1 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.

1.1 Research Questions

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

1.2 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?

2 Variable Definitions

2.1 Dependent Variables

Variable Definition Formula
\(BTFP_i\) Binary: Bank \(i\) borrowed from BTFP \(\mathbb{1}[\text{Bank } i \text{ borrowed from BTFP}]\)
\(DW_i\) Binary: Bank \(i\) borrowed from DW \(\mathbb{1}[\text{Bank } i \text{ borrowed from DW}]\)
\(BTFPAmount_i\) BTFP borrowing scaled by assets \(\frac{\text{BTFP Borrowing}_i}{\text{Assets}_i}\)
\(BTFP^{Acute}_i\) First BTFP borrow ≤ May 1, 2023 \(\mathbb{1}[\text{First BTFP date} \leq \text{May 1}]\)
\(BTFP^{PostAcute}_i\) First BTFP borrow ∈ (May 1, Oct 31] \(\mathbb{1}[\text{First BTFP date} \in (\text{May 1, Oct 31}]]\)
\(BTFP^{Arb}_i\) First BTFP borrow ∈ (Nov 1, Jan 24] \(\mathbb{1}[\text{First BTFP date} \in (\text{Nov 1, Jan 24}]]\)

2.2 Key Explanatory Variables

Variable Definition Formula
\(MTM^{BTFP}_i\) MTM loss on BTFP-eligible securities / Assets \(\frac{\text{MTM Loss on OMO-Eligible}_i}{\text{Total Assets}_i}\)
\(MTM^{Other}_i\) MTM loss on non-eligible assets / Assets \(\frac{\text{MTM Loss on Non-OMO}_i}{\text{Total Assets}_i}\)
\(UninsuredLev_i\) Uninsured deposits / Assets \(\frac{\text{Uninsured Deposits}_i}{\text{Total Assets}_i}\)
\(EligibleCollateral_i\) BTFP-eligible securities / Assets \(\frac{\text{OMO-Eligible Securities}_i}{\text{Total Assets}_i}\)
\(BorrowingSubsidy_i\) MTM loss rate on eligible collateral \(\frac{\text{MTM Loss on OMO-Eligible}_i}{\text{OMO-Eligible}_i}\)

2.3 Run Risk Measures

Variable Definition Formula
\(RunRisk1_i\) Continuous: Uninsured × MTM \(\%\text{Uninsured}_i \times \%\text{MTM Loss}_i\)
\(RunRisk2_i\) Continuous: Runable × MTM \(\%\text{Runable}_i \times \%\text{MTM Loss}_i\)
\(RunRisk1Dummy_i\) Binary: Both above median \(\mathbb{1}[\%\text{Uninsured} > \tilde{p}_{50} \cap \%\text{MTM} > \tilde{p}_{50}]\)
\(RunRisk2Dummy_i\) Binary: Both above median \(\mathbb{1}[\%\text{Runable} > \tilde{p}_{50} \cap \%\text{MTM} > \tilde{p}_{50}]\)

2.4 Jiang et al. Insolvency Measures

Following Jiang et al. (2023), we construct multiple insolvency measures under different uninsured deposit run scenarios:

2.4.1 Insured Deposit Coverage Ratio (IDCR)

\[IDCR_i(s) = \frac{MV\_Assets_i - s \times UninsuredDeposits_i - InsuredDeposits_i}{InsuredDeposits_i}\]

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 \(IDCR < 0\)

2.4.2 Capital Ratio Metric

\[Insolvency_i(s) = \frac{(TotalAssets_i - TotalLiabilities_i) - s \times UninsuredDeposits_i \times MV\_Adjustment_i}{TotalAssets_i}\]

where: \[MV\_Adjustment_i = \frac{TotalAssets_i}{MV\_Assets_i} - 1\]

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

2.4.3 Adjusted Equity (Jiang-Style)

\[AdjustedEquity_i = EquityRatio_i - MTMLoss_i\]

\[MTM\_Insolvent_i = \mathbb{1}[AdjustedEquity_i < 0]\]

2.5 Control Variables

Variable Definition Formula
\(\ln(Assets)_i\) Log of total assets \(\ln(\text{Total Assets}_i)\)
\(CashRatio_i\) Cash / Assets \(\frac{\text{Cash}_i}{\text{Total Assets}_i}\)
\(SecuritiesRatio_i\) Securities / Assets \(\frac{\text{Securities}_i}{\text{Total Assets}_i}\)
\(ROA_i\) Return on assets \(\frac{\text{Net Income}_i}{\text{Avg Assets}_i}\)
\(LoanToDeposit_i\) Loans / Deposits \(\frac{\text{Total Loans}_i}{\text{Total Deposits}_i}\)
\(WholesaleRatio_i\) Wholesale funding / Liabilities \(\frac{\text{Fed Funds + Repo + Other Borr}_i}{\text{Total Liabilities}_i}\)
\(RunableRatio_i\) Runable liabilities / Liabilities \(\frac{\text{Uninsured + Wholesale}_i}{\text{Total Liabilities}_i}\)
\(LiquidityRatio_i\) Liquid assets / Assets \(\frac{\text{Cash + Rerepo + FF Sold}_i}{\text{Total Assets}_i}\)
\(FHLBRatio_i\) FHLB advances / Assets \(\frac{\text{FHLB Advances}_i}{\text{Total Assets}_i}\)
\(BookEquityRatio_i\) Book equity / Assets \(\frac{\text{Total Equity}_i}{\text{Total Assets}_i}\)

3 Model Specifications

3.1 Step 1: Extensive Margin (Full Period)

3.1.1 Specification (Equation 1)

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

Run separately for BTFP and DW as dependent variables.

3.1.2 Expected Signs (Table 4 from Outline)

Variable BTFP Eq. DW Eq. Rationale
\(MTM^{BTFP}\) + (large) ≈ 0 Par valuation subsidy at BTFP only
\(MTM^{Other}\) ≈ 0 + No BTFP subsidy for non-eligible losses
\(MTM^{BTFP} \times UninsuredLev\) + (large) + (small) SVB channel strongest at BTFP

Key test: Is \(\beta_1^{BTFP} > \delta_1^{DW}\)? If so, par valuation generated differential selection.

3.2 Step 2: Temporal Analysis

3.2.1 Specification (Equation 2)

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

\[BTFP^p_i = \alpha + \beta^p_1 \cdot MTM^{BTFP}_i + \beta^p_2 \cdot MTM^{Other}_i + \beta^p_3 \cdot UninsuredLev_i + \beta^p_4 \cdot (MTM^{BTFP}_i \times UninsuredLev_i) + \beta^p_5 \cdot EligibleCollateral_i + \gamma'Z_i + \varepsilon_i\]

3.2.2 Expected Patterns (Table 3 from Outline)

Variable Period 1 (Acute) Period 2 (Post-Acute) Period 3 (Arbitrage)
\(\beta_{MTM^{BTFP}}\) Large + Moderate + Small or 0
\(\beta_{UninsuredLev}\) Large + Small + ≈ 0
\(\beta_{EligibleCollateral}\) + + Large +
Interpretation Need Subsidy Arbitrage capacity

3.3 Step 3: Intensive Margin

3.3.1 Specification (Equation 3)

Among BTFP users:

\[\frac{BTFPAmount_i}{Assets_i} = \alpha + \beta_1 \cdot MTM^{BTFP}_i + \beta_2 \cdot MTM^{Other}_i + \beta_3 \cdot UninsuredLev_i + \beta_4 \cdot EligibleCollateral_i + \gamma'Z_i + \varepsilon_i\]

Expected: \(\beta_1 > 0\) (subsidy capture); \(\beta_4 > 0\) (capacity)

3.4 Step 4: “Both” Banks and Collateral Constraints

3.4.1 Analysis 1: DW Usage Among BTFP Users (Equation 4)

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

3.4.2 Analysis 2: Maxing Out (Equation 5)

\[DW_i = \alpha + \theta \cdot MaxedOut_i + \gamma'Z_i + \varepsilon_i \quad | \quad BTFP_i = 1\]

3.4.3 Analysis 3: Facility Allocation (Equation 6)

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

4 Setup and Configuration

#> ✓ All packages loaded successfully
#> Working directory: C:/Users/mferdo2/OneDrive - Louisiana State University/Finance_PhD/DW_Stigma_paper/Liquidity_project_2025
#> 
#> ================================================================
#> BANK EMERGENCY BORROWING ANALYSIS - 2023 CRISIS
#> ================================================================
#> Crisis Phases:
#>   Period 1 (Acute):     Mar 13 - May 1, 2023
#>   Period 2 (Post-Acute): May 2 - Oct 31, 2023
#>   Period 3 (Arbitrage): Nov 1 - Jan 24, 2024
#> ================================================================
#> ✓ Helper functions loaded

5 Data Loading and Preparation

#> 
#> === LOADING DATA ===
#> ✓ Call reports loaded: 61002 obs
#> ✓ BTFP loans loaded: 6734 obs
#> ✓ DW loans loaded: 7724 obs
#> ✓ Full program usage: BTFP = 1327 banks, DW = 1090 banks
#> ✓ Baseline sample: 4292 banks
#> ✓ All variables constructed
#> ✓ Period-specific facility usage aggregated
#> BTFP Usage by Period:
#>   Acute (Mar 13 - May 1):      492 banks
#>   Post-Acute (May 2 - Oct 31): 816 banks
#>   Arbitrage (Nov 1 - Jan 24):  801 banks
#> 
#> DW Usage by Period:
#>   Acute (Mar 13 - May 1):      424 banks
#>   Post-Acute (May 2 - Oct 31): 844 banks
#>   Arbitrage (Nov 1 - Jan 24):  0 banks
#> ======================================================================
#> FACILITY USAGE SUMMARY BY PERIOD
#> ======================================================================
#> 
#> --- FULL PROGRAM (Mar 13, 2023 - Mar 11, 2024) ---
#>   BTFP only:     846 (19.7%)
#>   DW only:       589 (13.7%)
#>   Both:          413 (9.6%)
#>   Any Fed:       1848 (43.1%)
#> 
#> --- PERIOD 1: ACUTE (Mar 13 - May 1, 2023) ---
#>   BTFP only:     368 (8.6%)
#>   DW only:       299 (7.0%)
#>   Both:          94 (2.2%)
#>   Any Fed:       761 (17.7%)
#> 
#> --- PERIOD 2: POST-ACUTE (May 2 - Oct 31, 2023) ---
#>   BTFP only:     576 (13.4%)
#>   DW only:       572 (13.3%)
#>   Both:          199 (4.6%)
#>   Any Fed:       1347 (31.4%)
#> 
#> --- PERIOD 3: ARBITRAGE (Nov 1 - Jan 24, 2024) ---
#>   BTFP only:     766 (17.8%)
#>   DW only:       0 (0.0%)
#>   Both:          0 (0.0%)
#>   Any Fed:       766 (17.8%)
#> ======================================================================
#> ✓ Variables winsorized

6 Descriptive Statistics: Asset and Liability Composition

#> ================================================================================
#> ASSET AND LIABILITY COMPOSITION TABLES
#> ================================================================================
#> 
#> Generating descriptive tables for 2022Q4 and 2023Q1
#> ✓ Data Prepared successfully.
Bank Asset Composition, 2022Q4
(1)
(2)
(3)
(4)
(5)
Aggregate Full Sample Small Large GSIB
Number of Banks 4,737 4,737 3,967 737 33
Cash 11.0 8.1 (7.4) 8.5 (7.5) 5.2 (5.6) 18.7 (10.1)
Securities 24.0 24.0 (14.9) 24.7 (15.2) 20.5 (12.2) 17.4 (17.4)
Treasury 6.0 3.3 (4.8) 3.5 (5.0) 2.3 (3.7) 5.1 (6.1)
RMBS 11.2 3.0 (4.3) 2.4 (3.9) 6.1 (5.1) 4.9 (6.1)
CMBS 1.8 0.8 (1.4) 0.6 (1.3) 1.3 (1.6) 0.8 (1.4)
ABS 3.1 1.0 (1.7) 0.9 (1.6) 1.5 (1.9) 1.4 (2.3)
Other Securities 1.9 14.5 (12.2) 15.9 (12.4) 7.4 (7.7) 2.3 (5.9)
Total Loans 51.0 60.8 (16.5) 59.7 (16.6) 67.4 (13.6) 43.6 (18.9)
Real Estate Loans 24.2 45.9 (18.3) 45.4 (18.2) 49.7 (17.4) 22.0 (18.6)
Residential Mortgage 11.7 17.3 (12.8) 17.7 (13.0) 15.6 (11.7) 11.8 (15.4)
Commercial Mortgage 2.5 2.3 (2.8) 2.0 (2.6) 4.0 (3.1) 1.1 (2.1)
Other Real Estate 10.0 24.8 (12.9) 24.5 (12.7) 27.9 (12.8) 4.3 (6.2)
Agricultural Loans 0.3 3.0 (4.8) 3.4 (5.1) 0.8 (2.1) 0.1 (0.4)
Commercial & Industrial 9.8 7.2 (5.4) 6.8 (5.1) 9.4 (6.4) 4.4 (5.9)
Consumer Loans 8.6 2.4 (2.7) 2.3 (2.5) 2.5 (3.4) 3.5 (4.3)
Loans to Non-Depositories 3.2 0.1 (0.2) 0.0 (0.2) 0.2 (0.3) 0.4 (0.4)
Fed Funds Sold 0.1 0.8 (1.8) 0.9 (1.9) 0.1 (0.6) 0.6 (1.9)
Reverse Repo 1.3 0.0 (0.0) 0.0 (0.0) 0.0 (0.0) 0.0 (0.0)
Note:
Values are percentages of total assets. Row 1 shows number of banks. Column (1) is aggregate. Columns (2)-(5) are bank-level averages. Standard deviations in parentheses. All bank-level statistics (Cols 2-5) are winsorized at the 5th and 95th percentiles.
Bank Liability Composition, 2022Q4
(1)
(2)
(3)
(4)
(5)
Aggregate Full Sample Small Large GSIB
Number of Banks 4,737 4,737 3,967 737 33
Total Liabilities 90.6 90.3 (3.7) 90.3 (3.8) 90.4 (2.9) 86.9 (4.7)
Domestic Deposits 75.1 85.7 (6.4) 86.1 (6.4) 83.6 (5.7) 77.0 (7.9)
Insured Deposits 42.1 61.8 (12.7) 63.6 (11.9) 52.8 (12.0) 46.9 (18.4)
Uninsured Deposits 35.8 23.0 (11.0) 21.7 (10.4) 30.2 (11.0) 23.1 (17.0)
Uninsured Time Deposits (Total) 2.2 4.1 (3.4) 4.3 (3.4) 3.4 (3.0) 1.5 (2.4)
Long-term Time Deposits 0.3 1.1 (1.2) 1.1 (1.2) 0.8 (0.9) 0.1 (0.3)
Short-term Time Deposits 1.9 2.9 (2.6) 3.0 (2.6) 2.6 (2.4) 1.3 (2.2)
Foreign Deposits 6.3 0.0 (0.0) 0.0 (0.0) 0.0 (0.0) 0.0 (0.0)
Fed Funds Purchased 0.2 0.2 (0.5) 0.2 (0.5) 0.1 (0.4) 0.0 (0.0)
Repo 0.6 0.2 (0.7) 0.2 (0.6) 0.5 (0.9) 0.2 (0.6)
Other Liabilities 7.2 3.6 (4.0) 3.2 (3.9) 5.5 (4.1) 6.2 (4.4)
Total Equity 9.4 9.7 (3.7) 9.7 (3.8) 9.6 (2.9) 13.1 (4.7)
Common Stock 0.2 0.4 (0.6) 0.4 (0.6) 0.2 (0.6) 0.7 (1.0)
Preferred Stock 0.1 0.0 (0.0) 0.0 (0.0) 0.0 (0.0) 0.0 (0.0)
Retained Earnings 4.4 7.2 (4.2) 7.4 (4.3) 6.1 (3.2) 7.4 (5.3)
Note:
Values are percentages of total assets. Row 1 shows number of banks. Column (1) is aggregate. Columns (2)-(5) are bank-level averages. Standard deviations in parentheses. All bank-level statistics (Cols 2-5) are winsorized at the 5th and 95th percentiles.
Bank Asset Composition, 2023Q1
(1)
(2)
(3)
(4)
(5)
Aggregate Full Sample Small Large GSIB
Number of Banks 4,712 4,712 3,943 736 33
Cash 12.0 8.3 (7.1) 8.6 (7.2) 6.2 (5.6) 18.0 (9.5)
Securities 22.8 23.7 (14.9) 24.5 (15.2) 19.8 (11.8) 17.1 (17.1)
Treasury 5.5 3.1 (4.6) 3.3 (4.8) 2.1 (3.5) 4.9 (5.9)
RMBS 10.8 2.9 (4.3) 2.4 (3.8) 5.9 (5.0) 4.9 (6.2)
CMBS 1.7 0.8 (1.4) 0.7 (1.3) 1.3 (1.6) 0.8 (1.4)
ABS 3.0 0.9 (1.6) 0.8 (1.5) 1.5 (1.8) 1.4 (2.2)
Other Securities 1.9 14.4 (12.1) 15.9 (12.3) 7.3 (7.6) 2.2 (6.0)
Total Loans 50.6 60.8 (16.4) 59.7 (16.6) 67.4 (13.0) 44.3 (19.6)
Real Estate Loans 24.2 46.3 (18.3) 45.8 (18.3) 50.0 (17.1) 22.8 (20.3)
Residential Mortgage 11.7 17.5 (12.9) 17.9 (13.1) 15.7 (11.6) 12.0 (15.6)
Commercial Mortgage 2.5 2.3 (2.8) 2.0 (2.6) 4.1 (3.1) 1.1 (2.2)
Other Real Estate 10.0 25.0 (12.9) 24.6 (12.8) 28.0 (12.8) 4.3 (6.0)
Agricultural Loans 0.3 2.6 (4.2) 3.0 (4.5) 0.7 (1.8) 0.1 (0.3)
Commercial & Industrial 9.7 7.2 (5.4) 6.8 (5.1) 9.3 (6.3) 4.4 (5.9)
Consumer Loans 8.5 2.4 (2.7) 2.4 (2.6) 2.6 (3.5) 3.5 (4.3)
Loans to Non-Depositories 3.2 0.1 (0.2) 0.0 (0.2) 0.2 (0.3) 0.4 (0.4)
Fed Funds Sold 0.1 0.9 (1.8) 1.0 (2.0) 0.2 (0.7) 0.4 (1.6)
Reverse Repo 1.3 0.0 (0.0) 0.0 (0.0) 0.0 (0.0) 0.0 (0.0)
Note:
Values are percentages of total assets. Row 1 shows number of banks. Column (1) is aggregate. Columns (2)-(5) are bank-level averages. Standard deviations in parentheses. All bank-level statistics (Cols 2-5) are winsorized at the 5th and 95th percentiles.
Bank Liability Composition, 2023Q1
(1)
(2)
(3)
(4)
(5)
Aggregate Full Sample Small Large GSIB
Number of Banks 4,712 4,712 3,943 736 33
Total Liabilities 90.4 90.0 (3.7) 90.0 (3.8) 90.2 (2.7) 86.5 (4.8)
Domestic Deposits 72.9 85.1 (6.5) 85.7 (6.4) 82.6 (6.1) 75.3 (7.9)
Insured Deposits 42.9 62.8 (12.1) 64.5 (11.4) 54.5 (11.2) 47.8 (16.9)
Uninsured Deposits 32.7 21.6 (10.2) 20.4 (9.8) 27.7 (10.2) 21.4 (15.9)
Uninsured Time Deposits (Total) 2.6 4.9 (3.8) 5.0 (3.8) 4.1 (3.5) 1.7 (2.7)
Long-term Time Deposits 0.3 1.1 (1.2) 1.2 (1.2) 0.8 (0.9) 0.1 (0.3)
Short-term Time Deposits 2.3 3.6 (3.1) 3.7 (3.1) 3.2 (2.8) 1.5 (2.4)
Foreign Deposits 6.1 0.0 (0.0) 0.0 (0.0) 0.0 (0.0) 0.0 (0.0)
Fed Funds Purchased 0.1 0.0 (0.2) 0.0 (0.2) 0.1 (0.2) 0.0 (0.0)
Repo 1.1 0.2 (0.6) 0.2 (0.6) 0.4 (0.8) 0.3 (0.7)
Other Liabilities 8.8 4.0 (4.3) 3.5 (4.0) 6.3 (4.6) 7.1 (5.1)
Total Equity 9.6 10.0 (3.7) 10.0 (3.8) 9.8 (2.7) 13.5 (4.8)
Common Stock 0.2 0.4 (0.7) 0.4 (0.7) 0.2 (0.6) 0.7 (1.0)
Preferred Stock 0.0 0.0 (0.0) 0.0 (0.0) 0.0 (0.0) 0.0 (0.0)
Retained Earnings 4.5 7.2 (4.2) 7.4 (4.3) 6.1 (3.2) 7.7 (5.5)
Note:
Values are percentages of total assets. Row 1 shows number of banks. Column (1) is aggregate. Columns (2)-(5) are bank-level averages. Standard deviations in parentheses. All bank-level statistics (Cols 2-5) are winsorized at the 5th and 95th percentiles.

7 Summary Statistics

7.1 Table 1: Summary by Facility Choice (Full Program)

Table 1: Descriptive Statistics by Facility Choice (Full Program)
facility N Assets ($B) MTM BTFP (%) MTM Other (%) Uninsured (%) % Insolvent Eligible (%)
None 2444 1.175 60.141 438.714 21.793 16.228 10.946
BTFP Only 846 2.529 80.938 497.721 24.382 29.669 11.143
DW Only 589 4.365 61.178 464.517 25.949 14.092 8.707
Both 413 8.841 84.902 494.128 28.517 23.245 10.717

7.2 Table 1b: Summary by Facility Choice - ACUTE Period

Table 1b: Descriptive Statistics - Acute Period (Mar 13 - May 1, 2023)
Facility (Acute) N Assets ($B) MTM BTFP (%) MTM Other (%) Uninsured (%) % Insolvent Eligible (%)
None 3531 1.881 63.718 451.114 22.738 18.063 10.677
BTFP Only 368 5.421 85.258 500.998 26.123 30.435 11.386
DW Only 299 5.522 73.041 494.972 26.806 19.064 9.342
Both 94 10.039 89.236 487.667 32.290 21.277 11.151

7.3 Table 1c: Summary by Facility Choice - POST-ACUTE Period

Table 1c: Descriptive Statistics - Post-Acute Period (May 2 - Oct 31, 2023)
Facility (Post-Acute) N Assets ($B) MTM BTFP (%) MTM Other (%) Uninsured (%) % Insolvent Eligible (%)
None 2945 1.693 62.265 449.538 22.474 17.649 10.729
BTFP Only 576 2.062 86.017 491.216 24.518 28.993 11.845
DW Only 572 5.354 63.306 466.538 26.477 16.259 8.825
Both 199 10.036 87.679 489.361 27.634 23.618 11.382

7.4 Table 1d: Summary by Facility Choice - ARBITRAGE Period

Table 1d: Descriptive Statistics - Arbitrage Period (Nov 1 - Jan 24, 2024)
Facility (Arbitrage) N Assets ($B) MTM BTFP (%) MTM Other (%) Uninsured (%) % Insolvent Eligible (%)
None 3526 2.26 62.999 448.983 23.008 17.378 10.584
BTFP Only 766 4.26 84.135 506.466 25.881 27.937 10.983

7.5 Insolvency Summary

#> 
#> === INSOLVENCY MEASURES ===
#> % MTM Insolvent: 19.3%
#> % IDCR (s=0.5) < 0: 4.2%
#> % IDCR (s=1.0) < 0: 28.3%
#> % Capital (s=0.5) < 0: 2.2%
#> % Capital (s=1.0) < 0: 7.6%

8 Step 1: Extensive Margin Analysis

Table 2: Extensive Margin - BTFP vs DW
BTFP DW
* p < 0.1, ** p < 0.05, *** p < 0.01
MTM (BTFP) 0.065*** 0.012
(0.020) (0.017)
MTM (Other) 0.009** 0.002
(0.004) (0.003)
Uninsured Leverage 1.567*** 0.441
(0.351) (0.317)
MTM_btfp × Uninsured Leverage -0.106 0.006
(0.075) (0.066)
% Runnable Liabilities -0.011*** -0.003
(0.003) (0.003)
% Wholesale Liabilities 0.015*** 0.006*
(0.004) (0.003)
FHLB Ratio 0.007*** 0.002
(0.002) (0.002)
Cash Ratio -0.001 -0.001
(0.001) (0.002)
% Liquidity Available -0.004*** -0.001
(0.001) (0.001)
Log(Assets) 0.052*** 0.091***
(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 -0.001 0.001
(0.001) (0.001)
ROA -0.001 0.002
(0.007) (0.007)
Constant -0.542*** -0.952***
(0.096) (0.084)
Num.Obs. 4282 4282
R2 0.103 0.120

8.1 Run Risk Specifications

Run Risk Specifications
Run Risk (Cont) Run Risk (Dummy)
* p < 0.1, ** p < 0.05, *** p < 0.01
(Intercept) -0.457*** -0.457***
(0.090) (0.090)
mtm_btfp 0.074*** 0.074***
(0.021) (0.021)
mtm_other -0.015*** -0.015***
(0.005) (0.005)
uninsured_lev 1.029** 1.029**
(0.410) (0.410)
I(mtm_btfp * uninsured_lev) -0.228*** -0.228***
(0.077) (0.077)
pct_runable_liability -0.011*** -0.011***
(0.003) (0.003)
run_risk_1 0.000*** 0.000***
(0.000) (0.000)
ln_assets 0.052*** 0.052***
(0.006) (0.006)
cash_ratio 0.000 0.000
(0.002) (0.002)
pct_liquidity_available -0.005*** -0.005***
(0.001) (0.001)
securities_ratio 0.002*** 0.002***
(0.001) (0.001)
loan_to_deposit 0.000 0.000
(0.000) (0.000)
book_equity_ratio -0.004*** -0.004***
(0.001) (0.001)
pct_wholesale_liability 0.013*** 0.013***
(0.004) (0.004)
fhlb_ratio 0.005*** 0.005***
(0.002) (0.002)
roa 0.000 0.000
(0.007) (0.007)
Num.Obs. 4251 4251
R2 0.109 0.109

8.2 Insolvency Specifications

Insolvency Specifications (Jiang Integration)
Adj. Equity IDCR (s=1.0) Capital (s=1.0)
* p < 0.1, ** p < 0.05, *** p < 0.01
(Intercept) -0.493*** -0.514*** -0.481***
(0.084) (0.084) (0.087)
mtm_btfp 0.024** 0.039*** 0.044***
(0.011) (0.011) (0.011)
mtm_other -0.011** 0.008** 0.010***
(0.005) (0.004) (0.004)
uninsured_lev 0.463 1.039** 1.243***
(0.379) (0.407) (0.330)
pct_runable_liability -0.002 -0.007** -0.011***
(0.003) (0.003) (0.003)
ln_assets 0.053*** 0.051*** 0.049***
(0.006) (0.006) (0.006)
cash_ratio -0.000 -0.001 -0.000
(0.001) (0.001) (0.001)
pct_liquidity_available -0.004*** -0.004*** -0.004***
(0.001) (0.001) (0.001)
securities_ratio 0.002*** 0.003*** 0.003***
(0.001) (0.001) (0.001)
loan_to_deposit 0.000 0.000 0.000
(0.000) (0.000) (0.000)
book_equity_ratio 0.010*** -0.004** 0.007***
(0.002) (0.002) (0.002)
pct_wholesale_liability 0.005 0.010** 0.014***
(0.004) (0.004) (0.004)
fhlb_ratio 0.006*** 0.007*** 0.006***
(0.002) (0.002) (0.002)
roa -0.003 -0.003 0.001
(0.007) (0.007) (0.007)
adjusted_equity -0.017***
(0.004)
I(adjusted_equity * uninsured_lev) -0.013
(0.009)
idcr_2 0.007**
(0.003)
I(idcr_2 * uninsured_lev) -0.023**
(0.010)
insolvency_2 -1.286***
(0.297)
I(insolvency_2 * uninsured_lev) 1.997***
(0.725)
Num.Obs. 4282 4282 4282
R2 0.109 0.103 0.107

9 Step 2: Temporal Analysis

9.1 BTFP by Period

Table 3a: BTFP Usage by Period
BTFP Acute BTFP Post-Acute BTFP Arbitrage
* p < 0.1, ** p < 0.05, *** p < 0.01
MTM (BTFP) -0.002 0.029* 0.038**
(0.013) (0.018) (0.017)
MTM (Other) 0.002 0.001 0.008**
(0.002) (0.003) (0.003)
Uninsured Leverage 0.685*** 0.839*** 0.841***
(0.238) (0.286) (0.252)
MTM × Uninsured 0.076 0.011 -0.027
(0.055) (0.067) (0.063)
Log(Assets) 0.032*** 0.020*** 0.035***
(0.005) (0.005) (0.005)
Cash Ratio -0.001 -0.001 -0.002*
(0.001) (0.001) (0.001)
ROA -0.001 -0.000 -0.002
(0.004) (0.006) (0.006)
Num.Obs. 4282 4282 4282
R2 0.069 0.054 0.073

9.2 DW by Period

Table 3b: DW Usage by Period
DW Acute DW Post-Acute
* p < 0.1, ** p < 0.05, *** p < 0.01
Notes: Heteroskedasticity-robust standard errors in parentheses. Post-acute data through Sept 30.
MTM (BTFP Eligible) -0.004 0.011
(0.012) (0.017)
MTM (Other) 0.004* -0.001
(0.002) (0.003)
Uninsured Leverage 0.347 0.336
(0.216) (0.303)
MTM × Uninsured 0.049 -0.000
(0.052) (0.064)
Log(Assets) 0.046*** 0.062***
(0.005) (0.006)
Cash Ratio -0.001 -0.000
(0.001) (0.001)
ROA 0.002 0.002
(0.004) (0.006)
Num.Obs. 4282 4282
R2 0.067 0.079

9.3 Any Fed Facility by Period

Table 3c: Any Fed Facility by Period
Any Fed Acute Any Fed Post-Acute Any Fed Arbitrage
* p < 0.1, ** p < 0.05, *** p < 0.01
Notes: Heteroskedasticity-robust standard errors in parentheses. DW data avaiable through Sept 30.
MTM (BTFP Eligible) 0.007 0.045** 0.038**
(0.016) (0.020) (0.017)
MTM (Other) 0.006* -0.000 0.008**
(0.003) (0.004) (0.003)
Uninsured Leverage 0.922*** 1.006*** 0.841***
(0.280) (0.346) (0.252)
MTM × Uninsured 0.060 -0.060 -0.027
(0.061) (0.073) (0.063)
Log(Assets) 0.063*** 0.066*** 0.035***
(0.006) (0.006) (0.005)
Cash Ratio -0.002* -0.001 -0.002*
(0.001) (0.002) (0.001)
ROA 0.002 0.001 -0.002
(0.006) (0.007) (0.006)
Num.Obs. 4282 4282 4282
R2 0.106 0.091 0.073

9.4 Borrower Comparison

Borrower Characteristics by Period
btfp_period N MTM BTFP (%) Uninsured (%) % Insolvent
Acute 462 86.068 27.378 28.571
Arbitrage 242 73.223 25.075 28.099
PostAcute 522 83.675 24.647 26.628
Winddown 33 72.027 24.918 24.242

10 Step 3: Intensive Margin

Table 4: Intensive Margin
Main Run Risk Dummy
* p < 0.1, ** p < 0.05, *** p < 0.01
(Intercept) 78088.514*** 77939.496***
(18972.805) (18951.566)
mtm_btfp -4648.897** -4694.844**
(2338.224) (2361.659)
mtm_other -887.502*** -837.816**
(337.534) (384.399)
uninsured_lev 71528.640 76459.741
(68303.077) (71815.561)
I(mtm_btfp * uninsured_lev) 18317.937* 18691.410*
(9428.134) (9744.715)
pct_runable_liability -635.331 -672.507
(625.551) (649.664)
ln_assets -427.718 -438.174
(627.768) (636.291)
cash_ratio 328.617 325.787
(214.186) (214.041)
pct_liquidity_available -1242.640*** -1243.528***
(286.826) (287.146)
securities_ratio -498.682** -498.571**
(200.331) (200.494)
loan_to_deposit -710.016*** -711.798***
(197.285) (197.599)
book_equity_ratio 1180.259*** 1188.790***
(352.317) (355.725)
pct_wholesale_liability 1544.599** 1587.811**
(704.904) (733.901)
fhlb_ratio 1362.445*** 1365.710***
(293.918) (294.557)
roa -535.660 -521.559
(1279.534) (1271.930)
run_risk_1_dummy -536.514
(1555.028)
Num.Obs. 1259 1259
R2 0.097 0.097 
#> 
#> Subsidy: $ 404875.5 B borrowed at  7.9 % avg MTM = $ 36126.1 B implied subsidy

11 Step 4: Both Banks Analysis

Table 5: Both Banks Analysis
DW|BTFP (MTM) DW|BTFP (MaxOut)
* p < 0.1, ** p < 0.05, *** p < 0.01
(Intercept) -0.831** -0.625
(0.415) (0.425)
mtm_btfp 0.032 0.038
(0.041) (0.040)
mtm_other -0.016 -0.006
(0.017) (0.008)
uninsured_lev -0.764 -0.697
(1.087) (1.065)
I(mtm_btfp * uninsured_lev) -0.121 -0.116
(0.140) (0.142)
pct_runable_liability 0.011 0.010
(0.010) (0.010)
adjusted_equity -0.012
(0.017)
ln_assets 0.087*** 0.082***
(0.012) (0.012)
cash_ratio 0.002 0.002
(0.006) (0.006)
pct_liquidity_available -0.004 -0.005
(0.007) (0.007)
securities_ratio -0.002 -0.002
(0.004) (0.004)
loan_to_deposit -0.001 -0.001
(0.004) (0.004)
book_equity_ratio 0.008 -0.004
(0.017) (0.006)
pct_wholesale_liability -0.001 0.000
(0.012) (0.012)
fhlb_ratio 0.005 0.006
(0.005) (0.005)
roa 0.015 0.011
(0.020) (0.020)
maxed_out_btfp -0.108**
(0.051)
Num.Obs. 1259 1259
R2 0.106 0.109 
#> 
#> Collateral Utilization:
#>   Mean: 910211.5%
#>   % Maxed Out: 91.5%

12 Robustness Tests

12.1 By Bank Size

By Bank Size
Large Small
* p < 0.1, ** p < 0.05, *** p < 0.01
(Intercept) -0.167 -0.395*
(0.157) (0.216)
mtm_btfp 0.063 0.078***
(0.040) (0.023)
mtm_other 0.007 0.003
(0.006) (0.004)
uninsured_lev 1.817*** 0.932**
(0.557) (0.365)
I(mtm_btfp * uninsured_lev) -0.075 -0.205**
(0.124) (0.095)
pct_runable_liability -0.014*** -0.005*
(0.005) (0.003)
ln_assets 0.018* 0.057***
(0.011) (0.014)
cash_ratio 0.002 0.001
(0.006) (0.001)
pct_liquidity_available -0.009* -0.006***
(0.005) (0.002)
securities_ratio 0.006*** -0.000
(0.001) (0.002)
loan_to_deposit 0.001*** -0.002*
(0.000) (0.001)
book_equity_ratio -0.004 -0.001
(0.003) (0.001)
pct_wholesale_liability 0.015*** 0.010**
(0.006) (0.004)
fhlb_ratio 0.007*** 0.007**
(0.003) (0.003)
roa -0.007 -0.001
(0.013) (0.008)
Num.Obs. 2145 2137
R2 0.080 0.067

12.2 All Insolvency Measures

All Insolvency Measures
IDCR s=0.5 IDCR s=1.0 Cap s=0.5 Cap s=1.0 Adj Eq
* p < 0.1, ** p < 0.05, *** p < 0.01
(Intercept) -0.542*** -0.561*** -0.541*** -0.541*** -0.542***
(0.096) (0.093) (0.096) (0.096) (0.089)
insolvent_idcr_s50 0.029
(0.034)
mtm_btfp 0.066*** 0.066*** 0.065*** 0.065*** 0.064***
(0.020) (0.020) (0.020) (0.020) (0.020)
mtm_other 0.009** 0.009** 0.009** 0.009** 0.003
(0.004) (0.004) (0.004) (0.004) (0.004)
uninsured_lev 1.571*** 1.430*** 1.558*** 1.564*** 1.373***
(0.350) (0.348) (0.351) (0.355) (0.346)
I(mtm_btfp * uninsured_lev) -0.107 -0.102 -0.106 -0.106 -0.119
(0.075) (0.075) (0.075) (0.075) (0.075)
pct_runable_liability -0.011*** -0.010*** -0.011*** -0.011*** -0.010***
(0.003) (0.003) (0.003) (0.003) (0.003)
ln_assets 0.051*** 0.052*** 0.052*** 0.052*** 0.053***
(0.006) (0.006) (0.006) (0.006) (0.006)
cash_ratio -0.001 -0.001 -0.001 -0.001 -0.000
(0.001) (0.001) (0.001) (0.001) (0.001)
pct_liquidity_available -0.004*** -0.004*** -0.004*** -0.004*** -0.004***
(0.001) (0.001) (0.001) (0.001) (0.001)
securities_ratio 0.003*** 0.003*** 0.002*** 0.003*** 0.002***
(0.001) (0.001) (0.001) (0.001) (0.001)
loan_to_deposit -0.000 -0.000 -0.000 -0.000 0.000
(0.000) (0.000) (0.000) (0.000) (0.000)
book_equity_ratio -0.001 -0.001 -0.001 -0.001 -0.000
(0.001) (0.001) (0.001) (0.001) (0.001)
pct_wholesale_liability 0.015*** 0.015*** 0.015*** 0.015*** 0.013***
(0.004) (0.004) (0.004) (0.004) (0.004)
fhlb_ratio 0.007*** 0.008*** 0.007*** 0.007*** 0.007***
(0.002) (0.002) (0.002) (0.002) (0.002)
roa -0.001 -0.000 -0.001 -0.001 -0.002
(0.007) (0.007) (0.007) (0.007) (0.007)
insolvent_idcr_s100 0.043***
(0.016)
insolvent_cap_s50 0.016
(0.049)
insolvent_cap_s100 0.002
(0.029)
mtm_insolvent 0.076***
(0.022)
Num.Obs. 4282 4282 4282 4282 4282
R2 0.103 0.105 0.103 0.103 0.106

13 Visualization

14 Variable Dictionary

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
%Uninsured Continuous Uninsured / Total Deposit
%MTM Continuous MTM loss × / Asset
run_risk_1 Continuous %Uninsured × %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

15 Session Info

#> R version 4.3.1 (2023-06-16 ucrt)
#> Platform: x86_64-w64-mingw32/x64 (64-bit)
#> Running under: Windows 11 x64 (build 26100)
#> 
#> 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] psych_2.5.6        moments_0.14.1     DescTools_0.99.60  modelsummary_2.3.0
#>  [5] kableExtra_1.4.0   knitr_1.50         gridExtra_2.3      patchwork_1.3.0   
#>  [9] scales_1.3.0       ggthemes_5.1.0     ggplot2_3.5.1      broom_1.0.8       
#> [13] lmtest_0.9-40      zoo_1.8-12         sandwich_3.1-1     fixest_0.12.1     
#> [17] readr_2.1.5        stringr_1.5.1      lubridate_1.9.4    tibble_3.2.1      
#> [21] tidyr_1.3.1        dplyr_1.1.4        data.table_1.17.0 
#> 
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#>  [1] mnormt_2.1.1        gld_2.6.7           readxl_1.4.3       
#>  [4] rlang_1.1.2         magrittr_2.0.3      dreamerr_1.4.0     
#>  [7] e1071_1.7-14        compiler_4.3.1      mgcv_1.8-42        
#> [10] systemfonts_1.0.6   vctrs_0.6.4         pkgconfig_2.0.3    
#> [13] crayon_1.5.2        fastmap_1.1.1       backports_1.4.1    
#> [16] labeling_0.4.3      utf8_1.2.4          rmarkdown_2.29     
#> [19] tzdb_0.4.0          haven_2.5.4         purrr_1.0.2        
#> [22] bit_4.0.5           xfun_0.54           cachem_1.0.8       
#> [25] litedown_0.7        jsonlite_1.8.7      tinytable_0.15.1   
#> [28] stringmagic_1.1.2   parallel_4.3.1      R6_2.5.1           
#> [31] bslib_0.5.1         tables_0.9.31       stringi_1.7.12     
#> [34] RColorBrewer_1.1-3  boot_1.3-28.1       jquerylib_0.1.4    
#> [37] cellranger_1.1.0    numDeriv_2016.8-1.1 Rcpp_1.0.12        
#> [40] parameters_0.28.3   Matrix_1.5-4.1      splines_4.3.1      
#> [43] timechange_0.3.0    tidyselect_1.2.1    rstudioapi_0.16.0  
#> [46] yaml_2.3.7          lattice_0.21-8      withr_2.5.2        
#> [49] bayestestR_0.17.0   evaluate_0.23       proxy_0.4-27       
#> [52] xml2_1.3.6          pillar_1.9.0        checkmate_2.3.1    
#> [55] insight_1.4.3       generics_0.1.3      vroom_1.6.5        
#> [58] hms_1.1.3           munsell_0.5.0       rootSolve_1.8.2.4  
#> [61] class_7.3-22        glue_1.6.2          lmom_3.2           
#> [64] tools_4.3.1         forcats_1.0.0       Exact_3.3          
#> [67] fs_1.6.3            mvtnorm_1.3-3       grid_4.3.1         
#> [70] datawizard_1.3.0    colorspace_2.1-0    nlme_3.1-162       
#> [73] performance_0.15.3  Formula_1.2-5       cli_3.6.1          
#> [76] fansi_1.0.5         expm_1.0-0          viridisLite_0.4.2  
#> [79] svglite_2.1.3       gtable_0.3.6        sass_0.4.9         
#> [82] digest_0.6.33       farver_2.1.1        htmltools_0.5.7    
#> [85] lifecycle_1.0.4     httr_1.4.7          bit64_4.0.5        
#> [88] MASS_7.3-60