## 1. Balancing tests

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---

### Purpose and identification
- Aim: assess whether differences in banks’ liability structure (reliance on wholesale funding) affected their supply of mortgage credit during the 2005–2008 period, and to ensure observed differences are not driven by imbalances in borrower or loan characteristics.
- Identification sources of variation:
  - time variation in overall market liquidity (crisis period proxied by TED spread),
  - cross-sectional variation in the core deposit to assets ratio (CD/A), defined as deposits excluding time deposits over $100,000 divided by assets.
- Outcome of interest in micro analysis: change in bank-level rejection rates of conventional 1–4 family purchase mortgage applications (used as an indicator of supply shifts, less confounded by demand than aggregate volume).

### Matching procedure and sample construction
- Data merged: HMDA mortgage application data (2005–2008) matched to bank Call Report financials via agency IDs.
- HMDA sample restrictions:
  - owner-occupied home purchases of conventional one-to-four-family properties,
  - loans in counties within Metropolitan Statistical Areas (MSAs) — sample covers 295 MSAs (analysis elsewhere restricted to 773 counties covering around 80% of total HMDA originations in 2005),
  - exclude loans below $25,000 and above $1,000,000,
  - focus on depository institutions (banks) and their affiliates,
  - banks that originated at least 50 mortgage loans in a given year and that survived the whole sample period.
- Resulting samples and counts:
  - original sample includes 4,746 banks,
  - initial HMDA sample around 5.2 million applications,
  - restricting to banks with at least 50 loans reduces the sample to 555 banks and around 4.3 million applications,
  - excluding very small or very large loans removes around 0.3 million observations, leaving about 4 million applications for 2005–2008,
  - matching to construct characteristically identical pairs reduces the sample from around 2.6 million to less than 150 thousands observations on matched pairs.
- Definition of core deposits: sum of a bank’s deposits excluding time deposits over $100,000 (lagged CD/A used in analysis, including for 2008).

### Balancing variables used in matching
- Matching covariates (used to create retail vs. wholesale bank application pairs within the same MSA):
  - gender,
  - race,
  - income,
  - loan-to-income ratio,
  - income of the census tract of the applicant.
- Matching conducted within the same MSA to control for regional effects.
- Matching details:
  - Abadie and Imbens (2002) exact matching procedure used.
  - One-way (within-year) and two-way (across-years, with incomes deflated by county nominal income growth) matching implemented.
  - Caliper matching variant: matched pairs with distance in the upper 25th percentile in each matching group are dropped.

### Balancing tests and diagnostics
- Tests used:
  - Kolmogorov-Smirnov (KS) test of distributional differences,
  - t-test to compare means.
- Outcomes:
  - Neither the t-test nor the KS test rejects equality of means or distributions in the matched sample.
  - Authors target p-values above 10 percent for t-test and KS; this threshold is far exceeded in matched samples.
  - Example: mean and median income between Wholesale and Retail banks differ only at the third decimal point in matched sample.
- Practical implication:
  - Matching produced subsamples of retail and wholesale bank applications with almost identical distributions of observables, addressing concerns about poor overlap and potential confounding.

### Key summary statistics preserved from the source
- Aggregate lending in the 2005–2008 bank sample:
  - total originations around $898 billion,
  - this is more than 19% of the 4.7 trillion of 1–4 family purchase originations reported by the Mortgage Banker Association over the same period.
- Year-specific patterns:
  - 2005 saw the highest number of originations in the sample period;
  - volume of originations declined substantially in 2007 with the start of the mortgage crisis and declined by around 46% by 2008 compared to 2005.
- Rejection rates:
  - average rejection rate for banks shows an increase of 1.62% during 2008 from 2007.
- Sample counts reiterated:
  - balanced 2005–2008 sample consists of around 4 million applications at 555 banks,
  - the matching exercise reduces the sample to less than 150 thousands matched observations.
- CD/A distribution facts:
  - CD/A standard error 11%,
  - TED spread: hovered around 0.43% between 2005 and 2007, hiked to between 1% and 2.4% following August 2007, remained above 1% virtually during all of 2008, reached 5.76% in October 2008, and averaged 2.56% during the second half of 2008.

### Empirical findings from matched and full samples
- Main micro finding:
  - marginal effect of a one standard deviation decrease in CD/A is an increase in the rejection rate by around 3 percentage points during the crisis.
  - one standard deviation in CD/A corresponds to an increase by around 0.11 in CD/A; a one standard deviation increase in CD/A is associated with a 3% lower probability of rejection during the crisis.
- Robustness:
  - effect holds at the U.S. level controlling for MSA fixed effects interacted with the crisis dummy, in largest MSAs, and after excluding the largest banks.
  - relation holds in a subsample of least risky applications (higher income applicants in MSAs least affected by house price collapse).
  - matching on borrower observables produces near-identical distributions and results persist in reduced matched sample with only trivial changes to marginal impact estimate.
- Bank characteristic interactions:
  - higher leverage ratio and higher liquidity ratio as of end 2007 predict smaller increases in rejection during 2008;
  - higher provision for losses predicts higher rejection rates;
  - banks with higher shares of loans secured by properties continued to lend relative to banks less concentrated in this market.
- Subsample analyses:
  - small banks (lower 90% by total assets): interaction coefficient remains negative and significant, though smaller in magnitude.
  - MSAs with high housing supply elasticity and high-income borrowers: results hold.
  - MSA-level regressions: negative relation significant in 14 out of the top 18 MSAs.

### Demand-side checks
- Objective: test whether changes in rejection rates reflect supply shifts rather than demand heterogeneity across bank types.
- Demand regressions (bank-MSA-year panel):
  - Dependent variables:
    - A_k,m,t = log of number of loan applications at bank k in MSA m in year t,
    - V_k,m,t = log of ratio of dollar volume of applications at bank k in MSA m to total assets of the bank.
  - Key reported coefficients (Table 7 excerpts):
    - Crisis (2008 dropping 2007) = -1.0877** (col 1, Number log),
    - Crisis (2008 dropping 2007) = -0.9215*** (col 2, Number log),
    - Core deposits /Assets coefficients: -3.2485**, -3.3234** (cols 1-2, Number log),
    - CDA x Crisis coefficients: 1.16461, 1.2022 (cols 1-2, not statistically significant),
    - Core deposits /Assets coefficients: -2.5746*, -2.7102** (cols 3-4, Volume/Assets log),
    - CDA x Crisis coefficients: 0.54230, 0.5746 (cols 3-4, not statistically significant),
    - R-squared: 0.4489 (col 1), 0.4540 (col 2), 0.6795 (col 3), 0.6827 (col 4),
    - Observations: 11,412 in each specification.
- Interpretation:
  - The crisis led to a significant decline in demand for mortgages.
  - CDA x Crisis is insignificant in all four specifications, implying demand did not vary systematically with banks’ liability structure across retail vs. wholesale banks within MSAs.
  - Conclusion: changes in rejection rates are likely reflecting supply shifts rather than differential demand shifts across bank types.

### Aggregate (MSA-level) supply effects and magnitudes
- Purpose: assess whether wholesale funding exposure translated into aggregate mortgage credit effects across MSAs using weighted average CD/A within MSA.
- Key estimation methods reported: static fixed-effects, dynamic fixed-effects, FE-2SLS, Difference GMM, System GMM.
- Selected coefficients from Table 8 (Panel A: Log volume of originations in MSA):
  - Average CD/A X Crisis coefficients:
    - 1.1520** (col 1, standard error 0.5238),
    - 1.2062** (col 2, standard error 0.5172),
    - 1.5092*** (col 3, standard error 0.5298),
    - 2.0592*** (col 4, standard error 0.5022) — preferred specification for level equations cited in text,
    - 3.0824** (col 5, standard error 1.3015).
  - Diagnostics:
    - FE-2SLS first-stage F-stat (col 3): 13.09,
    - AR(2) test p-values: 0.5370 (col 4), 0.2190 (col 5),
    - Hansen J p-value (col 3): 0.6520.
- Panel B (Change in log volume of originations in MSA):
  - Average CD/A X Crisis coefficients:
    - 3.5687** (col 1),
    - 2.7799** (col 2),
    - 2.0330*** (col 3),
    - 3.5076** (col 4),
    - 2.9060** (col 5).
  - FE-2SLS first-stage F-stat (col 3): 6.89.
- Magnitude interpretation (text summary):
  - A reported coefficient of 1.91 in column (4) of panel A implies about 2% increase in volume of mortgage originations when the average CD/A in an MSA increases by 1%.
  - Comparison across quartiles: CD/A lower quartile 57% versus upper quartile 62% — "the fall in the volume of originations was about 10% steeper in the MSA with more wholesale funded banks."

### Robustness and estimation choices
- LPM versus Probit/Logit:
  - LPM preferred for consistency when N→∞ and T fixed; Logit on one-way matched sample still yields coefficient on CD/A × Crisis significant at 1%.
- Matching sample types:
  - One-Way matching reduces sample to 0.68 million applications;
  - Two-Way matching reduces sample to 0.13 million applications;
  - Two-Way matched sample: some coefficients lose significance (e.g., loan-to-income), but coefficient of interest remains stable.
- Clustering and inference:
  - Two-way clustering of standard errors by bank and MSA used in micro regressions.
- GMM and IV diagnostics:
  - First-stage F statistics and AR(2), Hansen J / Sargan tests reported and do not reject instruments/assumptions in preferred specifications.

### Key takeaways and conclusions
- Banks with lower CD/A (more wholesale funding) experienced larger contractions in mortgage lending in 2008 than banks with higher CD/A:
  - Percentage drop in lending volume in 2008 vs 2007: three times larger for low CD/A group in means, more than twice larger in medians.
- During the crisis, higher reliance on core deposits (higher CD/A) mitigated increases in rejection rates:
  - One standard deviation increase in CD/A (~0.11) → 3% lower probability of rejection during the crisis.
- Matching, balancing tests, and demand analyses strengthen causal interpretation that reliance on wholesale funding contributed to a sharper contraction in supply during the crisis rather than reflecting compositional demand differences.
- Aggregate implications:
  - Regions where mortgage credit relied more on wholesale funding experienced larger contractions in mortgage originations during the crisis, implying wholesale funding reliance contributed to a meaningful aggregate supply contraction.

*Source: _wp12155 - 1. Balancing tests (pages excerpted from the PDF chapter).*

### 1. Balancing tests  ..............................................................................................19

### 1. Balancing tests

### Purpose and identification
- Aim: assess whether differences in banks’ liability structure (reliance on wholesale funding) affected their supply of mortgage credit during the 2005–2008 period, and to ensure observed differences are not driven by imbalances in borrower or loan characteristics.
- Identification uses two sources of variation:
  - time variation in overall market liquidity (crisis period),
  - cross-sectional variation in the core deposit to assets ratio (CD/A), defined as deposits excluding time deposits over $100,000 divided by assets.
- Outcome of interest in the micro analysis: change in bank-level rejection rates of conventional 1–4 family purchase mortgage applications (used as an indicator of supply shifts, less confounded by demand than aggregate volume).

### Matching procedure and sample construction
- Data merged: HMDA mortgage application data (2005–2008) matched to bank Call Report financials via agency IDs.
- HMDA sample restrictions:
  - focus on owner-occupied home purchases of conventional one-to-four-family properties,
  - restrict to loans in counties within Metropolitan Statistical Areas (MSAs) — sample covers 295 MSAs,
  - exclude loans below $25,000 and above $1,000,000,
  - focus on depository institutions (banks) and their affiliates,
  - restrict to banks that originated at least 50 mortgage loans in a given year and that survived the whole sample period.
- Resulting samples and counts:
  - original sample includes 4,746 banks,
  - initial HMDA sample around 5.2 million applications,
  - restricting to banks with at least 50 loans reduces the sample to 555 banks and around 4.3 million applications,
  - excluding very small or very large loans removes around 0.3 million observations, leaving about 4 million applications for 2005–2008,
  - matching to construct characteristically identical pairs reduces the sample from around 2.6 million to less than 150 thousands observations on matched pairs.
- Definition of core deposits: sum of a bank’s deposits excluding time deposits over $100,000 (lagged CD/A used in analysis, including for 2008).

### Balancing variables used in matching
- Matching covariates (used to create retail vs. wholesale bank application pairs within the same MSA):
  - gender,
  - race,
  - income,
  - loan-to-income ratio,
  - income of the census tract of the applicant.
- Matching conducted within the same MSA to control for regional effects.

### Key summary statistics preserved from the source
- Aggregate lending in the 2005–2008 bank sample:
  - total originations around $898 billion,
  - this is more than 19% of the 4.7 trillion of 1–4 family purchase originations reported by the Mortgage Banker Association over the same period.
- Year-specific patterns:
  - 2005 saw the highest number of originations in the sample period;
  - volume of originations declined substantially in 2007 with the start of the mortgage crisis and declined by around 46% by 2008 compared to 2005.
- Rejection rates:
  - average rejection rate for banks shows an increase of 1.62% during 2008 from 2007.
- Sample counts reiterated:
  - balanced 2005–2008 sample consists of around 4 million applications at 555 banks.
  - the matching exercise reduces the sample to less than 150 thousands matched observations.

### Empirical findings relevant to balancing tests and matched sample
- Main micro finding (from the broader analysis that balancing supports):
  - the marginal effect of a one standard deviation decrease in the ratio of core deposits to assets is an increase in the rejection rate by around 3 percentage points during the crisis.
  - this effect holds at the U.S. level controlling for MSA fixed effects interacted with the crisis dummy, in largest MSAs, and after excluding the largest banks.
  - the relation holds in a subsample of least risky applications (higher income applicants in MSAs least affected by house price collapse).
- Role of matching/balancing:
  - matching on observable borrower characteristics produces subsamples of retail and wholesale bank applications with almost identical distributions of observables, addressing concerns about poor distributional overlap and potential confounding.
  - results persist in the reduced matched sample with only trivial changes to the estimate of the marginal impact of bank funding on rejection rates during the crisis.
- Demand checks:
  - number and volume of loan applications are examined to assess demand-side heterogeneity across banks; the core deposit to asset ratio is not a significant predictor of changes in demand (change in number and volume of mortgage applications), supporting the interpretation that observed rejection-rate changes reflect supply-side effects.

### Implications of balancing-test results
- The balancing/matching exercise strengthens causal interpretation that reliance on wholesale funding contributed to a sharper contraction in supply during the crisis by reducing concerns that observed differences are driven by compositional differences in applicants served by wholesale versus retail banks.
- Robustness of findings across the full and matched samples, across MSAs, and after excluding largest banks indicates the results are not driven by outliers or poor overlap in covariate distributions.

*Source: _wp12155 - 1. Balancing tests (pages excerpted from the PDF chapter).*

### 2005. The category of low CD/A comprises banks with a CD/A below the 33th percentile

### _wp12155 - 2005. The category of low CD/A comprises banks with a CD/A below the 33th percentile

### Definitions and sample construction
- Low CD/A: banks with a CD/A below the 33th percentile in 2005.  
- Medium CD/A: banks with a CD/A above this limit but below the 67th percentile.  
- High CD/A: the remainder of banks.  
- CD/A ratio is relatively stable over 2005–2007, with a slight overall decrease between 2005 and 2007. The choice of year to define CDA categories has no effect on the reported patterns.  
- The CD/A distribution shows significant variation across banks with a standard error of 11% and left-skewness (most banks above the mean CD/A).

### Descriptive patterns: credit volumes and rejection rates
- Volume of mortgage credit (log) over 2005–08:
  - Both in mean (upper panel) and in median (lower panel) low CD/A banks experienced a larger contraction in the volume of credit in 2008 compared to banks that relied more on core deposits.
  - Since bars represent changes in the log of volume, the percentage drop in volume of lending in 2008 compared to 2007 is three times larger for the low CD/A group compared to the high CD/A group in means, and more than twice larger in medians.
- Rejection rates evolution:
  - Relative to 2005 and 2006, the rejection rate increased substantially more for the low CD/A category than for the high CD/A category in both mean and median.
  - Rejection rates are on average higher for the low CD/A group.

### Empirical strategy and identification
- Research question: did vulnerability of wholesale-funded banks to liquidity shocks lead to a sharper decline in their credit supply relative to other banks during the crisis?
- Identification uses two sources of variation:
  - Time variation in overall market liquidity (TED Spread as a proxy).
  - Cross-sectional variation in banks’ reliance on core deposits (CD/A).
- TED Spread facts:
  - TED spread hovered around 0.43% between 2005 and 2007.
  - It hiked to levels between 1% and 2.4% following August 2007.
  - It remained above 1% virtually during all of 2008, reaching 5.76% in October 2008.
  - The TED spread averaged 2.56% during the second half of 2008.
- Exogeneity and controls:
  - Use lagged CD/A (CDA_{k,t−1}) as explanatory variable.
  - Controls for three broad categories: bank characteristics, borrower/loan characteristics (from HMDA), and regional characteristics.
  - Include bank fixed effects, time-varying balance sheet variables, applicant-level controls, MSA fixed effects and MSA×Crisis interactions.
  - Regressions also run within largest MSAs to test geographic robustness.
  - Two-way clustering of standard errors by bank and MSA.

### Model specification
- Binary dependent variable R_{i,k,m,t} = 1 if loan application i at bank k in year t for a property in MSA m is rejected.
- Benchmark equation (linear probability model, LPM):
  - R_{i,k,m,t} = α_t + λ_k + δ_m + β X_{i,t} + φ Z_{k,t−1} + γ (Crisis_t × CDA_{k,t−1}) + η δ_m × Crisis_t + θ (Crisis_t × Z_{k,t−1}) + ε_{i,k,t,m}
- X_{i,t} (HMDA applicant/loan controls): applicant income, loan value (used to compute loan-to-income), gender, race, median income of census tract.
- Z_{k,t−1} (bank characteristics, interacted with Crisis_t): (i) log of total assets, (ii) ratio of liquid assets to total assets, (iii) capital to assets, (iv) income to total assets, (v) provisions for losses to total assets, (vi) ratio of unused commitments to total assets, (vii) return on equity as a share of total assets, and shares of construction loans, loans secured by properties, and commercial and industrial loans to total assets.
- Crisis definition:
  - Primary specification excludes 2007 and compares 2008 with 2005 and 2006.
  - Authors justify excluding 2007 because including it either as crisis or non-crisis attenuates estimated effects; dropping 2007 yields larger measured crisis impact for 2008.

### Benchmark empirical results
- Coefficient of interest γ (Crisis × lagged CD/A):
  - γ is negative and significant at the 1% level in benchmark LPM specifications.
  - Interpretation: banks with higher reliance on retail deposits entering the crisis curtailed credit less.
  - Quantified effect: a one standard deviation increase in the CD/A ratio (which corresponds to an increase by around 0.11) is associated with a 3% lower probability of rejection of the mortgage application during the crisis, everything else held constant.
- Robustness to bank controls:
  - Introducing the Z variables and their interactions with the crisis slightly decreases the magnitude of γ but it remains very significant.
  - Interaction results: higher leverage ratio and higher liquidity ratio as of end 2007 predict smaller increases in rejection during 2008; higher provision for losses predicts higher rejection rates.
  - Banks with higher shares of loans secured by properties continued to lend relative to banks less concentrated in this market.
- Subsample analyses:
  - Small banks (lower 90% by total assets): γ remains negative and significant, though smaller in magnitude.
  - MSAs with high elasticity of housing supply and high-income borrowers (upper quartiles): results hold. Selecting MSAs with no drop in house prices yields similar results.
  - MSA-level regressions across top MSAs: the negative relation between retail funding and rejection rate during the crisis holds in all MSAs and is significant in 14 out of the top 18 MSAs; lack of significance in MSAs with smaller numbers of applications (e.g., Boston and Detroit).

### Matching and balance robustness
- Motivation: control for potential imbalance in applicant characteristics across wholesale and retail banks that could bias results.
- Bank-type cutoff for matching:
  - Define wholesale vs retail banks using a CD/A cutoff of 58% (the 25th percentile).
  - Rationale: banks above 58% CD/A are typically classified as traditional retail banks; this cutoff divides almost equally the volume of applications between wholesale and retail banks.
- Matching procedure:
  - Use Abadie and Imbens (2002) exact matching procedure.
  - Matching variables: (i) MSA, (ii) census tract income, (iii) applicant income, (iv) loan-to-income ratio, (v) race, (vi) gender.
  - Perform within-year (one-way) matching and across-years (two-way) matching. For two-way matching, deflate income by county nominal income growth.
- Sample sizes post-matching:
  - Original sample ≈ 2.7 million applications.
  - Subsample for high-elasticity MSAs and high-income borrowers reduced to around 80 thousand observations (from 2.7 million).
  - Within-year matching reduces sample to 0.68 million applications.
  - Two-way matching reduces sample to 0.13 million applications.
- Estimation after matching:
  - Matching is followed by the same regressions as in the benchmark (difference-in-differences style with controls).
  - Purpose: ensure results are not driven by imbalance in borrower or geographic distributions across bank types.

### Key takeaways
- Banks with lower CD/A (more wholesale funding) experienced larger contractions in mortgage lending in 2008 than banks with higher CD/A:
  - Percentage drop in lending volume in 2008 vs 2007: three times larger for low CD/A group in means, more than twice larger in medians.
- During the crisis, higher reliance on core deposits (higher CD/A) mitigated increases in rejection rates:
  - One standard deviation increase in CD/A (~0.11) → 3% lower probability of rejection during the crisis.
- Results are robust to:
  - Inclusion of rich bank-level and applicant-level controls.
  - Subsample analyses (small banks, high-elasticity MSAs, high-income borrowers).
  - Matching procedures that address distributional overlap concerns.
- Liquidity market indicators corroborate timing and severity of crisis:
  - TED spread dynamics (0.43% pre-crisis, spiking to between 1% and 2.4% post-August 2007, peaking at 5.76% in October 2008, averaging 2.56% in H2 2008) provide exogenous liquidity shock variation for identification.

*Source: _wp12155 - 2005. The category of low CD/A comprises banks with a CD/A below the 33th percentile.*

### 1. Balancing tests

### 1. Balancing tests

### Balancing tests methodology
- Objective: check the effectiveness of the matching and ensure that the distribution of the applicant’s characteristics does not significantly differ across groups in the matched sample.
- Tests used:
  - Kolmogorov-Smirnov (KS) test of distributional differences.
  - t-test to compare the means.
- Matching procedure detail:
  - After one-to-one matching of applicants between the two categories of banks we drop matches which are too far apart, using a variant of caliper matching (Cochran and Rubin, 1973).
  - Specifically, we drop matched pairs with distance in the upper 25th percentile in each matching group.

### Balancing tests results
- Post-matching comparisons are shown in panels B and D of Table 6; the original sample comparisons are shown in panels A and C of the same table.
- Test outcomes:
  - Neither the t-test nor the KS test can reject the equality of the mean or the distribution of the variables, respectively, in the matched sample.
  - The authors’ target is to have p-values for the t-test and the KS test above 10 percent; the tables show that this threshold is far exceeded.
- Practical implication:
  - The wealth of data allowed implementation of a strict matching leading to almost identical distributions between applicant characteristics across groups.
  - Example: a quick comparison of the mean and median income between Wholesale and Retail banks shows they are almost exactly the same with a difference at the third decimal point.
- Conclusion: Overall the results of the balancing tests give comfort that the matching achieved its goal.

### Matched-sample next steps
- After balancing tests, the analysis proceeds by fitting equation (1) to the matched sample; results are reported in Table (reference in source). 

*Source: _wp12155 - 1. Balancing tests*

### 4. For comparison purposes we show in columns 1 and 2 the results from our earlier bench-

### _wp12155 - 4. For comparison purposes we show in columns 1 and 2 the results from our earlier bench-

### Robustness, matching, and estimation methods
- LPM regressions on unmatched and matched samples:
  - Columns (1) and (3): coefficients on the interaction between CD/A and crisis remain unchanged qualitatively and quantitatively relative to the benchmark.
  - Columns (2) and (4): coefficients on the interaction between the retail dummy and crisis remain unchanged qualitatively and quantitatively relative to the benchmark.
- One-Way versus Two-Way matched samples:
  - Columns (5) and (6) (Two-Way matched sample): some coefficients lose significance (e.g., loan-to-income), but the coefficient on the interaction of interest remains remarkably stable.
  - Matching likely removes observations from the thinner tails of distributions, reducing significance for some coefficients.
- LPM versus Logit/Probit:
  - LPM advantage: "The LPM has an important advantage over Probit and Logit models when N−→∞ and T is fixed, since the estimates are generally inconsistent in Probit or Logit, but are √N consistent using LPM (Wooldridge, 2002)."
  - Logit robustness: coefficient on the interaction between CD/A and the crisis dummy remains significant at the 1% level in the Logit on the One-Way matched sample.

### Demand for credit (Section F)
- Objective: test whether wholesale lenders decreased their supply of credit more during the crisis, while controlling for demand-related effects.
- Dependent variables and estimations (equations (2) and (3)):
  - A_k,m,t = α_t + λ_k + δ_m + γ(Crisis_t × CDA_k,t−1) + η δ_m × Crisis_t + ε_k,t,m
    - A_k,m,t is the log of the number of loan applications at bank k in MSA m in year t.
  - V_k,m,t = α_t + λ_k + δ_m + γ(Crisis_t × CDA_k,t−1) + η δ_m × Crisis_t + ε_k,t,m
    - V_k,m,t is the ratio of the dollar volume of applications at bank k in MSA m to the total assets of the bank (logged in estimation).
  - Time, bank, and MSA effects controlled; crisis dummy interacted with lagged CD/A.
- Key results (Table 7):
  - Columns (1)-(2): dependent variable = Number (log)
    - Crisis (2008 dropping 2007) = -1.0877** in column (1)
    - Crisis (2008 dropping 2007) = -0.9215*** in column (2)
    - Core deposits /Assets coefficients: -3.2485**, -3.3234**
    - CDA x Crisis coefficients: 1.16461, 1.2022 (not statistically significant)
    - R-squared: 0.4489 (col 1), 0.4540 (col 2)
  - Columns (3)-(4): dependent variable = Volume / Assets (log)
    - Core deposits /Assets coefficients: -2.5746*, -2.7102**
    - CDA x Crisis coefficients: 0.54230, 0.5746 (not statistically significant)
    - R-squared: 0.6795 (col 3), 0.6827 (col 4)
  - Observations: 11,412 in each specification.
  - Clustering: residuals clustered at bank and MSA level.
- Interpretation:
  - The crisis led to a significant decline in demand for mortgages.
  - The coefficient of CDA x Crisis is insignificant in all four specifications, implying demand did not vary systematically with banks’ liability structure across retail vs. wholesale banks within MSAs.
  - Positive but insignificant coefficient on the interaction could indicate limited applicant reallocation from wholesale to retail banks, but not to a statistically significant extent.
- Conclusion from demand analysis: changes in rejection rates are likely reflecting supply shifts rather than differential demand shifts across bank types.

### Aggregate supply effects (Section IV)
- Motivation: assess whether wholesale funding exposure translated into consequential aggregate mortgage credit effects across MSAs by exploiting cross-regional variation in banks’ liability structure (weighted average CD/A within MSA).
- Models estimated (equations (4) and (5)):
  - Level and change specifications for V_m,t (log of dollar value of total mortgage originations in MSA m at time t), including interactions Crisis_t × CDA_m,t−1 and Crisis_t × Z_m,t−1; control for MSA characteristics M_m,t−1.
- Key empirical findings (Table 8):
  - Panel A (Log volume of originations in MSA):
    - Average CD/A X Crisis coefficients:
      - Static fixed-effects (col 1): 1.1520** (standard error 0.5238)
      - Dynamic fixed-effects (col 2): 1.2062** (standard error 0.5172)
      - FE-2SLS (col 3): 1.5092*** (standard error 0.5298)
      - Difference GMM (col 4): 2.0592*** (standard error 0.5022) — preferred specification for level equations cited in text
      - System GMM (col 5): 3.0824** (standard error 1.3015)
    - Average CD/A X 2007 coefficients:
      - 0.6958* (col 1), 0.7942** (col 2), 0.3257 (col 3), 0.8759* (col 4), 2.2977* (col 5)
    - Log volume lag coefficients vary across methods (e.g., 0.0224** in col 1; 0.3881** in col 2; 0.0549 in col 3; 0.9577*** in col 4).
    - First-stage F-stat (FE-2SLS): 13.09 (col 3).
    - AR(2) test p-values: 0.5370 (col 4), 0.2190 (col 5).
    - Sargan and Hansen test p-values reported (e.g., Hansen J p-value 0.6520 col 3; 0.3950 col 5).
  - Panel B (Change in log volume of originations in MSA):
    - Average CD/A X Crisis coefficients:
      - 3.5687** (col 1), 2.7799** (col 2), 2.0330*** (col 3), 3.5076** (col 4), 2.9060** (col 5)
    - Average CD/A X 2007 coefficients:
      - 5.0827** (col 1), 3.8614** (col 2), 0.5640 (col 3), 3.3103* (col 4), 2.2010 (col 5)
    - First-stage F-stat (FE-2SLS): 6.89 (col 3).
    - AR(2) test p-values: 0.5550 (col 4), 0.2810 (col 5).
- Magnitude interpretation (textual summary tied to Table 8 results):
  - The paper reports: "We observe that MSAs with higher reliance on mortgage lending by retail funded banks experienced a smaller decrease in credit, everything else equal."
  - The coefficient of 1.91 in column (4) of panel A (text reference) implies about 2% increase in volume of mortgage originations when the average CD/A in an MSA increases by 1%.
  - Comparison across quartiles: CD/A lower quartile 57% versus upper quartile 62% — "the fall in the volume of originations was about 10% steeper in the MSA with more wholesale funded banks."
- Robustness and diagnostics:
  - FE-2SLS first-stage F statistics reported (e.g., 13.83 and 6.65 in text for different specifications).
  - Post-estimation diagnostics: AR(2) does not reject higher-order autocorrelation; Hansen J and Sargan tests do not reject overidentifying restrictions in GMM specifications.

### Conclusion (Section V)
- Main empirical finding: wholesale funded banks increased their rejection rate significantly more than retail banks during the crisis, controlling for borrower, lender, and regional confounding factors.
- Methodological strengths:
  - Control for regional factors, including regressions within Metropolitan Statistical Areas.
  - Matching sub-samples of statistically indistinguishable applicants between retail and wholesale banks (reducing sample by more than 95 percent) — main results remain strong.
  - Demand analysis shows both wholesale and retail banks faced a similar decline in demand, supporting interpretation that rejection rate changes mainly reflect supply shifts.
- Aggregate implication:
  - Regions where mortgage credit relied more on wholesale funding experienced larger contractions in mortgage originations during the crisis, suggesting that wholesale funding reliance contributed to a meaningful aggregate supply contraction.

*Source: Excerpt from _wp12155 - 4. For comparison purposes we show in columns 1 and 2 the results from our earlier bench- (PDF chapter/section).*

### REFERENCES

### _wp12155 - REFERENCES

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### Data Appendix — HMDA Data
- Source: Home Mortgage Disclosure Act (HMDA) data collected by the Federal Reserve.
- Coverage and scope:
  - HMDA data covered around 95% of all mortgage originations in 2005.
  - HMDA data in the sample covering the sample period 2005 to 2008 contains around 5.2 million applications that are either approved or denied (Action code 1, 2, and 3), after restricting:
    - loan types to be conventional (excluding Federal Housing Agency, Veterans Administration, Farm Service Agency or Rural Housing Service),
    - property types to be one to four-family,
    - loan purpose to be home purchase only (excluding home improvement, refinancing purposes),
    - occupancy status to be owner-occupied as principal dwelling.
- Variables available in HMDA:
  - year of application (annual),
  - amount of the loan,
  - lender’s decision,
  - income of the applicant,
  - gender and race of the applicant,
  - census-tract information: median income and share of minority households.
- Lender classification:
  - Depository institutions and their affiliates (referred to as banks) listed under: Federal Deposit Insurance Corporation, Federal Reserve System, Office of the Comptroller of the Currency, Office of Thrift and Supervision, and National Credit Union Administration.
  - Non-bank mortgage originators (independents) listed under the Department of Housing and Urban Development.
- Sample restrictions for analysis:
  - Study restricted to mortgage originations by depository institutions in counties situated in a Metropolitan Statistical Area (MSA).
  - Resulting sample: 773 counties.
  - These 773 counties cover around 80% of total mortgage originations in HMDA in 2005.
- Footnote on HMDA reporting criteria (verbatim):
  - Lenders are required to report if they meet certain criteria related to size, geographical location, the extent of housing-related lending activity, and regulatory status. Regarding size, a depository institution is subject to HMDA reporting requirements if it has assets of $34 million or more, as of December 31, 2004. In 2010, the Board raised this threshold to $40 million. For a non depository institution, total assets must exceed $10 million, as of December 31 of the preceding year, taking into account the assets of any parent corporation. Regarding the geographical location, lenders must report if they have offices in a Metropolitan Statistical Area (MSA) or if they are non-depository institutions with lending activities on properties located in an MSA. Lenders must also report if they are depository institutions with at least one home purchase loan or if they are non-depository institutions and they originate 100 or more home-purchase and refinancing loans. As for the regulatory status, lenders must report if they are non-depository institutions or if they are depository institutions that are federally insured or regulated.

### Data Appendix — Call Report data
- Source: Reports of Condition and Income (Call Reports) filed with regulators via the Federal Financial Institutions Examination Council (FFIEC).
- Coverage and scope:
  - All regulated depository institutions in the United States are required to file Call Reports periodically (as of the close of business on the last day of each calendar quarter).
  - Specific reporting requirements depend on the size of the bank and whether it has foreign offices.
- Matching to HMDA:
  - Availability of agency-specific bank IDs in HMDA (Federal Reserve RSSD-ID, FDIC Certificate Number, and OCC Charter Number) allows matching HMDA depository lenders to their Call Report financials.

### Data Appendix — Federal Housing Finance Agency: House Prices
- Source: House Price Index (HPI) published quarterly by the U.S. Federal Housing Finance Agency.
- Description:
  - HPI is a weighted, repeated sales index measuring average price changes in repeat sales or refinancing on single family properties with mortgages purchased or securitized by Fannie Mae or Freddie Mac.
  - HPI includes indexes for all nine Census Divisions, the 50 states and the District of Columbia, and every Metropolitan Statistical Area (MSA) in the U.S., excluding Puerto Rico.
  - Compared to S&P/Case-Shiller indexes, HPI offers more comprehensive coverage of housing price trends in U.S. metropolitan areas.
- Usage in the study:
  - HPI data used at MSA level (most disaggregated level available).
  - Year-on-year changes computed as a measure of house price growth in a given MSA.

### Data Appendix — Housing Supply Elasticity
- Source: Saiz (2010) measure of housing supply elasticity at the MSA level.
- Construction:
  - Computed based on topological factors that are exogenous to house market conditions and population growth.
  - Factors computed using water and land slope constraint information obtained using Geographic Information System (GIS), United State Geographic Service (USGS), and USGS Digital Elevation Model (DEM).
- Coverage:
  - Data covers 269 Metropolitan areas using the 1999 county-based MSA or NECMA definitions.
  - Geographic data calculated using the principal city in the MSA (the first one on the list of an MSA name).

*Source: _wp12155 - REFERENCES (PDF chapter/section).*

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