` = round(mean(cash_ratio_raw, na.rm=T), 3),
`v` = round(mean(v_pp, na.rm=T), 3),
`Multi %` = round(100 * mean(btfp_multi), 1), .groups = "drop")
kbl(btfp_size, format = "html", escape = FALSE,
caption = "BTFP: ρ by Asset Size Quartile (Par/Face Value)") %>%
kable_styling(bootstrap_options = c("striped", "hover", "condensed"), full_width = FALSE)
BTFP: ρ by Asset Size Quartile (Par/Face Value)
|
size_bucket
|
N
|
ρ Mean
|
ρ Median
|
ρ SD
|
ℓ
|
ℓ_S
|
f^U
|
Cash/TA
|
v
|
Multi %
|
|
Q1 (Small)
|
39
|
0.6340
|
0.6919
|
0.3288
|
5.674
|
2.889
|
0.670
|
7.058
|
3.829
|
38.5
|
|
Q2
|
89
|
0.5797
|
0.5714
|
0.3275
|
6.266
|
2.939
|
0.950
|
5.903
|
3.415
|
52.8
|
|
Q3
|
143
|
0.6109
|
0.5991
|
0.3030
|
6.347
|
2.711
|
0.892
|
4.312
|
3.535
|
57.3
|
|
Q4 (Large)
|
225
|
0.5339
|
0.5168
|
0.3335
|
5.916
|
2.308
|
1.431
|
3.953
|
4.548
|
58.7
|
# ── DW by size (Added OMO & Non-OMO columns) ──
dw_size <- df_dw_valid %>%
group_by(size_bucket) %>%
summarise(
N = n(),
`ρ Overall Mean` = round(mean(rho_dw), 4),
`ρ OMO Mean` = round(mean(rho_dw_omo, na.rm=T), 4),
`ρ Non-OMO Mean` = round(mean(rho_dw_non_omo, na.rm=T), 4),
`ρ Median` = round(median(rho_dw), 4),
`ρ SD` = round(sd(rho_dw), 4),
`ℓ` = round(mean(mtm_total_raw, na.rm=T), 3),
`f^U` = round(mean(f_u_pp, na.rm=T), 3), `Cash/TA` = round(mean(cash_ratio_raw, na.rm=T), 3),
`v` = round(mean(v_pp, na.rm=T), 3),
`Multi %` = round(100 * mean(dw_multi), 1), .groups = "drop")
kbl(dw_size, format = "html", escape = FALSE,
caption = "DW: ρ by Asset Size Quartile (MV & Haircut Adjusted)") %>%
kable_styling(bootstrap_options = c("striped", "hover", "condensed"), full_width = FALSE) %>%
footnote(general = "Size quartiles from full model sample. Multi % = banks with >1 loan at that facility.")
DW: ρ by Asset Size Quartile (MV & Haircut Adjusted)
|
size_bucket
|
N
|
ρ Overall Mean
|
ρ OMO Mean
|
ρ Non-OMO Mean
|
ρ Median
|
ρ SD
|
ℓ
|
f^U
|
Cash/TA
|
v
|
Multi %
|
|
Q1 (Small)
|
25
|
1.2446
|
1.7555
|
1.2074
|
0.1246
|
2.1934
|
5.851
|
0.540
|
6.859
|
5.391
|
40.0
|
|
Q2
|
59
|
0.6294
|
16.7918
|
0.7140
|
0.0096
|
1.8447
|
5.634
|
0.821
|
8.243
|
4.135
|
25.4
|
|
Q3
|
120
|
0.9749
|
13.2611
|
0.7417
|
0.0336
|
2.6688
|
5.949
|
0.926
|
6.487
|
4.214
|
22.5
|
|
Q4 (Large)
|
226
|
1.0243
|
1968.0989
|
11.6831
|
0.0068
|
3.6775
|
5.620
|
1.429
|
4.632
|
5.666
|
30.5
|
|
Note:
|
|
Size quartiles from full model sample. Multi % = banks with
>1 loan at that facility.
|
save_kbl_latex(btfp_size, "Table_Rho_BTFP_SizeBuckets", caption = "BTFP $\\rho$ by Size")
## Saved: Table_Rho_BTFP_SizeBuckets.tex
save_kbl_latex(dw_size, "Table_Rho_DW_SizeBuckets", caption = "DW $\\rho$ by Size")
## Saved: Table_Rho_DW_SizeBuckets.tex
5.5 Multi-Loan vs
Single-Loan
# ── BTFP: single vs multi ──
btfp_multi_vars <- c("rho_btfp", "btfp_amt_ta", "btfp_collateral_ta",
"ln_assets_raw", "mtm_total_raw", "mtm_sec_raw",
"f_u_pp", "cash_ratio_raw", "v_pp")
btfp_multi_labs <- c("ρ_BTFP", "Amount/TA", "Collateral/TA",
"Log(Assets)", "MTM (ℓ)", "Securities MTM (ℓ_S)",
"f^U", "Cash/TA", "Run Value (v)")
df_btfp_valid <- df_btfp_valid %>%
mutate(multi_grp = ifelse(btfp_multi == 1, "Multi", "Single"))
btfp_multi_tbl <- make_desc_comparison(df_btfp_valid, "multi_grp", "Multi", "Single",
btfp_multi_vars, btfp_multi_labs)
kbl(btfp_multi_tbl %>% select(Variable, High, Low, Difference, p),
format = "html", escape = FALSE,
col.names = c("Variable", "Multi-Loan", "Single-Loan", "Difference", "p-value"),
caption = sprintf("BTFP: Multi-Loan (%d) vs Single-Loan (%d)",
sum(df_btfp_valid$btfp_multi), sum(!df_btfp_valid$btfp_multi))) %>%
kable_styling(bootstrap_options = c("striped", "hover", "condensed"), full_width = FALSE)
BTFP: Multi-Loan (276) vs Single-Loan (220)
|
Variable
|
Multi-Loan
|
Single-Loan
|
Difference
|
p-value
|
|
ρ_BTFP
|
0.531 (0.262)
|
0.624 (0.384)
|
-0.093***
|
0.0022886
|
|
Amount/TA
|
0.100 (0.123)
|
0.025 (0.029)
|
0.075***
|
0.0000000
|
|
Collateral/TA
|
0.234 (0.315)
|
0.042 (0.042)
|
0.192***
|
0.0000000
|
|
Log(Assets)
|
13.790 (1.403)
|
13.659 (1.746)
|
0.131
|
0.3664627
|
|
MTM (ℓ)
|
6.198 (1.967)
|
5.941 (1.903)
|
0.257
|
0.1418132
|
|
Securities MTM (ℓ_S)
|
2.676 (1.703)
|
2.467 (1.589)
|
0.209
|
0.1600984
|
|
f^U
|
1.153 (1.286)
|
1.100 (0.965)
|
0.053
|
0.6027277
|
|
Cash/TA
|
4.379 (4.810)
|
4.991 (4.435)
|
-0.612
|
0.1420094
|
|
Run Value (v)
|
4.002 (3.984)
|
3.988 (3.940)
|
0.014
|
0.9691570
|
# ── DW: single vs multi ──
dw_multi_vars <- c("rho_dw", "dw_amt_ta", "dw_collateral_ta",
"ln_assets_raw", "mtm_total_raw",
"f_u_pp", "cash_ratio_raw", "v_pp")
dw_multi_labs <- c("ρ_DW", "Amount/TA", "Collateral/TA",
"Log(Assets)", "MTM (ℓ)",
"f^U", "Cash/TA", "Run Value (v)")
df_dw_valid <- df_dw_valid %>%
mutate(multi_grp = ifelse(dw_multi == 1, "Multi", "Single"))
dw_multi_tbl <- make_desc_comparison(df_dw_valid, "multi_grp", "Multi", "Single",
dw_multi_vars, dw_multi_labs)
kbl(dw_multi_tbl %>% select(Variable, High, Low, Difference, p),
format = "html", escape = FALSE,
col.names = c("Variable", "Multi-Loan", "Single-Loan", "Difference", "p-value"),
caption = sprintf("DW: Multi-Loan (%d) vs Single-Loan (%d)",
sum(df_dw_valid$dw_multi), sum(!df_dw_valid$dw_multi))) %>%
kable_styling(bootstrap_options = c("striped", "hover", "condensed"), full_width = FALSE)
DW: Multi-Loan (121) vs Single-Loan (309)
|
Variable
|
Multi-Loan
|
Single-Loan
|
Difference
|
p-value
|
|
ρ_DW
|
3.222 (5.279)
|
0.087 (0.207)
|
3.136***
|
0.0000000
|
|
Amount/TA
|
0.288 (0.613)
|
0.002 (0.008)
|
0.286***
|
0.0000011
|
|
Collateral/TA
|
0.100 (0.094)
|
0.050 (0.071)
|
0.050***
|
0.0000003
|
|
Log(Assets)
|
14.040 (1.548)
|
14.014 (1.595)
|
0.025
|
0.8800942
|
|
MTM (ℓ)
|
5.894 (2.025)
|
5.662 (1.958)
|
0.232
|
0.2817347
|
|
f^U
|
1.330 (1.281)
|
1.084 (1.024)
|
0.246*
|
0.0605775
|
|
Cash/TA
|
4.295 (4.646)
|
6.354 (6.684)
|
-2.059***
|
0.0003389
|
|
Run Value (v)
|
4.490 (4.101)
|
5.249 (3.953)
|
-0.759*
|
0.0827915
|
save_kbl_latex(btfp_multi_tbl %>% select(Variable, High, Low, Difference, p),
"Table_BTFP_MultiVsSingle",
col.names = c("Variable", "Multi", "Single", "Diff", "p-value"),
caption = "BTFP: Multi-Loan vs Single-Loan")
## Saved: Table_BTFP_MultiVsSingle.tex
save_kbl_latex(dw_multi_tbl %>% select(Variable, High, Low, Difference, p),
"Table_DW_MultiVsSingle",
col.names = c("Variable", "Multi", "Single", "Diff", "p-value"),
caption = "DW: Multi-Loan vs Single-Loan")
## Saved: Table_DW_MultiVsSingle.tex
5.6 Facility-Type
Comparison
fac_summary <- df_cap %>%
group_by(borrower_type) %>%
summarise(
N = n(),
`ℓ` = round(mean(mtm_total_raw, na.rm=T), 3),
`ℓ_S` = round(mean(mtm_sec_raw, na.rm=T), 3),
`f^U` = round(mean(f_u_pp, na.rm=T), 3),
`Cash/TA` = round(mean(cash_ratio_raw, na.rm=T), 3),
`v` = round(mean(v_pp, na.rm=T), 3),
`Unins/TA` = round(mean(uninsured_lev_raw, na.rm=T), 3),
`β^U` = round(mean(beta_u_clipped, na.rm=T), 3),
`Log(TA)` = round(mean(ln_assets_raw, na.rm=T), 2),
.groups = "drop"
)
kbl(fac_summary, format = "html", escape = FALSE,
caption = "Characteristics by Facility Type") %>%
kable_styling(bootstrap_options = c("striped", "hover", "condensed"), full_width = FALSE)
Characteristics by Facility Type
|
borrower_type
|
N
|
ℓ
|
ℓ_S
|
f^U
|
Cash/TA
|
v
|
Unins/TA
|
β^U
|
Log(TA)
|
|
BTFP Only
|
392
|
6.165
|
2.608
|
1.054
|
4.677
|
3.904
|
26.173
|
0.337
|
13.50
|
|
Both
|
104
|
5.779
|
2.491
|
1.413
|
4.549
|
4.342
|
31.989
|
0.365
|
14.62
|
|
DW Only
|
326
|
5.710
|
2.112
|
1.071
|
6.166
|
5.256
|
26.737
|
0.341
|
13.83
|
save_kbl_latex(fac_summary, "Table_FacilityType_Chars",
caption = "Characteristics by Facility Type")
## Saved: Table_FacilityType_Chars.tex
REGRESSIONS: BTFP
BTFP: Realistic Implied Run Rate
BTFP offers par → recapitalization channel. Securities losses \(\ell_S\) determine capacity. Banks with
higher \(\ell \times f^U\) should draw
a larger share (expect worse runs). We use run_pct_btfp
(Cash + BTFP Draw / Uninsured Deposits) as our primary dependent
variable..
7.1 Main Table
# ── Prepare BTFP regression sample ──
df_btfp_reg <- df_btfp_valid %>%
mutate(
# Re-standardize within BTFP borrower sample
mtm_total_b = standardize_z(winsorize(mtm_total_raw)),
mtm_sec_b = standardize_z(winsorize(mtm_sec_raw)),
mtm_loan_b = standardize_z(winsorize(mtm_loan_raw)),
f_u_b = standardize_z(winsorize(f_u_pp)),
cash_b = standardize_z(winsorize(cash_ratio_raw)),
ln_assets_b = standardize_z(winsorize(ln_assets_raw)),
ltd_b = standardize_z(winsorize(loan_to_deposit_raw)),
equity_b = standardize_z(winsorize(book_equity_ratio_raw)),
wholesale_b = standardize_z(winsorize(wholesale_raw)),
roa_b = standardize_z(winsorize(roa_raw)),
unins_lev_b = standardize_z(winsorize(uninsured_lev_raw)),
one_minus_beta_b = standardize_z(winsorize(one_minus_beta)),
# Interactions
mtm_x_fu_b = mtm_total_b * f_u_b,
sec_x_fu_b = mtm_sec_b * f_u_b,
loan_x_fu_b = mtm_loan_b * f_u_b,
mtm_x_mu_b = mtm_total_b * unins_lev_b,
mtm_x_1mbeta_b = mtm_total_b * one_minus_beta_b,
mtm_x_mu_x_1mbeta_b = mtm_total_b * unins_lev_b * one_minus_beta_b,
# LHS: Revealed Run Rate (Percentage Points)
run_pct_btfp = run_rate_real_btfp * 100
)
cat(sprintf("BTFP regression sample: %d (after removing ρ=0)\n", nrow(df_btfp_reg)))
## BTFP regression sample: 496 (after removing ρ=0)
ctrl_b <- c("ln_assets_b", "cash_b", "ltd_b", "equity_b", "wholesale_b", "roa_b")
ctrl_b_str <- paste(ctrl_b, collapse = " + ")
coef_map_btfp <- c(
"mtm_total_b" = "ℓ (MTM Loss)", "mtm_sec_b" = "ℓ_S (Securities)",
"mtm_loan_b" = "ℓ_L (Loans)", "f_u_b" = "f^U (Uninsured Franchise)",
"mtm_x_fu_b" = "ℓ × f^U (expect > 0)",
"sec_x_fu_b" = "ℓ_S × f^U (expect > 0)",
"loan_x_fu_b" = "ℓ_L × f^U (expect ≈ 0)",
"cash_b" = "Cash/TA", "ln_assets_b" = "Log(Assets)",
"ltd_b" = "Loan/Dep", "equity_b" = "Equity/TA",
"wholesale_b" = "Wholesale", "roa_b" = "ROA")
# Updated formula using Implied Run %
fml_btfp <- as.formula(paste0("run_pct_btfp ~ mtm_total_b + f_u_b + mtm_x_fu_b + ", ctrl_b_str))
reg_btfp_main <- list(
"Run %: Full" = feols(fml_btfp, data = df_btfp_reg, vcov = "hetero"),
"Run %: Single" = feols(fml_btfp, data = df_btfp_reg %>% filter(btfp_multi == 0), vcov = "hetero"),
"Run %: Multi" = feols(fml_btfp, data = df_btfp_reg %>% filter(btfp_multi == 1), vcov = "hetero")
)
msummary(reg_btfp_main, stars = c("*"=.10, "**"=.05, "***"=.01), gof_omit = "AIC|BIC|Log|RMSE",
coef_rename = coef_map_btfp,
title = "BTFP: Revealed Run Expectation (%)",
notes = "LHS = (BTFP Draw + Cash) / Uninsured Deposits. Tests if fundamental vulnerability drives internal run expectations.")
BTFP: Revealed Run Expectation (%)
| |
Run %: Full |
Run %: Single |
Run %: Multi |
| * p < 0.1, ** p < 0.05, *** p < 0.01 |
| LHS = (BTFP Draw + Cash) / Uninsured Deposits. Tests if fundamental vulnerability drives internal run expectations. |
| (Intercept) |
56.357*** |
31.468*** |
75.401*** |
|
(5.786) |
(2.025) |
(9.454) |
| ℓ (MTM Loss) |
-3.037 |
4.147 |
-11.159 |
|
(6.840) |
(3.223) |
(12.305) |
| f^U (Uninsured Franchise) |
-35.928*** |
-16.475*** |
-45.797** |
|
(13.468) |
(4.178) |
(18.637) |
| ℓ × f^U (expect > 0) |
4.079 |
-2.496 |
6.949 |
|
(5.894) |
(4.695) |
(8.436) |
| Log(Assets) |
21.633 |
-2.378 |
39.314 |
|
(16.504) |
(2.746) |
(27.225) |
| Cash/TA |
27.729*** |
20.799*** |
41.494** |
|
(7.985) |
(4.148) |
(16.355) |
| Loan/Dep |
-31.377 |
-1.089 |
-48.461 |
|
(20.127) |
(4.803) |
(29.893) |
| Equity/TA |
16.816 |
2.404 |
19.276 |
|
(10.523) |
(4.235) |
(14.117) |
| Wholesale |
4.105 |
0.879 |
1.267 |
|
(3.228) |
(1.502) |
(5.933) |
| ROA |
5.850 |
1.962 |
8.307 |
|
(8.530) |
(2.571) |
(13.490) |
| Num.Obs. |
495 |
219 |
276 |
| R2 |
0.166 |
0.412 |
0.221 |
| R2 Adj. |
0.151 |
0.386 |
0.195 |
| Std.Errors |
Heteroskedasticity-robust |
Heteroskedasticity-robust |
Heteroskedasticity-robust |
save_reg_latex(reg_btfp_main, "Table_RunExp_BTFP_Main",
coef_rename = c("mtm_total_b"="$\\ell$", "f_u_b"="$f^U$",
"mtm_x_fu_b"="$\\ell \\times f^U$", "cash_b"="Cash/TA",
"ln_assets_b"="Log(Assets)", "ltd_b"="Loan/Dep",
"equity_b"="Equity/TA", "wholesale_b"="Wholesale", "roa_b"="ROA"),
title = "BTFP: Revealed Run Expectation (\\%)")
## Saved: Table_RunExp_BTFP_Main.tex
7.2 Signal
Decomposition: ℓ_S vs ℓ_L
# Col 1: Total MTM loss (Baseline)
fml_s1 <- as.formula(paste0("run_pct_btfp ~ mtm_total_b + f_u_b + mtm_x_fu_b + ", ctrl_b_str))
# Col 2: Split into Securities vs Loans (The actual signal decomposition)
fml_s2 <- as.formula(paste0("run_pct_btfp ~ mtm_sec_b + mtm_loan_b + f_u_b + sec_x_fu_b + loan_x_fu_b + ", ctrl_b_str))
reg_btfp_signal <- list(
"Total Loss (ℓ)" = feols(fml_s1, data = df_btfp_reg, vcov = "hetero"),
"Sec vs Loan Split" = feols(fml_s2, data = df_btfp_reg, vcov = "hetero")
)
msummary(reg_btfp_signal, stars = c("*"=.10, "**"=.05, "***"=.01), gof_omit = "AIC|BIC|Log|RMSE",
coef_rename = coef_map_btfp,
title = "BTFP Run Exp: Signal Decomposition ℓ_S vs ℓ_L",
notes = "Tests whether run expectations are driven strictly by pledgeable securities losses (ℓ_S) or general loan losses (ℓ_L).")
BTFP Run Exp: Signal Decomposition ℓ_S vs ℓ_L
| |
Total Loss (ℓ) |
Sec vs Loan Split |
| * p < 0.1, ** p < 0.05, *** p < 0.01 |
| Tests whether run expectations are driven strictly by pledgeable securities losses (ℓ_S) or general loan losses (ℓ_L). |
| (Intercept) |
56.357*** |
56.913*** |
|
(5.786) |
(5.944) |
| ℓ (MTM Loss) |
-3.037 |
|
|
(6.840) |
|
| f^U (Uninsured Franchise) |
-35.928*** |
-33.447*** |
|
(13.468) |
(11.264) |
| ℓ × f^U (expect > 0) |
4.079 |
|
|
(5.894) |
|
| Log(Assets) |
21.633 |
22.233 |
|
(16.504) |
(16.321) |
| Cash/TA |
27.729*** |
17.637** |
|
(7.985) |
(7.702) |
| Loan/Dep |
-31.377 |
-57.647 |
|
(20.127) |
(38.615) |
| Equity/TA |
16.816 |
12.271* |
|
(10.523) |
(7.414) |
| Wholesale |
4.105 |
6.977 |
|
(3.228) |
(4.307) |
| ROA |
5.850 |
6.071 |
|
(8.530) |
(8.636) |
| ℓ_S (Securities) |
|
-33.966 |
|
|
(27.603) |
| ℓ_L (Loans) |
|
7.991 |
|
|
(5.691) |
| ℓ_S × f^U (expect > 0) |
|
9.470 |
|
|
(8.065) |
| ℓ_L × f^U (expect ≈ 0) |
|
7.964 |
|
|
(7.706) |
| Num.Obs. |
495 |
495 |
| R2 |
0.166 |
0.198 |
| R2 Adj. |
0.151 |
0.179 |
| Std.Errors |
Heteroskedasticity-robust |
Heteroskedasticity-robust |
save_reg_latex(reg_btfp_signal, "Table_RunExp_BTFP_Signal",
coef_rename = c("mtm_total_b"="$\\ell$", "mtm_sec_b"="$\\ell_S$", "mtm_loan_b"="$\\ell_L$",
"f_u_b"="$f^U$", "mtm_x_fu_b"="$\\ell \\times f^U$",
"sec_x_fu_b"="$\\ell_S \\times f^U$", "loan_x_fu_b"="$\\ell_L \\times f^U$",
"cash_b"="Cash/TA", "ln_assets_b"="Log(Assets)", "ltd_b"="Loan/Dep",
"equity_b"="Equity/TA", "wholesale_b"="Wholesale", "roa_b"="ROA"),
title = "BTFP Run Expectation: Securities vs Loan Losses")
## Saved: Table_RunExp_BTFP_Signal.tex
7.3 Decomposition: ℓ
× μ × (1 − β^U)
fml_d1 <- as.formula(paste0("run_pct_btfp ~ mtm_total_b + f_u_b + mtm_x_fu_b + ", ctrl_b_str))
fml_d2 <- as.formula(paste0("run_pct_btfp ~ mtm_total_b + unins_lev_b + one_minus_beta_b + ",
"mtm_x_mu_b + mtm_x_1mbeta_b + ", ctrl_b_str))
fml_d3 <- as.formula(paste0("run_pct_btfp ~ mtm_total_b + unins_lev_b + one_minus_beta_b + ",
"mtm_x_mu_x_1mbeta_b + ", ctrl_b_str))
reg_btfp_decomp <- list(
"ℓ × f^U" = feols(fml_d1, data = df_btfp_reg, vcov = "hetero"),
"ℓ×μ + ℓ×(1−β^U)" = feols(fml_d2, data = df_btfp_reg, vcov = "hetero"),
"ℓ × μ × (1−β^U)" = feols(fml_d3, data = df_btfp_reg, vcov = "hetero")
)
decomp_map <- c(
"mtm_total_b" = "ℓ", "f_u_b" = "f^U",
"unins_lev_b" = "μ (Uninsured Leverage)",
"one_minus_beta_b" = "1−β^U (Deposit Sensitivity)",
"mtm_x_fu_b" = "ℓ × f^U",
"mtm_x_mu_b" = "ℓ × μ", "mtm_x_1mbeta_b" = "ℓ × (1−β^U)",
"mtm_x_mu_x_1mbeta_b" = "ℓ × μ × (1−β^U)",
"cash_b" = "Cash/TA", "ln_assets_b" = "Log(Assets)", "ltd_b" = "Loan/Dep",
"equity_b" = "Equity/TA", "wholesale_b" = "Wholesale", "roa_b" = "ROA")
msummary(reg_btfp_decomp, stars = c("*"=.10, "**"=.05, "***"=.01), gof_omit = "AIC|BIC|Log|RMSE",
coef_rename = decomp_map,
title = "BTFP Run Exp: Decomposition ℓ × f^U → ℓ × μ × (1−β^U)",
notes = "Col 1: baseline. Col 2: separate interactions. Col 3: triple interaction capturing fundamental vulnerability.")
BTFP Run Exp: Decomposition ℓ × f^U → ℓ × μ × (1−β^U)
| |
ℓ × f^U |
ℓ×μ + ℓ×(1−β^U) |
ℓ × μ × (1−β^U) |
| * p < 0.1, ** p < 0.05, *** p < 0.01 |
| Col 1: baseline. Col 2: separate interactions. Col 3: triple interaction capturing fundamental vulnerability. |
| (Intercept) |
56.357*** |
53.883*** |
57.234*** |
|
(5.786) |
(4.501) |
(5.220) |
| ℓ |
-3.037 |
-7.484 |
-0.970 |
|
(6.840) |
(7.219) |
(5.039) |
| f^U |
-35.928*** |
|
|
|
(13.468) |
|
|
| ℓ × f^U |
4.079 |
|
|
|
(5.894) |
|
|
| Log(Assets) |
21.633 |
22.992* |
20.854* |
|
(16.504) |
(13.901) |
(11.481) |
| Cash/TA |
27.729*** |
27.129*** |
25.132*** |
|
(7.985) |
(6.874) |
(6.011) |
| Loan/Dep |
-31.377 |
-34.043* |
-40.772* |
|
(20.127) |
(19.027) |
(21.109) |
| Equity/TA |
16.816 |
12.995 |
17.007* |
|
(10.523) |
(8.486) |
(9.315) |
| Wholesale |
4.105 |
1.033 |
3.070 |
|
(3.228) |
(3.127) |
(3.009) |
| ROA |
5.850 |
6.944 |
4.420 |
|
(8.530) |
(7.600) |
(6.102) |
| μ (Uninsured Leverage) |
|
-49.021*** |
-36.555*** |
|
|
(15.434) |
(8.663) |
| 1−β^U (Deposit Sensitivity) |
|
-14.987* |
-30.376** |
|
|
(8.570) |
(15.267) |
| ℓ × μ |
|
6.707 |
|
|
|
(7.793) |
|
| ℓ × (1−β^U) |
|
20.347* |
|
|
|
(11.275) |
|
| ℓ × μ × (1−β^U) |
|
|
-28.872* |
|
|
|
(15.894) |
| Num.Obs. |
495 |
495 |
495 |
| R2 |
0.166 |
0.288 |
0.349 |
| R2 Adj. |
0.151 |
0.272 |
0.336 |
| Std.Errors |
Heteroskedasticity-robust |
Heteroskedasticity-robust |
Heteroskedasticity-robust |
save_reg_latex(reg_btfp_decomp, "Table_RunExp_BTFP_Decomp",
coef_rename = c("mtm_total_b"="$\\ell$", "f_u_b"="$f^U$",
"unins_lev_b"="$\\mu$", "one_minus_beta_b"="$1-\\beta^U$",
"mtm_x_fu_b"="$\\ell \\times f^U$",
"mtm_x_mu_b"="$\\ell \\times \\mu$",
"mtm_x_1mbeta_b"="$\\ell \\times (1-\\beta^U)$",
"mtm_x_mu_x_1mbeta_b"="$\\ell \\times \\mu \\times (1-\\beta^U)$"),
title = "BTFP Run Expectation: Uninsured Deposit Decomposition")
## Saved: Table_RunExp_BTFP_Decomp.tex
REGRESSIONS: DW
DW: Realistic Implied Run Rate
DW accepts broad collateral (OMO at MV, non-OMO at MV−haircut). Banks
borrow for immediate cash needs. Cash should be strongly negative. We
use run_pct_dw (Cash + DW Draw / Uninsured Deposits) as our
primary dependent variable to measure internal run expectations.
8.1 Main Table
df_dw_reg <- df_dw_valid %>%
mutate(
# Re-standardize within DW borrower sample
mtm_total_b = standardize_z(winsorize(mtm_total_raw)),
mtm_sec_b = standardize_z(winsorize(mtm_sec_raw)),
mtm_loan_b = standardize_z(winsorize(mtm_loan_raw)),
f_u_b = standardize_z(winsorize(f_u_pp)),
cash_b = standardize_z(winsorize(cash_ratio_raw)),
ln_assets_b = standardize_z(winsorize(ln_assets_raw)),
ltd_b = standardize_z(winsorize(loan_to_deposit_raw)),
equity_b = standardize_z(winsorize(book_equity_ratio_raw)),
wholesale_b = standardize_z(winsorize(wholesale_raw)),
roa_b = standardize_z(winsorize(roa_raw)),
unins_lev_b = standardize_z(winsorize(uninsured_lev_raw)),
one_minus_beta_b = standardize_z(winsorize(one_minus_beta)),
# Interactions
mtm_x_fu_b = mtm_total_b * f_u_b,
sec_x_fu_b = mtm_sec_b * f_u_b,
loan_x_fu_b = mtm_loan_b * f_u_b,
mtm_x_mu_b = mtm_total_b * unins_lev_b,
mtm_x_1mbeta_b = mtm_total_b * one_minus_beta_b,
mtm_x_mu_x_1mbeta_b = mtm_total_b * unins_lev_b * one_minus_beta_b,
# LHS: Revealed Run Rate (Percentage Points)
run_pct_dw = run_rate_real_dw * 100
)
cat(sprintf("DW regression sample: %d (after removing ρ=0)\n", nrow(df_dw_reg)))
## DW regression sample: 430 (after removing ρ=0)
ctrl_b <- c("ln_assets_b", "cash_b", "ltd_b", "equity_b", "wholesale_b", "roa_b")
ctrl_b_str <- paste(ctrl_b, collapse = " + ")
coef_map_dw <- c(
"mtm_total_b" = "ℓ (MTM Loss)", "mtm_sec_b" = "ℓ_S (Securities)",
"mtm_loan_b" = "ℓ_L (Loans)", "f_u_b" = "f^U (Uninsured Franchise)",
"mtm_x_fu_b" = "ℓ × f^U (expect > 0)",
"sec_x_fu_b" = "ℓ_S × f^U",
"loan_x_fu_b" = "ℓ_L × f^U",
"cash_b" = "Cash/TA", "ln_assets_b" = "Log(Assets)",
"ltd_b" = "Loan/Dep", "equity_b" = "Equity/TA",
"wholesale_b" = "Wholesale", "roa_b" = "ROA")
fml_dw <- as.formula(paste0("run_pct_dw ~ mtm_total_b + f_u_b + mtm_x_fu_b + ", ctrl_b_str))
reg_dw_main <- list(
"Run %: Full" = feols(fml_dw, data = df_dw_reg, vcov = "hetero"),
"Run %: Single" = feols(fml_dw, data = df_dw_reg %>% filter(dw_multi == 0), vcov = "hetero"),
"Run %: Multi" = feols(fml_dw, data = df_dw_reg %>% filter(dw_multi == 1), vcov = "hetero")
)
msummary(reg_dw_main, stars = c("*"=.10, "**"=.05, "***"=.01), gof_omit = "AIC|BIC|Log|RMSE",
coef_rename = coef_map_dw,
title = "DW: Revealed Run Expectation (%)",
notes = "LHS = (DW Draw + Cash) / Uninsured Deposits. DW uses standing pool (max). OMO at MV, non-OMO at MV−haircut.")
DW: Revealed Run Expectation (%)
| |
Run %: Full |
Run %: Single |
Run %: Multi |
| * p < 0.1, ** p < 0.05, *** p < 0.01 |
| LHS = (DW Draw + Cash) / Uninsured Deposits. DW uses standing pool (max). OMO at MV, non-OMO at MV−haircut. |
| (Intercept) |
85.496*** |
57.478* |
140.201*** |
|
(28.879) |
(31.782) |
(24.265) |
| ℓ (MTM Loss) |
72.323 |
105.115 |
-1.070 |
|
(68.358) |
(98.576) |
(24.160) |
| f^U (Uninsured Franchise) |
-58.780 |
-83.119 |
-40.618** |
|
(40.766) |
(67.484) |
(18.629) |
| ℓ × f^U (expect > 0) |
-23.172 |
-45.934 |
3.108 |
|
(28.311) |
(47.036) |
(17.740) |
| Log(Assets) |
16.100 |
10.053 |
50.661* |
|
(11.383) |
(14.683) |
(29.677) |
| Cash/TA |
18.945* |
28.484** |
33.987 |
|
(9.914) |
(12.032) |
(36.146) |
| Loan/Dep |
6.861 |
8.079 |
-45.578* |
|
(26.084) |
(19.131) |
(26.765) |
| Equity/TA |
58.078 |
92.559 |
-0.754 |
|
(56.758) |
(84.982) |
(24.341) |
| Wholesale |
2.202 |
-5.555 |
4.869 |
|
(12.232) |
(13.547) |
(14.918) |
| ROA |
88.932 |
131.358 |
-1.611 |
|
(85.222) |
(129.249) |
(15.479) |
| Num.Obs. |
430 |
309 |
121 |
| R2 |
0.042 |
0.065 |
0.090 |
| R2 Adj. |
0.022 |
0.037 |
0.017 |
| Std.Errors |
Heteroskedasticity-robust |
Heteroskedasticity-robust |
Heteroskedasticity-robust |
save_reg_latex(reg_dw_main, "Table_RunExp_DW_Main",
coef_rename = c("mtm_total_b"="$\\ell$", "f_u_b"="$f^U$",
"mtm_x_fu_b"="$\\ell \\times f^U$", "cash_b"="Cash/TA",
"ln_assets_b"="Log(Assets)", "ltd_b"="Loan/Dep",
"equity_b"="Equity/TA", "wholesale_b"="Wholesale", "roa_b"="ROA"),
title = "DW: Revealed Run Expectation (\\%)")
## Saved: Table_RunExp_DW_Main.tex
8.2 Signal
Decomposition
# Col 1: Total MTM loss (Baseline)
fml_dw_s1 <- as.formula(paste0("run_pct_dw ~ mtm_total_b + f_u_b + mtm_x_fu_b + ", ctrl_b_str))
# Col 2: Split into Securities vs Loans
fml_dw_s2 <- as.formula(paste0(
"run_pct_dw ~ mtm_sec_b + mtm_loan_b + f_u_b + sec_x_fu_b + loan_x_fu_b + ", ctrl_b_str))
reg_dw_sig <- list(
"Total Loss (ℓ)" = feols(fml_dw_s1, data = df_dw_reg, vcov = "hetero"),
"Sec vs Loan Split" = feols(fml_dw_s2, data = df_dw_reg, vcov = "hetero")
)
msummary(reg_dw_sig, stars = c("*"=.10, "**"=.05, "***"=.01), gof_omit = "AIC|BIC|Log|RMSE",
coef_rename = coef_map_dw,
title = "DW Run Exp: Signal Decomposition ℓ_S vs ℓ_L",
notes = "Tests whether run expectations are driven strictly by pledgeable securities losses (ℓ_S) or general loan losses (ℓ_L). DW accepts broad collateral; signal decomposition may differ from BTFP.")
DW Run Exp: Signal Decomposition ℓ_S vs ℓ_L
| |
Total Loss (ℓ) |
Sec vs Loan Split |
| * p < 0.1, ** p < 0.05, *** p < 0.01 |
| Tests whether run expectations are driven strictly by pledgeable securities losses (ℓ_S) or general loan losses (ℓ_L). DW accepts broad collateral; signal decomposition may differ from BTFP. |
| (Intercept) |
85.496*** |
80.703*** |
|
(28.879) |
(22.366) |
| ℓ (MTM Loss) |
72.323 |
|
|
(68.358) |
|
| f^U (Uninsured Franchise) |
-58.780 |
-58.706 |
|
(40.766) |
(40.839) |
| ℓ × f^U (expect > 0) |
-23.172 |
|
|
(28.311) |
|
| Log(Assets) |
16.100 |
15.642 |
|
(11.383) |
(12.043) |
| Cash/TA |
18.945* |
3.535 |
|
(9.914) |
(20.801) |
| Loan/Dep |
6.861 |
-37.424 |
|
(26.084) |
(32.790) |
| Equity/TA |
58.078 |
57.328 |
|
(56.758) |
(55.437) |
| Wholesale |
2.202 |
7.759 |
|
(12.232) |
(9.972) |
| ROA |
88.932 |
92.821 |
|
(85.222) |
(87.930) |
| ℓ_S (Securities) |
|
14.616 |
|
|
(22.416) |
| ℓ_L (Loans) |
|
75.629 |
|
|
(68.814) |
| ℓ_S × f^U |
|
8.509 |
|
|
(23.257) |
| ℓ_L × f^U |
|
-46.394 |
|
|
(64.273) |
| Num.Obs. |
430 |
430 |
| R2 |
0.042 |
0.050 |
| R2 Adj. |
0.022 |
0.025 |
| Std.Errors |
Heteroskedasticity-robust |
Heteroskedasticity-robust |
save_reg_latex(reg_dw_sig, "Table_RunExp_DW_Signal",
coef_rename = c("mtm_total_b"="$\\ell$", "mtm_sec_b"="$\\ell_S$", "mtm_loan_b"="$\\ell_L$",
"f_u_b"="$f^U$", "mtm_x_fu_b"="$\\ell \\times f^U$",
"sec_x_fu_b"="$\\ell_S \\times f^U$", "loan_x_fu_b"="$\\ell_L \\times f^U$",
"cash_b"="Cash/TA", "ln_assets_b"="Log(Assets)", "ltd_b"="Loan/Dep",
"equity_b"="Equity/TA", "wholesale_b"="Wholesale", "roa_b"="ROA"),
title = "DW Run Expectation: Securities vs Loan Signal")
## Saved: Table_RunExp_DW_Signal.tex
8.3 Decomposition: ℓ
× μ × (1 − β^U)
fml_d1 <- as.formula(paste0("run_pct_dw ~ mtm_total_b + f_u_b + mtm_x_fu_b + ", ctrl_b_str))
fml_d2 <- as.formula(paste0("run_pct_dw ~ mtm_total_b + unins_lev_b + one_minus_beta_b + ",
"mtm_x_mu_b + mtm_x_1mbeta_b + ", ctrl_b_str))
fml_d3 <- as.formula(paste0("run_pct_dw ~ mtm_total_b + unins_lev_b + one_minus_beta_b + ",
"mtm_x_mu_x_1mbeta_b + ", ctrl_b_str))
reg_dw_decomp <- list(
"ℓ × f^U" = feols(fml_d1, data = df_dw_reg, vcov = "hetero"),
"ℓ×μ + ℓ×(1−β^U)" = feols(fml_d2, data = df_dw_reg, vcov = "hetero"),
"ℓ × μ × (1−β^U)" = feols(fml_d3, data = df_dw_reg, vcov = "hetero")
)
decomp_map_dw <- c(
"mtm_total_b" = "ℓ", "f_u_b" = "f^U",
"unins_lev_b" = "μ (Uninsured Leverage)",
"one_minus_beta_b" = "1−β^U (Deposit Sensitivity)",
"mtm_x_fu_b" = "ℓ × f^U",
"mtm_x_mu_b" = "ℓ × μ", "mtm_x_1mbeta_b" = "ℓ × (1−β^U)",
"mtm_x_mu_x_1mbeta_b" = "ℓ × μ × (1−β^U)",
"cash_b" = "Cash/TA", "ln_assets_b" = "Log(Assets)", "ltd_b" = "Loan/Dep",
"equity_b" = "Equity/TA", "wholesale_b" = "Wholesale", "roa_b" = "ROA")
msummary(reg_dw_decomp, stars = c("*"=.10, "**"=.05, "***"=.01), gof_omit = "AIC|BIC|Log|RMSE",
coef_rename = decomp_map_dw,
title = "DW Run Exp: Decomposition ℓ × f^U → ℓ × μ × (1−β^U)",
notes = "Col 1: baseline. Col 2: separate interactions. Col 3: triple interaction capturing fundamental vulnerability.")
DW Run Exp: Decomposition ℓ × f^U → ℓ × μ × (1−β^U)
| |
ℓ × f^U |
ℓ×μ + ℓ×(1−β^U) |
ℓ × μ × (1−β^U) |
| * p < 0.1, ** p < 0.05, *** p < 0.01 |
| Col 1: baseline. Col 2: separate interactions. Col 3: triple interaction capturing fundamental vulnerability. |
| (Intercept) |
85.496*** |
92.092*** |
83.589*** |
|
(28.879) |
(34.998) |
(26.770) |
| ℓ |
72.323 |
70.231 |
73.127 |
|
(68.358) |
(66.629) |
(70.124) |
| f^U |
-58.780 |
|
|
|
(40.766) |
|
|
| ℓ × f^U |
-23.172 |
|
|
|
(28.311) |
|
|
| Log(Assets) |
16.100 |
34.591* |
33.343* |
|
(11.383) |
(20.646) |
(19.683) |
| Cash/TA |
18.945* |
23.457** |
28.127* |
|
(9.914) |
(10.967) |
(14.500) |
| Loan/Dep |
6.861 |
-2.338 |
0.738 |
|
(26.084) |
(20.734) |
(22.999) |
| Equity/TA |
58.078 |
48.985 |
54.712 |
|
(56.758) |
(49.103) |
(55.421) |
| Wholesale |
2.202 |
4.512 |
0.305 |
|
(12.232) |
(10.686) |
(13.883) |
| ROA |
88.932 |
96.771 |
92.713 |
|
(85.222) |
(90.629) |
(86.437) |
| μ (Uninsured Leverage) |
|
-88.506 |
-99.298 |
|
|
(61.640) |
(73.215) |
| 1−β^U (Deposit Sensitivity) |
|
-48.021 |
-22.586 |
|
|
(42.928) |
(18.516) |
| ℓ × μ |
|
-33.312 |
|
|
|
(38.979) |
|
| ℓ × (1−β^U) |
|
-43.499 |
|
|
|
(46.167) |
|
| ℓ × μ × (1−β^U) |
|
|
24.461 |
|
|
|
(28.972) |
| Num.Obs. |
430 |
430 |
430 |
| R2 |
0.042 |
0.059 |
0.055 |
| R2 Adj. |
0.022 |
0.034 |
0.032 |
| Std.Errors |
Heteroskedasticity-robust |
Heteroskedasticity-robust |
Heteroskedasticity-robust |
save_reg_latex(reg_dw_decomp, "Table_RunExp_DW_Decomp",
coef_rename = c("mtm_total_b"="$\\ell$", "f_u_b"="$f^U$",
"unins_lev_b"="$\\mu$", "one_minus_beta_b"="$1-\\beta^U$",
"mtm_x_fu_b"="$\\ell \\times f^U$",
"mtm_x_mu_b"="$\\ell \\times \\mu$",
"mtm_x_1mbeta_b"="$\\ell \\times (1-\\beta^U)$",
"mtm_x_mu_x_1mbeta_b"="$\\ell \\times \\mu \\times (1-\\beta^U)$"),
title = "DW Run Expectation: Uninsured Deposit Decomposition")
## Saved: Table_RunExp_DW_Decomp.tex
