Summary

This analysis examines bank borrowing behavior across Federal Reserve emergency facilities (BTFP and Discount Window) during the March 2023 banking crisis. We exploit the institutional differences between facilities – particularly BTFP’s par valuation of eligible collateral – to test whether banks strategically selected facilities based on balance sheet vulnerabilities.

Research Questions

Extensive Margin: Did BTFP’s par valuation generate systematic selection, with banks sorting into facilities based on MTM losses?
Temporal Dynamics: Did borrowing determinants differ across crisis phases (acute crisis vs. post-acute vs. arbitrage)?
Intensive Margin: Conditional on borrowing, did banks with larger MTM losses borrow more?
Collateral Constraints: Did banks “max out” BTFP-eligible collateral and turn to DW for additional needs?

Empirical Strategy Overview

Step	Analysis	Question Answered
1	Extensive margin (full period)	Did MTM losses drive BTFP selection?
2	Temporal analysis	Did determinants differ across phases?
3	Intensive margin	Did distressed banks borrow more?
4	“Both” banks	Did collateral constraints bind?

Variable Definitions

Dependent Variables

Variable	Definition	Formula
BTFP_i	Binary: Bank i borrowed from BTFP	1[Bank i borrowed from BTFP]
DW_i	Binary: Bank i borrowed from DW	1[Bank i borrowed from DW]
BTFPAmount_i	BTFP borrowing scaled by assets	BTFP Borrowing_i / Assets_i
BTFP_Acute_i	First BTFP borrow <= May 1, 2023	1[First BTFP date <= May 1]
BTFP_PostAcute_i	First BTFP borrow in (May 1, Oct 31]	1[First BTFP date in (May 1, Oct 31]]
BTFP_Arb_i	First BTFP borrow in (Nov 1, Jan 24]	1[First BTFP date in (Nov 1, Jan 24]]

Key Explanatory Variables

Variable	Definition	Formula
MTM_BTFP_i	MTM loss on BTFP-eligible securities / Assets	MTM Loss on OMO-Eligible_i / Total Assets_i
MTM_Other_i	MTM loss on non-eligible assets / Assets	MTM Loss on Non-OMO_i / Total Assets_i
UninsuredLev_i	Uninsured deposits / Assets	Uninsured Deposits_i / Total Assets_i
EligibleCollateral_i	BTFP-eligible securities / Assets	OMO-Eligible Securities_i / Total Assets_i
BorrowingSubsidy_i	MTM loss rate on eligible collateral	MTM Loss on OMO-Eligible_i / OMO-Eligible_i

Run Risk Measures

Variable	Definition	Formula
RunRisk1_i	Continuous: Uninsured x MTM	%Uninsured_i x %MTM Loss_i
RunRisk2_i	Continuous: Runable x MTM	%Runable_i x %MTM Loss_i
RunRisk1Dummy_i	Binary: Both above median	1[%Uninsured > p50 AND %MTM > p50]
RunRisk2Dummy_i	Binary: Both above median	1[%Runable > p50 AND %MTM > p50]

Jiang et al. Insolvency Measures

Insured Deposit Coverage Ratio (IDCR)

IDCR_i(s) = (MV_Assets_i - s x UninsuredDeposits_i - InsuredDeposits_i) / InsuredDeposits_i

where s in {0.5, 1.0} represents the fraction of uninsured deposits that run.

Variable	Run Scenario	Interpretation
IDCR_1	s = 0.5 (50% run)	Coverage ratio under moderate run
IDCR_2	s = 1.0 (100% run)	Coverage ratio under complete run

Insolvency: Bank is insolvent if IDCR < 0

Capital Ratio Metric

Insolvency_i(s) = [(TotalAssets_i - TotalLiabilities_i) - s x UninsuredDeposits_i x MV_Adjustment_i] / TotalAssets_i

where: MV_Adjustment_i = (TotalAssets_i / MV_Assets_i) - 1

Variable	Run Scenario	Interpretation
Insolvency_1	s = 0.5	Capital metric under 50% run
Insolvency_2	s = 1.0	Capital metric under 100% run

Adjusted Equity (Jiang-Style)

AdjustedEquity_i = EquityRatio_i - MTMLoss_i

MTM_Insolvent_i = 1[AdjustedEquity_i < 0]

Control Variables

Variable	Definition	Formula
ln_assets	Log of total assets	ln(Total Assets_i)
cash_ratio	Cash / Assets	Cash_i / Total Assets_i
securities_ratio	Securities / Assets	Securities_i / Total Assets_i
roa	Return on assets	Net Income_i / Avg Assets_i
loan_to_deposit	Loans / Deposits	Total Loans_i / Total Deposits_i
book_equity_ratio	Book equity / Assets	Total Equity_i / Total Assets_i
pct_wholesale_liability	Wholesale funding / Liabilities	(Fed Funds + Repo + Other Borr)_i / Total Liabilities_i
pct_runable_liability	Runable liabilities / Liabilities	(Uninsured + Wholesale)_i / Total Liabilities_i
pct_liquidity_available	Liquid assets / Assets	(Cash + Rerepo + FF Sold)_i / Total Assets_i
fhlb_ratio	FHLB advances / Assets	FHLB Advances_i / Total Assets_i

Facility Choice Variables

Variable	Definition
btfp	Binary: Used BTFP during full program
dw	Binary: Used DW during full program (post-BTFP)
dw_pre_btfp	Binary: Used DW in pre-BTFP period (Jan 1 - Mar 12, 2023)
both	Binary: Used both BTFP and DW
btfp_only	Binary: Used BTFP but not DW
dw_only	Binary: Used DW but not BTFP
any_fed	Binary: Used either facility
facility	Categorical: None / BTFP Only / DW Only / Both

Period-Specific Variables

Variable	Period	Date Range
btfp_acute / dw_acute	Acute Crisis	Mar 13 - May 1, 2023
btfp_post / dw_post	Post-Acute	May 2 - Oct 31, 2023
btfp_arb / dw_arb	Arbitrage	Nov 1, 2023 - Jan 24, 2024
dw_pre	Pre-BTFP (Baseline)	Jan 1 - Mar 12, 2023

Intensive Margin Variables

Variable	Definition	Formula
btfp_amount_pct	BTFP borrowing as % of assets	(BTFP Amount / Assets) x 100
dw_amount_pct	DW borrowing as % of assets	(DW Amount / Assets) x 100
total_borrowed_pct	Total Fed borrowing as % of assets	(BTFP + DW Amount) / Assets x 100
btfp_share	BTFP share of total Fed borrowing	BTFP Amount / (BTFP + DW) x 100
btfp_utilization	Collateral utilization rate	BTFP Amount / Collateral Capacity
maxed_out_btfp	Binary: Utilization > 90%	1[btfp_utilization > 0.90]

Step 1: Extensive Margin (Full Period)

\[BTFP_i = \alpha + \beta_1 \cdot MTM^{BTFP}_i + \beta_2 \cdot MTM^{Other}_i + \beta_3 \cdot UninsuredLev_i + \beta_4 \cdot (MTM^{BTFP}_i \times UninsuredLev_i) + \beta_5 \cdot EligibleCollateral_i + \gamma'Z_i + \varepsilon_i\]

Run separately for BTFP and DW as dependent variables.

Step 2: Temporal Analysis

For each period $p \in \{Acute, PostAcute, Arbitrage\}$:

\[BTFP^p_i = \alpha + \beta^p_1 \cdot MTM^{BTFP}_i + \beta^p_2 \cdot MTM^{Other}_i + \beta^p_3 \cdot UninsuredLev_i + \gamma'Z_i + \varepsilon_i\]

Step 3: Intensive Margin

Among BTFP users:

\[\frac{BTFPAmount_i}{Assets_i} = \alpha + \beta_1 \cdot MTM^{BTFP}_i + \beta_2 \cdot MTM^{Other}_i + \beta_3 \cdot UninsuredLev_i + \gamma'Z_i + \varepsilon_i\]

Step 4: Both Banks and Collateral Constraints

\[DW_i = \alpha + \beta_1 \cdot MTM^{BTFP}_i + \beta_2 \cdot MTM^{Other}_i + \beta_3 \cdot EligibleCollateral_i + \gamma'Z_i + \varepsilon_i \quad | \quad BTFP_i = 1\]

# SETUP AND PACKAGES

BASE_PATH <- "C:/Users/mohua/OneDrive - Louisiana State University/Finance_PhD/DW_Stigma_paper/Liquidity_project_2025"
knitr::opts_knit$set(root.dir = BASE_PATH)

options(repos = c(CRAN = "https://cloud.r-project.org"))
options(scipen = 999)
set.seed(20230313)

required_packages <- c(
  "data.table", "dplyr", "tidyr", "tibble", "lubridate", "stringr", "readr",

"fixest", "sandwich", "lmtest", "broom",
  "ggplot2", "ggthemes", "scales", "patchwork", "gridExtra",
  "knitr", "kableExtra", "modelsummary", "htmltools", "fastmap",
  "bslib", "sass", "jquerylib", "rlang",
  "DescTools", "moments", "psych"
)

check_and_install <- function(pkg, min_version = NULL) {
  needs_install <- FALSE
  if (!requireNamespace(pkg, quietly = TRUE)) {
    needs_install <- TRUE
  } else if (!is.null(min_version)) {
    if (packageVersion(pkg) < min_version) {
      needs_install <- TRUE
    }
  }
  if (needs_install) {
    message(paste("Installing/Updating", pkg))
    tryCatch(
      install.packages(pkg, quiet = TRUE),
      error = function(e) warning(paste("Could not install", pkg))
    )
  }
}

check_and_install("fastmap", "1.2.0")
check_and_install("htmltools", "0.5.8")
check_and_install("bslib")

missing <- required_packages[!required_packages %in% installed.packages()[,"Package"]]
if(length(missing) > 0) install.packages(missing)

suppressPackageStartupMessages({
  library(data.table)
  library(dplyr)
  library(tidyr)
  library(tibble)
  library(lubridate)
  library(stringr)
  library(readr)
  library(fixest)
  library(sandwich)
  library(lmtest)
  library(broom)
  library(ggplot2)
  library(ggthemes)
  library(scales)
  library(patchwork)
  library(gridExtra)
  library(knitr)
  library(kableExtra)
  library(modelsummary)
  library(DescTools)
  library(moments)
  library(psych)
  library(tidyverse)
})

theme_journal <- function(base_size = 12) {
  theme_classic(base_size = base_size) +
    theme(
      plot.title = element_text(face = "bold"),
      legend.position = "bottom",
      panel.grid = element_blank()
    )
}

# CONFIGURE PATHS

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/btfp_analysis_new")
FIG_PATH    <- file.path(DOC_PATH, "figures/btfp_analysis_new")

dir.create(TABLE_PATH, recursive = TRUE, showWarnings = FALSE)
dir.create(FIG_PATH, recursive = TRUE, showWarnings = FALSE)

Crisis Timeline

# CRISIS PARAMETERS

CRISIS_START      <- as.Date("2023-03-13")
SVB_FAIL          <- as.Date("2023-03-10")
FRC_FAIL          <- as.Date("2023-05-01")
DW_HAIRCUT_RETURN <- as.Date("2023-10-31")
ARB_OPEN          <- as.Date("2023-11-06")
ARB_CLOSE         <- as.Date("2024-01-24")
BTFP_CLOSE        <- as.Date("2024-03-11")

PRE_BTFP_START    <- as.Date("2023-01-01")
PRE_BTFP_END      <- as.Date("2023-03-12")
PERIOD_1_END      <- as.Date("2023-05-01")
PERIOD_2_END      <- as.Date("2023-10-31")
PERIOD_3_END      <- as.Date("2024-01-24")

BASELINE_DATE     <- "2022Q4"

cat("================================================================\n")

#> ================================================================

cat("CRISIS TIMELINE\n")

#> CRISIS TIMELINE

cat("================================================================\n")

#> ================================================================

cat("Pre-BTFP (DW Only):    Jan 1 - Mar 12, 2023\n")

#> Pre-BTFP (DW Only):    Jan 1 - Mar 12, 2023

cat("Period 1 (Acute):      Mar 13 - May 1, 2023\n")

#> Period 1 (Acute):      Mar 13 - May 1, 2023

cat("Period 2 (Post-Acute): May 2 - Oct 31, 2023\n")

#> Period 2 (Post-Acute): May 2 - Oct 31, 2023

cat("Period 3 (Arbitrage):  Nov 1 - Jan 24, 2024\n")

#> Period 3 (Arbitrage):  Nov 1 - Jan 24, 2024

cat("================================================================\n")

#> ================================================================

Helper Functions

# HELPER FUNCTIONS

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])
}

safe_div <- function(num, denom) {
  ifelse(is.na(denom) | denom == 0, NA_real_, num / denom)
}

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)
}

theme_pub <- function(base_size = 11) {
  theme_minimal(base_size = base_size) +
    theme(
      plot.title = element_text(face = "bold", size = rel(1.2), hjust = 0),
      plot.subtitle = element_text(size = rel(0.9), hjust = 0, color = "gray40"),
      plot.caption = element_text(size = rel(0.7), hjust = 1, color = "gray50"),
      panel.grid.minor = element_blank(),
      panel.grid.major = element_line(color = "gray90", linewidth = 0.3),
      axis.title = element_text(face = "bold", size = rel(0.9)),
      legend.position = "bottom",
      strip.text = element_text(face = "bold"),
      plot.margin = margin(10, 10, 10, 10)
    )
}

crisis_colors <- c("Pre-BTFP" = "#636363", "Acute" = "#d73027",
                   "Post-Acute" = "#fc8d59", "Arbitrage" = "#4575b4")
facility_colors <- c("BTFP" = "#2166ac", "DW" = "#b2182b", "Both" = "#762a83", "None" = "#d9d9d9")

Data Loading

Load Data

# LOAD DATA

cat("\n=== LOADING DATA ===\n")

#> 
#> === LOADING 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:", nrow(call_q), "obs\n")

#> Call reports: 61002 obs

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),
    btfp_maturity_date = parse_date_safe(btfp_maturity_date),
    btfp_repayment_date = parse_date_safe(btfp_repayment_date)
  )
cat("BTFP loans:", nrow(btfp_raw), "records\n")

#> BTFP loans: 6734 records

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),
    dw_maturity_date = parse_date_safe(dw_maturity_date),
    dw_repayment_date = parse_date_safe(dw_repayment_date)
  )
cat("DW loans:", nrow(dw_raw), "records\n")

#> DW loans: 20219 records

Assign Periods

# ASSIGN CRISIS PERIODS

assign_period <- function(date) {
  case_when(
    date >= PRE_BTFP_START & date <= PRE_BTFP_END ~ "Pre-BTFP",
    date >= CRISIS_START & date <= PERIOD_1_END ~ "Acute",
    date > PERIOD_1_END & date <= PERIOD_2_END ~ "Post-Acute",
    date > PERIOD_2_END & date <= PERIOD_3_END ~ "Arbitrage",
    TRUE ~ NA_character_
  )
}

btfp_loans <- btfp_raw %>%
  mutate(
    period = assign_period(btfp_loan_date),
    period = factor(period, levels = c("Pre-BTFP", "Acute", "Post-Acute", "Arbitrage"))
  ) %>%
  filter(!is.na(period))

dw_loans <- dw_raw %>%
  mutate(
    period = assign_period(dw_loan_date),
    period = factor(period, levels = c("Pre-BTFP", "Acute", "Post-Acute", "Arbitrage"))
  ) %>%
  filter(!is.na(period))

cat("\nLoans by period:\n")

#> 
#> Loans by period:

cat("BTFP:", table(btfp_loans$period), "\n")

#> BTFP: 0 1087 1972 3279

cat("DW:", table(dw_loans$period), "\n")

#> DW: 1871 1619 4237 0

Loan-Level Summary Tables

Table 1: Loan Characteristics by Period

Total ($B) represents the sum for amounts; ‘Cumulative’ row shows issuance to date. Mean, Median, Min, and Max statistics are reported in $Millions for monetary variables. Data includes observations up to September 30.

library(tidyverse)
library(lubridate)
library(kableExtra)

# --- 1. PRE-CALCULATION ---
dw_loans <- dw_loans %>%
  arrange(dw_loan_date) %>%
  mutate(dw_cumulative_global = cumsum(dw_loan_amount))

btfp_loans <- btfp_loans %>%
  arrange(btfp_loan_date) %>%
  mutate(btfp_cumulative_global = cumsum(btfp_loan_amount))

# --- 2. CONFIGURATION ---
# IMPORTANT: Avoid $ signs - they break HTML rendering
vars_dw <- list(
  "dw_loan_amount"      = "Loan Amount (Millions)",
  "dw_interest_rate"    = "Interest Rate (%)",
  "dw_term"             = "Term (Days)",
  "dw_total_collateral" = "Collateral Pledged (Millions)",
  "utilization"         = "Utilization (%)",
  "pct_omo"             = "BTFP Eligible Share (%)"
)

vars_btfp <- list(
  "btfp_loan_amount"      = "Loan Amount (Millions)",
  "btfp_interest_rate"    = "Interest Rate (%)",
  "btfp_term"             = "Term (Days)",
  "btfp_total_collateral" = "Collateral Pledged (Millions)",
  "utilization"           = "Utilization (%)",
  "pct_tsy"               = "Treasury Share (%)"
)

# --- 3. HELPER FUNCTION ---
get_period_stats <- function(data, period_name, var_list, facility_type = "DW") {
  
  df_period <- data %>% filter(period == period_name)
  n_banks <- n_distinct(df_period$rssd_id)
  
  cum_col <- if(facility_type == "DW") "dw_cumulative_global" else "btfp_cumulative_global"
  cum_val <- max(df_period[[cum_col]], na.rm = TRUE) / 1e9
  
  row_unique <- tibble(
    Variable = "Unique Borrowers (Count)",
    N = n_banks, Total_B = NA, Mean = NA, Median = NA, SD = NA, Min = NA, Max = NA
  )
  
  row_cumulative <- tibble(
    Variable = "Cumulative Issuance (Billions)",
    N = NA, Total_B = cum_val, Mean = NA, Median = NA, SD = NA, Min = NA, Max = NA
  )
  
  stats_rows <- map_dfr(names(var_list), function(v_col) {
    vals <- df_period[[v_col]]
    is_money <- str_detect(v_col, "amount|collateral")
    total_val <- if(is_money) sum(vals, na.rm = TRUE) / 1e9 else NA
    calc_vals <- if(is_money) vals / 1e6 else vals
    
    tibble(
      Variable = var_list[[v_col]],
      N      = sum(!is.na(vals)),
      Total_B = total_val,
      Mean   = mean(calc_vals, na.rm = TRUE),
      Median = median(calc_vals, na.rm = TRUE),
      SD     = sd(calc_vals, na.rm = TRUE),
      Min    = min(calc_vals, na.rm = TRUE),
      Max    = max(calc_vals, na.rm = TRUE)
    )
  })
  
  bind_rows(row_unique, row_cumulative, stats_rows)
}

# --- 4. PREPARE DATA ---
dw_ready <- dw_loans %>%
  mutate(
    utilization = (dw_loan_amount / dw_total_collateral) * 100,
    pct_omo = (dw_omo_eligible / dw_total_collateral) * 100
  )

btfp_ready <- btfp_loans %>%
  mutate(
    utilization = (btfp_loan_amount / btfp_total_collateral) * 100,
    pct_tsy = (btfp_treasury_sec / btfp_total_collateral) * 100
  )

# --- 5. GENERATE TABLE 1 (DW) ---
d1 <- get_period_stats(dw_ready, "Pre-BTFP", vars_dw, "DW")
d2 <- get_period_stats(dw_ready, "Acute", vars_dw, "DW")
d3 <- get_period_stats(dw_ready, "Post-Acute", vars_dw, "DW")
d4 <- get_period_stats(dw_ready, "Arbitrage", vars_dw, "DW")

tab1_data <- bind_rows(d1, d2, d3, d4)

kbl(tab1_data, 
    format = "html",
    caption = "Table 1: Discount Window (DW) Detailed Statistics by Period",
    digits = 2,
    col.names = c("Variable", "N", "Total (B)", "Mean", "Median", "SD", "Min", "Max"),
    escape = FALSE) %>%
  kable_styling(
    bootstrap_options = c("striped", "hover", "condensed"),
    full_width = FALSE
  ) %>%
  pack_rows("Panel A: Pre-BTFP", 1, nrow(d1)) %>%
  pack_rows("Panel B: Acute Crisis", nrow(d1) + 1, nrow(d1) + nrow(d2)) %>%
  pack_rows("Panel C: Post-Acute", nrow(d1) + nrow(d2) + 1, nrow(d1) + nrow(d2) + nrow(d3)) %>%
  pack_rows("Panel D: Arbitrage Period", nrow(tab1_data) - nrow(d4) + 1, nrow(tab1_data))

Table 1: Discount Window (DW) Detailed Statistics by Period
Variable	N	Total (B)	Mean	Median	SD	Min	Max
Panel A: Pre-BTFP
Unique Borrowers (Count)	292	NA	NA	NA	NA	NA	NA
Cumulative Issuance (Billions)	NA	123.59	NA	NA	NA	NA	NA
Loan Amount (Millions)	1871	123.59	66.06	12.40	585.43	0.00	20377.61
Interest Rate (%)	1871	NA	4.63	4.75	0.13	4.50	4.75
Term (Days)	1871	NA	4.54	1.00	11.98	1.00	90.00
Collateral Pledged (Millions)	1871	892.23	476.87	85.79	6322.08	0.01	268687.26
Utilization (%)	1871	NA	23.95	14.98	23.75	0.00	100.00
BTFP Eligible Share (%)	1871	NA	32.64	0.00	45.69	0.00	100.00
Panel B: Acute Crisis
Unique Borrowers (Count)	424	NA	NA	NA	NA	NA	NA
Cumulative Issuance (Billions)	NA	3257.07	NA	NA	NA	NA	NA
Loan Amount (Millions)	1619	3133.48	1935.44	10.00	12075.23	0.00	127500.00
Interest Rate (%)	1619	NA	4.92	5.00	0.12	4.75	5.00
Term (Days)	1619	NA	4.51	1.00	12.73	1.00	91.00
Collateral Pledged (Millions)	1619	4745.72	2931.27	81.90	15706.74	0.00	272872.11
Utilization (%)	1619	NA	28.78	17.78	30.12	0.00	242.97
BTFP Eligible Share (%)	1619	NA	36.74	0.00	46.28	0.00	100.00
Panel C: Post-Acute
Unique Borrowers (Count)	846	NA	NA	NA	NA	NA	NA
Cumulative Issuance (Billions)	NA	3368.62	NA	NA	NA	NA	NA
Loan Amount (Millions)	4237	111.55	26.33	5.40	99.01	0.00	5600.00
Interest Rate (%)	4237	NA	5.35	5.25	0.13	4.95	6.00
Term (Days)	4237	NA	5.44	1.00	13.58	1.00	92.00
Collateral Pledged (Millions)	4237	2457.74	580.07	59.93	7515.33	0.00	309683.66
Utilization (%)	4237	NA	22.57	14.39	23.61	0.00	100.00
BTFP Eligible Share (%)	4237	NA	34.35	0.00	45.70	0.00	100.00
Panel D: Arbitrage Period
Unique Borrowers (Count)	0	NA	NA	NA	NA	NA	NA
Cumulative Issuance (Billions)	NA	-Inf	NA	NA	NA	NA	NA
Loan Amount (Millions)	0	0.00	NaN	NA	NA	Inf	-Inf
Interest Rate (%)	0	NA	NaN	NA	NA	Inf	-Inf
Term (Days)	0	NA	NaN	NA	NA	Inf	-Inf
Collateral Pledged (Millions)	0	0.00	NaN	NA	NA	Inf	-Inf
Utilization (%)	0	NA	NaN	NA	NA	Inf	-Inf
BTFP Eligible Share (%)	0	NA	NaN	NA	NA	Inf	-Inf

# BTFP Table
b1 <- get_period_stats(btfp_ready, "Acute", vars_btfp, "BTFP")
b2 <- get_period_stats(btfp_ready, "Post-Acute", vars_btfp, "BTFP")
b3 <- get_period_stats(btfp_ready, "Arbitrage", vars_btfp, "BTFP")

tab2_data <- bind_rows(b1, b2, b3)

kbl(tab2_data, 
    format = "html",
    caption = "Table 2: BTFP Detailed Statistics by Period",
    digits = 2,
    col.names = c("Variable", "N", "Total (B)", "Mean", "Median", "SD", "Min", "Max")) %>%
  kable_styling(
    bootstrap_options = c("striped", "hover", "condensed"),
    full_width = FALSE
  ) %>%
  pack_rows("Panel A: Acute Crisis", 1, nrow(b1)) %>%
  pack_rows("Panel B: Post-Acute", nrow(b1) + 1, nrow(b1) + nrow(b2)) %>%
  pack_rows("Panel C: Arbitrage Period", nrow(tab2_data) - nrow(b3) + 1, nrow(tab2_data))

Table 2: BTFP Detailed Statistics by Period
Variable	N	Total (B)	Mean	Median	SD	Min	Max
Panel A: Acute Crisis
Unique Borrowers (Count)	492	NA	NA	NA	NA	NA	NA
Cumulative Issuance (Billions)	NA	145.33	NA	NA	NA	NA	NA
Loan Amount (Millions)	1087	145.33	133.70	14.00	658.38	0.00	8900.00
Interest Rate (%)	1087	NA	4.69	4.70	0.20	4.37	5.03
Term (Days)	1087	NA	311.66	365.00	125.27	1.00	369.00
Collateral Pledged (Millions)	1087	390.33	359.09	34.00	1626.91	0.01	17598.44
Utilization (%)	1087	NA	52.45	49.78	35.05	0.00	100.00
Treasury Share (%)	1087	NA	25.43	0.00	38.15	0.00	100.00
Panel B: Post-Acute
Unique Borrowers (Count)	816	NA	NA	NA	NA	NA	NA
Cumulative Issuance (Billions)	NA	196.71	NA	NA	NA	NA	NA
Loan Amount (Millions)	1972	51.38	26.06	5.00	103.68	0.00	3500.00
Interest Rate (%)	1972	NA	5.20	5.35	0.31	4.37	5.59
Term (Days)	1972	NA	272.37	365.00	154.72	1.00	369.00
Collateral Pledged (Millions)	1972	556.95	282.43	26.11	2763.23	0.00	53797.57
Utilization (%)	1972	NA	34.72	22.72	32.35	0.00	100.00
Treasury Share (%)	1972	NA	24.08	0.00	36.61	0.00	100.00
Panel C: Arbitrage Period
Unique Borrowers (Count)	801	NA	NA	NA	NA	NA	NA
Cumulative Issuance (Billions)	NA	426.52	NA	NA	NA	NA	NA
Loan Amount (Millions)	3279	229.81	70.09	15.00	259.09	0.00	3900.00
Interest Rate (%)	3279	NA	4.97	4.89	0.19	4.76	5.49
Term (Days)	3279	NA	334.63	365.00	97.12	1.00	369.00
Collateral Pledged (Millions)	3279	744.68	227.11	41.10	1470.39	0.01	52925.81
Utilization (%)	3279	NA	49.62	42.81	33.64	0.00	100.00
Treasury Share (%)	3279	NA	19.79	0.00	31.43	0.00	100.00

Visualizations

Figure 1: Daily Borrowing Volume

# FIGURE 1: DAILY BORROWING VOLUME

daily_combined <- bind_rows(
  btfp_loans %>%
    group_by(d = btfp_loan_date) %>%
    summarise(v = sum(btfp_loan_amount, na.rm = TRUE), .groups = "drop") %>%
    mutate(Fac = "BTFP"),
  dw_loans %>%
    group_by(d = dw_loan_date) %>%
    summarise(v = sum(dw_loan_amount, na.rm = TRUE), .groups = "drop") %>%
    mutate(Fac = "DW")
)

p1 <- ggplot(daily_combined, aes(x = d, y = v / 1e9, color = Fac)) +
  geom_line(linewidth = 0.8) +
  scale_color_manual(values = c("BTFP" = "#2b8cbe", "DW" = "#e34a33")) +
  labs(
    title = "Figure 1: Daily Borrowing Volume",
    subtitle = "Discount Window spikes early; BTFP builds gradually",
    y = "Volume ($ Billions)",
    x = NULL,
    color = NULL
  ) +
  theme_journal() +
  theme(legend.position = c(0.8, 0.8))

print(p1)

btfp_daily <- btfp_loans %>%
  group_by(btfp_loan_date) %>%
  summarise(volume = sum(btfp_loan_amount, na.rm = TRUE) / 1e9, .groups = "drop") %>%
  mutate(facility = "BTFP") %>%
  rename(date = btfp_loan_date)

dw_daily <- dw_loans %>%
  group_by(dw_loan_date) %>%
  summarise(volume = sum(dw_loan_amount, na.rm = TRUE) / 1e9, .groups = "drop") %>%
  mutate(facility = "DW") %>%
  rename(date = dw_loan_date)

daily_combined <- bind_rows(btfp_daily, dw_daily)

Figure 2: Cumulative Borrowing

# FIGURE 2: CUMULATIVE BORROWING

btfp_cumul <- btfp_daily %>% arrange(date) %>% mutate(cumulative = cumsum(volume))
dw_cumul <- dw_daily %>% arrange(date) %>% mutate(cumulative = cumsum(volume))
cumul_combined <- bind_rows(btfp_cumul, dw_cumul)

p2 <- ggplot(cumul_combined, aes(x = date, y = cumulative, color = facility)) +
  geom_line(linewidth = 1.2) +
  geom_vline(xintercept = c(SVB_FAIL, FRC_FAIL, ARB_OPEN),
             linetype = "dashed", color = "gray50", linewidth = 0.5) +
  scale_color_manual(values = facility_colors, name = "Facility") +
  scale_x_date(date_breaks = "1 month", date_labels = "%b\n%Y") +
  scale_y_continuous(labels = scales::dollar_format(suffix = "B")) +
  labs(
    title = "Figure 2: Cumulative Emergency Lending",
    x = NULL,
    y = "Cumulative ($B)"
  ) +
  theme_pub()

print(p2)

Figure 3: Interest Rate Evolution

# FIGURE 3: INTEREST RATES

btfp_weekly <- btfp_loans %>%
  mutate(week = floor_date(btfp_loan_date, "week")) %>%
  group_by(week) %>%
  summarise(
    rate = weighted.mean(btfp_interest_rate, btfp_loan_amount, na.rm = TRUE),
    n = n(),
    .groups = "drop"
  ) %>%
  mutate(facility = "BTFP")

dw_weekly <- dw_loans %>%
  mutate(week = floor_date(dw_loan_date, "week")) %>%
  group_by(week) %>%
  summarise(
    rate = weighted.mean(dw_interest_rate, dw_loan_amount, na.rm = TRUE),
    n = n(),
    .groups = "drop"
  ) %>%
  mutate(facility = "DW")

weekly_rates <- bind_rows(btfp_weekly, dw_weekly)

p3 <- ggplot(weekly_rates, aes(x = week, y = rate, color = facility)) +
  geom_line(linewidth = 1) +
  geom_point(aes(size = n), alpha = 0.5) +
  annotate("rect", xmin = ARB_OPEN, xmax = ARB_CLOSE,
           ymin = -Inf, ymax = Inf, fill = "blue", alpha = 0.1) +
  scale_color_manual(values = facility_colors, name = "Facility") +
  scale_size_continuous(name = "N Loans", range = c(1, 4)) +
  scale_x_date(date_breaks = "1 month", date_labels = "%b\n%Y") +
  scale_y_continuous(labels = scales::percent_format(scale = 1)) +
  labs(
    title = "Figure 3: Weekly Average Interest Rates",
    subtitle = "Blue shading = Arbitrage window (BTFP rate < IORB)",
    x = NULL,
    y = "Interest Rate (%)"
  ) +
  theme_pub()

print(p3)

Figure 4: Term Distribution

# FIGURE 4: TERM DISTRIBUTION

all_loans <- bind_rows(
  btfp_loans %>%
    filter(period %in% c("Acute", "Post-Acute", "Arbitrage")) %>%
    transmute(period, facility = "BTFP", term = btfp_term),
  dw_loans %>%
    filter(period %in% c("Acute", "Post-Acute", "Arbitrage")) %>%
    transmute(period, facility = "DW", term = dw_term)
)

p4 <- ggplot(all_loans, aes(x = term, fill = facility)) +
  geom_histogram(alpha = 0.6, position = "identity", bins = 40) +
  facet_wrap(~period, ncol = 3, scales = "free_y") +
  scale_fill_manual(values = facility_colors, name = "Facility") +
  scale_x_continuous(limits = c(0, 400)) +
  labs(
    title = "Figure 4: Loan Term Distribution",
    subtitle = "BTFP offers 1-year terms (365 days); DW terms typically shorter",
    x = "Term (Days)",
    y = "Count"
  ) +
  theme_pub()

print(p4)

Figure 5: DW Collateral Composition

# FIGURE 5: DW COLLATERAL COMPOSITION OVER TIME

dw_monthly_collat <- dw_loans %>%
  mutate(month = floor_date(dw_loan_date, "month")) %>%
  group_by(month) %>%
  summarise(
    `BTFP-eligible`    = sum(dw_omo_eligible, na.rm = TRUE) / 1e9,
    `DW eligible only` = sum(dw_non_omo_eligible, na.rm = TRUE) / 1e9,
    .groups = "drop"
  ) %>%
  pivot_longer(
    cols = c(`BTFP-eligible`, `DW eligible only`),
    names_to = "type",
    values_to = "value"
  )

p5_levels <- ggplot(dw_monthly_collat, aes(month, value, color = type)) +
  geom_line(linewidth = 1) +
  geom_vline(xintercept = c(CRISIS_START, FRC_FAIL, ARB_OPEN),
             linetype = "dashed", color = "gray40", linewidth = 0.4) +
  scale_color_manual(values = c(`BTFP-eligible` = "#4575b4",
                                `DW eligible only` = "#d73027")) +
  scale_x_date(date_breaks = "2 months", date_labels = "%b\n%Y") +
  scale_y_continuous(labels = scales::dollar_format(suffix = "B")) +
  labs(
    title = "Figure 5: DW Collateral Amounts Over Time",
    subtitle = "BTFP-eligible vs. DW-only eligible collateral posted at the Discount Window",
    x = NULL,
    y = "Collateral ($B)",
    color = "Collateral Type"
  ) +
  theme_classic(base_size = 11) +
  theme(legend.position = "bottom")

print(p5_levels)

# FIGURE 6: EFFECTIVE MATURITY VS CONTRACTUAL TERM

btfp_mat <- btfp_loans %>%
  filter(period %in% c("Acute", "Post-Acute", "Arbitrage")) %>%
  transmute(
    period,
    facility = "BTFP",
    term = btfp_term,
    eff_mat = btfp_effective_maturity_days
  )

dw_mat <- dw_loans %>%
  filter(period %in% c("Acute", "Post-Acute", "Arbitrage")) %>%
  transmute(
    period,
    facility = "DW",
    term = dw_term,
    eff_mat = dw_effective_maturity_days
  )

mat_data <- bind_rows(btfp_mat, dw_mat) %>%
  mutate(early_repay = term - eff_mat)

p6b <- ggplot(mat_data, aes(x = term, y = term - eff_mat, color = facility)) +
  geom_hline(yintercept = 0, linetype = "dashed", color = "gray50") +
  geom_point(alpha = 0.3, size = 1) +
  facet_wrap(~period, ncol = 3) +
  scale_color_manual(values = facility_colors, name = "Facility") +
  labs(
    title = "Figure 6: Early Repayment by Contractual Term",
    subtitle = "0 = held to term; higher = repaid earlier",
    x = "Contractual Term (Days)",
    y = "Days Repaid Early"
  ) +
  theme_classic(base_size = 11)

print(p6b)

Bank-Level Analysis Dataset Construction

# AGGREGATE FULL PROGRAM FACILITY USAGE

btfp_full <- btfp_raw %>%
  filter(btfp_loan_date >= CRISIS_START, btfp_loan_date <= BTFP_CLOSE) %>%
  group_by(rssd_id) %>%
  summarise(
    btfp = 1L,
    btfp_amount = sum(btfp_loan_amount, na.rm = TRUE),
    btfp_first_date = min(btfp_loan_date),
    btfp_n_loans = n(),
    .groups = "drop"
  ) %>%
  rename(idrssd = rssd_id)

dw_full <- dw_raw %>%
  filter(dw_loan_date >= CRISIS_START, dw_loan_date <= BTFP_CLOSE) %>%
  group_by(rssd_id) %>%
  summarise(
    dw = 1L,
    dw_amount = sum(dw_loan_amount, na.rm = TRUE),
    dw_first_date = min(dw_loan_date),
    dw_n_loans = n(),
    .groups = "drop"
  ) %>%
  rename(idrssd = rssd_id)

dw_pre_btfp <- dw_raw %>%
  filter(dw_loan_date >= PRE_BTFP_START, dw_loan_date <= PRE_BTFP_END) %>%
  group_by(rssd_id) %>%
  summarise(
    dw_pre_btfp = 1L,
    dw_pre_btfp_amount = sum(dw_loan_amount, na.rm = TRUE),
    dw_pre_btfp_first = min(dw_loan_date),
    dw_pre_btfp_n = n(),
    .groups = "drop"
  ) %>%
  rename(idrssd = rssd_id)

cat("Full program usage: BTFP =", nrow(btfp_full), "banks, DW (post-BTFP) =", nrow(dw_full), "banks\n")

#> Full program usage: BTFP = 1327 banks, DW (post-BTFP) = 1092 banks

cat("Pre-BTFP DW usage:", nrow(dw_pre_btfp), "banks\n")

#> Pre-BTFP DW usage: 292 banks

# CREATE 2022Q4 BASELINE

has_failed_bank <- "failed_bank" %in% names(call_q)
has_gsib <- "gsib" %in% names(call_q)
has_mv_asset <- "mm_asset" %in% names(call_q)

baseline <- call_q %>%
  filter(quarter == BASELINE_DATE) %>%
  transmute(
    idrssd = as.character(idrssd),
    failed_bank = if (has_failed_bank) failed_bank else 0L,
    gsib = if (has_gsib) gsib else 0L,
    size_bin = if ("size_bin" %in% names(call_q)) size_bin else NA_character_,
    total_asset, total_liability, total_equity, total_deposit, uninsured_deposit_to_total_asset,
    insured_deposit = pmax(insured_deposit, 1),
    uninsured_deposit = pmax(uninsured_deposit, 0),
    ln_assets = log(pmax(total_asset, 1)),
    assets = total_asset,
    cash, fed_fund_sold, rerepo,
    security, omo_eligible, non_omo_eligible, omo_eligible_to_total_asset, non_omo_eligible_to_total_asset,
    total_loan, roa,
    mv_asset = mm_asset,
    mtm_total_loss, mtm_loss_to_total_asset, equity_after_mtm,
    mtm_loss_omo_eligible, mtm_loss_omo_eligible_to_total_asset, mtm_loss_omo_eligible_to_omo_eligible,
    mtm_loss_non_omo_eligible, mtm_loss_non_omo_eligible_to_total_asset,
    repo, fed_fund_purchase, other_borr, other_borrowed_less_than_1yr,
    fhlb_adv, fhlb_to_total_asset,
    cash_to_total_asset, security_to_total_asset, book_equity_to_total_asset, loan_to_deposit
  ) %>%
  filter(
    gsib == 0 | is.na(gsib),
    failed_bank == 0 | is.na(failed_bank),
    !is.na(omo_eligible) & omo_eligible > 0
  )

cat("Baseline sample:", nrow(baseline), "banks\n")

#> Baseline sample: 4292 banks

# CONSTRUCT ALL VARIABLES

baseline <- baseline %>%
  mutate(
    mtm_btfp = mtm_loss_omo_eligible_to_total_asset,
    mtm_other = mtm_loss_non_omo_eligible_to_total_asset,
    uninsured_lev = uninsured_deposit_to_total_asset,
    eligible_collateral = omo_eligible_to_total_asset,
    borrowing_subsidy = mtm_loss_omo_eligible_to_omo_eligible,
    pct_uninsured = safe_div(uninsured_deposit, total_deposit) * 100,
    pct_wholesale_liability = safe_div(fed_fund_purchase + repo + other_borrowed_less_than_1yr, total_liability) * 100,
    pct_runable_liability = safe_div(uninsured_deposit + fed_fund_purchase + repo + other_borrowed_less_than_1yr, total_liability) * 100,
    pct_liquidity_available = safe_div(cash + rerepo + fed_fund_sold, total_asset) * 100,
    pct_mtm_loss = mtm_loss_to_total_asset * 100,
    cash_ratio = cash_to_total_asset,
    securities_ratio = security_to_total_asset,
    equity_ratio = safe_div(total_equity, total_asset) * 100,
    book_equity_ratio = book_equity_to_total_asset,
    fhlb_ratio = fhlb_to_total_asset,
    loan_to_deposit = loan_to_deposit,
    run_risk_1 = pct_uninsured * pct_mtm_loss,
    run_risk_2 = pct_runable_liability * pct_mtm_loss
  )

baseline <- baseline %>%
  mutate(
    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 = as.integer(pct_uninsured > median_pct_uninsured & pct_mtm_loss > median_pct_mtm_loss),
    run_risk_2_dummy = as.integer(pct_runable_liability > median_pct_runable & pct_mtm_loss > median_pct_mtm_loss)
  )

# JIANG INSOLVENCY MEASURES
baseline <- baseline %>%
  mutate(
    mv_adjustment = if_else(mv_asset == 0 | is.na(mv_asset), NA_real_, (total_asset / mv_asset) - 1),
    idcr_1 = safe_div(mv_asset - 0.5 * uninsured_deposit - insured_deposit, insured_deposit),
    idcr_2 = safe_div(mv_asset - 1.0 * uninsured_deposit - insured_deposit, insured_deposit),
    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),
    adjusted_equity = equity_ratio - mtm_loss_to_total_asset,
    mtm_insolvent = as.integer(adjusted_equity < 0) * 100,
    insolvent_idcr_s50 = as.integer(idcr_1 < 0),
    insolvent_idcr_s100 = as.integer(idcr_2 < 0),
    insolvent_cap_s50 = as.integer(insolvency_1 < 0),
    insolvent_cap_s100 = as.integer(insolvency_2 < 0)
  )

baseline <- baseline %>%
  mutate(
    mtm_btfp_x_uninsured = mtm_btfp * uninsured_lev,
    adj_equity_x_uninsured = adjusted_equity * uninsured_lev
  )

cat("All variables constructed\n")

#> All variables constructed

# AGGREGATE FACILITY USAGE BY PERIOD

btfp_acute <- btfp_raw %>%
  filter(btfp_loan_date >= CRISIS_START, btfp_loan_date <= PERIOD_1_END) %>%
  group_by(rssd_id) %>%
  summarise(
    btfp_acute = 1L,
    btfp_acute_amount = sum(btfp_loan_amount, na.rm = TRUE),
    btfp_acute_first = min(btfp_loan_date),
    btfp_acute_n = n(),
    .groups = "drop"
  ) %>%
  rename(idrssd = rssd_id)

btfp_post <- btfp_raw %>%
  filter(btfp_loan_date > PERIOD_1_END, btfp_loan_date <= PERIOD_2_END) %>%
  group_by(rssd_id) %>%
  summarise(
    btfp_post = 1L,
    btfp_post_amount = sum(btfp_loan_amount, na.rm = TRUE),
    btfp_post_first = min(btfp_loan_date),
    btfp_post_n = n(),
    .groups = "drop"
  ) %>%
  rename(idrssd = rssd_id)

btfp_arb <- btfp_raw %>%
  filter(btfp_loan_date > PERIOD_2_END, btfp_loan_date <= PERIOD_3_END) %>%
  group_by(rssd_id) %>%
  summarise(
    btfp_arb = 1L,
    btfp_arb_amount = sum(btfp_loan_amount, na.rm = TRUE),
    btfp_arb_first = min(btfp_loan_date),
    btfp_arb_n = n(),
    .groups = "drop"
  ) %>%
  rename(idrssd = rssd_id)

dw_pre <- dw_raw %>%
  filter(dw_loan_date >= PRE_BTFP_START, dw_loan_date <= PRE_BTFP_END) %>%
  group_by(rssd_id) %>%
  summarise(
    dw_pre = 1L,
    dw_pre_amount = sum(dw_loan_amount, na.rm = TRUE),
    dw_pre_first = min(dw_loan_date, na.rm = TRUE),
    dw_pre_n = n(),
    .groups = "drop"
  ) %>%
  rename(idrssd = rssd_id)

dw_acute <- dw_raw %>%
  filter(dw_loan_date >= CRISIS_START, dw_loan_date <= PERIOD_1_END) %>%
  group_by(rssd_id) %>%
  summarise(
    dw_acute = 1L,
    dw_acute_amount = sum(dw_loan_amount, na.rm = TRUE),
    dw_acute_first = min(dw_loan_date),
    dw_acute_n = n(),
    .groups = "drop"
  ) %>%
  rename(idrssd = rssd_id)

dw_post <- dw_raw %>%
  filter(dw_loan_date > PERIOD_1_END, dw_loan_date <= PERIOD_2_END) %>%
  group_by(rssd_id) %>%
  summarise(
    dw_post = 1L,
    dw_post_amount = sum(dw_loan_amount, na.rm = TRUE),
    dw_post_first = min(dw_loan_date),
    dw_post_n = n(),
    .groups = "drop"
  ) %>%
  rename(idrssd = rssd_id)

dw_arb <- dw_raw %>%
  filter(dw_loan_date > PERIOD_2_END, dw_loan_date <= PERIOD_3_END) %>%
  group_by(rssd_id) %>%
  summarise(
    dw_arb = 1L,
    dw_arb_amount = sum(dw_loan_amount, na.rm = TRUE),
    dw_arb_first = min(dw_loan_date),
    dw_arb_n = n(),
    .groups = "drop"
  ) %>%
  rename(idrssd = rssd_id)

cat("Period-specific facility usage aggregated\n\n")

#> Period-specific facility usage aggregated

cat("BTFP Usage by Period:\n")

#> BTFP Usage by Period:

cat("  Acute (Mar 13 - May 1):     ", nrow(btfp_acute), "banks\n")

#>   Acute (Mar 13 - May 1):      492 banks

cat("  Post-Acute (May 2 - Oct 31):", nrow(btfp_post), "banks\n")

#>   Post-Acute (May 2 - Oct 31): 816 banks

cat("  Arbitrage (Nov 1 - Jan 24): ", nrow(btfp_arb), "banks\n")

#>   Arbitrage (Nov 1 - Jan 24):  801 banks

cat("\nDW Usage by Period:\n")

#> 
#> DW Usage by Period:

cat("  Pre-BTFP (January 1 - March 12):     ", nrow(dw_pre), "banks\n")

#>   Pre-BTFP (January 1 - March 12):      292 banks

cat("  Acute (Mar 13 - May 1):     ", nrow(dw_acute), "banks\n")

#>   Acute (Mar 13 - May 1):      424 banks

cat("  Post-Acute (May 2 - Oct 31):", nrow(dw_post), "banks\n")

#>   Post-Acute (May 2 - Oct 31): 846 banks

cat("  Arbitrage (Nov 1 - Jan 24): ", nrow(dw_arb), "banks\n")

#>   Arbitrage (Nov 1 - Jan 24):  0 banks

# MERGE ALL BORROWING DATA

df <- baseline %>%
  left_join(btfp_full, by = "idrssd") %>%
  left_join(dw_full, by = "idrssd") %>%
  left_join(dw_pre_btfp, by = "idrssd") %>%
  left_join(btfp_acute, by = "idrssd") %>%
  left_join(btfp_post, by = "idrssd") %>%
  left_join(btfp_arb, by = "idrssd") %>%
  left_join(dw_pre, by = "idrssd") %>%
  left_join(dw_acute, by = "idrssd") %>%
  left_join(dw_post, by = "idrssd") %>%
  left_join(dw_arb, by = "idrssd") %>%
  mutate(
    btfp = coalesce(btfp, 0L),
    dw = coalesce(dw, 0L),
    btfp_amount = coalesce(btfp_amount, 0),
    dw_amount = coalesce(dw_amount, 0),
    dw_pre_btfp = coalesce(dw_pre_btfp, 0L),
    dw_pre_btfp_amount = coalesce(dw_pre_btfp_amount, 0),
    btfp_acute = coalesce(btfp_acute, 0L),
    btfp_post = coalesce(btfp_post, 0L),
    btfp_arb = coalesce(btfp_arb, 0L),
    btfp_acute_amount = coalesce(btfp_acute_amount, 0),
    btfp_post_amount = coalesce(btfp_post_amount, 0),
    btfp_arb_amount = coalesce(btfp_arb_amount, 0),
    dw_acute = coalesce(dw_acute, 0L),
    dw_post = coalesce(dw_post, 0L),
    dw_arb = coalesce(dw_arb, 0L),
    dw_acute_amount = coalesce(dw_acute_amount, 0),
    dw_post_amount = coalesce(dw_post_amount, 0),
    dw_arb_amount = coalesce(dw_arb_amount, 0),
    both = as.integer(btfp == 1 & dw == 1),
    btfp_only = as.integer(btfp == 1 & dw == 0),
    dw_only = as.integer(btfp == 0 & dw == 1),
    any_fed = as.integer(btfp == 1 | dw == 1),
    dw_pre_only = as.integer(dw_pre_btfp == 1),
    any_fed_pre = as.integer(dw_pre_btfp == 1),
    both_acute = as.integer(btfp_acute == 1 & dw_acute == 1),
    btfp_only_acute = as.integer(btfp_acute == 1 & dw_acute == 0),
    dw_only_acute = as.integer(btfp_acute == 0 & dw_acute == 1),
    any_fed_acute = as.integer(btfp_acute == 1 | dw_acute == 1),
    both_post = as.integer(btfp_post == 1 & dw_post == 1),
    btfp_only_post = as.integer(btfp_post == 1 & dw_post == 0),
    dw_only_post = as.integer(btfp_post == 0 & dw_post == 1),
    any_fed_post = as.integer(btfp_post == 1 | dw_post == 1),
    both_arb = as.integer(btfp_arb == 1 & dw_arb == 1),
    btfp_only_arb = as.integer(btfp_arb == 1 & dw_arb == 0),
    dw_only_arb = as.integer(btfp_arb == 0 & dw_arb == 1),
    any_fed_arb = as.integer(btfp_arb == 1 | dw_arb == 1),
    d_assets = assets * 1000,
    btfp_amount_pct = safe_div(btfp_amount, d_assets) * 100,
    dw_amount_pct = safe_div(dw_amount, d_assets) * 100,
    total_borrowed = btfp_amount + dw_amount,
    total_borrowed_pct = safe_div(total_borrowed, d_assets) * 100,
    btfp_acute_amount_pct = safe_div(btfp_acute_amount, d_assets) * 100,
    btfp_post_amount_pct = safe_div(btfp_post_amount, d_assets) * 100,
    btfp_arb_amount_pct = safe_div(btfp_arb_amount, d_assets) * 100,
    dw_acute_amount_pct = safe_div(dw_acute_amount, d_assets) * 100,
    dw_post_amount_pct = safe_div(dw_post_amount, d_assets) * 100,
    dw_arb_amount_pct = safe_div(dw_arb_amount, d_assets) * 100,
    dw_pre_btfp_amount_pct = safe_div(dw_pre_btfp_amount, d_assets) * 100,
    btfp_share = ifelse(both == 1, safe_div(btfp_amount, total_borrowed) * 100, NA_real_),
    btfp_share_acute = ifelse(both_acute == 1,
                              safe_div(btfp_acute_amount, btfp_acute_amount + dw_acute_amount) * 100,
                              NA_real_),
    btfp_share_post = ifelse(both_post == 1,
                             safe_div(btfp_post_amount, btfp_post_amount + dw_post_amount) * 100,
                             NA_real_),
    btfp_share_arb = ifelse(both_arb == 1,
                            safe_div(btfp_arb_amount, btfp_arb_amount + dw_arb_amount) * 100,
                            NA_real_),
    collateral_capacity = (eligible_collateral / 100) * d_assets,
    btfp_utilization = safe_div(btfp_amount, collateral_capacity),
    maxed_out_btfp = as.integer(btfp_utilization > 0.90),
    btfp_util_acute = safe_div(btfp_acute_amount, collateral_capacity),
    btfp_util_post = safe_div(btfp_post_amount, collateral_capacity),
    btfp_util_arb = safe_div(btfp_arb_amount, collateral_capacity),
    btfp_period = case_when(
      btfp == 0 ~ NA_character_,
      btfp_first_date <= PERIOD_1_END ~ "Acute",
      btfp_first_date <= PERIOD_2_END ~ "PostAcute",
      btfp_first_date <= PERIOD_3_END ~ "Arbitrage",
      TRUE ~ "Winddown"
    ),
    facility = factor(case_when(
      btfp == 0 & dw == 0 ~ "None",
      btfp == 1 & dw == 0 ~ "BTFP Only",
      btfp == 0 & dw == 1 ~ "DW Only",
      TRUE ~ "Both"
    ), levels = c("None", "BTFP Only", "DW Only", "Both")),
    facility_pre = factor(case_when(
      dw_pre_btfp == 1 ~ "DW Only",
      TRUE ~ "None"
    ), levels = c("None", "DW Only")),
    facility_acute = factor(case_when(
      btfp_acute == 0 & dw_acute == 0 ~ "None",
      btfp_acute == 1 & dw_acute == 0 ~ "BTFP Only",
      btfp_acute == 0 & dw_acute == 1 ~ "DW Only",
      TRUE ~ "Both"
    ), levels = c("None", "BTFP Only", "DW Only", "Both")),
    facility_post = factor(case_when(
      btfp_post == 0 & dw_post == 0 ~ "None",
      btfp_post == 1 & dw_post == 0 ~ "BTFP Only",
      btfp_post == 0 & dw_post == 1 ~ "DW Only",
      TRUE ~ "Both"
    ), levels = c("None", "BTFP Only", "DW Only", "Both")),
    facility_arb = factor(case_when(
      btfp_arb == 0 & dw_arb == 0 ~ "None",
      btfp_arb == 1 & dw_arb == 0 ~ "BTFP Only",
      btfp_arb == 0 & dw_arb == 1 ~ "DW Only",
      TRUE ~ "Both"
    ), levels = c("None", "BTFP Only", "DW Only", "Both"))
  )

cat("\n")

cat(strrep("=", 70), "\n")

#> ======================================================================

cat("FACILITY USAGE SUMMARY BY PERIOD\n")

#> FACILITY USAGE SUMMARY BY PERIOD

cat(strrep("=", 70), "\n")

#> ======================================================================

cat("\n--- PRE-BTFP (Jan 1 - Mar 12, 2023) DW ONLY ---\n")

#> 
#> --- PRE-BTFP (Jan 1 - Mar 12, 2023) DW ONLY ---

cat("  DW only:      ", sum(df$dw_pre_only), sprintf("(%.1f%%)", 100 * mean(df$dw_pre_only)), "\n")

#>   DW only:       266 (6.2%)

cat("  Any Fed:      ", sum(df$any_fed_pre), sprintf("(%.1f%%)", 100 * mean(df$any_fed_pre)), "\n")

#>   Any Fed:       266 (6.2%)

cat("\n--- FULL PROGRAM (Mar 13, 2023 - Mar 11, 2024) ---\n")

#> 
#> --- FULL PROGRAM (Mar 13, 2023 - Mar 11, 2024) ---

cat("  BTFP only:    ", sum(df$btfp_only), sprintf("(%.1f%%)", 100 * mean(df$btfp_only)), "\n")

#>   BTFP only:     846 (19.7%)

cat("  DW only:      ", sum(df$dw_only), sprintf("(%.1f%%)", 100 * mean(df$dw_only)), "\n")

#>   DW only:       591 (13.8%)

cat("  Both:         ", sum(df$both), sprintf("(%.1f%%)", 100 * mean(df$both)), "\n")

#>   Both:          413 (9.6%)

cat("  Any Fed:      ", sum(df$any_fed), sprintf("(%.1f%%)", 100 * mean(df$any_fed)), "\n")

#>   Any Fed:       1850 (43.1%)

cat(strrep("=", 70), "\n")

#> ======================================================================

# WINSORIZE

vars_to_winsorize <- c("mtm_btfp", "mtm_other", "uninsured_lev", "eligible_collateral",
                       "borrowing_subsidy", "pct_uninsured", "pct_mtm_loss",
                       "cash_ratio", "securities_ratio", "ln_assets", "roa",
                       "idcr_1", "idcr_2", "insolvency_1", "insolvency_2", "adjusted_equity")

df <- df %>%
  mutate(across(any_of(vars_to_winsorize), ~winsorize(.x, c(0.01, 0.99)))) %>%
  mutate(
    mtm_btfp_x_uninsured = mtm_btfp * uninsured_lev,
    adj_equity_x_uninsured = adjusted_equity * uninsured_lev
  )

cat("Variables winsorized\n")

#> Variables winsorized

Summary Statistics

Table: Summary by Facility Choice (Full Program)

desc_stats <- df %>%
  group_by(facility) %>%
  summarize(
    N = n(),
    `Assets ($B)` = mean(assets, na.rm = TRUE) / 1e6,
    `MTM BTFP (%)` = mean(mtm_btfp, na.rm = TRUE),
    `MTM Other (%)` = mean(mtm_other, na.rm = TRUE),
    `Uninsured (%)` = mean(uninsured_lev, na.rm = TRUE),
    `% Insolvent` = mean(mtm_insolvent, na.rm = TRUE),
    `Eligible (%)` = mean(eligible_collateral, na.rm = TRUE),
    .groups = "drop"
  )

desc_stats %>%
  kbl(
    caption = "Descriptive Statistics by Facility Choice (January 2023 - March 2024)",
    digits = 3
  ) %>%
  kable_styling(bootstrap_options = c("striped", "hover"), full_width = FALSE)

Descriptive Statistics by Facility Choice (January 2023 - March 2024)
facility	N	Assets ($B)	MTM BTFP (%)	MTM Other (%)	Uninsured (%)	% Insolvent	Eligible (%)
None	2442	1.172	0.602	4.389	21.806	16.242	10.953
BTFP Only	846	2.529	0.809	4.977	24.382	29.669	11.143
DW Only	591	4.366	0.610	4.635	25.880	14.044	8.687
Both	413	8.841	0.849	4.941	28.517	23.245	10.717

Insolvency Summary

cat("\n=== INSOLVENCY MEASURES ===\n")

#> 
#> === INSOLVENCY MEASURES ===

cat("% MTM Insolvent:", sprintf("%.1f%%", mean(df$mtm_insolvent, na.rm = TRUE) * 100), "\n")

#> % MTM Insolvent: 1926.7%

cat("% IDCR (s=0.5) < 0:", sprintf("%.1f%%", mean(df$insolvent_idcr_s50, na.rm = TRUE) * 100), "\n")

#> % IDCR (s=0.5) < 0: 4.2%

cat("% IDCR (s=1.0) < 0:", sprintf("%.1f%%", mean(df$insolvent_idcr_s100, na.rm = TRUE) * 100), "\n")

#> % IDCR (s=1.0) < 0: 28.3%

cat("% Capital (s=0.5) < 0:", sprintf("%.1f%%", mean(df$insolvent_cap_s50, na.rm = TRUE) * 100), "\n")

#> % Capital (s=0.5) < 0: 2.2%

cat("% Capital (s=1.0) < 0:", sprintf("%.1f%%", mean(df$insolvent_cap_s100, na.rm = TRUE) * 100), "\n")

#> % Capital (s=1.0) < 0: 7.6%

Step 1: Extensive Margin Analysis

# STEP 1: EXTENSIVE MARGIN

controls <- "ln_assets + cash_ratio + securities_ratio + loan_to_deposit + book_equity_ratio + pct_wholesale_liability + fhlb_ratio + roa"

rhs <- paste(
  "mtm_btfp + mtm_other + uninsured_lev + I(mtm_btfp * uninsured_lev)",
  controls,
  sep = " + "
)

lpm_btfp <- feols(as.formula(paste("btfp ~", rhs)),
                  data = df, vcov = "hetero")

lpm_dw <- feols(as.formula(paste("dw ~", rhs)),
                data = df, vcov = "hetero")

modelsummary(
  list("BTFP" = lpm_btfp, "DW" = lpm_dw),
  stars = c('*' = .1, '**' = .05, '***' = .01),
  coef_map = c(
    "mtm_btfp" = "MTM (BTFP)",
    "mtm_other" = "MTM (Other)",
    "uninsured_lev" = "Uninsured Leverage",
    "I(mtm_btfp * uninsured_lev)" = "MTM_btfp x Uninsured Leverage",
    "pct_wholesale_liability" = "% Wholesale Liabilities",
    "fhlb_ratio" = "FHLB Ratio",
    "cash_ratio" = "Cash Ratio",
    "ln_assets" = "Log(Assets)",
    "securities_ratio" = "Securities Ratio",
    "loan_to_deposit" = "Loan-to-Deposit Ratio",
    "book_equity_ratio" = "Book Equity Ratio",
    "roa" = "ROA",
    "(Intercept)" = "Constant"
  ),
  gof_map = c("nobs", "r.squared"),
  title = "Extensive Margin - BTFP vs DW"
)

Extensive Margin - BTFP vs DW
	BTFP	DW
* p < 0.1, p < 0.05, * p < 0.01
MTM (BTFP)	0.063***	0.009
	(0.020)	(0.017)
MTM (Other)	0.010***	0.001
	(0.004)	(0.003)
Uninsured Leverage	0.003***	0.001
	(0.001)	(0.001)
MTM_btfp x Uninsured Leverage	-0.001	0.000
	(0.001)	(0.001)
% Wholesale Liabilities	0.003	0.002
	(0.002)	(0.002)
FHLB Ratio	0.007***	0.002
	(0.002)	(0.002)
Cash Ratio	-0.005***	-0.001
	(0.001)	(0.001)
Log(Assets)	0.055***	0.093***
	(0.006)	(0.006)
Securities Ratio	0.003***	-0.001
	(0.001)	(0.001)
Loan-to-Deposit Ratio	0.000	-0.000
	(0.000)	(0.000)
Book Equity Ratio	-0.002***	0.000
	(0.001)	(0.001)
ROA	-0.002	-0.001
	(0.010)	(0.009)
Constant	-0.589***	-0.962***
	(0.082)	(0.081)
Num.Obs.	4282	4282
R2	0.100	0.120

Run Risk Specifications

controls <- "ln_assets + cash_ratio + securities_ratio + loan_to_deposit + book_equity_ratio + pct_wholesale_liability + fhlb_ratio + roa"

base_rhs <- paste(
  "mtm_btfp + mtm_other + uninsured_lev + I(mtm_btfp * uninsured_lev)",
  controls,
  sep = " + "
)

rhs_cont <- paste(base_rhs, "run_risk_1", sep = " + ")
lpm_run_cont <- feols(as.formula(paste("btfp ~", rhs_cont)),
                      data = df, vcov = "hetero")

rhs_dummy <- paste(base_rhs, "run_risk_1_dummy", sep = " + ")
lpm_run <- feols(as.formula(paste("btfp ~", rhs_dummy)),
                 data = df, vcov = "hetero")

modelsummary(
  list("Run Risk (Cont)" = lpm_run_cont, "Run Risk (Dummy)" = lpm_run),
  stars = c('*' = 0.1, '**' = 0.05, '***' = 0.01),
  gof_map = c("nobs", "r.squared"),
  title = "Run Risk Specifications"
)

Run Risk Specifications
	Run Risk (Cont)	Run Risk (Dummy)
* p < 0.1, p < 0.05, * p < 0.01
(Intercept)	-0.544***	-0.564***
	(0.082)	(0.081)
mtm_btfp	0.071***	0.069***
	(0.021)	(0.021)
mtm_other	-0.014**	0.005
	(0.006)	(0.004)
uninsured_lev	-0.002*	0.002**
	(0.001)	(0.001)
I(mtm_btfp * uninsured_lev)	-0.002***	-0.001*
	(0.001)	(0.001)
ln_assets	0.057***	0.055***
	(0.006)	(0.006)
cash_ratio	-0.004***	-0.005***
	(0.001)	(0.001)
securities_ratio	0.003***	0.003***
	(0.001)	(0.001)
loan_to_deposit	0.001***	0.000
	(0.000)	(0.000)
book_equity_ratio	-0.007***	-0.002***
	(0.001)	(0.001)
pct_wholesale_liability	0.001	0.003
	(0.002)	(0.002)
fhlb_ratio	0.004**	0.007***
	(0.002)	(0.002)
roa	-0.013	-0.003
	(0.011)	(0.010)
run_risk_1	0.000***
	(0.000)
run_risk_1_dummy		0.064***
		(0.021)
Num.Obs.	4251	4279
R2	0.107	0.102

Insolvency Specifications

controls <- "ln_assets + cash_ratio + securities_ratio + loan_to_deposit + book_equity_ratio + pct_wholesale_liability + fhlb_ratio + roa"

base_rhs <- paste(
  "mtm_btfp + mtm_other + uninsured_lev + I(mtm_btfp * uninsured_lev)",
  controls,
  sep = " + "
)

rhs_jiang <- paste(base_rhs, "adjusted_equity", sep = " + ")
lpm_jiang <- feols(as.formula(paste("btfp ~", rhs_jiang)),
                   data = df, vcov = "hetero")

rhs_idcr <- paste(base_rhs, "idcr_2", sep = " + ")
lpm_idcr <- feols(as.formula(paste("btfp ~", rhs_idcr)),
                  data = df, vcov = "hetero")

rhs_cap <- paste(base_rhs, "insolvency_2", sep = " + ")
lpm_cap <- feols(as.formula(paste("btfp ~", rhs_cap)),
                 data = df, vcov = "hetero")

modelsummary(
  list(
    "Adj. Equity" = lpm_jiang,
    "IDCR (s = 1.0)" = lpm_idcr,
    "Capital (s = 1.0)" = lpm_cap
  ),
  stars = c('*' = 0.1, '**' = 0.05, '***' = 0.01),
  gof_map = c("nobs", "r.squared"),
  title = "Insolvency Specifications (Jiang Integration)"
)

Insolvency Specifications (Jiang Integration)
	Adj. Equity	IDCR (s = 1.0)	Capital (s = 1.0)
* p < 0.1, p < 0.05, * p < 0.01
(Intercept)	-0.593***	-0.588***	-0.575***
	(0.090)	(0.079)	(0.079)
mtm_btfp	0.048**	0.063***	0.061***
	(0.020)	(0.020)	(0.020)
mtm_other	-0.012***	0.010***	0.011***
	(0.005)	(0.004)	(0.004)
uninsured_lev	0.003***	0.003***	0.002*
	(0.001)	(0.001)	(0.001)
I(mtm_btfp * uninsured_lev)	-0.001	-0.001	-0.001
	(0.001)	(0.001)	(0.001)
ln_assets	0.057***	0.055***	0.053***
	(0.006)	(0.006)	(0.006)
cash_ratio	-0.004***	-0.005***	-0.004***
	(0.001)	(0.001)	(0.001)
securities_ratio	0.003***	0.003***	0.003***
	(0.001)	(0.001)	(0.001)
loan_to_deposit	0.001	0.000	0.000
	(0.001)	(0.000)	(0.000)
book_equity_ratio	0.013***	-0.004***	0.002*
	(0.002)	(0.001)	(0.001)
pct_wholesale_liability	0.003	0.003	0.003
	(0.002)	(0.002)	(0.002)
fhlb_ratio	0.006***	0.007***	0.006***
	(0.002)	(0.002)	(0.002)
roa	-0.010	-0.007	0.001
	(0.010)	(0.010)	(0.010)
adjusted_equity	-0.023***
	(0.003)
idcr_2		0.006*
		(0.003)
insolvency_2			-0.650***
			(0.164)
Num.Obs.	4282	4282	4282
R2	0.108	0.101	0.103

Step 2: Temporal Analysis

BTFP by Period

# STEP 2: TEMPORAL ANALYSIS - BTFP BY PERIOD

controls <- "ln_assets + cash_ratio + securities_ratio + loan_to_deposit + book_equity_ratio + pct_wholesale_liability + fhlb_ratio + roa"

base_rhs <- paste(
  "mtm_btfp + mtm_other + uninsured_lev + I(mtm_btfp * uninsured_lev)",
  controls,
  sep = " + "
)

lpm_btfp_acute <- feols(as.formula(paste("btfp_acute ~", base_rhs)),
                        data = df, vcov = "hetero")

lpm_btfp_post <- feols(as.formula(paste("btfp_post ~", base_rhs)),
                       data = df, vcov = "hetero")

lpm_btfp_arb <- feols(as.formula(paste("btfp_arb ~", base_rhs)),
                      data = df, vcov = "hetero")

modelsummary(
  list(
    "BTFP Acute" = lpm_btfp_acute,
    "BTFP Post-Acute" = lpm_btfp_post,
    "BTFP Arbitrage" = lpm_btfp_arb
  ),
  stars = c('*' = 0.1, '**' = 0.05, '***' = 0.01),
  coef_map = c(
    "mtm_btfp" = "MTM (BTFP)",
    "mtm_other" = "MTM (Other)",
    "uninsured_lev" = "Uninsured Leverage",
    "I(mtm_btfp * uninsured_lev)" = "MTM_btfp x Uninsured",
    "ln_assets" = "Log(Assets)",
    "cash_ratio" = "Cash Ratio",
    "securities_ratio" = "Securities Ratio",
    "loan_to_deposit" = "Loan/Deposit",
    "book_equity_ratio" = "Book Equity Ratio",
    "pct_wholesale_liability" = "% Wholesale Liab.",
    "fhlb_ratio" = "FHLB Ratio",
    "roa" = "ROA"
  ),
  gof_map = list(
    list("raw" = "nobs", "clean" = "N", "fmt" = 0),
    list("raw" = "r.squared", "clean" = "R2", "fmt" = 3)
  ),
  title = "BTFP Usage by Period"
)

BTFP Usage by Period
	BTFP Acute	BTFP Post-Acute	BTFP Arbitrage
* p < 0.1, p < 0.05, * p < 0.01
MTM (BTFP)	-0.002	0.028	0.037**
	(0.013)	(0.017)	(0.017)
MTM (Other)	0.002	0.002	0.008***
	(0.002)	(0.003)	(0.003)
Uninsured Leverage	0.001*	0.001	0.002**
	(0.001)	(0.001)	(0.001)
MTM_btfp x Uninsured	0.001	0.000	-0.000
	(0.001)	(0.001)	(0.001)
Log(Assets)	0.032***	0.023***	0.037***
	(0.005)	(0.005)	(0.005)
Cash Ratio	-0.002***	-0.004***	-0.004***
	(0.001)	(0.001)	(0.001)
Securities Ratio	0.001**	0.003***	0.002***
	(0.001)	(0.001)	(0.001)
Loan/Deposit	-0.000	0.000	0.000
	(0.000)	(0.000)	(0.000)
Book Equity Ratio	-0.001*	-0.002***	-0.000
	(0.000)	(0.001)	(0.001)
% Wholesale Liab.	0.005**	0.002	0.001
	(0.002)	(0.002)	(0.002)
FHLB Ratio	0.007***	0.003*	0.007***
	(0.001)	(0.002)	(0.002)
ROA	0.006	-0.003	-0.007
	(0.007)	(0.008)	(0.008)
N	4282	4282	4282
R2	0.068	0.052	0.072

DW by Period

# STEP 2: TEMPORAL ANALYSIS - DW BY PERIOD

controls <- "ln_assets + cash_ratio + securities_ratio + loan_to_deposit + book_equity_ratio + pct_wholesale_liability + fhlb_ratio + roa"

base_rhs <- paste(
  "mtm_btfp + mtm_other + uninsured_lev + I(mtm_btfp * uninsured_lev)",
  controls,
  sep = " + "
)

lpm_dw_pre <- feols(as.formula(paste("dw_pre_btfp ~", base_rhs)),
                    data = df, vcov = "hetero")

lpm_dw_acute <- feols(as.formula(paste("dw_acute ~", base_rhs)),
                      data = df, vcov = "hetero")

lpm_dw_post <- feols(as.formula(paste("dw_post ~", base_rhs)),
                     data = df, vcov = "hetero")

modelsummary(
  list(
    "DW Pre-BTFP" = lpm_dw_pre,
    "DW Acute" = lpm_dw_acute,
    "DW Post-Acute" = lpm_dw_post
  ),
  stars = c('*' = 0.1, '**' = 0.05, '***' = 0.01),
  coef_map = c(
    "mtm_btfp" = "MTM (BTFP Eligible)",
    "mtm_other" = "MTM (Other)",
    "uninsured_lev" = "Uninsured Leverage",
    "I(mtm_btfp * uninsured_lev)" = "MTM x Uninsured",
    "ln_assets" = "Log(Assets)",
    "cash_ratio" = "Cash Ratio",
    "securities_ratio" = "Securities Ratio",
    "loan_to_deposit" = "Loan/Deposit",
    "book_equity_ratio" = "Book Equity Ratio",
    "pct_wholesale_liability" = "% Wholesale Liab.",
    "fhlb_ratio" = "FHLB Ratio",
    "roa" = "ROA"
  ),
  gof_map = list(
    list("raw" = "nobs", "clean" = "N", "fmt" = 0),
    list("raw" = "r.squared", "clean" = "R2", "fmt" = 3)
  ),
  title = "DW Usage by Period"
)

DW Usage by Period
	DW Pre-BTFP	DW Acute	DW Post-Acute
* p < 0.1, p < 0.05, * p < 0.01
MTM (BTFP Eligible)	-0.001	-0.005	0.008
	(0.011)	(0.012)	(0.016)
MTM (Other)	-0.001	0.004*	-0.002
	(0.002)	(0.002)	(0.003)
Uninsured Leverage	-0.000	0.000	0.001
	(0.000)	(0.001)	(0.001)
MTM x Uninsured	0.001	0.001	0.000
	(0.000)	(0.001)	(0.001)
Log(Assets)	0.035***	0.045***	0.064***
	(0.004)	(0.005)	(0.006)
Cash Ratio	-0.001***	-0.000	-0.002**
	(0.000)	(0.001)	(0.001)
Securities Ratio	0.001*	0.000	-0.001
	(0.000)	(0.000)	(0.001)
Loan/Deposit	-0.000	-0.000	0.000
	(0.000)	(0.000)	(0.000)
Book Equity Ratio	0.000	0.000	0.000
	(0.000)	(0.000)	(0.000)
% Wholesale Liab.	0.004**	0.005**	0.001
	(0.002)	(0.002)	(0.002)
FHLB Ratio	0.001	0.002	0.001
	(0.001)	(0.001)	(0.002)
ROA	0.002	0.003	0.001
	(0.005)	(0.006)	(0.009)
N	4282	4282	4282
R2	0.059	0.066	0.079

Borrower Comparison

df %>%
  filter(btfp == 1) %>%
  group_by(btfp_period) %>%
  summarize(
    N = n(),
    `MTM BTFP (%)` = mean(mtm_btfp, na.rm = TRUE),
    `Uninsured (%)` = mean(uninsured_lev, na.rm = TRUE),
    `% Insolvent` = mean(mtm_insolvent, na.rm = TRUE),
    .groups = "drop"
  ) %>%
  kbl(caption = "Borrower Characteristics by Period", digits = 3) %>%
  kable_styling(bootstrap_options = c("striped", "hover"), full_width = FALSE)

Borrower Characteristics by Period
btfp_period	N	MTM BTFP (%)	Uninsured (%)	% Insolvent
Acute	462	0.861	27.378	28.571
Arbitrage	242	0.732	25.075	28.099
PostAcute	522	0.837	24.647	26.628
Winddown	33	0.720	24.918	24.242

Step 3: Intensive Margin

# STEP 3: INTENSIVE MARGIN

btfp_users <- df %>% filter(btfp == 1)

controls <- "ln_assets + cash_ratio + securities_ratio + loan_to_deposit + book_equity_ratio + pct_wholesale_liability + fhlb_ratio + roa"

base_rhs <- paste(
  "uninsured_lev + eligible_collateral + borrowing_subsidy + adjusted_equity",
  controls,
  sep = " + "
)

intensive_pct <- feols(as.formula(paste("btfp_amount_pct ~", base_rhs)),
                       data = btfp_users, vcov = "hetero")

rhs_run <- paste(base_rhs, "run_risk_1_dummy", sep = " + ")
intensive_run <- feols(as.formula(paste("btfp_amount_pct ~", rhs_run)),
                       data = btfp_users, vcov = "hetero")

modelsummary(
  list("Main" = intensive_pct, "Run Risk Dummy" = intensive_run),
  stars = c('*' = 0.1, '**' = 0.05, '***' = 0.01),
  gof_map = c("nobs", "r.squared"),
  title = "Intensive Margin"
)

Intensive Margin
	Main	Run Risk Dummy
* p < 0.1, p < 0.05, * p < 0.01
(Intercept)	43.272***	43.342***
	(15.185)	(15.144)
uninsured_lev	0.130*	0.126
	(0.075)	(0.084)
eligible_collateral	0.143*	0.143*
	(0.085)	(0.085)
borrowing_subsidy	-0.118	-0.119
	(0.121)	(0.121)
adjusted_equity	0.229	0.245
	(0.363)	(0.402)
ln_assets	-0.157	-0.156
	(0.557)	(0.559)
cash_ratio	-0.666***	-0.665***
	(0.182)	(0.182)
securities_ratio	-0.241	-0.241
	(0.185)	(0.185)
loan_to_deposit	-0.466***	-0.465***
	(0.170)	(0.170)
book_equity_ratio	0.546	0.531
	(0.497)	(0.527)
pct_wholesale_liability	0.668***	0.667***
	(0.253)	(0.254)
fhlb_ratio	1.182***	1.181***
	(0.293)	(0.294)
roa	1.699	1.688
	(1.661)	(1.647)
run_risk_1_dummy		0.151
		(1.412)
Num.Obs.	1259	1259
R2	0.082	0.082

Step 4: Both Banks Analysis

# STEP 4: BOTH BANKS

btfp_users <- df %>% filter(btfp == 1)

controls <- "ln_assets + cash_ratio + securities_ratio + loan_to_deposit + book_equity_ratio + pct_wholesale_liability + fhlb_ratio + roa"

base_rhs <- paste(
  "mtm_btfp + mtm_other + uninsured_lev + I(mtm_btfp * uninsured_lev)",
  controls,
  sep = " + "
)

rhs_other <- paste(base_rhs, "adjusted_equity", sep = " + ")
both_other <- feols(as.formula(paste("dw ~", rhs_other)),
                    data = btfp_users, vcov = "hetero")

rhs_maxout <- paste(base_rhs, "maxed_out_btfp", sep = " + ")
both_maxout <- feols(as.formula(paste("dw ~", rhs_maxout)),
                     data = btfp_users, vcov = "hetero")

modelsummary(
  list("DW | BTFP (Adj. Equity)" = both_other, "DW | BTFP (MaxOut)" = both_maxout),
  stars = c('*' = 0.1, '**' = 0.05, '***' = 0.01),
  gof_map = c("nobs", "r.squared"),
  title = "Both Banks Analysis"
)

Both Banks Analysis
	DW \| BTFP (Adj. Equity)	DW \| BTFP (MaxOut)
* p < 0.1, p < 0.05, * p < 0.01
(Intercept)	-0.974***	-0.941***
	(0.342)	(0.341)
mtm_btfp	0.024	0.025
	(0.041)	(0.040)
mtm_other	-0.013	-0.005
	(0.017)	(0.008)
uninsured_lev	0.004**	0.004**
	(0.002)	(0.002)
I(mtm_btfp * uninsured_lev)	-0.001	-0.001
	(0.001)	(0.001)
ln_assets	0.091***	0.090***
	(0.012)	(0.012)
cash_ratio	-0.000	-0.001
	(0.004)	(0.004)
securities_ratio	-0.001	-0.001
	(0.004)	(0.004)
loan_to_deposit	0.000	0.000
	(0.003)	(0.003)
book_equity_ratio	0.007	-0.002
	(0.017)	(0.005)
pct_wholesale_liability	0.009	0.009
	(0.006)	(0.006)
fhlb_ratio	0.003	0.003
	(0.005)	(0.005)
roa	-0.012	-0.014
	(0.028)	(0.028)
adjusted_equity	-0.008
	(0.017)
maxed_out_btfp		-0.024
		(0.027)
Num.Obs.	1259	1259
R2	0.105	0.105

Robustness Tests

By Bank Size

controls <- "ln_assets + cash_ratio + securities_ratio + loan_to_deposit + book_equity_ratio + pct_wholesale_liability + fhlb_ratio + roa"

base_rhs <- paste(
  "mtm_btfp + mtm_other + uninsured_lev + I(mtm_btfp * uninsured_lev)",
  controls,
  sep = " + "
)

lpm_large <- feols(as.formula(paste("btfp ~", base_rhs)),
                   data = df %>% filter(size_bin == "large"),
                   vcov = "hetero")

lpm_small <- feols(as.formula(paste("btfp ~", base_rhs)),
                   data = df %>% filter(size_bin == "small"),
                   vcov = "hetero")

modelsummary(
  list("Large" = lpm_large, "Small" = lpm_small),
  stars = c('*' = 0.1, '**' = 0.05, '***' = 0.01),
  gof_map = list(
    list("raw" = "nobs", "clean" = "N", "fmt" = 0),
    list("raw" = "r.squared", "clean" = "R2", "fmt" = 3)
  ),
  title = "By Bank Size"
)

By Bank Size
	Large	Small
* p < 0.1, p < 0.05, * p < 0.01
(Intercept)	-0.182	-0.944***
	(0.447)	(0.107)
mtm_btfp	-0.018	0.080***
	(0.057)	(0.021)
mtm_other	0.023**	0.004
	(0.010)	(0.004)
uninsured_lev	0.003	0.002**
	(0.002)	(0.001)
I(mtm_btfp * uninsured_lev)	0.002	-0.002**
	(0.002)	(0.001)
ln_assets	-0.001	0.089***
	(0.020)	(0.009)
cash_ratio	-0.005	-0.004***
	(0.004)	(0.001)
securities_ratio	0.008**	0.003***
	(0.004)	(0.001)
loan_to_deposit	0.002	-0.000
	(0.003)	(0.000)
book_equity_ratio	0.000	-0.002**
	(0.003)	(0.001)
pct_wholesale_liability	-0.008	0.004*
	(0.007)	(0.002)
fhlb_ratio	0.013**	0.005***
	(0.005)	(0.002)
roa	0.022	-0.006
	(0.035)	(0.010)
N	716	3566
R2	0.086	0.093

Visualization

# MTM by Facility
ggplot(df, aes(x = facility, y = mtm_btfp * 100, fill = facility)) +
  geom_boxplot(alpha = 0.7) +
  scale_fill_brewer(palette = "Set2") +
  labs(title = "MTM Losses by Facility Choice", y = "MTM Loss (%)") +
  theme_minimal() +
  theme(legend.position = "none")

# Insolvency Distribution
ggplot(df, aes(x = adjusted_equity * 100, fill = factor(btfp))) +
  geom_histogram(alpha = 0.6, position = "identity", bins = 50) +
  geom_vline(xintercept = 0, linetype = "dashed", color = "red") +
  scale_fill_manual(values = c("gray60", "steelblue"), labels = c("Non-Borrower", "BTFP")) +
  labs(title = "Adjusted Equity Distribution", x = "Adjusted Equity (%)", fill = "") +
  theme_minimal()

# Create bins for MTM losses for visualization
df_plot <- df %>%
  mutate(mtm_bin = cut(mtm_btfp, breaks = quantile(mtm_btfp, probs = seq(0, 1, 0.1), na.rm = TRUE), include.lowest = TRUE)) %>%
  group_by(mtm_bin) %>%
  summarise(
    prob_btfp = mean(btfp, na.rm = TRUE),
    prob_dw = mean(dw, na.rm = TRUE),
    avg_mtm = mean(mtm_btfp * 100, na.rm = TRUE),
    .groups = "drop"
  )

ggplot(df_plot) +
  geom_line(aes(x = avg_mtm, y = prob_btfp, color = "BTFP Probability"), linewidth = 1.2) +
  geom_line(aes(x = avg_mtm, y = prob_dw, color = "DW Probability"), linewidth = 1.2, linetype = "dashed") +
  geom_point(aes(x = avg_mtm, y = prob_btfp, color = "BTFP Probability")) +
  geom_point(aes(x = avg_mtm, y = prob_dw, color = "DW Probability")) +
  scale_color_manual(values = c("BTFP Probability" = "steelblue", "DW Probability" = "darkorange")) +
  labs(
    title = "Facility Selection by MTM Loss Magnitude",
    subtitle = "Probability of borrowing increases with subsidy value (MTM loss)",
    x = "MTM Loss on BTFP-Eligible Securities (%)",
    y = "Probability of Borrowing",
    color = "Facility"
  ) +
  theme_minimal()

# Collateral Max-Out Scatter (Intensive Margin)
df %>%
  filter(any_fed == 1) %>%
  ggplot(aes(x = eligible_collateral, y = btfp_amount_pct)) +
  geom_point(aes(color = factor(dw)), alpha = 0.6) +
  geom_abline(intercept = 0, slope = 1, linetype = "dashed", color = "red") +
  annotate("text", x = 15, y = 18, label = "Maxed Out BTFP Collateral", color = "red", angle = 35) +
  scale_color_manual(values = c("0" = "gray", "1" = "darkred"), labels = c("BTFP Only", "Used Both")) +
  labs(
    title = "BTFP Borrowing vs. Available Collateral",
    subtitle = "Banks using both facilities (red) often cluster near the collateral limit",
    x = "BTFP-Eligible Collateral (% of Assets)",
    y = "Actual BTFP Borrowing (% of Assets)",
    color = "Facility Choice"
  ) +
  theme_minimal()

# Temporal Distribution of First-Time Borrowers
df %>%
  filter(!is.na(btfp_period)) %>%
  group_by(btfp_period) %>%
  summarise(
    `Avg MTM Loss` = mean(mtm_btfp, na.rm = TRUE),
    `Avg Uninsured` = mean(uninsured_lev, na.rm = TRUE),
    .groups = "drop"
  ) %>%
  pivot_longer(cols = -btfp_period) %>%
  ggplot(aes(x = factor(btfp_period, levels = c("Acute", "PostAcute", "Arbitrage")), y = value, fill = name)) +
  geom_bar(stat = "identity", position = "dodge") +
  scale_fill_brewer(palette = "Paired") +
  labs(
    title = "Characteristics of New BTFP Borrowers Over Time",
    subtitle = "Acute phase borrowers had higher vulnerability (MTM & Uninsured)",
    x = "Period of First Borrowing",
    y = "Mean Percentage (%)",
    fill = "Metric"
  ) +
  theme_minimal()

# Coefficient Plot
modelplot(
  list("BTFP (Selection)" = lpm_btfp, "DW (Liquidity)" = lpm_dw),
  coef_map = c(
    "mtm_btfp" = "MTM (BTFP-Eligible)",
    "mtm_other" = "MTM (Other)",
    "uninsured_lev" = "Uninsured Leverage"
  )
) +
  geom_vline(xintercept = 0, color = "red", linetype = "dotted") +
  labs(
    title = "Comparison of Borrowing Determinants",
    subtitle = "MTM losses drive BTFP selection but not necessarily DW usage",
    x = "Coefficient Estimate"
  ) +
  theme_minimal()

# Jiang-Style Vulnerability Map
ggplot(df, aes(x = uninsured_lev, y = mtm_btfp)) +
  annotate("rect", xmin = 25, xmax = Inf, ymin = 2, ymax = Inf,
           fill = "red", alpha = 0.1) +
  geom_point(aes(color = factor(btfp), alpha = factor(btfp)), size = 2) +
  scale_color_manual(values = c("0" = "gray70", "1" = "#2c7fb8"),
                     labels = c("Non-Borrower", "BTFP Borrower")) +
  scale_alpha_manual(values = c("0" = 0.3, "1" = 0.8), guide = "none") +
  geom_vline(xintercept = median(df$uninsured_lev, na.rm = TRUE), linetype = "dotted") +
  geom_hline(yintercept = median(df$mtm_btfp, na.rm = TRUE), linetype = "dotted") +
  labs(
    title = "Bank Vulnerability and BTFP Selection",
    subtitle = "Blue dots (BTFP users) cluster in the high-uninsured, high-MTM loss quadrant",
    x = "Uninsured Deposits / Total Assets (%)",
    y = "MTM Loss on BTFP-Eligible Securities (%)",
    color = "Facility Usage"
  ) +
  annotate("text", x = 60, y = 8, label = "High Vulnerability\nZone", color = "red", fontface = "bold") +
  theme_minimal() +
  theme(legend.position = "bottom")

# BTFP Intensive Margin: Borrowing vs. Subsidy Value
btfp_users <- df %>% filter(btfp == 1)

ggplot(btfp_users, aes(x = mtm_btfp, y = btfp_amount_pct)) +
  geom_point(color = "#2c7fb8", alpha = 0.6) +
  geom_smooth(method = "lm", color = "darkblue", se = TRUE) +
  geom_text(
    data = subset(btfp_users, btfp_amount_pct > quantile(btfp_amount_pct, 0.95)),
    aes(label = idrssd),
    vjust = -1,
    size = 3,
    check_overlap = TRUE
  ) +
  labs(
    title = "BTFP Intensive Margin - Subsidy Capture",
    subtitle = "Conditional on borrowing, larger MTM losses correlate with larger borrowing amounts",
    x = "MTM Loss on Eligible Collateral (The Subsidy %)",
    y = "BTFP Borrowing / Total Assets (%)"
  ) +
  theme_minimal()

Variable Dictionary

tribble(
  ~Variable, ~Type, ~Description,
  "btfp", "Binary", "Bank borrowed from BTFP",
  "dw", "Binary", "Bank borrowed from DW",
  "mtm_btfp", "Continuous", "MTM loss on BTFP-eligible / Assets",
  "mtm_other", "Continuous", "MTM loss on non-eligible / Assets",
  "uninsured_lev", "Continuous", "Uninsured deposits / Assets",
  "eligible_collateral", "Continuous", "BTFP-eligible / Assets",
  "borrowing_subsidy", "Continuous", "MTM loss on OMO-eligible/ OMO-eligible",
  "run_risk_1", "Continuous", "%Uninsured x %MTM",
  "run_risk_1_dummy", "Binary", "Both above median",
  "idcr_1", "Continuous", "IDCR (s=0.5)",
  "idcr_2", "Continuous", "IDCR (s=1.0)",
  "insolvency_1", "Continuous", "Capital metric (s=0.5)",
  "insolvency_2", "Continuous", "Capital metric (s=1.0)",
  "adjusted_equity", "Continuous", "Equity ratio - MTM loss",
  "mtm_insolvent", "Binary", "Adjusted equity < 0"
) %>%
  kbl(caption = "Variable Dictionary") %>%
  kable_styling(bootstrap_options = c("striped", "hover"), full_width = FALSE)

Variable Dictionary
Variable	Type	Description
btfp	Binary	Bank borrowed from BTFP
dw	Binary	Bank borrowed from DW
mtm_btfp	Continuous	MTM loss on BTFP-eligible / Assets
mtm_other	Continuous	MTM loss on non-eligible / Assets
uninsured_lev	Continuous	Uninsured deposits / Assets
eligible_collateral	Continuous	BTFP-eligible / Assets
borrowing_subsidy	Continuous	MTM loss on OMO-eligible/ OMO-eligible
run_risk_1	Continuous	%Uninsured x %MTM
run_risk_1_dummy	Binary	Both above median
idcr_1	Continuous	IDCR (s=0.5)
idcr_2	Continuous	IDCR (s=1.0)
insolvency_1	Continuous	Capital metric (s=0.5)
insolvency_2	Continuous	Capital metric (s=1.0)
adjusted_equity	Continuous	Equity ratio - MTM loss
mtm_insolvent	Binary	Adjusted equity < 0

Session Info

sessionInfo()

#> R version 4.3.1 (2023-06-16 ucrt)
#> Platform: x86_64-w64-mingw32/x64 (64-bit)
#> Running under: Windows 11 x64 (build 26200)
#> 
#> Matrix products: default
#> 
#> 
#> locale:
#> [1] LC_COLLATE=English_United States.utf8 
#> [2] LC_CTYPE=English_United States.utf8   
#> [3] LC_MONETARY=English_United States.utf8
#> [4] LC_NUMERIC=C                          
#> [5] LC_TIME=English_United States.utf8    
#> 
#> time zone: America/Chicago
#> tzcode source: internal
#> 
#> attached base packages:
#> [1] stats     graphics  grDevices utils     datasets  methods   base     
#> 
#> other attached packages:
#>  [1] forcats_1.0.0      purrr_1.0.4        tidyverse_2.0.0    psych_2.5.6       
#>  [5] moments_0.14.1     DescTools_0.99.60  modelsummary_2.4.0 kableExtra_1.4.0  
#>  [9] knitr_1.50         gridExtra_2.3      patchwork_1.3.2    scales_1.4.0      
#> [13] ggthemes_5.1.0     ggplot2_3.5.2      broom_1.0.9        lmtest_0.9-40     
#> [17] zoo_1.8-13         sandwich_3.1-1     fixest_0.12.1      readr_2.1.5       
#> [21] stringr_1.5.1      lubridate_1.9.4    tibble_3.2.1       tidyr_1.3.1       
#> [25] dplyr_1.1.4        data.table_1.17.0 
#> 
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#>  [4] rootSolve_1.8.2.4   farver_2.1.2        fastmap_1.2.0      
#>  [7] bayestestR_0.16.1   digest_0.6.33       timechange_0.3.0   
#> [10] estimability_1.5.1  lifecycle_1.0.4     dreamerr_1.4.0     
#> [13] lmom_3.2            magrittr_2.0.3      compiler_4.3.1     
#> [16] rlang_1.1.1         sass_0.4.10         tools_4.3.1        
#> [19] yaml_2.3.10         labeling_0.4.3      bit_4.6.0          
#> [22] mnormt_2.1.1        xml2_1.3.8          RColorBrewer_1.1-3 
#> [25] tinytable_0.13.0    expm_1.0-0          withr_3.0.2        
#> [28] numDeriv_2016.8-1.1 datawizard_1.2.0    grid_4.3.1         
#> [31] fansi_1.0.6         xtable_1.8-4        e1071_1.7-16       
#> [34] emmeans_1.11.2-8    MASS_7.3-60         insight_1.3.1      
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#> [67] gtable_0.3.6        tables_0.9.31       pillar_1.11.0      
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#> [73] evaluate_1.0.4      lattice_0.21-8      haven_2.5.4        
#> [76] backports_1.5.0     bslib_0.9.0         class_7.3-22       
#> [79] Rcpp_1.0.14         checkmate_2.3.2     svglite_2.1.3      
#> [82] coda_0.19-4.1       nlme_3.1-162        mgcv_1.8-42        
#> [85] xfun_0.52           fs_1.6.5            pkgconfig_2.0.3

Borrowing Analysis

Bank Emergency Borrowing During the March 2023 Crisis

Mohua Ferdousi

2025-12-19

Summary

Research Questions

Empirical Strategy Overview

Variable Definitions

Variable Definitions

Dependent Variables

Key Explanatory Variables

Run Risk Measures

Jiang et al. Insolvency Measures

Insured Deposit Coverage Ratio (IDCR)

Capital Ratio Metric

Adjusted Equity (Jiang-Style)

Control Variables

Facility Choice Variables

Period-Specific Variables

Intensive Margin Variables

Step 1: Extensive Margin (Full Period)

Step 2: Temporal Analysis

Step 3: Intensive Margin

Step 4: Both Banks and Collateral Constraints

Crisis Timeline

Helper Functions

Data Loading

Load Data

Assign Periods

Loan-Level Summary Tables

Table 1: Loan Characteristics by Period

Visualizations

Figure 1: Daily Borrowing Volume

Figure 2: Cumulative Borrowing

Figure 3: Interest Rate Evolution

Figure 4: Term Distribution

Figure 5: DW Collateral Composition

Bank-Level Analysis Dataset Construction

Summary Statistics

Table: Summary by Facility Choice (Full Program)

Insolvency Summary

Step 1: Extensive Margin Analysis

Run Risk Specifications

Insolvency Specifications

Step 2: Temporal Analysis

BTFP by Period

DW by Period

Borrower Comparison

Step 3: Intensive Margin

Step 4: Both Banks Analysis

Robustness Tests

By Bank Size

Visualization

Variable Dictionary

Session Info