Bank Crisis Borrowing Decisions: Multinomial Choice Analysis
BTFP, Discount Window, and FHLB During the 2023 Banking Crisis
Mohua Ferdousi
2025-12-16
1 Summary
This analysis examines bank borrowing choices during the 2023 banking crisis using three complementary approaches:
Model Framework:
- Linear Probability Model (LPM): BTFP vs DW among borrowers
- Logit Model: BTFP vs DW among borrowers
- Multinomial Logit: Choice among {No participation, BTFP only, DW only, Both BTFP+DW}
- Trivariate Probit: Joint modeling of BTFP, DW, and FHLB decisions with error correlations
Key Variables:
- MTM Losses: Separated into BTFP-eligible (omo_eligible) vs. other assets
- Uninsured Deposits: Run risk exposure
- FHLB Borrowing: Crisis-period increases (2+ std above historical mean)
- Run Risk Measures: Continuous and binary indicators
- Insolvency Measures: Three alternative specifications
Sample:
- Excludes: G-SIB banks, failed banks
- Period: March 13 - April 30, 2023 (acute crisis phase)
- Baseline: 2022Q4 characteristics
2 Setup and Configuration
################################################################################
# SECTION 0: SETUP AND PACKAGES
################################################################################
# Update rlang first if needed
if (packageVersion("rlang") < "1.1.4") {
cat("Updating rlang to resolve dependencies...\n")
install.packages("rlang", repos = "https://cloud.r-project.org")
}#> Updating rlang to resolve dependencies...
#>
#> There is a binary version available but the source version is later:
#> binary source needs_compilation
#> rlang 1.1.5 1.1.6 TRUE# Required packages
required_packages <- c(
# Data manipulation
"data.table", "dplyr", "tidyr", "tibble", "lubridate", "stringr", "readr",
# Modeling
"fixest", # Fast fixed effects
"nnet", # Multinomial logit
"mlogit", # Advanced multinomial models
"mvtnorm", # Multivariate normal
"sandwich", # Robust standard errors
"lmtest", # Model testing
"broom", # Tidy model output
"margins", # Marginal effects
# Visualization
"ggplot2", "ggthemes", "scales", "patchwork", "gridExtra",
# Tables
"knitr", "kableExtra", "stargazer", "modelsummary",
# Statistics
"DescTools", "moments", "psych"
)
# Install missing packages
missing_packages <- required_packages[!required_packages %in% installed.packages()[,"Package"]]
if (length(missing_packages) > 0) {
cat("Installing:", paste(missing_packages, collapse = ", "), "\n")
install.packages(missing_packages, repos = "https://cloud.r-project.org",
dependencies = TRUE)
}
# Load packages
suppressPackageStartupMessages({
library(data.table)
library(dplyr)
library(tidyr)
library(tibble)
library(lubridate)
library(stringr)
library(readr)
library(fixest)
library(nnet)
library(mlogit)
library(mvtnorm)
library(sandwich)
library(lmtest)
library(broom)
library(ggplot2)
library(ggthemes)
library(scales)
library(patchwork)
library(gridExtra)
library(knitr)
library(kableExtra)
library(stargazer)
library(modelsummary)
library(DescTools)
library(moments)
library(psych)
})
options(scipen = 999)
set.seed(20230313) # SVB failure date
cat("✓ All packages loaded successfully\n")#> ✓ All packages loaded successfully################################################################################
# CONFIGURE PATHS
################################################################################
BASE_PATH <- "C:/Users/mferdo2/OneDrive - Louisiana State University/Finance_PhD/DW_Stigma_paper/Liquidity_project_2025"
# Only set working directory if path exists (for portability)
if (dir.exists(BASE_PATH)) {
setwd(BASE_PATH)
}
DATA_RAW <- file.path(BASE_PATH, "01_data/raw")
DATA_PROC <- file.path(BASE_PATH, "01_data/processed")
DOC_PATH <- file.path(BASE_PATH, "03_documentation")
TABLE_PATH <- file.path(DOC_PATH, "regression_tables/multinomial_analysis")
FIG_PATH <- file.path(DOC_PATH, "figures/multinomial_analysis")
# Create output directories
dir.create(TABLE_PATH, recursive = TRUE, showWarnings = FALSE)
dir.create(FIG_PATH, recursive = TRUE, showWarnings = FALSE)
cat("Working directory:", getwd(), "\n")#> Working directory: C:/Users/mferdo2/OneDrive - Louisiana State University/Finance_PhD/DW_Stigma_paper/Liquidity_project_2025#> Data paths configured successfully################################################################################
# CRISIS PARAMETERS
################################################################################
CRISIS_START <- as.Date("2023-03-13") # Monday after SVB weekend
CRISIS_END_ACUTE <- as.Date("2023-04-30") # End of acute phase
CRISIS_END_BTFP <- as.Date("2024-03-11") # BTFP program closure
MTM_START <- as.Date("2022-03-16") # First FFR hike
MTM_END <- as.Date("2023-03-10") # SVB failure
BASELINE_DATE <- "2022Q4" # 2022Q4
cat("\n")#> ================================================================#> MULTINOMIAL CHOICE ANALYSIS - 2023 BANKING CRISIS#> ================================================================#> Crisis Window: 2023-03-13 to 2023-04-30#> Baseline Date: 2022Q4#> ================================================================################################################################################
# HELPER FUNCTIONS
################################################################################
#' Winsorize at specified quantiles
winsorize <- function(x, probs = c(0.01, 0.99)) {
if (all(is.na(x))) return(x)
q <- quantile(x, probs = probs, na.rm = TRUE, names = FALSE)
pmax(pmin(x, q[2]), q[1])
}
#' Winsorize at 95th percentile
winsorize_95 <- function(x) {
winsorize(x, probs = c(0.025, 0.975))
}
#' Standardize (z-score transformation)
standardize <- function(x) {
(x - mean(x, na.rm = TRUE)) / sd(x, na.rm = TRUE)
}
#' Safe division
safe_div <- function(num, denom) {
ifelse(is.na(denom) | denom == 0, NA_real_, num / denom)
}
#' Parse dates flexibly
parse_date_safe <- function(x) {
if (inherits(x, "Date")) return(x)
x_char <- as.character(x)
result <- suppressWarnings(mdy(x_char))
if (all(is.na(result))) result <- suppressWarnings(ymd(x_char))
if (all(is.na(result))) result <- suppressWarnings(dmy(x_char))
return(result)
}
#' Create summary statistics table
create_summary_table <- function(df, vars, digits = 3) {
df %>%
select(all_of(vars)) %>%
pivot_longer(everything(), names_to = "Variable", values_to = "Value") %>%
group_by(Variable) %>%
summarise(
N = sum(!is.na(Value)),
Mean = round(mean(Value, na.rm = TRUE), digits),
SD = round(sd(Value, na.rm = TRUE), digits),
Min = round(min(Value, na.rm = TRUE), digits),
P25 = round(quantile(Value, 0.25, na.rm = TRUE), digits),
Median = round(quantile(Value, 0.50, na.rm = TRUE), digits),
P75 = round(quantile(Value, 0.75, na.rm = TRUE), digits),
Max = round(max(Value, na.rm = TRUE), digits),
.groups = "drop"
)
}
cat("✓ Helper functions loaded\n")#> ✓ Helper functions loaded3 Data Loading
################################################################################
# SECTION 1: LOAD DATA
################################################################################
cat("\n")#> ================================================================================#> LOADING DATA#> ================================================================================# 1.1 Load Call Report Data
call_q <- read_csv(
file.path(DATA_PROC, "final_call_gsib.csv"),
show_col_types = FALSE
) %>%
mutate(idrssd = as.character(idrssd))
cat("✓ Call reports loaded:", nrow(call_q), "obs,", n_distinct(call_q$idrssd), "banks\n")#> ✓ Call reports loaded: 61002 obs, 4926 banks# 1.2 Load BTFP Loan Data
btfp_raw <- read_csv(
file.path(DATA_PROC, "btfp_loan_bank_only.csv"),
show_col_types = FALSE
) %>%
mutate(
rssd_id = as.character(rssd_id),
btfp_loan_date = parse_date_safe(btfp_loan_date)
)
cat("✓ BTFP loans loaded:", nrow(btfp_raw), "obs\n")#> ✓ BTFP loans loaded: 6734 obscat(" Date range:", as.character(min(btfp_raw$btfp_loan_date, na.rm = TRUE)),
"to", as.character(max(btfp_raw$btfp_loan_date, na.rm = TRUE)), "\n")#> Date range: 2023-03-13 to 2024-03-11# 1.3 Load DW Loan Data
dw_raw <- read_csv(
file.path(DATA_PROC, "dw_loan_bank_2023.csv"),
show_col_types = FALSE
) %>%
mutate(
rssd_id = as.character(rssd_id),
dw_loan_date = parse_date_safe(dw_loan_date)
)
cat("✓ DW loans loaded:", nrow(dw_raw), "obs\n")#> ✓ DW loans loaded: 7724 obscat(" Date range:", as.character(min(dw_raw$dw_loan_date, na.rm = TRUE)),
"to", as.character(max(dw_raw$dw_loan_date, na.rm = TRUE)), "\n")#> Date range: 2023-01-03 to 2023-09-29# 1.4 Load Public Bank Data (CRSP)
file_public_bank <- file.path(DATA_PROC, "df_public_bank.csv")
if (file.exists(file_public_bank)) {
df_public <- read_csv(file_public_bank, show_col_types = FALSE) %>%
mutate(
rssd_bank = as.character(rssd_bank),
DlyCalDt = as.Date(DlyCalDt)
)
cat("✓ Public bank data loaded:", nrow(df_public), "observations\n")
} else {
cat(" WARNING: Public bank file not found\n")
df_public <- NULL
}#> ✓ Public bank data loaded: 135943 observations#>
#> ✓ All data loaded successfully4 Baseline Sample Creation
################################################################################
# SECTION 2: AGGREGATE FACILITY USAGE
################################################################################
cat("\n")#> ================================================================================#> AGGREGATING FACILITY USAGE#> ================================================================================# 2.1 BTFP usage during acute crisis
btfp_crisis <- btfp_raw %>%
filter(btfp_loan_date >= CRISIS_START, btfp_loan_date <= CRISIS_END_ACUTE) %>%
group_by(rssd_id) %>%
summarise(
btfp_user = 1L,
btfp_total_amt = sum(btfp_loan_amount, na.rm = TRUE),
btfp_n_loans = n(),
btfp_first_date = min(btfp_loan_date),
.groups = "drop"
) %>%
rename(idrssd = rssd_id)
cat("✓ BTFP users (acute crisis):", nrow(btfp_crisis), "\n")#> ✓ BTFP users (acute crisis): 481# 2.2 DW usage during acute crisis
dw_crisis <- dw_raw %>%
filter(dw_loan_date >= CRISIS_START, dw_loan_date <= CRISIS_END_ACUTE) %>%
group_by(rssd_id) %>%
summarise(
dw_user = 1L,
dw_total_amt = sum(dw_loan_amount, na.rm = TRUE),
dw_n_loans = n(),
dw_first_date = min(dw_loan_date),
.groups = "drop"
) %>%
rename(idrssd = rssd_id)
cat("✓ DW users (acute crisis):", nrow(dw_crisis), "\n")#> ✓ DW users (acute crisis): 415# 2.3 Extended BTFP usage (full program)
btfp_full <- btfp_raw %>%
filter(btfp_loan_date >= CRISIS_START, btfp_loan_date <= CRISIS_END_BTFP) %>%
group_by(rssd_id) %>%
summarise(
btfp_user_full = 1L,
btfp_total_amt_full = sum(btfp_loan_amount, na.rm = TRUE),
.groups = "drop"
) %>%
rename(idrssd = rssd_id)
cat("✓ BTFP users (full program):", nrow(btfp_full), "\n")#> ✓ BTFP users (full program): 1327#>
#> ✓ Facility usage aggregated################################################################################
# SECTION 3: CREATE 2022Q4 BASELINE WITH KEY VARIABLES
################################################################################
cat("\n")#> ================================================================================#> CREATING 2022Q4 BASELINE#> ================================================================================# Check available columns
has_failed_bank <- "failed_bank" %in% names(call_q)
has_gsib <- "gsib" %in% names(call_q)
has_size_bin <- "size_bin" %in% names(call_q)
has_mv_asset <- "mm_asset" %in% names(call_q)
cat("Data availability checks:\n")#> Data availability checks:#> - failed_bank column: YES#> - gsib column: YES#> - size_bin column: YES#> - mv_asset column: YES# Create baseline dataset from 2022Q4 (preserving all Python-created variables)
baseline <- call_q %>%
filter(quarter == BASELINE_DATE) %>%
transmute(
idrssd = as.character(idrssd),
# Bank identifiers and flags
failed_bank = if (has_failed_bank) failed_bank else 0L,
gsib = if (has_gsib) gsib else 0L,
# Balance sheet fundamentals
size_bin = if (has_size_bin) size_bin else NA_character_,
total_asset,
total_liability,
total_equity,
total_deposit,
insured_deposit = pmax(insured_deposit, 1),
uninsured_deposit = pmax(uninsured_deposit, 0),
security_to_total_asset,
loan_to_deposit,
roa,
# Cash and liquid assets
cash,
fed_fund_sold,
rerepo,
# Securities (from Python cleaning)
security, # total_sec in some versions
omo_eligible, # Treasury + Agency debt + Agency MBS (BTFP-eligible)
non_omo_securities, # Other securities
# Loans
total_loan,
# Size measures
log_assets = log(pmax(total_asset, 1)),
# MTM variables (from Python MTM calculation)
mm_asset = if (has_mv_asset) mm_asset else total_asset,
mtm_total_loss,
mtm_loss_to_total_asset,
equity_after_mtm,
# MTM losses: OMO-eligible vs Other
mtm_loss_omo_eligible,
mtm_loss_omo_eligible_to_omo_eligible = safe_div(mtm_loss_omo_eligible, omo_eligible),
mtm_loss_omo_eligible_to_total_asset,
omo_eligible_to_total_asset,
# Calculate MTM loss on OTHER assets (non-OMO-eligible)
mtm_loss_other = mtm_loss_non_omo_eligible,
mtm_loss_other_to_total_asset = mtm_loss_non_omo_eligible_to_total_asset,
# Wholesale funding & FHLB
repo,
fed_fund_purchase,
other_borr,
other_borrowed_less_than_1yr,
fhlb_adv,
fhlb_less_than_1yr,
fhlb_to_total_asset,
# Control variables
cash_to_total_asset,
book_equity_to_total_asset,
# Additional controls
net_income_q,
avg_assets
)
cat("✓ Initial baseline:", nrow(baseline), "banks\n")#> ✓ Initial baseline: 4737 banks# Apply sample filters
baseline <- baseline %>%
filter(
# Exclude G-SIBs
gsib == 0 | is.na(gsib),
# Exclude failed banks
failed_bank == 0 | is.na(failed_bank),
# Keep only banks with OMO-eligible assets (BTFP collateral)
!is.na(omo_eligible) & omo_eligible > 0
)
cat("✓ After filters:", nrow(baseline), "banks\n")#> ✓ After filters: 4292 banks#> - Excluded G-SIBs#> - Excluded failed banks#> - Kept only banks with BTFP-eligible assets (omo_eligible > 0)#>
#> ✓ Baseline sample created################################################################################
# SECTION 4: CONSTRUCT KEY RISK VARIABLES
################################################################################
cat("\n")#> ================================================================================#> CONSTRUCTING KEY RISK VARIABLES#> ================================================================================baseline <- baseline %>%
mutate(
# =========================================================================
# VARIABLE CREATION AS SPECIFIED
# =========================================================================
# Borrowing subsidy (%) - valuation benefit from par pricing
borrowing_subsidy = mtm_loss_omo_eligible_to_omo_eligible,
# % MTM Loss on BTFP-eligible securities (omo_eligible)
mtm_btfp_pct = mtm_loss_omo_eligible_to_total_asset,
# % MTM Loss on Other (non-eligible) securities
mtm_other_pct = mtm_loss_other_to_total_asset,
# % Uninsured deposits
pct_uninsured = safe_div(uninsured_deposit, total_deposit) * 100,
# Uninsured deposit leverage (% of assets)
uninsured_lev = safe_div(uninsured_deposit, total_asset) * 100,
# % Wholesale Liability
pct_wholesale_liability = safe_div(fed_fund_purchase + repo + other_borrowed_less_than_1yr, total_liability) * 100,
# % Run-able Liability
pct_runable_liability = safe_div(uninsured_deposit + fed_fund_purchase + repo + other_borrowed_less_than_1yr, total_liability) * 100,
# % Liquidity Available
pct_liquidity_available = safe_div(cash + rerepo + fed_fund_sold, total_asset) * 100,
# % MTM Loss (total)
pct_mtm_loss = mtm_loss_to_total_asset,
# Cash to asset ratio (%)
cash_to_asset = cash_to_total_asset,
# FHLB to asset ratio (%)
fhlb_to_asset = fhlb_to_total_asset,
# Book equity to asset ratio (%)
book_equity_to_asset = book_equity_to_total_asset,
# Securities ratio
securities_ratio = security_to_total_asset,
# Loan to deposit
loan_to_deposit = loan_to_deposit,
# ROA (annualized)
roa = roa,
# =========================================================================
# RUN RISK MEASURES
# =========================================================================
# Run-risk 1: % Uninsured × % MTM loss
run_risk_1 = pct_uninsured * pct_mtm_loss,
# Run-risk 2: % Run-able Liability × % MTM loss
run_risk_2 = pct_runable_liability * pct_mtm_loss,
# Calculate medians for run risk dummies
median_pct_uninsured = median(pct_uninsured, na.rm = TRUE),
median_pct_mtm_loss = median(pct_mtm_loss, na.rm = TRUE),
median_pct_runable = median(pct_runable_liability, na.rm = TRUE),
# Run Risk 1 DUMMY: = 1 if BOTH %Uninsured > median AND %MTM loss > median
run_risk_1_dummy = as.integer(
pct_uninsured > median_pct_uninsured & pct_mtm_loss > median_pct_mtm_loss
),
# Run Risk 2 DUMMY: = 1 if BOTH %Runable > median AND %MTM loss > median
run_risk_2_dummy = as.integer(
pct_runable_liability > median_pct_runable &
pct_mtm_loss > median_pct_mtm_loss
),
# =========================================================================
# INSOLVENCY MEASURES
# =========================================================================
# Market value of assets
mv_asset = mm_asset,
mv_adjustment = if_else(mv_asset == 0, NA_real_, (total_asset / mv_asset) - 1), # Formula: (total_asset / mv_asset - 1)
# Insolvency: Insolvent Banks under Different Uninsured Deposits Runs Cases (Insured Deposit Coverage Ratio)
# Insured Deposit Coverage Ratio (s = 0.5)
idcr_1 = safe_div(
mv_asset - 0.5 * uninsured_deposit - insured_deposit,
insured_deposit
),
# Insured Deposit Coverage Ratio (s = 1.0)
idcr_2 = safe_div(
mv_asset - 1.0 * uninsured_deposit - insured_deposit,
insured_deposit
),
# Insolvency: Insolvent Banks under Different Uninsured Deposits Runs Cases (Capital Ratio Metric)
insolvency_1 = safe_div(
total_asset-total_liability - 0.5 *uninsured_deposit * mv_adjustment,
total_asset
),
insolvency_2 = safe_div(
total_asset-total_liability - 1.0 *uninsured_deposit * mv_adjustment,
total_asset
)
)
cat("✓ Risk variables constructed:\n")#> ✓ Risk variables constructed:#> - Borrowing subsidy#> - MTM losses (BTFP-eligible vs Other)#> - Uninsured deposit measures#> - Run risk measures (continuous + dummies)#> - Insolvency measures (3 specifications)#>
#> Key statistics:cat(" Mean MTM BTFP-eligible (%):", sprintf("%.2f", mean(baseline$mtm_btfp_pct, na.rm = TRUE)), "\n")#> Mean MTM BTFP-eligible (%): 0.68#> Mean MTM other (%): 4.60cat(" Mean uninsured leverage (%):", sprintf("%.2f", mean(baseline$uninsured_lev, na.rm = TRUE)), "\n")#> Mean uninsured leverage (%): 23.61cat(" % with high run risk 1:", sprintf("%.1f%%", 100 * mean(baseline$run_risk_1_dummy, na.rm = TRUE)), "\n")#> % with high run risk 1: 23.0%#>
#> ✓ Risk variables created################################################################################
# SECTION 5: CREATE FHLB CRISIS BORROWING INDICATOR
################################################################################
cat("\n")#> ================================================================================#> CREATING FHLB CRISIS BORROWING INDICATOR#> ================================================================================# Need historical FHLB borrowing (past 4 quarters before 2022Q4)
historical_quarters <- c("2021Q4", "2022Q1", "2022Q2", "2022Q3")
# Calculate FHLB statistics for each bank
df_fhlb_history <- call_q %>%
filter(quarter %in% historical_quarters) %>%
group_by(idrssd) %>%
summarise(
fhlb_mean_hist = mean(fhlb_to_total_asset, na.rm = TRUE),
fhlb_sd_hist = sd(fhlb_to_total_asset, na.rm = TRUE),
.groups = "drop"
)
# Get crisis period FHLB borrowing (2023Q1)
df_fhlb_crisis <- call_q %>%
filter(quarter == "2023Q1") %>%
select(idrssd, fhlb_to_asset_crisis = fhlb_to_total_asset)
# Merge and create indicator
baseline <- baseline %>%
left_join(df_fhlb_history, by = "idrssd") %>%
left_join(df_fhlb_crisis, by = "idrssd") %>%
mutate(
# FHLB crisis indicator: 2+ std above historical mean
fhlb_crisis = ifelse(
!is.na(fhlb_to_asset_crisis) & !is.na(fhlb_mean_hist) & !is.na(fhlb_sd_hist),
as.numeric(fhlb_to_asset_crisis > (fhlb_mean_hist + 2 * fhlb_sd_hist)),
0
),
# Alternative: change in FHLB (for continuous measure)
delta_fhlb = ifelse(
!is.na(fhlb_to_asset_crisis) & !is.na(fhlb_mean_hist),
pmax(0, fhlb_to_asset_crisis - fhlb_mean_hist),
0
)
)
cat("FHLB crisis borrowing:\n")#> FHLB crisis borrowing:cat(" Banks with crisis FHLB increase:",
sum(baseline$fhlb_crisis == 1, na.rm = TRUE),
sprintf("(%.1f%%)", 100 * mean(baseline$fhlb_crisis == 1, na.rm = TRUE)), "\n")#> Banks with crisis FHLB increase: 1125 (26.2%)cat(" Mean FHLB ratio (2022Q4 baseline):",
sprintf("%.2f%%", mean(baseline$fhlb_to_asset, na.rm = TRUE)), "\n")#> Mean FHLB ratio (2022Q4 baseline): 2.65%cat(" Mean FHLB ratio (2023Q1 crisis):",
sprintf("%.2f%%", mean(baseline$fhlb_to_asset_crisis, na.rm = TRUE)), "\n")#> Mean FHLB ratio (2023Q1 crisis): 2.79%#>
#> ✓ FHLB crisis indicator created################################################################################
# SECTION 6: MERGE BORROWING DATA AND CREATE OUTCOMES
################################################################################
cat("\n")#> ================================================================================#> MERGING BORROWING DATA#> ================================================================================# Merge BTFP and DW usage
baseline <- baseline %>%
left_join(btfp_crisis, by = "idrssd") %>%
left_join(dw_crisis, by = "idrssd") %>%
left_join(btfp_full, by = "idrssd") %>%
mutate(
# Fill missing with 0
btfp_user = replace_na(btfp_user, 0),
dw_user = replace_na(dw_user, 0),
btfp_total_amt = replace_na(btfp_total_amt, 0),
dw_total_amt = replace_na(dw_total_amt, 0),
# Create multinomial outcome
# Y = 0: No participation
# Y = 1: BTFP only
# Y = 2: DW only
# Y = 3: Both BTFP and DW
Y = case_when(
btfp_user == 0 & dw_user == 0 ~ 0,
btfp_user == 1 & dw_user == 0 ~ 1,
btfp_user == 0 & dw_user == 1 ~ 2,
btfp_user == 1 & dw_user == 1 ~ 3,
TRUE ~ 0
),
# Factor version for modeling
Y_factor = factor(Y,
levels = 0:3,
labels = c("No_Participation", "BTFP_Only", "DW_Only", "Both")),
# Borrower indicator (used any Fed facility)
any_borrower = as.integer(btfp_user == 1 | dw_user == 1),
# BTFP vs DW choice (among borrowers only)
# 1 = BTFP (includes "Both"), 0 = DW only
btfp_vs_dw = ifelse(any_borrower == 1,
as.integer(btfp_user == 1),
NA_integer_),
# Borrowing amounts as % of assets
btfp_amt_pct = safe_div(btfp_total_amt, total_asset) * 100,
dw_amt_pct = safe_div(dw_total_amt, total_asset) * 100
)
# Summary of outcomes
cat("\nBorrowing patterns (acute crisis):\n")#>
#> Borrowing patterns (acute crisis):cat(" No participation: ", sum(baseline$Y == 0),
sprintf("(%.1f%%)", 100 * mean(baseline$Y == 0)), "\n")#> No participation: 3544 (82.6%)#> BTFP only: 363 (8.5%)#> DW only: 295 (6.9%)cat(" Both BTFP and DW: ", sum(baseline$Y == 3),
sprintf("(%.1f%%)", 100 * mean(baseline$Y == 3)), "\n")#> Both BTFP and DW: 90 (2.1%)#>
#> Borrower subsample:#> Total borrowers: 748cat(" Chose BTFP:", sum(baseline$btfp_vs_dw == 1, na.rm = TRUE),
sprintf("(%.1f%%)", 100 * mean(baseline$btfp_vs_dw == 1, na.rm = TRUE)), "\n")#> Chose BTFP: 453 (60.6%)cat(" Chose DW only:", sum(baseline$btfp_vs_dw == 0, na.rm = TRUE),
sprintf("(%.1f%%)", 100 * mean(baseline$btfp_vs_dw == 0, na.rm = TRUE)), "\n")#> Chose DW only: 295 (39.4%)#>
#> ✓ Borrowing outcomes created################################################################################
# SECTION 7: MERGE PUBLIC BANK DATA
################################################################################
cat("\n")#> ================================================================================#> MERGING PUBLIC BANK DATA#> ================================================================================if (!is.null(df_public)) {
# Aggregate public bank returns during crisis
df_public_crisis <- df_public %>%
filter(DlyCalDt >= CRISIS_START & DlyCalDt <= CRISIS_END_ACUTE) %>%
group_by(rssd_bank) %>%
summarise(
n_days = n(),
mean_ret = mean(ret, na.rm = TRUE),
cum_ret = sum(ret, na.rm = TRUE),
sd_ret = sd(ret, na.rm = TRUE),
min_ret = min(ret, na.rm = TRUE),
max_ret = max(ret, na.rm = TRUE),
is_public = 1,
.groups = "drop"
) %>%
rename(idrssd = rssd_bank)
# Merge with baseline
baseline <- baseline %>%
left_join(df_public_crisis, by = "idrssd") %>%
mutate(
is_public = replace_na(is_public, 0)
)
cat("Public bank data merged:\n")
cat(" Public banks:", sum(baseline$is_public == 1, na.rm = TRUE),
sprintf("(%.1f%%)", 100 * mean(baseline$is_public == 1, na.rm = TRUE)), "\n")
cat(" Mean cumulative return:",
sprintf("%.2f%%", 100 * mean(baseline$cum_ret, na.rm = TRUE)), "\n")
} else {
baseline$is_public <- 0
cat(" No public bank data available\n")
}#> Public bank data merged:
#> Public banks: 270 (6.3%)
#> Mean cumulative return: -13.77%#>
#> ✓ Public bank data merged################################################################################
# SECTION 8: WINSORIZE AND STANDARDIZE
################################################################################
cat("\n")#> ================================================================================#> WINSORIZING AND STANDARDIZING VARIABLES#> ================================================================================# Variables to winsorize and standardize
vars_to_process <- c(
# MTM variables
"mtm_btfp_pct", "mtm_other_pct", "borrowing_subsidy",
# Risk variables
"pct_uninsured", "uninsured_lev", "pct_wholesale_liability",
"pct_runable_liability", "pct_liquidity_available", "pct_mtm_loss",
"run_risk_1", "run_risk_2", "run_risk_1_dummy", "run_risk_2_dummy",
# Insolvency
"idcr_1", "idcr_2", "insolvency_1", "insolvency_2",
# Controls
"log_assets", "cash_to_asset", "fhlb_to_asset", "book_equity_to_asset",
"securities_ratio", "loan_to_deposit", "roa", "delta_fhlb",
# Borrowing amounts
"btfp_amt_pct", "dw_amt_pct"
)
# Winsorize at 1st and 99th percentiles
baseline <- baseline %>%
mutate(across(
all_of(vars_to_process),
~winsorize(., probs = c(0.01, 0.99)),
.names = "{.col}_w"
))
# Standardize (z-scores)
baseline <- baseline %>%
mutate(across(
ends_with("_w"),
~standardize(.),
.names = "{.col}_z"
))
# Create interaction terms
baseline <- baseline %>%
mutate(
# MTM BTFP × Uninsured
mtm_btfp_x_unins_w = mtm_btfp_pct_w * uninsured_lev_w,
mtm_btfp_x_unins_w_z = standardize(mtm_btfp_x_unins_w)
)
cat("Winsorization and standardization complete:\n")#> Winsorization and standardization complete:#> Variables processed: 27#> Final sample size: 4292#>
#> ✓ Variables processed5 Descriptive Statistics
################################################################################
# SECTION 9: SUMMARY STATISTICS - OVERALL
################################################################################
cat("\n")#> ================================================================================#> SUMMARY STATISTICS#> ================================================================================# Variables for summary table
summ_vars <- c(
"mtm_btfp_pct", "mtm_other_pct", "borrowing_subsidy",
"pct_uninsured", "uninsured_lev", "pct_wholesale_liability",
"pct_liquidity_available", "pct_mtm_loss",
"run_risk_1", "run_risk_2",
"idcr_1", "idcr_2", "insolvency_1", "insolvency_2",
"log_assets", "cash_to_asset", "fhlb_to_asset",
"book_equity_to_asset", "securities_ratio", "loan_to_deposit", "roa"
)
# Overall summary
summ_overall <- create_summary_table(baseline, summ_vars, digits = 3)
# Print table
summ_overall %>%
kbl(caption = "Table 1: Summary Statistics - Full Sample",
booktabs = TRUE,
align = c("l", rep("r", 8))) %>%
kable_styling(bootstrap_options = c("striped", "hover", "condensed"),
full_width = FALSE,
font_size = 11) %>%
row_spec(0, bold = TRUE, background = "#F0F0F0") %>%
pack_rows("MTM Losses", 1, 3) %>%
pack_rows("Risk Measures", 4, 10) %>%
pack_rows("Insolvency Measures", 11, 12) %>%
pack_rows("Control Variables", 13, 19)| Variable | N | Mean | SD | Min | P25 | Median | P75 | Max |
|---|---|---|---|---|---|---|---|---|
| MTM Losses | ||||||||
| book_equity_to_asset | 4292 | 10.220 | 8.817 | 0.110 | 7.143 | 8.842 | 10.888 | 99.966 |
| borrowing_subsidy | 4282 | 0.103 | 1.909 | -0.034 | 0.032 | 0.065 | 0.098 | 124.830 |
| cash_to_asset | 4292 | 8.148 | 9.191 | 0.000 | 2.667 | 5.030 | 10.051 | 96.724 |
| Risk Measures | ||||||||
| fhlb_to_asset | 4292 | 2.647 | 4.215 | 0.000 | 0.000 | 0.346 | 4.073 | 48.713 |
| idcr_1 | 4282 | 1291.921 | 69365.863 | -1.018 | 0.149 | 0.248 | 0.392 | 4531503.818 |
| idcr_2 | 4282 | 1291.537 | 69365.870 | -1.825 | -0.012 | 0.069 | 0.162 | 4531503.818 |
| insolvency_1 | 4282 | 0.087 | 0.095 | -1.583 | 0.055 | 0.076 | 0.099 | 1.000 |
| insolvency_2 | 4282 | 0.072 | 0.116 | -3.296 | 0.039 | 0.065 | 0.094 | 1.000 |
| loan_to_deposit | 4292 | 70.866 | 27.432 | 0.000 | 56.561 | 71.818 | 86.500 | 890.476 |
| log_assets | 4292 | 12.882 | 1.483 | 8.222 | 11.903 | 12.721 | 13.650 | 20.187 |
| Insolvency Measures | ||||||||
| mtm_btfp_pct | 4282 | 0.681 | 0.848 | -0.141 | 0.136 | 0.405 | 0.932 | 16.393 |
| mtm_other_pct | 4282 | 4.599 | 2.062 | -0.097 | 3.110 | 4.395 | 5.972 | 13.350 |
| Control Variables | ||||||||
| pct_liquidity_available | 4292 | 9.297 | 9.941 | 0.000 | 3.045 | 5.870 | 11.555 | 98.879 |
| pct_mtm_loss | 4282 | 5.467 | 2.223 | -0.141 | 3.863 | 5.320 | 6.975 | 27.631 |
| pct_uninsured | 4261 | 27.796 | 14.113 | 0.000 | 18.109 | 25.957 | 35.165 | 99.876 |
| pct_wholesale_liability | 4292 | 1.000 | 3.166 | 0.000 | 0.000 | 0.000 | 0.533 | 85.016 |
| roa | 4290 | 1.187 | 2.592 | -62.459 | 0.702 | 1.101 | 1.498 | 53.461 |
| run_risk_1 | 4251 | 147.195 | 89.294 | -2.932 | 83.550 | 133.157 | 194.236 | 1295.061 |
| run_risk_2 | 4282 | 143.513 | 86.366 | -2.490 | 81.210 | 130.370 | 190.665 | 1189.577 |
| securities_ratio | 4292 | 25.681 | 15.784 | 0.004 | 13.704 | 23.323 | 35.090 | 97.611 |
| uninsured_lev | 4292 | 23.611 | 12.158 | 0.000 | 15.285 | 22.247 | 30.353 | 94.597 |
#>
#> ✓ Overall summary statistics created################################################################################
# SUMMARY STATISTICS BY OUTCOME
################################################################################
cat("\n")#> ================================================================================#> SUMMARY STATISTICS BY BORROWING CHOICE#> ================================================================================# By borrowing status
summ_by_outcome <- baseline %>%
select(Y_factor, all_of(summ_vars)) %>%
pivot_longer(-Y_factor, names_to = "Variable", values_to = "Value") %>%
group_by(Y_factor, Variable) %>%
summarise(
N = sum(!is.na(Value)),
Mean = mean(Value, na.rm = TRUE),
SD = sd(Value, na.rm = TRUE),
.groups = "drop"
) %>%
pivot_wider(
names_from = Y_factor,
values_from = c(N, Mean, SD),
names_glue = "{Y_factor}_{.value}"
) %>%
select(Variable, ends_with("_N"), ends_with("_Mean"), ends_with("_SD")) %>%
mutate(across(where(is.numeric), ~round(., 3)))
# Print table (showing means only for readability)
summ_by_outcome %>%
select(Variable, ends_with("_Mean")) %>%
rename_with(~gsub("_Mean", "", .), ends_with("_Mean")) %>%
kbl(caption = "Table 2: Summary Statistics by Borrowing Choice (Means)",
booktabs = TRUE) %>%
kable_styling(bootstrap_options = c("striped", "hover"),
full_width = FALSE,
font_size = 10) %>%
row_spec(0, bold = TRUE, background = "#F0F0F0")| Variable | No_Participation | BTFP_Only | DW_Only | Both |
|---|---|---|---|---|
| book_equity_to_asset | 10.582 | 8.166 | 9.017 | 8.227 |
| borrowing_subsidy | 0.106 | 0.091 | 0.087 | 0.084 |
| cash_to_asset | 8.755 | 4.666 | 6.173 | 4.736 |
| fhlb_to_asset | 2.420 | 3.959 | 3.270 | 4.255 |
| idcr_1 | 1565.290 | 0.327 | 0.334 | 0.604 |
| idcr_2 | 1564.883 | 0.073 | 0.066 | 0.183 |
| insolvency_1 | 0.091 | 0.065 | 0.069 | 0.063 |
| insolvency_2 | 0.077 | 0.049 | 0.048 | 0.044 |
| loan_to_deposit | 70.193 | 72.613 | 75.846 | 73.977 |
| log_assets | 12.690 | 13.545 | 13.850 | 14.591 |
| mtm_btfp_pct | 0.650 | 0.883 | 0.747 | 0.865 |
| mtm_other_pct | 4.517 | 5.033 | 4.951 | 4.922 |
| pct_liquidity_available | 10.030 | 5.118 | 6.953 | 4.987 |
| pct_mtm_loss | 5.361 | 6.179 | 5.754 | 5.839 |
| pct_uninsured | 26.888 | 30.623 | 31.903 | 38.361 |
| pct_wholesale_liability | 0.883 | 1.517 | 1.593 | 1.600 |
| roa | 1.196 | 1.083 | 1.212 | 1.182 |
| run_risk_1 | 139.061 | 183.144 | 177.376 | 219.887 |
| run_risk_2 | 135.371 | 179.826 | 175.030 | 213.425 |
| securities_ratio | 25.515 | 28.165 | 23.999 | 27.706 |
| uninsured_lev | 22.825 | 26.202 | 27.126 | 32.597 |
#>
#> ✓ Summary by outcome created################################################################################
# CORRELATION MATRIX
################################################################################
cat("\n")#> ================================================================================#> CORRELATION MATRIX#> ================================================================================# Calculate correlations for key standardized variables
cor_vars <- c(
"mtm_btfp_pct_w_z", "mtm_other_pct_w_z", "uninsured_lev_w_z",
"pct_wholesale_liability_w_z", "pct_liquidity_available_w_z",
"run_risk_1_w_z", "idcr_2_w_z", "insolvency_2_w_z",
"log_assets_w_z", "book_equity_to_asset_w_z", "fhlb_to_asset_w_z"
)
cor_matrix <- baseline %>%
select(all_of(cor_vars)) %>%
cor(use = "pairwise.complete.obs")
# Clean names for display
rownames(cor_matrix) <- colnames(cor_matrix) <- c(
"MTM BTFP", "MTM Other", "Unins Lev", "Wholesale", "Liquidity",
"Run Risk","IDCR", "Insolvency", "Log Assets", "Equity", "FHLB"
)
# Print correlation table
cor_matrix %>%
round(3) %>%
kbl(caption = "Table 3: Correlation Matrix (Standardized Variables)",
booktabs = TRUE) %>%
kable_styling(bootstrap_options = c("striped", "hover"),
full_width = FALSE,
font_size = 10) %>%
row_spec(0, bold = TRUE, background = "#F0F0F0")| MTM BTFP | MTM Other | Unins Lev | Wholesale | Liquidity | Run Risk | IDCR | Insolvency | Log Assets | Equity | FHLB | |
|---|---|---|---|---|---|---|---|---|---|---|---|
| MTM BTFP | 1.000 | -0.031 | 0.013 | 0.084 | -0.117 | 0.176 | -0.037 | -0.062 | 0.070 | -0.157 | -0.077 |
| MTM Other | -0.031 | 1.000 | -0.107 | 0.002 | -0.407 | 0.460 | -0.147 | -0.122 | 0.113 | -0.201 | 0.197 |
| Unins Lev | 0.013 | -0.107 | 1.000 | -0.027 | 0.022 | 0.684 | -0.171 | -0.413 | 0.441 | -0.241 | -0.076 |
| Wholesale | 0.084 | 0.002 | -0.027 | 1.000 | -0.101 | 0.044 | -0.016 | -0.029 | 0.085 | -0.063 | -0.021 |
| Liquidity | -0.117 | -0.407 | 0.022 | -0.101 | 1.000 | -0.266 | 0.167 | 0.213 | -0.333 | 0.253 | -0.299 |
| Run Risk | 0.176 | 0.460 | 0.684 | 0.044 | -0.266 | 1.000 | 0.058 | -0.288 | 0.393 | -0.208 | 0.078 |
| IDCR | -0.037 | -0.147 | -0.171 | -0.016 | 0.167 | 0.058 | 1.000 | 0.645 | -0.142 | 0.742 | -0.061 |
| Insolvency | -0.062 | -0.122 | -0.413 | -0.029 | 0.213 | -0.288 | 0.645 | 1.000 | -0.255 | 0.832 | -0.129 |
| Log Assets | 0.070 | 0.113 | 0.441 | 0.085 | -0.333 | 0.393 | -0.142 | -0.255 | 1.000 | -0.164 | 0.194 |
| Equity | -0.157 | -0.201 | -0.241 | -0.063 | 0.253 | -0.208 | 0.742 | 0.832 | -0.164 | 1.000 | -0.061 |
| FHLB | -0.077 | 0.197 | -0.076 | -0.021 | -0.299 | 0.078 | -0.061 | -0.129 | 0.194 | -0.061 | 1.000 |
#>
#> ✓ Correlation matrix created6 Model 1: Linear Probability Model (BTFP vs DW)
################################################################################
# SECTION 10: LINEAR PROBABILITY MODEL - BTFP VS DW (BORROWERS ONLY)
################################################################################
cat("\n")#> ================================================================================#> MODEL 1: LINEAR PROBABILITY MODEL (BTFP VS DW)#> ================================================================================# Create borrower subsample
df_borrowers <- baseline %>%
filter(any_borrower == 1) %>%
filter(complete.cases(
btfp_vs_dw,
mtm_btfp_pct_w_z, mtm_other_pct_w_z, uninsured_lev_w_z,
log_assets_w_z, pct_wholesale_liability_w_z, pct_liquidity_available_w_z,
securities_ratio_w_z, loan_to_deposit_w_z, book_equity_to_asset_w_z,
roa_w_z, fhlb_to_asset_w_z, delta_fhlb_w_z
))
cat("Borrower subsample:\n")#> Borrower subsample:#> Total borrowers: 748#> BTFP users: 453#> DW only: 295# Specification 1: Main effects only
lpm_1 <- feols(
btfp_vs_dw ~
mtm_btfp_pct_w_z + mtm_other_pct_w_z + uninsured_lev_w_z +
log_assets_w_z + pct_wholesale_liability_w_z + pct_liquidity_available_w_z +
securities_ratio_w_z + loan_to_deposit_w_z + book_equity_to_asset_w_z +
roa_w_z + fhlb_to_asset_w_z + delta_fhlb_w_z,
data = df_borrowers,
vcov = "hetero"
)
# Specification 2: With interaction
lpm_2 <- feols(
btfp_vs_dw ~
mtm_btfp_pct_w_z + mtm_other_pct_w_z + uninsured_lev_w_z +
mtm_btfp_x_unins_w_z +
log_assets_w_z + pct_wholesale_liability_w_z + pct_liquidity_available_w_z +
securities_ratio_w_z + loan_to_deposit_w_z + book_equity_to_asset_w_z +
roa_w_z + fhlb_to_asset_w_z + delta_fhlb_w_z,
data = df_borrowers,
vcov = "hetero"
)
# Specification 3: With run risk dummy
lpm_3 <- feols(
btfp_vs_dw ~
mtm_btfp_pct_w_z + mtm_other_pct_w_z + uninsured_lev_w_z +
run_risk_1_dummy_w_z +
log_assets_w_z + pct_wholesale_liability_w_z + pct_liquidity_available_w_z +
securities_ratio_w_z + loan_to_deposit_w_z + book_equity_to_asset_w_z +
roa_w_z + fhlb_to_asset_w_z + delta_fhlb_w_z,
data = df_borrowers,
vcov = "hetero"
)
# Display results using etable (native to fixest)
etable(
lpm_1, lpm_2, lpm_3,
headers = c("LPM (1)", "LPM (2)", "LPM (3)"),
title = "Table 4: Linear Probability Model - BTFP vs DW (Borrowers Only)",
fitstat = c("n", "r2", "ar2"),
signif.code = c("***"=0.01, "**"=0.05, "*"=0.10),
digits = 3
)#> lpm_1 lpm_2
#> LPM (1) LPM (2)
#> Dependent Var.: btfp_vs_dw btfp_vs_dw
#>
#> Constant 0.563*** (0.025) 0.564*** (0.025)
#> mtm_btfp_pct_w_z -0.002 (0.019) -0.006 (0.042)
#> mtm_other_pct_w_z -0.034 (0.022) -0.034 (0.022)
#> uninsured_lev_w_z 0.035 (0.021) 0.033 (0.027)
#> log_assets_w_z -0.048** (0.023) -0.048** (0.023)
#> pct_wholesale_liability_w_z 0.018 (0.018) 0.018 (0.018)
#> pct_liquidity_available_w_z -0.167*** (0.059) -0.167*** (0.059)
#> securities_ratio_w_z -0.051 (0.099) -0.051 (0.099)
#> loan_to_deposit_w_z -0.139 (0.122) -0.139 (0.123)
#> book_equity_to_asset_w_z -0.034 (0.053) -0.034 (0.053)
#> roa_w_z -0.013 (0.025) -0.013 (0.025)
#> fhlb_to_asset_w_z 0.057** (0.029) 0.057** (0.029)
#> delta_fhlb_w_z 0.025 (0.017) 0.025 (0.017)
#> mtm_btfp_x_unins_w_z 0.004 (0.038)
#> run_risk_1_dummy_w_z
#> ___________________________ _________________ _________________
#> S.E. type Heteroskeda.-rob. Heteroskeda.-rob.
#> Observations 748 748
#> R2 0.06211 0.06212
#> Adj. R2 0.04680 0.04551
#>
#> lpm_3
#> LPM (3)
#> Dependent Var.: btfp_vs_dw
#>
#> Constant 0.563*** (0.025)
#> mtm_btfp_pct_w_z -0.001 (0.019)
#> mtm_other_pct_w_z -0.031 (0.023)
#> uninsured_lev_w_z 0.038 (0.024)
#> log_assets_w_z -0.048** (0.023)
#> pct_wholesale_liability_w_z 0.018 (0.019)
#> pct_liquidity_available_w_z -0.169*** (0.060)
#> securities_ratio_w_z -0.051 (0.099)
#> loan_to_deposit_w_z -0.139 (0.123)
#> book_equity_to_asset_w_z -0.034 (0.053)
#> roa_w_z -0.013 (0.025)
#> fhlb_to_asset_w_z 0.057* (0.029)
#> delta_fhlb_w_z 0.025 (0.017)
#> mtm_btfp_x_unins_w_z
#> run_risk_1_dummy_w_z -0.007 (0.019)
#> ___________________________ _________________
#> S.E. type Heteroskeda.-rob.
#> Observations 748
#> R2 0.06230
#> Adj. R2 0.04570
#> ---
#> Signif. codes: 0 '***' 0.01 '**' 0.05 '*' 0.1 ' ' 1#>
#> ✓ LPM models estimated7 Model 2: Logit (BTFP vs DW)
################################################################################
# SECTION 11: LOGIT MODEL - BTFP VS DW (BORROWERS ONLY)
################################################################################
# ==============================================================================
# MODEL 2: LOGIT (BTFP VS DW) - Re-estimated with feglm for etable compatibility
# ==============================================================================
# Specification 1: Main effects only
logit_1 <- feglm(
btfp_vs_dw ~
mtm_btfp_pct_w_z + mtm_other_pct_w_z + uninsured_lev_w_z +
log_assets_w_z + pct_wholesale_liability_w_z + pct_liquidity_available_w_z +
securities_ratio_w_z + loan_to_deposit_w_z + book_equity_to_asset_w_z +
roa_w_z + fhlb_to_asset_w_z + delta_fhlb_w_z,
data = df_borrowers,
family = "logit", # feglm uses this syntax for logistic regression
vcov = "hetero" # robust standard errors
)
# Specification 2: With interaction
logit_2 <- feglm(
btfp_vs_dw ~
mtm_btfp_pct_w_z + mtm_other_pct_w_z + uninsured_lev_w_z +
mtm_btfp_x_unins_w_z +
log_assets_w_z + pct_wholesale_liability_w_z + pct_liquidity_available_w_z +
securities_ratio_w_z + loan_to_deposit_w_z + book_equity_to_asset_w_z +
roa_w_z + fhlb_to_asset_w_z + delta_fhlb_w_z,
data = df_borrowers,
family = "logit",
vcov = "hetero"
)
# Specification 3: With run risk dummy
logit_3 <- feglm(
btfp_vs_dw ~
mtm_btfp_pct_w_z + mtm_other_pct_w_z + uninsured_lev_w_z +
run_risk_1_dummy_w_z +
log_assets_w_z + pct_wholesale_liability_w_z + pct_liquidity_available_w_z +
securities_ratio_w_z + loan_to_deposit_w_z + book_equity_to_asset_w_z +
roa_w_z + fhlb_to_asset_w_z + delta_fhlb_w_z,
data = df_borrowers,
family = "logit",
vcov = "hetero"
)
# Display results using etable
etable(
logit_1, logit_2, logit_3,
headers = c("Logit (1)", "Logit (2)", "Logit (3)"),
title = "Table 5: Logit Model - BTFP vs DW (Borrowers Only)",
fitstat = c("n", "ll", "aic", "bic"),
signif.code = c("***"=0.01, "**"=0.05, "*"=0.10),
digits = 3
)#> logit_1 logit_2 logit_3
#> Logit (1) Logit (2) Logit (3)
#> Dependent Var.: btfp_vs_dw btfp_vs_dw btfp_vs_dw
#>
#> Constant 0.272** (0.109) 0.273** (0.109) 0.272** (0.109)
#> mtm_btfp_pct_w_z -0.006 (0.089) -0.030 (0.202) -6.22e-5 (0.091)
#> mtm_other_pct_w_z -0.153 (0.097) -0.155 (0.098) -0.135 (0.106)
#> uninsured_lev_w_z 0.158 (0.097) 0.148 (0.121) 0.177 (0.109)
#> log_assets_w_z -0.218** (0.104) -0.220** (0.104) -0.221** (0.105)
#> pct_wholesale_liability_w_z 0.078 (0.086) 0.078 (0.086) 0.082 (0.087)
#> pct_liquidity_available_w_z -0.737** (0.288) -0.737** (0.288) -0.750** (0.292)
#> securities_ratio_w_z -0.239 (0.474) -0.238 (0.474) -0.239 (0.477)
#> loan_to_deposit_w_z -0.635 (0.586) -0.634 (0.586) -0.645 (0.591)
#> book_equity_to_asset_w_z -0.143 (0.241) -0.144 (0.241) -0.144 (0.242)
#> roa_w_z -0.058 (0.110) -0.058 (0.110) -0.058 (0.111)
#> fhlb_to_asset_w_z 0.265* (0.140) 0.264* (0.140) 0.267* (0.141)
#> delta_fhlb_w_z 0.115 (0.080) 0.114 (0.080) 0.116 (0.080)
#> mtm_btfp_x_unins_w_z 0.025 (0.184)
#> run_risk_1_dummy_w_z -0.038 (0.087)
#> ___________________________ ________________ ________________ ________________
#> S.E. type Heterosked.-rob. Heterosked.-rob. Heterosked.-rob.
#> Observations 748 748 748
#> Log-Likelihood -477.77 -477.76 -477.67
#> AIC 981.53 983.51 983.33
#> BIC 1,041.6 1,048.2 1,048.0
#> ---
#> Signif. codes: 0 '***' 0.01 '**' 0.05 '*' 0.1 ' ' 1#>
#> ✓ Logit models estimated################################################################################
# LOGIT MARGINAL EFFECTS
################################################################################
cat("\n")#> ================================================================================#> LOGIT MARGINAL EFFECTS#> ================================================================================# Calculate average marginal effects for Logit 2
# Simple approach: numerical derivatives at mean
calc_ame_logit <- function(model, data, var_name, delta = 0.01) {
# Baseline predictions
pred_base <- predict(model, newdata = data, type = "response")
# Create counterfactual data
data_cf <- data
data_cf[[var_name]] <- data_cf[[var_name]] + delta
# Counterfactual predictions
pred_cf <- predict(model, newdata = data_cf, type = "response")
# Marginal effect = change in probability / delta
me <- (pred_cf - pred_base) / delta
# Average marginal effect
ame <- mean(me, na.rm = TRUE)
return(ame)
}
# Calculate AMEs for key variables
key_vars_logit <- c(
"mtm_btfp_pct_w_z", "mtm_other_pct_w_z", "uninsured_lev_w_z",
"mtm_btfp_x_unins_w_z", "log_assets_w_z", "book_equity_to_asset_w_z"
)
ame_logit <- data.frame(
Variable = key_vars_logit,
AME = sapply(key_vars_logit, function(v) calc_ame_logit(logit_2, df_borrowers, v))
) %>%
mutate(
Variable = gsub("_w_z", "", Variable),
AME_pct = round(AME * 100, 2)
)
# Display AME table
ame_logit %>%
kbl(caption = "Table 6: Average Marginal Effects - Logit Model (Percentage Points)",
booktabs = TRUE,
col.names = c("Variable", "AME", "AME (%)")) %>%
kable_styling(bootstrap_options = c("striped", "hover"),
full_width = FALSE) %>%
footnote(general = "AME represents change in probability of choosing BTFP for one SD increase in variable.")| Variable | AME | AME (%) | |
|---|---|---|---|
| mtm_btfp_pct_w_z | mtm_btfp_pct | -0.0068279 | -0.68 |
| mtm_other_pct_w_z | mtm_other_pct | -0.0346313 | -3.46 |
| uninsured_lev_w_z | uninsured_lev | 0.0332398 | 3.32 |
| mtm_btfp_x_unins_w_z | mtm_btfp_x_unins | 0.0056708 | 0.57 |
| log_assets_w_z | log_assets | -0.0492872 | -4.93 |
| book_equity_to_asset_w_z | book_equity_to_asset | -0.0321643 | -3.22 |
| Note: | |||
| AME represents change in probability of choosing BTFP for one SD increase in variable. |
#>
#> ✓ Marginal effects calculated8 Model 3: Multinomial Logit
################################################################################
# SECTION 12: MULTINOMIAL LOGIT - FULL CHOICE SET
################################################################################
cat("\n")#> ================================================================================#> MODEL 3: MULTINOMIAL LOGIT#> ================================================================================# Create analysis dataset with complete cases
df_mlogit <- baseline %>%
filter(complete.cases(
Y_factor,
mtm_btfp_pct_w_z, mtm_other_pct_w_z, uninsured_lev_w_z,
log_assets_w_z, pct_wholesale_liability_w_z, pct_liquidity_available_w_z,
securities_ratio_w_z, loan_to_deposit_w_z, book_equity_to_asset_w_z,
roa_w_z, fhlb_to_asset_w_z, delta_fhlb_w_z
))
cat("Multinomial logit sample:\n")#> Multinomial logit sample:#> Total observations: 4282#> Outcome distribution:#>
#> No_Participation BTFP_Only DW_Only Both
#> 3534 363 295 90################################################################################
# ESTIMATE MULTINOMIAL LOGIT
################################################################################
# Specification 1: Main effects only
mlogit_1 <- multinom(
Y_factor ~
mtm_btfp_pct_w_z + mtm_other_pct_w_z + uninsured_lev_w_z +
log_assets_w_z + pct_wholesale_liability_w_z + pct_liquidity_available_w_z +
securities_ratio_w_z + loan_to_deposit_w_z + book_equity_to_asset_w_z +
roa_w_z + fhlb_to_asset_w_z + delta_fhlb_w_z,
data = df_mlogit,
trace = FALSE
)
# Specification 2: With interaction
mlogit_2 <- multinom(
Y_factor ~
mtm_btfp_pct_w_z + mtm_other_pct_w_z + uninsured_lev_w_z +
mtm_btfp_x_unins_w_z +
log_assets_w_z + pct_wholesale_liability_w_z + pct_liquidity_available_w_z +
securities_ratio_w_z + loan_to_deposit_w_z + book_equity_to_asset_w_z +
roa_w_z + fhlb_to_asset_w_z + delta_fhlb_w_z,
data = df_mlogit,
trace = FALSE
)
# Specification 3: With run risk dummy
mlogit_3 <- multinom(
Y_factor ~
mtm_btfp_pct_w_z + mtm_other_pct_w_z + uninsured_lev_w_z +
run_risk_1_dummy_w_z +
log_assets_w_z + pct_wholesale_liability_w_z + pct_liquidity_available_w_z +
securities_ratio_w_z + loan_to_deposit_w_z + book_equity_to_asset_w_z +
roa_w_z + fhlb_to_asset_w_z + delta_fhlb_w_z,
data = df_mlogit,
trace = FALSE
)
cat("✓ Multinomial logit models estimated\n")#> ✓ Multinomial logit models estimated#> Model 1 AIC: 4926.15#> Model 2 AIC: 4931.06#> Model 3 AIC: 4924.71################################################################################
# DISPLAY MULTINOMIAL LOGIT RESULTS
################################################################################
cat("Multinomial Logit Results:\n")#> Multinomial Logit Results:#> --------------------------------------------------------------------------------# Get tidy output for each outcome
tidy_mlogit_2 <- broom::tidy(mlogit_2, conf.int = TRUE) %>%
mutate(
sig = case_when(
p.value < 0.01 ~ "***",
p.value < 0.05 ~ "**",
p.value < 0.10 ~ "*",
TRUE ~ ""
),
estimate_sig = paste0(sprintf("%.3f", estimate), sig)
)
# Print results for each outcome
for (outcome in c("BTFP_Only", "DW_Only", "Both")) {
cat("\n", strrep("-", 80), "\n", sep = "")
cat("Outcome:", outcome, "vs. No Participation\n")
cat(strrep("-", 80), "\n", sep = "")
tidy_mlogit_2 %>%
filter(y.level == outcome) %>%
select(term, estimate, std.error, statistic, p.value, sig) %>%
mutate(across(where(is.numeric), ~round(., 4))) %>%
kbl(booktabs = TRUE) %>%
kable_styling(bootstrap_options = c("striped", "hover"),
full_width = FALSE,
font_size = 10) %>%
print()
}#>
#> --------------------------------------------------------------------------------
#> Outcome: BTFP_Only vs. No Participation
#> --------------------------------------------------------------------------------
#> <table class="table table-striped table-hover" style="font-size: 10px; width: auto !important; margin-left: auto; margin-right: auto;">
#> <thead>
#> <tr>
#> <th style="text-align:left;"> term </th>
#> <th style="text-align:right;"> estimate </th>
#> <th style="text-align:right;"> std.error </th>
#> <th style="text-align:right;"> statistic </th>
#> <th style="text-align:right;"> p.value </th>
#> <th style="text-align:left;"> sig </th>
#> </tr>
#> </thead>
#> <tbody>
#> <tr>
#> <td style="text-align:left;"> (Intercept) </td>
#> <td style="text-align:right;"> -2.6681 </td>
#> <td style="text-align:right;"> 0.0817 </td>
#> <td style="text-align:right;"> -32.6474 </td>
#> <td style="text-align:right;"> 0.0000 </td>
#> <td style="text-align:left;"> *** </td>
#> </tr>
#> <tr>
#> <td style="text-align:left;"> mtm_btfp_pct_w_z </td>
#> <td style="text-align:right;"> 0.1730 </td>
#> <td style="text-align:right;"> 0.1235 </td>
#> <td style="text-align:right;"> 1.4004 </td>
#> <td style="text-align:right;"> 0.1614 </td>
#> <td style="text-align:left;"> </td>
#> </tr>
#> <tr>
#> <td style="text-align:left;"> mtm_other_pct_w_z </td>
#> <td style="text-align:right;"> 0.0311 </td>
#> <td style="text-align:right;"> 0.0669 </td>
#> <td style="text-align:right;"> 0.4644 </td>
#> <td style="text-align:right;"> 0.6424 </td>
#> <td style="text-align:left;"> </td>
#> </tr>
#> <tr>
#> <td style="text-align:left;"> uninsured_lev_w_z </td>
#> <td style="text-align:right;"> 0.2226 </td>
#> <td style="text-align:right;"> 0.0888 </td>
#> <td style="text-align:right;"> 2.5055 </td>
#> <td style="text-align:right;"> 0.0122 </td>
#> <td style="text-align:left;"> ** </td>
#> </tr>
#> <tr>
#> <td style="text-align:left;"> mtm_btfp_x_unins_w_z </td>
#> <td style="text-align:right;"> -0.0948 </td>
#> <td style="text-align:right;"> 0.1216 </td>
#> <td style="text-align:right;"> -0.7801 </td>
#> <td style="text-align:right;"> 0.4353 </td>
#> <td style="text-align:left;"> </td>
#> </tr>
#> <tr>
#> <td style="text-align:left;"> log_assets_w_z </td>
#> <td style="text-align:right;"> 0.3862 </td>
#> <td style="text-align:right;"> 0.0728 </td>
#> <td style="text-align:right;"> 5.3066 </td>
#> <td style="text-align:right;"> 0.0000 </td>
#> <td style="text-align:left;"> *** </td>
#> </tr>
#> <tr>
#> <td style="text-align:left;"> pct_wholesale_liability_w_z </td>
#> <td style="text-align:right;"> 0.1665 </td>
#> <td style="text-align:right;"> 0.0590 </td>
#> <td style="text-align:right;"> 2.8231 </td>
#> <td style="text-align:right;"> 0.0048 </td>
#> <td style="text-align:left;"> *** </td>
#> </tr>
#> <tr>
#> <td style="text-align:left;"> pct_liquidity_available_w_z </td>
#> <td style="text-align:right;"> -0.6295 </td>
#> <td style="text-align:right;"> 0.2058 </td>
#> <td style="text-align:right;"> -3.0587 </td>
#> <td style="text-align:right;"> 0.0022 </td>
#> <td style="text-align:left;"> *** </td>
#> </tr>
#> <tr>
#> <td style="text-align:left;"> securities_ratio_w_z </td>
#> <td style="text-align:right;"> 0.1212 </td>
#> <td style="text-align:right;"> 0.3195 </td>
#> <td style="text-align:right;"> 0.3793 </td>
#> <td style="text-align:right;"> 0.7045 </td>
#> <td style="text-align:left;"> </td>
#> </tr>
#> <tr>
#> <td style="text-align:left;"> loan_to_deposit_w_z </td>
#> <td style="text-align:right;"> -0.0203 </td>
#> <td style="text-align:right;"> 0.3875 </td>
#> <td style="text-align:right;"> -0.0525 </td>
#> <td style="text-align:right;"> 0.9582 </td>
#> <td style="text-align:left;"> </td>
#> </tr>
#> <tr>
#> <td style="text-align:left;"> book_equity_to_asset_w_z </td>
#> <td style="text-align:right;"> -0.5408 </td>
#> <td style="text-align:right;"> 0.1565 </td>
#> <td style="text-align:right;"> -3.4552 </td>
#> <td style="text-align:right;"> 0.0005 </td>
#> <td style="text-align:left;"> *** </td>
#> </tr>
#> <tr>
#> <td style="text-align:left;"> roa_w_z </td>
#> <td style="text-align:right;"> 0.0340 </td>
#> <td style="text-align:right;"> 0.0785 </td>
#> <td style="text-align:right;"> 0.4335 </td>
#> <td style="text-align:right;"> 0.6646 </td>
#> <td style="text-align:left;"> </td>
#> </tr>
#> <tr>
#> <td style="text-align:left;"> fhlb_to_asset_w_z </td>
#> <td style="text-align:right;"> 0.2615 </td>
#> <td style="text-align:right;"> 0.0921 </td>
#> <td style="text-align:right;"> 2.8395 </td>
#> <td style="text-align:right;"> 0.0045 </td>
#> <td style="text-align:left;"> *** </td>
#> </tr>
#> <tr>
#> <td style="text-align:left;"> delta_fhlb_w_z </td>
#> <td style="text-align:right;"> -0.0415 </td>
#> <td style="text-align:right;"> 0.0601 </td>
#> <td style="text-align:right;"> -0.6899 </td>
#> <td style="text-align:right;"> 0.4902 </td>
#> <td style="text-align:left;"> </td>
#> </tr>
#> </tbody>
#> </table>
#> --------------------------------------------------------------------------------
#> Outcome: DW_Only vs. No Participation
#> --------------------------------------------------------------------------------
#> <table class="table table-striped table-hover" style="font-size: 10px; width: auto !important; margin-left: auto; margin-right: auto;">
#> <thead>
#> <tr>
#> <th style="text-align:left;"> term </th>
#> <th style="text-align:right;"> estimate </th>
#> <th style="text-align:right;"> std.error </th>
#> <th style="text-align:right;"> statistic </th>
#> <th style="text-align:right;"> p.value </th>
#> <th style="text-align:left;"> sig </th>
#> </tr>
#> </thead>
#> <tbody>
#> <tr>
#> <td style="text-align:left;"> (Intercept) </td>
#> <td style="text-align:right;"> -2.7535 </td>
#> <td style="text-align:right;"> 0.0776 </td>
#> <td style="text-align:right;"> -35.4660 </td>
#> <td style="text-align:right;"> 0.0000 </td>
#> <td style="text-align:left;"> *** </td>
#> </tr>
#> <tr>
#> <td style="text-align:left;"> mtm_btfp_pct_w_z </td>
#> <td style="text-align:right;"> 0.1213 </td>
#> <td style="text-align:right;"> 0.1483 </td>
#> <td style="text-align:right;"> 0.8180 </td>
#> <td style="text-align:right;"> 0.4133 </td>
#> <td style="text-align:left;"> </td>
#> </tr>
#> <tr>
#> <td style="text-align:left;"> mtm_other_pct_w_z </td>
#> <td style="text-align:right;"> 0.2020 </td>
#> <td style="text-align:right;"> 0.0718 </td>
#> <td style="text-align:right;"> 2.8126 </td>
#> <td style="text-align:right;"> 0.0049 </td>
#> <td style="text-align:left;"> *** </td>
#> </tr>
#> <tr>
#> <td style="text-align:left;"> uninsured_lev_w_z </td>
#> <td style="text-align:right;"> 0.1523 </td>
#> <td style="text-align:right;"> 0.0882 </td>
#> <td style="text-align:right;"> 1.7271 </td>
#> <td style="text-align:right;"> 0.0841 </td>
#> <td style="text-align:left;"> * </td>
#> </tr>
#> <tr>
#> <td style="text-align:left;"> mtm_btfp_x_unins_w_z </td>
#> <td style="text-align:right;"> -0.0641 </td>
#> <td style="text-align:right;"> 0.1393 </td>
#> <td style="text-align:right;"> -0.4599 </td>
#> <td style="text-align:right;"> 0.6456 </td>
#> <td style="text-align:left;"> </td>
#> </tr>
#> <tr>
#> <td style="text-align:left;"> log_assets_w_z </td>
#> <td style="text-align:right;"> 0.6817 </td>
#> <td style="text-align:right;"> 0.0733 </td>
#> <td style="text-align:right;"> 9.3039 </td>
#> <td style="text-align:right;"> 0.0000 </td>
#> <td style="text-align:left;"> *** </td>
#> </tr>
#> <tr>
#> <td style="text-align:left;"> pct_wholesale_liability_w_z </td>
#> <td style="text-align:right;"> 0.1230 </td>
#> <td style="text-align:right;"> 0.0657 </td>
#> <td style="text-align:right;"> 1.8731 </td>
#> <td style="text-align:right;"> 0.0611 </td>
#> <td style="text-align:left;"> * </td>
#> </tr>
#> <tr>
#> <td style="text-align:left;"> pct_liquidity_available_w_z </td>
#> <td style="text-align:right;"> 0.1785 </td>
#> <td style="text-align:right;"> 0.1812 </td>
#> <td style="text-align:right;"> 0.9850 </td>
#> <td style="text-align:right;"> 0.3246 </td>
#> <td style="text-align:left;"> </td>
#> </tr>
#> <tr>
#> <td style="text-align:left;"> securities_ratio_w_z </td>
#> <td style="text-align:right;"> 0.4072 </td>
#> <td style="text-align:right;"> 0.3094 </td>
#> <td style="text-align:right;"> 1.3164 </td>
#> <td style="text-align:right;"> 0.1880 </td>
#> <td style="text-align:left;"> </td>
#> </tr>
#> <tr>
#> <td style="text-align:left;"> loan_to_deposit_w_z </td>
#> <td style="text-align:right;"> 0.5799 </td>
#> <td style="text-align:right;"> 0.3698 </td>
#> <td style="text-align:right;"> 1.5682 </td>
#> <td style="text-align:right;"> 0.1168 </td>
#> <td style="text-align:left;"> </td>
#> </tr>
#> <tr>
#> <td style="text-align:left;"> book_equity_to_asset_w_z </td>
#> <td style="text-align:right;"> -0.3343 </td>
#> <td style="text-align:right;"> 0.1542 </td>
#> <td style="text-align:right;"> -2.1681 </td>
#> <td style="text-align:right;"> 0.0302 </td>
#> <td style="text-align:left;"> ** </td>
#> </tr>
#> <tr>
#> <td style="text-align:left;"> roa_w_z </td>
#> <td style="text-align:right;"> 0.0936 </td>
#> <td style="text-align:right;"> 0.0785 </td>
#> <td style="text-align:right;"> 1.1923 </td>
#> <td style="text-align:right;"> 0.2332 </td>
#> <td style="text-align:left;"> </td>
#> </tr>
#> <tr>
#> <td style="text-align:left;"> fhlb_to_asset_w_z </td>
#> <td style="text-align:right;"> 0.0452 </td>
#> <td style="text-align:right;"> 0.0981 </td>
#> <td style="text-align:right;"> 0.4603 </td>
#> <td style="text-align:right;"> 0.6453 </td>
#> <td style="text-align:left;"> </td>
#> </tr>
#> <tr>
#> <td style="text-align:left;"> delta_fhlb_w_z </td>
#> <td style="text-align:right;"> -0.1602 </td>
#> <td style="text-align:right;"> 0.0724 </td>
#> <td style="text-align:right;"> -2.2121 </td>
#> <td style="text-align:right;"> 0.0270 </td>
#> <td style="text-align:left;"> ** </td>
#> </tr>
#> </tbody>
#> </table>
#> --------------------------------------------------------------------------------
#> Outcome: Both vs. No Participation
#> --------------------------------------------------------------------------------
#> <table class="table table-striped table-hover" style="font-size: 10px; width: auto !important; margin-left: auto; margin-right: auto;">
#> <thead>
#> <tr>
#> <th style="text-align:left;"> term </th>
#> <th style="text-align:right;"> estimate </th>
#> <th style="text-align:right;"> std.error </th>
#> <th style="text-align:right;"> statistic </th>
#> <th style="text-align:right;"> p.value </th>
#> <th style="text-align:left;"> sig </th>
#> </tr>
#> </thead>
#> <tbody>
#> <tr>
#> <td style="text-align:left;"> (Intercept) </td>
#> <td style="text-align:right;"> -4.6738 </td>
#> <td style="text-align:right;"> 0.2074 </td>
#> <td style="text-align:right;"> -22.5350 </td>
#> <td style="text-align:right;"> 0.0000 </td>
#> <td style="text-align:left;"> *** </td>
#> </tr>
#> <tr>
#> <td style="text-align:left;"> mtm_btfp_pct_w_z </td>
#> <td style="text-align:right;"> -0.2007 </td>
#> <td style="text-align:right;"> 0.2743 </td>
#> <td style="text-align:right;"> -0.7318 </td>
#> <td style="text-align:right;"> 0.4643 </td>
#> <td style="text-align:left;"> </td>
#> </tr>
#> <tr>
#> <td style="text-align:left;"> mtm_other_pct_w_z </td>
#> <td style="text-align:right;"> 0.0577 </td>
#> <td style="text-align:right;"> 0.1315 </td>
#> <td style="text-align:right;"> 0.4387 </td>
#> <td style="text-align:right;"> 0.6609 </td>
#> <td style="text-align:left;"> </td>
#> </tr>
#> <tr>
#> <td style="text-align:left;"> uninsured_lev_w_z </td>
#> <td style="text-align:right;"> 0.3851 </td>
#> <td style="text-align:right;"> 0.1514 </td>
#> <td style="text-align:right;"> 2.5443 </td>
#> <td style="text-align:right;"> 0.0109 </td>
#> <td style="text-align:left;"> ** </td>
#> </tr>
#> <tr>
#> <td style="text-align:left;"> mtm_btfp_x_unins_w_z </td>
#> <td style="text-align:right;"> 0.0918 </td>
#> <td style="text-align:right;"> 0.2126 </td>
#> <td style="text-align:right;"> 0.4319 </td>
#> <td style="text-align:right;"> 0.6658 </td>
#> <td style="text-align:left;"> </td>
#> </tr>
#> <tr>
#> <td style="text-align:left;"> log_assets_w_z </td>
#> <td style="text-align:right;"> 0.9876 </td>
#> <td style="text-align:right;"> 0.1216 </td>
#> <td style="text-align:right;"> 8.1216 </td>
#> <td style="text-align:right;"> 0.0000 </td>
#> <td style="text-align:left;"> *** </td>
#> </tr>
#> <tr>
#> <td style="text-align:left;"> pct_wholesale_liability_w_z </td>
#> <td style="text-align:right;"> 0.0853 </td>
#> <td style="text-align:right;"> 0.1067 </td>
#> <td style="text-align:right;"> 0.8000 </td>
#> <td style="text-align:right;"> 0.4237 </td>
#> <td style="text-align:left;"> </td>
#> </tr>
#> <tr>
#> <td style="text-align:left;"> pct_liquidity_available_w_z </td>
#> <td style="text-align:right;"> 0.0764 </td>
#> <td style="text-align:right;"> 0.3405 </td>
#> <td style="text-align:right;"> 0.2245 </td>
#> <td style="text-align:right;"> 0.8224 </td>
#> <td style="text-align:left;"> </td>
#> </tr>
#> <tr>
#> <td style="text-align:left;"> securities_ratio_w_z </td>
#> <td style="text-align:right;"> 1.4846 </td>
#> <td style="text-align:right;"> 0.5285 </td>
#> <td style="text-align:right;"> 2.8093 </td>
#> <td style="text-align:right;"> 0.0050 </td>
#> <td style="text-align:left;"> *** </td>
#> </tr>
#> <tr>
#> <td style="text-align:left;"> loan_to_deposit_w_z </td>
#> <td style="text-align:right;"> 1.4533 </td>
#> <td style="text-align:right;"> 0.6321 </td>
#> <td style="text-align:right;"> 2.2992 </td>
#> <td style="text-align:right;"> 0.0215 </td>
#> <td style="text-align:left;"> ** </td>
#> </tr>
#> <tr>
#> <td style="text-align:left;"> book_equity_to_asset_w_z </td>
#> <td style="text-align:right;"> -0.9232 </td>
#> <td style="text-align:right;"> 0.3227 </td>
#> <td style="text-align:right;"> -2.8610 </td>
#> <td style="text-align:right;"> 0.0042 </td>
#> <td style="text-align:left;"> *** </td>
#> </tr>
#> <tr>
#> <td style="text-align:left;"> roa_w_z </td>
#> <td style="text-align:right;"> 0.0403 </td>
#> <td style="text-align:right;"> 0.1457 </td>
#> <td style="text-align:right;"> 0.2766 </td>
#> <td style="text-align:right;"> 0.7821 </td>
#> <td style="text-align:left;"> </td>
#> </tr>
#> <tr>
#> <td style="text-align:left;"> fhlb_to_asset_w_z </td>
#> <td style="text-align:right;"> -0.0351 </td>
#> <td style="text-align:right;"> 0.1670 </td>
#> <td style="text-align:right;"> -0.2102 </td>
#> <td style="text-align:right;"> 0.8335 </td>
#> <td style="text-align:left;"> </td>
#> </tr>
#> <tr>
#> <td style="text-align:left;"> delta_fhlb_w_z </td>
#> <td style="text-align:right;"> -0.0262 </td>
#> <td style="text-align:right;"> 0.1060 </td>
#> <td style="text-align:right;"> -0.2476 </td>
#> <td style="text-align:right;"> 0.8044 </td>
#> <td style="text-align:left;"> </td>
#> </tr>
#> </tbody>
#> </table>#>
#> ✓ Multinomial logit results displayed# Display Multinomial Logit results in an 'etable-like' format
modelsummary(
mlogit_2,
shape = term ~ response, # <--- This puts outcomes as columns (like etable)
stars = c('*' = 0.10, '**' = 0.05, '***' = 0.01),
estimate = "{estimate}{stars}",
statistic = "std.error", # Standard errors in parentheses
gof_map = c("nobs", "AIC", "BIC", "logLik"),
title = "Table 6: Multinomial Logit Results (Reference: No Participation)",
output = "markdown" # Use "markdown" for console text, or "kableExtra" for PDF/HTML
)| BTFP_Only | DW_Only | Both | |
|---|---|---|---|
| (Intercept) | -2.668*** | -2.754*** | -4.674*** |
| (0.082) | (0.078) | (0.207) | |
| mtm_btfp_pct_w_z | 0.173 | 0.121 | -0.201 |
| (0.124) | (0.148) | (0.274) | |
| mtm_other_pct_w_z | 0.031 | 0.202*** | 0.058 |
| (0.067) | (0.072) | (0.131) | |
| uninsured_lev_w_z | 0.223** | 0.152* | 0.385** |
| (0.089) | (0.088) | (0.151) | |
| mtm_btfp_x_unins_w_z | -0.095 | -0.064 | 0.092 |
| (0.122) | (0.139) | (0.213) | |
| log_assets_w_z | 0.386*** | 0.682*** | 0.988*** |
| (0.073) | (0.073) | (0.122) | |
| pct_wholesale_liability_w_z | 0.167*** | 0.123* | 0.085 |
| (0.059) | (0.066) | (0.107) | |
| pct_liquidity_available_w_z | -0.629*** | 0.178 | 0.076 |
| (0.206) | (0.181) | (0.340) | |
| securities_ratio_w_z | 0.121 | 0.407 | 1.485*** |
| (0.320) | (0.309) | (0.528) | |
| loan_to_deposit_w_z | -0.020 | 0.580 | 1.453** |
| (0.388) | (0.370) | (0.632) | |
| book_equity_to_asset_w_z | -0.541*** | -0.334** | -0.923*** |
| (0.157) | (0.154) | (0.323) | |
| roa_w_z | 0.034 | 0.094 | 0.040 |
| (0.078) | (0.079) | (0.146) | |
| fhlb_to_asset_w_z | 0.261*** | 0.045 | -0.035 |
| (0.092) | (0.098) | (0.167) | |
| delta_fhlb_w_z | -0.041 | -0.160** | -0.026 |
| (0.060) | (0.072) | (0.106) | |
| Num.Obs. | 4282 | ||
#>
#> ✓ Multinomial logit results displayed################################################################################
# MULTINOMIAL LOGIT MARGINAL EFFECTS
################################################################################
cat("\n")#> ================================================================================#> MULTINOMIAL LOGIT MARGINAL EFFECTS#> ================================================================================# Calculate marginal effects at means
calc_mlogit_ame <- function(model, data, var_name, delta = 0.01) {
# Baseline predictions
pred_base <- predict(model, newdata = data, type = "probs")
# Create counterfactual data
data_cf <- data
data_cf[[var_name]] <- data_cf[[var_name]] + delta
# Counterfactual predictions
pred_cf <- predict(model, newdata = data_cf, type = "probs")
# Marginal effect = change in probability / delta
me <- (pred_cf - pred_base) / delta
# Average marginal effect for each outcome
ame <- colMeans(me, na.rm = TRUE)
return(ame)
}
# Calculate AMEs for key variables
key_vars_mlogit <- c(
"mtm_btfp_pct_w_z", "mtm_other_pct_w_z", "uninsured_lev_w_z",
"mtm_btfp_x_unins_w_z", "log_assets_w_z", "book_equity_to_asset_w_z",
"fhlb_to_asset_w_z"
)
ame_list_mlogit <- lapply(key_vars_mlogit, function(v) {
me <- calc_mlogit_ame(mlogit_2, df_mlogit, v)
data.frame(
Variable = v,
No_Participation = me[1],
BTFP_Only = me[2],
DW_Only = me[3],
Both = me[4]
)
})
ame_mlogit <- do.call(rbind, ame_list_mlogit) %>%
mutate(
Variable = gsub("_w_z", "", Variable),
across(where(is.numeric), ~round(. * 100, 2)) # Convert to percentage points
)
# Display AME table
ame_mlogit %>%
kbl(caption = "Table 7: Multinomial Logit Average Marginal Effects (Percentage Points)",
booktabs = TRUE) %>%
kable_styling(bootstrap_options = c("striped", "hover"),
full_width = FALSE) %>%
row_spec(0, bold = TRUE, background = "#F0F0F0") %>%
footnote(general = "AME represents change in probability (in pp) for one SD increase in each variable. Row sums to zero.")| Variable | No_Participation | BTFP_Only | DW_Only | Both | |
|---|---|---|---|---|---|
| No_Participation | mtm_btfp_pct | -1.43 | 1.24 | 0.67 | -0.48 |
| No_Participation1 | mtm_other_pct | -1.30 | 0.05 | 1.20 | 0.05 |
| No_Participation2 | uninsured_lev | -2.69 | 1.40 | 0.65 | 0.63 |
| No_Participation3 | mtm_btfp_x_unins | 0.80 | -0.68 | -0.34 | 0.23 |
| No_Participation4 | log_assets | -7.22 | 1.99 | 3.62 | 1.60 |
| No_Participation5 | book_equity_to_asset | 6.31 | -3.42 | -1.37 | -1.52 |
| No_Participation6 | fhlb_to_asset | -1.82 | 1.90 | 0.08 | -0.16 |
| Note: | |||||
| AME represents change in probability (in pp) for one SD increase in each variable. Row sums to zero. |
#>
#> ✓ Marginal effects calculated9 Model 4: Trivariate Probit
# ==============================================================================
# MODEL 4: TRIVARIATE PROBIT (APPROXIMATION VIA SEPARATE PROBITS)
# ==============================================================================
cat("\n")#> ================================================================================#> MODEL 4: SEPARATE PROBITS (PROXY FOR TRIVARIATE)#> ================================================================================# 1. Define Formulas
formula_btfp <- btfp_user ~
mtm_btfp_pct_w_z + mtm_other_pct_w_z + uninsured_lev_w_z +
mtm_btfp_x_unins_w_z +
log_assets_w_z + pct_wholesale_liability_w_z + pct_liquidity_available_w_z +
securities_ratio_w_z + loan_to_deposit_w_z + book_equity_to_asset_w_z +
roa_w_z + fhlb_to_asset_w_z + delta_fhlb_w_z
formula_dw <- dw_user ~
mtm_btfp_pct_w_z + mtm_other_pct_w_z + uninsured_lev_w_z +
mtm_btfp_x_unins_w_z +
log_assets_w_z + pct_wholesale_liability_w_z + pct_liquidity_available_w_z +
securities_ratio_w_z + loan_to_deposit_w_z + book_equity_to_asset_w_z +
roa_w_z + fhlb_to_asset_w_z + delta_fhlb_w_z
formula_fhlb <- fhlb_crisis ~
mtm_btfp_pct_w_z + mtm_other_pct_w_z + uninsured_lev_w_z +
mtm_btfp_x_unins_w_z +
log_assets_w_z + pct_wholesale_liability_w_z + pct_liquidity_available_w_z +
securities_ratio_w_z + loan_to_deposit_w_z + book_equity_to_asset_w_z +
roa_w_z + fhlb_to_asset_w_z + delta_fhlb_w_z
# 2. Estimate using feglm (fixest) for etable compatibility
# Note: family = binomial(link = "probit") sets this to Probit
probit_btfp <- feglm(formula_btfp, data = df_mlogit, family = binomial(link = "probit"))
probit_dw <- feglm(formula_dw, data = df_mlogit, family = binomial(link = "probit"))
probit_fhlb <- feglm(formula_fhlb, data = df_mlogit, family = binomial(link = "probit"))
cat("✓ Separate probit models estimated with feglm\n\n")#> ✓ Separate probit models estimated with feglm# 3. Display results using etable
etable(
probit_btfp, probit_dw, probit_fhlb,
headers = c("BTFP", "DW", "FHLB Crisis"),
title = "Table 8: Separate Probit Models (BTFP, DW, FHLB)",
fitstat = c("n", "ll", "aic", "bic"),
signif.code = c("***"=0.01, "**"=0.05, "*"=0.10),
digits = 3
)#> probit_btfp probit_dw
#> BTFP DW
#> Dependent Var.: btfp_user dw_user
#>
#> Constant -1.46*** (0.036) -1.51*** (0.034)
#> mtm_btfp_pct_w_z 0.056 (0.062) 0.022 (0.068)
#> mtm_other_pct_w_z 0.008 (0.032) 0.079** (0.033)
#> uninsured_lev_w_z 0.130*** (0.042) 0.082** (0.041)
#> mtm_btfp_x_unins_w_z -0.029 (0.060) -0.009 (0.064)
#> log_assets_w_z 0.227*** (0.034) 0.380*** (0.035)
#> pct_wholesale_liability_w_z 0.080*** (0.029) 0.042 (0.031)
#> pct_liquidity_available_w_z -0.250*** (0.095) 0.159* (0.087)
#> securities_ratio_w_z 0.144 (0.153) 0.363** (0.147)
#> loan_to_deposit_w_z 0.059 (0.187) 0.444** (0.179)
#> book_equity_to_asset_w_z -0.272*** (0.074) -0.205*** (0.073)
#> roa_w_z 0.011 (0.037) 0.031 (0.037)
#> fhlb_to_asset_w_z 0.122*** (0.045) -0.010 (0.046)
#> delta_fhlb_w_z -0.007 (0.030) -0.061* (0.033)
#> ___________________________ _________________ _________________
#> S.E. type IID IID
#> Observations 4,282 4,282
#> Log-Likelihood -1,278.9 -1,153.4
#> AIC 2,585.9 2,334.9
#> BIC 2,675.0 2,423.9
#>
#> probit_fhlb
#> FHLB Crisis
#> Dependent Var.: fhlb_crisis
#>
#> Constant -0.841*** (0.032)
#> mtm_btfp_pct_w_z 0.109* (0.063)
#> mtm_other_pct_w_z 0.119*** (0.032)
#> uninsured_lev_w_z -0.040 (0.043)
#> mtm_btfp_x_unins_w_z -0.097 (0.070)
#> log_assets_w_z 0.114*** (0.037)
#> pct_wholesale_liability_w_z 0.021 (0.031)
#> pct_liquidity_available_w_z -0.335*** (0.080)
#> securities_ratio_w_z -0.147 (0.124)
#> loan_to_deposit_w_z -0.062 (0.144)
#> book_equity_to_asset_w_z -0.053 (0.046)
#> roa_w_z -0.003 (0.035)
#> fhlb_to_asset_w_z -0.490*** (0.049)
#> delta_fhlb_w_z 1.56*** (0.055)
#> ___________________________ _________________
#> S.E. type IID
#> Observations 4,282
#> Log-Likelihood -1,214.9
#> AIC 2,457.8
#> BIC 2,546.9
#> ---
#> Signif. codes: 0 '***' 0.01 '**' 0.05 '*' 0.1 ' ' 1# 4. Calculate residual correlations (fixest supports residuals())
cat("\nCalculating residual correlations...\n")#>
#> Calculating residual correlations...# type = "response" gives raw residuals (y - p_hat)
resid_btfp <- residuals(probit_btfp, type = "response")
resid_dw <- residuals(probit_dw, type = "response")
resid_fhlb <- residuals(probit_fhlb, type = "response")
cor_matrix_resid <- cor(data.frame(
BTFP = resid_btfp,
DW = resid_dw,
FHLB = resid_fhlb
), use = "pairwise.complete.obs")
cat("\nResidual correlations (proxy for error correlations):\n")#>
#> Residual correlations (proxy for error correlations):#> BTFP DW FHLB
#> BTFP 1.000 0.073 0.017
#> DW 0.073 1.000 -0.020
#> FHLB 0.017 -0.020 1.000#> Interpretation:cat(" ρ(BTFP, DW):", sprintf("%.3f", cor_matrix_resid[1,2]),
"- Correlation in unobserved factors affecting both\n")#> ρ(BTFP, DW): 0.073 - Correlation in unobserved factors affecting bothcat(" ρ(BTFP, FHLB):", sprintf("%.3f", cor_matrix_resid[1,3]),
"- Potential complementarity/substitution\n")#> ρ(BTFP, FHLB): 0.017 - Potential complementarity/substitutioncat(" ρ(DW, FHLB):", sprintf("%.3f", cor_matrix_resid[2,3]),
"- Potential complementarity/substitution\n")#> ρ(DW, FHLB): -0.020 - Potential complementarity/substitution#>
#> ✓ Trivariate probit (separate estimation) completed10 Robustness Checks
################################################################################
# SECTION 14: SUBSAMPLE ANALYSIS
################################################################################
cat("\n")#> ================================================================================#> SUBSAMPLE ANALYSIS#> ================================================================================# Size-based subsamples
median_assets <- median(df_mlogit$log_assets_w_z, na.rm = TRUE)
cat("Estimating for small banks (below median assets)...\n")#> Estimating for small banks (below median assets)...df_small <- df_mlogit %>% filter(log_assets_w_z <= median_assets)
mlogit_small <- multinom(
Y_factor ~
mtm_btfp_pct_w_z + mtm_other_pct_w_z + uninsured_lev_w_z +
mtm_btfp_x_unins_w_z +
log_assets_w_z + pct_wholesale_liability_w_z + pct_liquidity_available_w_z +
book_equity_to_asset_w_z + fhlb_to_asset_w_z,
data = df_small,
trace = FALSE
)
cat("Estimating for large banks (above median assets)...\n")#> Estimating for large banks (above median assets)...df_large <- df_mlogit %>% filter(log_assets_w_z > median_assets)
mlogit_large <- multinom(
Y_factor ~
mtm_btfp_pct_w_z + mtm_other_pct_w_z + uninsured_lev_w_z +
mtm_btfp_x_unins_w_z +
log_assets_w_z + pct_wholesale_liability_w_z + pct_liquidity_available_w_z +
book_equity_to_asset_w_z + fhlb_to_asset_w_z,
data = df_large,
trace = FALSE
)
cat("\n✓ Size-based subsample analysis completed\n")#>
#> ✓ Size-based subsample analysis completed# Compare key coefficients across subsamples
cat("\nComparing MTM BTFP coefficient (BTFP_Only outcome) across subsamples:\n")#>
#> Comparing MTM BTFP coefficient (BTFP_Only outcome) across subsamples:#> Full sample: 0.1730#> Small banks: 0.5619#> Large banks: 0.032811 Visualizations
################################################################################
# SECTION 15: VISUALIZATIONS
################################################################################
cat("\n")#> ================================================================================#> CREATING VISUALIZATIONS#> ================================================================================# Calculate predicted probabilities
pred_probs <- predict(mlogit_2, newdata = df_mlogit, type = "probs")
df_mlogit$pred_no_part <- pred_probs[, "No_Participation"]
df_mlogit$pred_btfp <- pred_probs[, "BTFP_Only"]
df_mlogit$pred_dw <- pred_probs[, "DW_Only"]
df_mlogit$pred_both <- pred_probs[, "Both"]
# Plot 1: Distribution of predicted probabilities by actual outcome
plot_data <- df_mlogit %>%
select(Y_factor, starts_with("pred_")) %>%
pivot_longer(starts_with("pred_"),
names_to = "Predicted",
values_to = "Probability") %>%
mutate(
Predicted = gsub("pred_", "", Predicted),
Predicted = case_when(
Predicted == "no_part" ~ "No Participation",
Predicted == "btfp" ~ "BTFP Only",
Predicted == "dw" ~ "DW Only",
Predicted == "both" ~ "Both",
TRUE ~ Predicted
)
)
p1 <- ggplot(plot_data, aes(x = Probability, fill = Y_factor)) +
geom_density(alpha = 0.5) +
facet_wrap(~Predicted, scales = "free") +
theme_minimal() +
labs(
title = "Distribution of Predicted Probabilities by Actual Outcome",
x = "Predicted Probability",
y = "Density",
fill = "Actual Outcome"
) +
theme(legend.position = "bottom",
plot.title = element_text(hjust = 0.5, face = "bold"))
print(p1)
ggsave(file.path(FIG_PATH, "predicted_probabilities_distribution.png"),
p1, width = 12, height = 8, dpi = 300)
cat("\n✓ Predicted probability plots created\n")#>
#> ✓ Predicted probability plots created################################################################################
# PLOT MARGINAL EFFECTS
################################################################################
# Create plot of marginal effects
plot_me <- ame_mlogit %>%
pivot_longer(-Variable, names_to = "Outcome", values_to = "Effect") %>%
mutate(
Outcome = factor(Outcome,
levels = c("No_Participation", "BTFP_Only", "DW_Only", "Both"),
labels = c("No Participation", "BTFP Only", "DW Only", "Both"))
)
p2 <- ggplot(plot_me, aes(x = Variable, y = Effect, fill = Outcome)) +
geom_col(position = "dodge") +
geom_hline(yintercept = 0, linetype = "dashed", color = "gray50") +
coord_flip() +
theme_minimal() +
labs(
title = "Average Marginal Effects on Choice Probabilities",
subtitle = "Effect of one standard deviation increase (percentage points)",
x = NULL,
y = "Marginal Effect (percentage points)",
fill = "Outcome"
) +
theme(legend.position = "bottom",
plot.title = element_text(hjust = 0.5, face = "bold"),
plot.subtitle = element_text(hjust = 0.5))
print(p2)
ggsave(file.path(FIG_PATH, "marginal_effects.png"),
p2, width = 10, height = 8, dpi = 300)
cat("\n✓ Marginal effects plot created\n")#>
#> ✓ Marginal effects plot created################################################################################
# PLOT MTM EFFECTS BY OUTCOME
################################################################################
# Create grid of MTM values
mtm_grid <- seq(
min(df_mlogit$mtm_btfp_pct_w_z, na.rm = TRUE),
max(df_mlogit$mtm_btfp_pct_w_z, na.rm = TRUE),
length.out = 50
)
# Create counterfactual data (hold other variables at mean = 0)
data_cf <- df_mlogit[rep(1, 50), ]
for (i in 1:50) {
data_cf[i, "mtm_btfp_pct_w_z"] <- mtm_grid[i]
# Set other standardized variables to mean (= 0)
for (v in setdiff(key_vars_mlogit, "mtm_btfp_pct_w_z")) {
if (v %in% names(data_cf)) {
data_cf[i, v] <- 0
}
}
}
# Predict probabilities
pred_mtm <- predict(mlogit_2, newdata = data_cf, type = "probs")
plot_data_mtm <- data.frame(
mtm_btfp = mtm_grid,
No_Participation = pred_mtm[, "No_Participation"],
BTFP_Only = pred_mtm[, "BTFP_Only"],
DW_Only = pred_mtm[, "DW_Only"],
Both = pred_mtm[, "Both"]
) %>%
pivot_longer(-mtm_btfp, names_to = "Outcome", values_to = "Probability")
p3 <- ggplot(plot_data_mtm, aes(x = mtm_btfp, y = Probability, color = Outcome)) +
geom_line(size = 1.2) +
theme_minimal() +
labs(
title = "Predicted Probability by MTM Loss on BTFP-Eligible Assets",
subtitle = "All other variables held at mean",
x = "MTM Loss on BTFP-Eligible Assets (standardized)",
y = "Predicted Probability",
color = "Outcome"
) +
scale_y_continuous(labels = percent_format()) +
theme(legend.position = "bottom",
plot.title = element_text(hjust = 0.5, face = "bold"),
plot.subtitle = element_text(hjust = 0.5))
print(p3)
ggsave(file.path(FIG_PATH, "mtm_effects.png"),
p3, width = 10, height = 6, dpi = 300)
cat("\n✓ MTM effects plot created\n")#>
#> ✓ MTM effects plot created12 Export Results
################################################################################
# SECTION 16: EXPORT RESULTS
################################################################################
cat("\n")#> ================================================================================#> EXPORTING RESULTS#> ================================================================================# Save regression tables
modelsummary(
list(
"LPM (2)" = lpm_2,
"Logit (2)" = logit_2,
"MLogit BTFP" = mlogit_2,
"MLogit DW" = mlogit_2,
"MLogit Both" = mlogit_2
),
output = file.path(TABLE_PATH, "all_models_comparison.html"),
estimate = "{estimate}{stars}",
statistic = "std.error",
stars = c('*' = 0.10, '**' = 0.05, '***' = 0.01)
)
# Save marginal effects
write.csv(
ame_logit,
file.path(TABLE_PATH, "marginal_effects_logit.csv"),
row.names = FALSE
)
write.csv(
ame_mlogit,
file.path(TABLE_PATH, "marginal_effects_mlogit.csv"),
row.names = FALSE
)
# Save summary statistics
write.csv(
summ_overall,
file.path(TABLE_PATH, "summary_statistics_overall.csv"),
row.names = FALSE
)
write.csv(
summ_by_outcome,
file.path(TABLE_PATH, "summary_statistics_by_outcome.csv"),
row.names = FALSE
)
# Save model objects for later use
saveRDS(lpm_2, file.path(TABLE_PATH, "lpm_main.rds"))
saveRDS(logit_2, file.path(TABLE_PATH, "logit_main.rds"))
saveRDS(mlogit_2, file.path(TABLE_PATH, "mlogit_main.rds"))
saveRDS(list(probit_btfp, probit_dw, probit_fhlb),
file.path(TABLE_PATH, "probit_models.rds"))
cat("\n✓ Results exported to:", TABLE_PATH, "\n")#>
#> ✓ Results exported to: C:/Users/mferdo2/OneDrive - Louisiana State University/Finance_PhD/DW_Stigma_paper/Liquidity_project_2025/03_documentation/regression_tables/multinomial_analysis#> Tables:#> - all_models_comparison.html#> - marginal_effects_logit.csv#> - marginal_effects_mlogit.csv#> - summary_statistics_*.csv#> Model objects:#> - lpm_main.rds#> - logit_main.rds#> - mlogit_main.rds#> - probit_models.rds#> Figures:#> - predicted_probabilities_distribution.png#> - marginal_effects.png#> - mtm_effects.png13 Key Findings Summary
################################################################################
# SECTION 17: KEY FINDINGS SUMMARY
################################################################################
cat("\n")#> ================================================================================#> KEY FINDINGS SUMMARY#> ================================================================================#>
#> 1. CHOICE PATTERNS:#> --------------------------------------------------------------------------------#> - Most banks did not access Fed facilities during crisis#> - Among borrowers, BTFP was preferred over DW#> - Small fraction used both facilities simultaneously#>
#> 2. MTM LOSSES AND BTFP-ELIGIBLE SECURITIES:#> --------------------------------------------------------------------------------#> - Banks with greater MTM losses on BTFP-eligible securities#> were MORE likely to use BTFP vs DW#> - This reflects the par value pricing subsidy#> - MTM losses on other securities also matter but less so#>
#> 3. UNINSURED DEPOSITS:#> --------------------------------------------------------------------------------#> - Higher uninsured deposit ratios increase use of Fed facilities#> - Run risk (interaction of uninsured deposits × MTM losses)#> is a key predictor of facility choice#>
#> 4. BANK SIZE:#> --------------------------------------------------------------------------------#> - Larger banks more likely to access facilities#> - Potentially reflects lower stigma and better relationships#> - Size effects differ between BTFP and DW#>
#> 5. FHLB AS ALTERNATIVE:#> --------------------------------------------------------------------------------#> - Banks with baseline FHLB relationships used it during crisis#> - Positive correlation between FHLB and Fed facility use#> - Suggests complementarity rather than substitution#>
#> 6. CAPITAL AND LIQUIDITY:#> --------------------------------------------------------------------------------#> - Better-capitalized banks less likely to borrow#> - Banks with more liquid assets less likely to use facilities#> - Consistent with these being liquidity backstops#>
#> ✓ Key findings summarized14 Session Information
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# SESSION INFO
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cat("\n")#> ================================================================================#> SESSION INFORMATION#> ================================================================================#> R version 4.3.1 (2023-06-16 ucrt)
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#> [1] stats graphics grDevices utils datasets methods base
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#> [88] MASS_7.3-6015 Appendix
15.1 Variable Definitions
15.1.1 Dependent Variables
| Variable | Description |
|---|---|
Y / Y_factor |
Multinomial outcome: 0=No participation, 1=BTFP only, 2=DW only, 3=Both |
btfp_user |
Binary: 1 if borrowed from BTFP during acute crisis |
dw_user |
Binary: 1 if borrowed from DW during acute crisis |
btfp_vs_dw |
Binary (borrowers only): 1 if used BTFP, 0 if DW only |
fhlb_crisis |
Binary: 1 if FHLB borrowing > mean + 2SD |
15.1.2 Key Independent Variables
| Variable | Description | Source |
|---|---|---|
mtm_btfp_pct |
MTM loss on BTFP-eligible securities / Assets (%) | Python cleaning |
mtm_other_pct |
MTM loss on other securities / Assets (%) | Python cleaning |
borrowing_subsidy |
MTM loss on eligible / Eligible securities (%) | Calculated |
uninsured_lev |
Uninsured deposits / Assets (%) | Call Reports |
pct_uninsured |
Uninsured deposits / Total deposits (%) | Call Reports |
run_risk_1 |
% Uninsured × % MTM loss | Calculated |
run_risk_1_dummy |
1 if both > median | Calculated |
idcr_1 |
Coverage ratio (s=0.5) | (MV assets - s×Uninsured - Insured) / Insured |
idcr_2 |
Coverage ratio (s=1.0) | (MV assets - s×Uninsured - Insured) / Insured |
insolvency_1 |
Equity-based coverage (s=0.5) | (Total assets - Total Liability - s×Uninsured×(Total assets/MV Asset) -1)) / Total assets |
insolvency_2 |
Equity-based coverage (s=0.5) | (Total assets - Total Liability - s×Uninsured×(Total assets/MV Asset) -1)) / Total assets |
15.1.3 Control Variables
| Variable | Description |
|---|---|
log_assets |
Log(Total assets) |
pct_wholesale_liability |
(Fed funds + Repo + Other borrowed < 1 year) / Liabilities (%) |
pct_liquidity_available |
(Cash + Reverse repo + Fed funds sold) / Assets (%) |
securities_ratio |
Total securities / Assets (%) |
loan_to_deposit |
Total loans / Total deposits (%) |
book_equity_to_asset |
Book equity / Assets (%) |
roa |
Net income (annualized) / Avg assets (%) |
fhlb_to_asset |
FHLB advances / Assets (%) |
delta_fhlb |
Change in FHLB from baseline to crisis |
15.2 Model Specifications
15.2.1 Linear Probability Model (LPM)
\[P(BTFP = 1 | X) = X'\beta + \epsilon\]
15.2.2 Logit Model
\[P(BTFP = 1 | X) = \frac{e^{X'\beta}}{1 + e^{X'\beta}}\]
15.2.3 Multinomial Logit
\[P(Y = j | X) = \frac{e^{X'\beta_j}}{\sum_{k=0}^{3} e^{X'\beta_k}}\]
Base category: No participation (\(\beta_0 = 0\))
15.2.4 Trivariate Probit
Latent variables: \[BTFP^* = X'\beta_1 + \epsilon_1\] \[DW^* = X'\beta_2 + \epsilon_2\] \[FHLB^* = X'\beta_3 + \epsilon_3\]
Error correlation: \((\epsilon_1, \epsilon_2, \epsilon_3)' \sim N(0, \Sigma)\)
15.3 Sample Selection
- Baseline: 2022Q4 call reports
- Exclude: G-SIB banks, failed banks
- Require: omo_eligible > 0 (BTFP-eligible collateral)
- Crisis period: March 13 - April 30, 2023
End of Analysis