## wp18157 - 2005. Such risk taking pattern was associated with real economic outcomes during the

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### Metadata and classification
- JEL Classification Numbers: G21, G28, E24
- Keywords: Bank competition, risk taking, mortgage market, unemployment
- Author’s E-Mail Address: xfeng@imf.org

### Research question and conceptual framework
- Examines the risk shifting hypothesis: bank competition induces excessive risk taking because limited liability makes bank equityholders' payoff option-like and thus more valuable with higher asset-return volatility.
- Focus: U.S. mortgage market during the run-up to the financial crisis (primarily lending behavior between 2000 and 2005) and subsequent real economic outcomes during the crisis.
- Key theoretical prediction: banks in high-competition local mortgage markets optimally choose higher exposure to house-price volatility by lowering lending standards (e.g., increasing loan-to-income ratios), especially for local banks facing local competition versus national banks.

### Identification strategy and instruments
- Cross-sectional exploitation at the U.S. county level of:
  - Local house price volatility (HPV) measured by magnitude of house price movement during a boom-bust cycle.
  - Local mortgage-market competition measured by Concentration Ratio (CR = combined market share of the top ten lenders in each county) and Herfindahl index (HHI = sum of market share squared of all lenders in a county), both as of 2000.
- Instrument for historical local house price volatility:
  - Housing Supply Elasticity (HSE) from Saiz (2010) transformed to housing supply inelasticity = (5−HSE)/5, measure in [0,1].
  - Historical house price volatility over 1982–1996 used as prior.
- Distinction by lender type:
  - National banks: operating in ten or more U.S. states (alternative definition: more than ten states); local/regional banks: operating in fewer than ten states.
- Empirical specification key regressor: interaction HPV_i × CONC_i; coefficient β2 on interaction captures whether loan risk response to HPV varies with local competition.

### Data sources and variables
- Loan-level and aggregated mortgage measures:
  - HMDA (2000–2005): loan-to-income (LTI) ratios, acceptance rates, fraction of high-interest mortgage loans.
  - MIRS: average loan-to-value (LTV) ratio at zip-code/county level.
- House prices: S&P/Case-Shiller Home Price Index and Zillow House Price Index.
- Other controls and outcomes:
  - County Business Patterns (CBP) for employment.
  - FDIC for failed banks.
  - QCEW for population and wages.
  - Controls include local employment and wage growth, employment in financial and construction sectors, shares of investment homes and refinancing loans, local debt-to-income ratio.

### Theoretical framework and predictions
- Model summary:
  - Banks invest in risky asset S with geometric Brownian motion: dS/S = μ dt + σ dB (under risk-neutral probability), with σ(l; σ_hp) = l σ_hp and constant risk-free rate r.
  - Banks choose lending risk l given cost M(l) with M′>0, M′′>0; bank value is a European call option with strike K and cost M(l).
  - First-order condition: ∂C/∂l* − M′(l*) = 0.
- Propositions and comparative statics:
  - Proposition 1: ∂l*/∂σ_hp > 0 — banks increase lending risk l when house price volatility σ_hp rises exogenously.
  - Proposition 2: ∂^2 l*/(∂σ_hp ∂S0) < 0 — banks in higher-competition environments increase lending risk more strongly when σ_hp rises (competition captured by S0/K; higher competition → smaller S0/K).
- Empirical predictions:
  - Prediction 1a: Banks increase loan-to-income ratio when house price volatility is high; response diminishes as local market competition decreases.
  - Prediction 1b: Local competition affects lending decisions of local banks but not national banks.
  - Prediction 2a: During the crisis, higher HPV implies greater mortgage losses and potentially greater bank failures; relationship diminishes with local market concentration.
  - Prediction 2b: For local employment after the crisis, higher HPV is especially damaging where local bank competition is high.

### Main empirical findings on loan risk before the crisis (2000–2005)
- Aggregate and heterogeneity results:
  - Banks in high-competition markets lowered mortgage lending standards in response to higher house price volatility by twice as much as banks in low-competition markets between 2000 and 2005.
  - Effect present for local banks; not present for national banks.
- Magnitudes (cross-section s.d. = 0.05):
  - One standard-deviation increase in house price volatility associated with:
    - 0.20 percent (or 10 percent) increase in the loan-to-income ratio (reported magnitude language preserved from source).
    - 1.5 percentage point increase in the acceptance rate.
  - Effects reported for counties with high competition (CR below 0.45 quintile); change in lending standards in high-competition counties doubles that in low-competition counties (CR above 0.65 quintile).
- Key regression coefficients (selected, preserve exact figures):
  - Table 3 (local banks): HP Vol. = 5.31*** (0.96); HP Vol. × CR = -7.51*** (1.66).
  - Table 3 (national banks subset): HP Vol. = 1.30** (0.59); HP Vol. × CR = -1.35 (1.02) [statistically insignificant].
  - Table 4 (acceptance rate, local banks): HP Vol. = 2.09*** (0.66); HP Vol. × CR = -2.79** (1.32).
  - Table 5 (combined): HP Vol. = 3.86*** (0.66) in Δln(LTI); HP Vol. × CR = -4.92*** (1.32) in Δln(LTI).
- Bank-level portfolio reallocation (2000–2005):
  - Banks with lower weighted-average HHI (higher local competition) intentionally increased issuance in inelastic-supply counties.
  - Table 9: Weighted Average HHI coefficients include 2.71*** (0.77) and related positive significant estimates across specifications.

### Robustness and alternative empirical specifications
- Alternative competition measures:
  - HHI (sum of market share squared) yields similar patterns; HHI as of 1995 also yields similar results.
  - Table 6 reports Change in LTI, local banks: HP Vol. = 1.98*** (0.46); HP Vol. × CR = -23.80*** (6.51).
- Alternative loan-risk measures and volatility treatments:
  - Share of high-spread loans, LTV changes, realized HPV (2000–2011) treated as exogenous; Table 7 shows consistent negative HP Vol. × CR interaction for local banks.
  - Table 7 (share of high-spread loans): HP Vol. = 1.03*** (0.51); HP Vol. × CR = -2.57*** (1.00).
- Within-county bank comparisons and bank-county fixed effects:
  - Table 8 bank-level regressions with county fixed effects: Bank Average Local Concentration × Elasticity positive and significant (e.g., 1.50*** (0.56)).
- Robustness notes:
  - Results robust to excluding securitized loans and to a wide range of local controls (employment, wages, sectoral employment, shares of investment/construction/refinance, local debt-to-income).
  - Acceptance rate measure acknowledged to partly reflect demand-side applicant composition; other measures (LTV, share of high-spread loans) corroborate findings.

### Real economic effects during and after the crisis
- Foreclosures and bank failures (illustrative stylized evidence):
  - Foreclosure rates (2007Q1–2008Q2): in high-competition counties, negative correlation between foreclosure rate and housing supply elasticity; inelastic-supply areas experienced larger foreclosure rates; relationship absent in low-competition counties.
  - Bank failures (2008Q1–2014Q3): nearly 500 U.S. banks failed (FDIC). In most inelastic-supply areas (HSE between 0 and 1), 3 percent of banks that had lending activities in these areas failed during this period. Bank failure rate declines as HSE increases; negative relationship much weaker in low-competition regions.
  - Caveat: bank failures may arise from non-mortgage business lines; evidence is illustrative of risk-shifting incentives.
- Local non-financial employment (2007–2009):
  - Outcome: percentage change in non-financial sector employment between 2007 and 2009 (exclude financial sector, real estate, construction).
  - Instrumented HPV × HHI interaction strongly positive in regressions (Table 10).
  - Magnitude: one standard deviation increase in HPV (s.d. = 0.05) associated with a 1.5 percent larger drop in the employment rate between 2007 and 2009 in high-competition counties; no such relationship in low-competition counties.
  - Firm-size heterogeneity:
    - Effect strongest for small-sized firms (fewer than 50 employees); coefficient loses significance as firm size increases.
  - Tradable-sector evidence (Table 11):
    - HP Vol. coefficients negative and HP Vol. × CR interaction positive and significant for tradable employment 2007–2009.
    - Placebo 2003–2007: coefficients on HP Vol. and interaction statistically insignificant, supporting causal interpretation for 2007–2009.

### Selected empirical results — key statistics and coefficients (preserved exactly)
- Table 1 summary statistics (N = 789 counties):
  - CR (top-10), 2000: Mean 0.53 SD 0.10 10th 0.41 90th 0.67 Weighted Mean 0.48 Weighted SD 0.08
  - Herfindahl Index, 2000: Mean 0.05 SD 0.03 10th 0.03 90th 0.1 Weighted Mean 0.04 Weighted SD 0.02
  - House price volatility measure, 2001-2011: Mean 0.42 SD 0.33 10th 0.14 90th 0.85 Weighted Mean 0.61 Weighted SD 0.42
  - Housing supply elasticity (Saiz): Mean 2.32 SD 1.00 10th 1.02 90th 3.66 Weighted Mean 1.74 Weighted SD 0.94
  - Percentage change in loan-to-income ratio, 2000–2005: Mean 0.20 SD 0.10 10th 0.07 90th 0.35 Weighted Mean 0.22 Weighted SD 0.12
  - Change in acceptance rate, 2000–2005: Mean -0.06 SD 0.05 10th -0.12 90th 0 Weighted Mean -0.07 Weighted SD 0.04
  - Share of high-spread mortgage loans, 2005: Mean 0.26 SD 0.08 10th 0.17 90th 0.36 Weighted Mean 0.27 Weighted SD 0.08
  - Employment growth (tradable + nontradable), 2007–2009: Mean -0.03 SD -0.08 10th -0.11 90th 0.05 Weighted Mean -0.03 Weighted SD 0.05
  - Share of securitized loans, 2005: Mean 0.54 SD 0.09 10th 0.4 90th 0.65 Weighted Mean 0.59 Weighted SD 0.07
- Table 2 first-stage (N = 789):
  - HP Vol 1982–1996 on Housing Supply Inelasticity: 0.56*** (0.22); Constant -0.28** (0.12); R^2 0.10
  - HP Vol 2000–2011 on Housing Supply Inelasticity: 1.37*** (0.15); Constant -0.28*** (0.08); R^2 0.37
  - Wage Change, 2000–2005 on Housing Supply Inelasticity: 0.004 (0.015); Constant 0.15*** (0.01); R^2 0.00
- Table 3 (selected):
  - Local Banks: HP Vol. = 5.31*** (0.96); HP Vol. × CR = -7.51*** (1.66)
  - National Banks: HP Vol. = 1.30** (0.59); HP Vol. × CR = -1.35 (1.02)
  - HP Vol. × CR × National Bank: 4.48** (2.00) in pooled specification
- Table 4 (selected acceptance rate):
  - Local Banks: HP Vol. = 2.09*** (0.66); HP Vol. × CR = -2.79** (1.32)
  - Pooled: HP Vol. × CR × National Bank: 1.81* (1.03)
- Table 5 (selected Δln(LTI), N = 789):
  - HP Vol.: 3.86*** (0.66); HP Vol. × CR: -4.92*** (1.32); CR: 0.43*** (0.09); R^2: 0.39
  - Absolute ΔLTI: HP Vol.: 8.44*** (1.87); HP Vol. × CR: -9.26*** (3.28); CR: 0.82*** (0.19); R^2: 0.44
- Table 10 (employment 2007–2009, selected):
  - HP Vol. coefficients vary across firm-size splits, e.g., -0.30** (0.13) in some columns; HP Vol. × CR ranges, e.g., 6.01** (2.43); R^2 range 0.01–0.17.
- Table 11 (tradable employment, N ≈ 728):
  - HP Vol.: -1.32** (0.56) in some specifications; HP Vol. × CR: 2.25** (1.02) in one specification; placebo 2003–2007 HP Vol. coefficients statistically insignificant.

### Conclusions and interpretation
- Main empirical finding:
  - Banks in high-competition markets lowered lending standards (raising LTI and acceptance rate) in anticipation of high house price volatility between 2000 and 2005; banks in low-competition markets did not. This pattern is consistent with the risk-shifting hypothesis.
- Real effects during crisis:
  - Between 2007 and 2009, non-financial sector employment in high-competition markets fell by 1.5 percent for one standard deviation increase in local house price volatility; relationship insignificant in low-competition markets.
  - Evidence supports a credit-supply channel through which pre-crisis bank risk-taking amplified real-sector employment losses during the Great Recession, particularly for small firms and in tradable sectors.
- Contributions and caveats:
  - Contribution: provides novel evidence on competition-induced risk shifting using exogenous cross-sectional variation in asset risk and traces credit supply shocks to real-sector outcomes.
  - Caveat: study focuses on the U.S. mortgage market and period 2000–2005 and does not claim bank competition is without efficiency benefits in other contexts.

*Source: wp18157 (excerpt).*

### 2005. Such risk taking pattern was associated with real economic outcomes during the

### wp18157 - 2005. Such risk taking pattern was associated with real economic outcomes during the

### Metadata and classification
- JEL Classification Numbers: G21, G28, E24
- Keywords: Bank competition, risk taking, mortgage market, unemployment
- Author’s E-Mail Address: xfeng@imf.org

### Research question and conceptual framework
- Examines the risk shifting hypothesis: bank competition induces excessive risk taking because limited liability makes bank equityholders' payoff option-like and thus more valuable with higher asset-return volatility.
- Focus: U.S. mortgage market during the run-up to the financial crisis (primarily lending behavior between 2000 and 2005) and subsequent real economic outcomes during the crisis.
- Key theoretical prediction: banks in high-competition local mortgage markets optimally choose higher exposure to house-price volatility by lowering lending standards (e.g., increasing loan-to-income ratios), especially for local banks facing local competition versus national banks.

### Identification strategy and instruments
- Cross-sectional exploitation of local house price volatility and local mortgage-market competition at the U.S. county level.
- House price volatility measurement: magnitude of house price movement during a boom-bust housing cycle; historical local house price volatility instrumented using Saiz (2010) housing supply elasticity constructed from land-topology (satellite) data, measured over 1982–1996.
- Local competition measures: Concentration Ratio (CR) and Herfindahl index as of 2000 constructed from HMDA database (CR = combined market share of the top ten lenders in each county; Herfindahl = sum of market share squared of all lenders in a county).
- Distinction between local banks and national banks: national banks defined as operating in more than five or ten U.S. states; local competition predicted to affect primarily local banks.
- Empirical specification key regressor: interaction term between house price volatility and bank competition; dependent variables capture changes in mortgage lending standards.

### Data sources and variables
- Mortgage loan measures: loan-to-income ratio, loan-to-value ratio, acceptance rate, fraction of high-interest mortgage loans (HMDA), average loan-to-value ratio aggregated from Monthly Interest Rate Survey (MIRS) at the zip-code/county level.
- Historical house price volatility considered 1982–1996 as prior; verified that the 2000s housing cycle followed the pattern predicted by housing supply elasticity.
- County-bank pair data used to include county fixed effects and to examine portfolio shifts (extensive margin) of bank mortgages.
- Robustness controls include local employment and wage growth, local employment in financial and construction sectors, shares of investment homes and refinancing loans, and local debt-to-income ratio.

### Main empirical findings on loan risk before the crisis (2000–2005)
- Banks in high-competition markets lowered mortgage lending standards in response to higher house price volatility by twice as much as banks in low-competition markets between 2000 and 2005.
- The effect of local competition was present for loans issued by local banks but did not exist for national banks.
- Results robust to:
  - Excluding securitized loans.
  - Controlling for a wide range of local factors (employment, wages, sectoral employment, investment/refinance shares).
  - Alternative measures of loan risk: loan-to-value ratio and fraction of high-interest mortgage loans.
  - Alternative competition measure: Herfindahl index.
  - Treating realized house price volatility as exogenous.
- Alternative hypotheses without local-competition incentive distortions are turned down by the finding that the competition effect is limited to local banks.

### Real economic effects during and after the crisis
- Lower-quality mortgage loans in high-competition markets were associated with:
  - Higher rates of foreclosures and bank failures when house prices declined.
  - Stronger negative effects on local employment through impaired local financial sectors (credit-supply channel).
- Quantified employment effect:
  - In high-competition local markets, a one standard-deviation increase in local house price volatility was associated with a 1.5 percent larger drop in the employment rate between 2007 and 2009.
  - No such relationship was found in low-competition markets.
  - The adverse employment effect was especially strong for smaller-sized firms.
- These credit-supply effects are documented in addition to the demand-side channels emphasized in the literature (e.g., household balance-sheet channels).

### Robustness on real-outcome channels
- Employment results robust to:
  - Inclusion of local demand-side controls such as local debt-to-income ratio (Mian and Sufi (2014) proxy).
  - Exclusion of non-tradable sectors (to isolate supply-side effects).
  - Considering only tradable sectors in sensitivity checks.

### Contributions and caveats
- Contributions:
  - Provides novel evidence on the risk shifting incentive associated with bank competition using exogenous cross-sectional variation in asset risk.
  - Develops an empirical strategy to trace credit supply shocks (originating from pre-crisis risk taking) to real-sector outcomes during the crisis.
- Caveats:
  - The paper studies welfare costs of risk shifting associated with bank competition in a specific market (U.S. mortgage market) and time period (2000–2005) and does not argue that bank competition lacks efficiency benefits (e.g., lower interest margins, increased pass-through of monetary policy).
  - Acknowledges complementary literature finding competition can improve efficiency and stability in other contexts.

*Source: wp18157 (2005). Such risk taking pattern was associated with real economic outcomes during the*

### Section IV.C, a few alternative measures and empirical specifications are used to show

### Section IV.C, a few alternative measures and empirical specifications are used to show robustness of results

### Theoretical framework and predictions
- Model setup:
  - Banks borrow from deposits and invest in a risky asset S that follows geometric Brownian motion: dS/S = μ dt + σ dB (under risk-neutral probability), with σ(l; σ_hp) = l σ_hp and constant risk-free rate r.
  - Banks choose lending risk l given cost function M(l) with M′>0 and M′′>0; bank value is a European call option with strike K and additional cost M(l).
  - First-order condition: ∂C/∂l* − M′(l*) = 0.
  - Assumption: log(S0/K) + rT > 1/2 σ(l)^2 T for all l (call option sufficiently in-the-money).
- Key propositions:
  - Proposition 1: ∂l*/∂σ_hp > 0 — banks increase lending risk l when house price volatility σ_hp goes up exogenously.
  - Proposition 2: ∂^2 l*/(∂σ_hp ∂S0) < 0 — banks in higher-competition environments increase lending risk more strongly when σ_hp rises (competition captured by S0/K; higher competition → smaller S0/K).
- Empirical predictions:
  - Prediction 1a: Banks increase loan-to-income ratio when house price volatility is high; this response diminishes as local market competition decreases.
  - Prediction 1b: Local competition affects lending decisions of local banks but should not affect national banks.
  - Prediction 2a: During the crisis, higher house price volatility implies greater mortgage losses and potentially greater bank failures; this relationship diminishes as local market competition decreases.
  - Prediction 2b: For local employment in non-financial sectors after the crisis, higher house price volatility is especially damaging where local bank competition is high.

### Data, market structure, and identification
- Mortgage market and competition measures:
  - County-level concentration measures: CR (total market share of the top ten lenders in the county) and Herfindahl index (HHI = sum of market share squared for all lenders in a county), both measured as of 2000 (also HHI as of 1995 considered).
  - 3,185 U.S. counties have HMDA coverage during 1995–2005.
  - Empirical distinction between lender types:
    - National banks: operating in ten or more U.S. states (also noted as operating in more than ten states in another definition) and total loans exceeded 10,000 reported in HMDA database as of 2000.
    - Local/regional banks: operating in fewer than ten states.
- Key data sources:
  - Loan-level mortgage data: HMDA (2000–2005 coverage), used to construct loan-to-income (LTI) ratios and acceptance rates; lender identifier allows lender-level aggregation.
  - County-level loan-to-value (LTV) from MIRS.
  - House prices: S&P/Case-Shiller Home Price Index and Zillow House Price Index (availability back to 1980s).
  - Housing Supply Elasticity (HSE) from Saiz (2010), transformed to housing supply inelasticity = (5−HSE)/5, resulting measure in [0,1]; lower HSE (higher inelasticity) associated with larger house price volatility.
  - Employment: County Business Patterns (CBP); other sources: FDIC for failed banks, QCEW for population and wages.
- Identification strategy:
  - Instrument for expected local house price volatility using historical HSE-derived housing supply inelasticity and historical house price volatility (1982–1996) as the prior for banks entering the 2000s cycle.
  - First-stage evidence: Table 2 shows regressions of house price volatility (peak-trough distance in percentage) on housing supply inelasticity with t-statistics greater than 3; wage growth regression on HSE coefficient statistically insignificant.
  - Important identification note: coefficient of interest is on interaction between house price volatility and local competition; estimates remain valid provided correlated instruments do not differentially affect loan risk across competition levels.
  - Robustness: bank-county pair specifications with county fixed effects included in robustness checks.

### Empirical specification and main results
- Main empirical model:
  - ∆LTI_i 2000−2005 = β0 + β1 HPV_i + β2 (HPV_i × CONC_i) + β3 CONC_i + γ X_i + ε_i
    - ∆LTI_i 2000−2005: 2000–2005 change in loan risk (loan-to-income ratio, acceptance rate) for county i.
    - HPV_i: expected local house price volatility.
    - CONC_i: CR or HHI for county i as of 2000.
    - X_i: control variables (mortgage market characteristics and real economy).
  - Coefficient of interest: β2 on the interaction term; negative β2 implies loan risk became higher under house price uncertainty only in competitive mortgage markets.
- Results (loan-to-income ratio as risk measure; Tables 3–5):
  - Local banks:
    - Columns (1)–(3) (lending by local banks): coefficient on HPV × CR is negative and statistically significant, robust to controls.
  - National banks:
    - Column (4): coefficient on HPV × CR is statistically insignificant for national banks.
  - Combined tests:
    - Columns (5)–(6): triple interaction (HPV × CR × national-bank indicator) is strongly positive, indicating national-bank responses are significantly less negative than local-bank responses.
  - Acceptance rate (Tables 4):
    - For local banks, HPV × CR coefficient negative and statistically significant.
    - For national banks, HPV × CR coefficient statistically insignificant.
    - Coefficients on interaction term statistically different between local and national banks.
- Magnitude (Table 5):
  - One standard-deviation increase in house price volatility in the cross section (s.d. = 0.05) is associated with:
    - 0.20 percent (or 10 percent) increase in the loan-to-income ratio
    - 1.5 percentage point increase in the acceptance rate
  - These effects are for counties with high competition (quintile of counties with CR below 0.45).
  - Compared to counties with low competition (quintile with CR above 0.65), the magnitude of change in lending standards in high-competition counties doubles that in low-competition counties.
- Graphical evidence:
  - Figure 4:
    - Upper panel: percentage change in LTI from 1998 to 2005 shows larger divergence in inelastic-supply vs elastic-supply areas when mortgage market competition is high (solid lines) than when concentrated (dashed lines).
    - Lower panel: absolute change in LTI (2000–2005) across 789 U.S. counties in sample shows similar conclusions.

### Robustness and alternative empirical specifications
- Alternative measures of local competition:
  - Use HHI (sum of market share squared) as county-level competition measure; lower HHI indicates greater competition.
  - HHI as of 1995 (well before the housing cycle) yields similar empirical results.
- Alternative specifications:
  - Bank-county pair regressions include county fixed effects to absorb time-invariant county characteristics; results qualitatively similar.
  - The paper also examines portfolio shifts (extensive margin of risk taking) in addition to lending standards (intensive margin).
- Additional identification and measurement notes:
  - When measuring acceptance rate, recognize it also reflects demand-side shifts (inflow of low-quality applicants mechanically affects acceptance rate even absent lender behavior changes).
  - Robustness section uses alternative empirical measures and specifications to address endogeneity and omitted-variable concerns; results remain consistent with predictions that local competition amplifies risk-taking responses to house price volatility for local banks but not for national banks.

*Italic source: wp18157 - Section IV.C, a few alternative measures and empirical specifications are used to show (PDF).*

### 2000. Columns (1)–(3) show the estimates of coefficients where the dependent variable is the

### wp18157 - 2000. Columns (1)–(3) show the estimates of coefficients where the dependent variable is the 

### Regression results on lending standards (2000–2005)
- Dependent variables: percentage change in the loan-to-income (LTI) ratio between 2000 and 2005; change in the acceptance rate of mortgage loans.
- Columns (1)–(3): regressions for percentage change in LTI.
  - Column (1): only lending decisions by local banks.
  - Column (2): only lending decisions by national banks.
  - Column (3): both groups included; difference between local and national banks is statistically significant.
- Key empirical pattern:
  - Interaction term between house price volatility and the Herfindahl index (HHI) is strongly significant and negative for local banks but not for national banks.
  - Columns (4)–(6): analogous results for change in acceptance rate — local competition encouraged lowering lending standards by local banks but not by national banks; difference statistically significant.

### Robustness checks: alternative measures of bank competition, loan risk, and volatility
- Alternative loan-risk measures used:
  - Interest rate (share of mortgage loans as of 2005 with an interest spread higher than the HMDA reporting threshold after 2004).
  - Loan-to-value (LTV) ratio (zip-code level MIRS survey data, population-weighted to county level).
- Alternative volatility measure:
  - Realized house price volatility between 2000 and 2001 treated as exogenous; also realized volatility between 2000 and 2011 used in simple OLS.
- Table 7 results:
  - Columns (1)–(2): coefficient estimates for share of high-spread loans originated.
  - Columns (3)–(4): estimates for percentage change in loan-to-value ratio.
  - Columns (5)–(6): OLS treating realized house price volatility between 2000 and 2011 as exogenous.
  - Consistent finding: coefficient on interaction between house price volatility and CR (competition measure) is negative and statistically significant for local banks; statistically insignificant and economically negligible for national banks.

### Controlling for county fixed effects (within-county bank comparisons)
- Objective: compare two banks A and B in same county C with different exposure to competitive mortgage markets.
- Regression framework (bank b in county c):
  - ∆LTI_{b,c 00−05} = α_c + β1 wHHI_b + β2 (wHHI_b × Hsupply_c) + β3 X_b + ε_{b,c}
  - Definitions:
    - ∆LTI_{b,c 00−05}: 2000–2005 percentage point change in average loan-to-income ratios issued by bank b in county c.
    - α_c: county fixed effects.
    - wHHI_b: value-weighted average of Herfindahl indexes for bank b across counties as of 2000.
    - Hsupply_c: housing supply elasticity of county c.
    - X_b: bank controls (size, type, total loan amounts).
  - Sample restriction: county must represent at least 1 percent and at most 50 percent of the bank’s total mortgage portfolio.
- Table 8 results:
  - Column (1): wHHI alone — slightly negative, statistically insignificant.
  - Columns (2)–(3): include interaction with housing supply elasticity.
    - β1 < 0 and β2 > 0; both statistically significant.
    - Interpretation: in very inelastic-supply counties (high house price volatility), lower HHI (higher competition) associated with larger increase in LTI from 2000 to 2005; effect weaker in elastic-supply counties.
  - Columns (4)–(6): similar results when using CR instead of HHI.

### Bank-level loan portfolio changes (2000–2005)
- Mechanism: multi-branch banks facing high local competition may increase lending in inelastic areas to raise portfolio correlation with aggregate housing shocks.
- Measurement:
  - For each bank, compute wHHI_b (value-weighted average HHI of counties where bank lent as of 2000).
  - Compute value-weighted average of county elasticities in 2000 and 2005; difference ∆Hsupply_b 00−05 measures change in loan portfolio across counties.
  - Construct counterfactual AvReflectChange_b 00−05: change if bank maintained same market shares across counties; intentional change = actual change − counterfactual.
- Regression:
  - ∆Hsupply_b 00−05 − AvReflectChange_b 00−05 = β0 + β1 wHHI_b + β2 X_b + ε_b
  - X_b: bank controls (size, total mortgage issuance, bank type).
  - Sample focus: banks with housing supply elasticity available for at least 70 percent of total mortgage portfolio as of 2000 (and robustness at 99 percent coverage).
- Table 9 results:
  - Column (1): positive and significant coefficient on wHHI_b — banks with low local concentration HHI (high competition) intentionally increased issuance in inelastic counties.
  - Column (2): similar when restricting to >99 percent coverage.
  - Column (3): similar after including bank controls (bank size, securitized share, bank type).
  - Columns (4)–(5): include headquarter state fixed effects; coefficient remains positive and significant.
  - Columns (6)–(7): using weighted average CR in place of HHI yields similar conclusion: higher bank-level local competition predicted greater shifts toward inelastic areas.

### Real economic effects during and after the crisis
- Two dimensions for welfare assessment:
  1. Direct damage to debt holders via excessive risk-taking and resulting foreclosures and bank failures.
  2. Spillovers to the real economy via the credit supply channel, measured by local non-financial sector unemployment.
- Stylized evidence on foreclosures and bank failures:
  - Foreclosure rates (county level, 2007Q1–2008Q2): negative correlation between foreclosure rate and housing supply elasticity in high-competition counties (inelastic-supply areas with larger house price volatility experienced greater foreclosure rates); relationship absent in low-competition counties. Difference statistically significant.
  - Bank failures (2008Q1–2014Q3): nearly 500 U.S. banks failed (FDIC). Bank failure rate calculated as number failed in region divided by total number of banks with lending activities as of 2005.
    - In most inelastic-supply areas (HSE between 0 and 1), 3 percent of banks that had lending activities in these areas failed during this period.
    - Bank failure rate declines as HSE increases; negative relationship much weaker in low-competition regions.
  - Caveat: bank failures may arise from non-mortgage business lines; evidence is illustrative of risk-shifting incentives.
- Local unemployment in the real sector (2007–2009)
  - Outcome: change in non-financial sector employment between 2007 and 2009 (exclude financial sector, real estate, construction).
  - Specification includes instrumented house price volatility, Herfindahl index, and their interaction; interest in coefficient on interaction.
  - Data treatment: drop 5 percent of counties with lowest competition due to data noise/confidentiality.
  - Table 10 results:
    - Columns (3)–(5): coefficient on interaction between bank competition and house price volatility is strongly positive whether or not local controls included.
    - Magnitude: one standard deviation increase in house price volatility (s.d. = 0.05) implies a drop in employment by 1.5 percent in high-competition counties; relationship diminishes to zero in low-competition counties.
    - Column (4): controlling for local debt-to-income ratio does not change results significantly.
  - Firm-size heterogeneity (columns (6)–(9)):
    - Employment changes calculated by establishment sizes: below 20 employees; 20–50; 50–100; 100–500; above 500.
    - CBP data limitations: firms with over 500 employees typically not accurately reported; results for >500 not reported.
    - As firm size increases, coefficient on interaction loses statistical significance.
    - Effect strongest for small-sized firms (fewer than 50 employees), consistent with larger sensitivity of smaller firms to adverse credit shocks.
  - Tradable-sector robustness (Table 11):
    - Following Mian and Sufi (2014) definition of tradable vs nontradable sectors.
    - Columns (1)–(4): percentage change in tradable employment between 2007 and 2009 — interaction term statistically significant and positive.
    - Local controls (debt-to-income as of 2006, population change) not correlated with change in tradable employment.
    - Placebo (columns (5)–(6)): change in tradable employment between 2003 and 2007 — house price volatility and its interaction with bank competition statistically insignificant, supporting causal interpretation for 2007–2009.

### Conclusions and interpretation
- Main empirical finding:
  - Banks in high-competition markets lowered lending standards (raising LTI and acceptance rate) in anticipation of high house price volatility between 2000 and 2005; banks in low-competition markets did not. This pattern is consistent with the risk-shifting hypothesis.
- Real effects:
  - Between 2007 and 2009, non-financial sector employment in high-competition markets fell by 1.5 percent for one standard deviation increase in local house price volatility; relationship insignificant in low-competition markets.
  - Evidence supports a credit-supply channel through which pre-crisis bank risk-taking amplified real-sector employment losses during the Great Recession, particularly for small firms and in tradable sectors.
- Broader implication:
  - Competition-induced risk-taking incentives can lead banks to accumulate mortgage risk prior to large house price reversals, with consequences for both bank solvency (foreclosures, failures) and local real economic outcomes.  

*Source: wp18157 (excerpt).*

### APPENDIX 1. PROOFS OF PROPOSITIONS

### wp18157 - APPENDIX 1. PROOFS OF PROPOSITIONS

### A. Proof of Proposition 1
- Vega of the European call option:
  - ∂C/∂σ = K e^{−rT} n(μ2/2) √T, where n is the density of the standard normal distribution and
  - μ2 = [log(S0/K) + (r + 1/2 σ^2) T] / (σ √T) − σ √T.
  - Note: Vega of a European call option is positive.
- First-order condition (bank’s maximization) and comparative statics:
  - Chain rule applied to first-order condition yields: (∂C/∂σ)_{σ_hpp} − M′(l^*) = 0.
  - Since M′′ > 0 and ∂^2C/∂σ^2 > 0, the solution l^* increases with σ_hpp:
    - ∂l^*/∂σ_hpp > 0.

### B. Proof of Proposition 2
- Vanna of the European call option:
  - ∂^2 C / (∂σ ∂S0) = ν / S0 [1 − μ1/(σ √T)], where ν is the Vega and μ2 defined as above.
  - Note: Vega of a European call option is positive.
- Under Assumption 1:
  - ∂^2 (∂C/∂σ) / (∂σ ∂S0) < 0 (Vanna < 0 under assumptions).
  - First-order condition: (∂C/∂σ)_{σ_hpp} − M′(l^*) = 0.
  - With M′′ > 0, ∂^2(∂C/∂σ)/∂σ∂S0 < 0 and ∂^2C/∂σ^2 > 0, the solution l^* increases with σ_hpp but sensitivity declines with S0:
    - ∂^2 l^*/(∂σ_hpp ∂S0) < 0.

### Figures — descriptive summaries (selected)
- Figure 1:
  - Evolution of CR (top-10) from 1995 to 2005 at county level; CR measure declined nationally but relative ranking across counties remained similar.
- Figure 2:
  - Historical House Price Volatility: 1982–1996 — most inelastic areas experienced much larger house price volatility than elastic areas.
- Figure 3:
  - House Price Volatility Over the Recent Cycle and Exclusion Restriction — upper panel S&P/Case-Shiller indices by supply elasticity quintiles; middle panel new building permits 2000–2005; lower panel growth of real wages.
- Figure 4:
  - Loan-to-Income Ratio by House Price Volatility and Local Bank Competition — evolution percentage change (1998–2005) for 789 counties and absolute change (2000–2005).
- Figure 5:
  - Foreclosure and Bank Failure Rates During the Crisis — foreclosure rate 2007Q1–2008Q2 vs. Saiz elasticity; bank failure rate 2008Q1–2014Q2 vs. Saiz elasticity, with splits by competitive vs. concentrated mortgage markets.
- Figure 6:
  - Non-Financial Employment After the Crisis — percentage change of tradable non-financial employment 2007–2009 for establishments with size below 100 against housing supply elasticity, separate for competitive and concentrated mortgage markets.

### Selected empirical results — key statistics and coefficients

- Table 1. Summary statistics (N = 789 counties)
  - CR (top-10), 2000: Mean 0.53 SD 0.10 10th 0.41 90th 0.67 Weighted Mean 0.48 Weighted SD 0.08
  - CR (top-10), 1995: Mean 0.62 SD 0.18 10th 0.4 90th 0.9 Weighted Mean 0.48 Weighted SD 0.13
  - Herfindahl Index, 2000: Mean 0.05 SD 0.03 10th 0.03 90th 0.1 Weighted Mean 0.04 Weighted SD 0.02
  - House price volatility measure, 1982-1996: Mean 0.02 SD 0.3 10th -0.36 90th 0.27 Weighted Mean 0.06 Weighted SD 0.34
  - House price volatility measure, 2001-2011: Mean 0.42 SD 0.33 10th 0.14 90th 0.85 Weighted Mean 0.61 Weighted SD 0.42
  - Housing supply elasticity (Saiz): Mean 2.32 SD 1.00 10th 1.02 90th 3.66 Weighted Mean 1.74 Weighted SD 0.94
  - Population, 2000 (thousands): Mean 243.3 SD 522.08 10th 20.72 90th 569.95 Weighted Mean 1362.08 Weighted SD 2160.09
  - Percentage change in loan-to-income ratio, 2000–2005: Mean 0.20 SD 0.10 10th 0.07 90th 0.35 Weighted Mean 0.22 Weighted SD 0.12
  - Change in acceptance rate, 2000–2005: Mean -0.06 SD 0.05 10th -0.12 90th 0 Weighted Mean -0.07 Weighted SD 0.04
  - Change in loan-to-value ratio, 2001–2005: Mean -0.02 SD 0.08 10th -0.1 90th 0.07 Weighted Mean -0.04 Weighted SD 0.06
  - Share of high-spread mortgage loans, 2005: Mean 0.26 SD 0.08 10th 0.17 90th 0.36 Weighted Mean 0.27 Weighted SD 0.08
  - Employment growth (tradable + nontradable), 2007–2009: Mean -0.03 SD -0.08 10th -0.11 90th 0.05 Weighted Mean -0.03 Weighted SD 0.05
  - Share of securitized loans, 2005: Mean 0.54 SD 0.09 10th 0.4 90th 0.65 Weighted Mean 0.59 Weighted SD 0.07
  - Share of national banks, 2000 (Table 5 variable): coefficient reported in regressions as 0.16*** (see Table 5).

- Table 2. First Stage Regression and Exclusion Restriction (N = 789)
  - Column (1): HP Vol 1982–1996
    - Housing Supply Inelasticity 0.56*** (0.22)
    - Constant -0.28** (0.12)
    - R^2 0.10
  - Column (2): HP Vol 2000–2011
    - Housing Supply Inelasticity 1.37*** (0.15)
    - Constant -0.28*** (0.08)
    - R^2 0.37
  - Column (3): validation (N = 789)
    - Housing Supply Inelasticity 1.34*** (0.16)
    - Constant -0.20 (0.20)
    - R^2 0.37
  - Column (4): Wage Change, 2000–2005
    - Housing Supply Inelasticity 0.004 (0.015)
    - Constant 0.15*** (0.01)
    - R^2 0.00

- Table 3. Loan-to-Income Ratio for National Banks versus Local Banks (N = 789; pooled N = 1578)
  - Key coefficients (standard errors in parentheses)
  - HP Vol.:
    - Local Banks: 5.31*** (0.96)
    - National Banks: 1.30** (0.59) in column (4) for National Banks subset
    - All (pooled): 3.87*** (0.95)
  - HP Vol. × CR:
    - Local Banks: -7.51*** (1.66)
    - National Banks: -1.35 (1.02) in column (4)
    - All: -6.32*** (1.61)
  - HP Vol. × CR × National Bank:
    - 4.48** (2.00) reported in pooled interaction specifications
  - CR:
    - 0.64*** (0.12) for Local Banks; pooled 0.54*** (0.10)
  - %Δ Wage: 0.47** (0.21) in some specifications; pooled 0.43*** (0.10)
  - R^2 ranges reported: e.g., 0.36, 0.42, 0.45, 0.67, 0.35, 0.52 across columns.

- Table 4. Acceptance Rate for National Banks versus Local Banks (N = 789; pooled N = 1578)
  - HP Vol.:
    - Local Banks: 2.09*** (0.66)
    - National Banks: 0.51 (0.35) in column (4)
    - All: 1.75*** (0.66)
  - HP Vol. × CR:
    - Local Banks: -2.79** (1.32)
    - All: -2.20* (1.15)
  - HP Vol. × CR × National Bank:
    - 1.81* (1.03) in pooled interaction specifications
  - CR: 0.16* (0.09) in some columns; pooled similar
  - R^2 ranges: 0.17, 0.20, 0.27, 0.11, 0.35, 0.38.

- Table 5. Combining National and Local Banks (N = 789)
  - Δln(Loan-to-Income), 2000-2005 (columns 1–3):
    - HP Vol.: 3.86*** (0.66), 3.19*** (0.64), 2.00*** (0.51)
    - HP Vol. × CR: -4.92*** (1.32), -3.78*** (1.14), -3.08*** (0.88)
    - CR: 0.43*** (0.09), 0.39*** (0.09), 0.25** (0.06)
    - R^2: 0.39, 0.44, 0.67 respectively.
  - ΔLoan-to-Income, 2000-2005 (absolute change, columns 4–6):
    - HP Vol.: 8.44*** (1.87), 6.72*** (1.68), 4.14*** (1.23)
    - HP Vol. × CR: -9.26*** (3.28), -6.77** (3.13), -6.05*** (2.11)
    - CR: 0.82*** (0.19), 0.85*** (0.21), 0.57** (0.16)
    - R^2: 0.44, 0.48, 0.72
  - ΔAcceptance Rate, 2000-2005 (columns 7–8):
    - HP Vol.: 0.66** (0.66) and 0.54* (0.30) in other columns
    - HP Vol. × CR: -0.96* (0.54) and -0.81 (0.53)
    - R^2: 0.35, 0.33

- Table 6. Robustness Using the Herfindahl Index (N = 789, pooled N = 1578)
  - Change in Loan-to-Income Ratio, Local Banks:
    - HP Vol.: 1.98*** (0.46)
    - HP Vol. × CR: -23.80*** (6.51)
    - CR: 2.06*** (0.44)
    - R^2: 0.45
  - Change in Loan-to-Income Ratio, National Banks:
    - HP Vol.: 0.85*** (0.29)
    - HP Vol. × CR: -5.24 (4.63)
    - CR: 0.48 (0.33)
    - R^2: 0.67
  - Change in Acceptance Rate, All:
    - HP Vol.: 1.25*** (0.30)
    - HP Vol. × CR: -13.26** (5.82)
    - CR: 0.11 (0.06)
    - R^2: 0.40

- Table 7. Alternative Measures for Loan Risk and House Price Volatility (N = 789; pooled N = 1578)
  - Share of high-spread loans (columns 1–2):
    - HP Vol.: 1.03*** (0.51) and 0.84* (0.44)
    - HP Vol. × CR: -2.57*** (1.00) and -2.00** (0.80)
    - CR: -0.27*** (0.03) and -0.18*** (0.06)
    - R^2: 0.17, 0.32
  - Percentage change in LTV (columns 3–4):
    - HP Vol.: 0.37 (0.35) and 0.36 (0.32)
    - HP Vol. × CR: -0.88+ (0.61) and -0.84+ (0.58)
    - R^2: 0.14, 0.29
  - %ΔLTI, Realized HP Volatility (columns 5–6, pooled N = 1578):
    - HP Vol.: 0.49** (0.21) and 0.59*** (0.17)
    - HP Vol. × CR: -0.62+ (0.40) and -0.86*** (0.33)
    - R^2: 0.43, 0.61

- Table 8. Banks in the Same County (Bank-level regressions, N = 2,159)
  - Percentage change in loan-to-income ratio, 2000-2005:
    - Bank Average Local Concentration: coefficients include -0.31 (1.01), -3.19** (1.30), -3.44* (2.36), -0.17 (0.21), -0.75** (1.30), -1.07*** (0.33) across specifications.
    - Bank Average Local Concentration × Elasticity: 1.50*** (0.56), 1.68*** (0.57), 0.35*** (0.13), 0.42*** (0.13) in various specs.
    - Share of Loans Securitized: -0.03 (0.02) and 0.05* (0.03) in different specs.
    - R^2: 0.06, 0.07, 0.08, 0.06, 0.07, 0.10.

- Table 9. Bank Loan Portfolio Shift and Local Competition (N varies; e.g., 2,203)
  - Change in average elasticity:
    - Weighted Average HHI: 2.71*** (0.77), 3.24** (1.47), 2.78*** (0.79), 0.96 (0.64), 1.65*** (0.71) across specifications.
    - Weighted Average CR: 0.78*** (0.10) and 0.39*** (0.12) in some specifications.
    - Total Mortgage Loans: 0.97*** (0.25), 0.62*** (0.13), 0.62*** (0.24).
    - R^2 up to 0.43 in specifications with headquarter state fixed effects.

- Table 10. Change in Employment in Real Sectors (N = 789; firm-size splits)
  - Percentage Change in Employment, 2007-2009:
    - HP Vol. coefficients across columns: -0.08* (0.04), -0.14 (0.10), -0.30** (0.13), -0.20+ (0.13), -0.16 (0.12), -0.18** (0.08), -0.35*** (0.13), -0.34* (0.19), -0.04 (0.24).
    - HP Vol. × CR: coefficients include 2.01 (1.56), 6.01** (2.43), 4.82** (2.40), 4.24* (2.33), 3.08** (1.35), 4.87* (2.64), 3.67 (4.06), 1.30 (4.71).
    - R^2 range: 0.01 to 0.17 depending on specification and firm size.

- Table 11. Change in Tradable-Sector Employment (N ≈ 728)
  - Percentage Change in Employment, 2007-2009:
    - HP Vol.: -0.20* (0.12), -1.32** (0.56), -1.38** (0.54), -1.45* (0.79) across specifications.
    - HP Vol. × CR: 2.25** (1.02), 2.23** (1.02), 2.41* (1.42).
    - Placebo (2003-2007): HP Vol. coefficients -0.69 (1.10) and 0.35 (0.95).
    - R^2: 0.01 to 0.11 across specifications.

### Empirical interpretation (from tables)
- Housing supply inelasticity is a strong predictor of historical house price volatility:
  - Coefficients: 0.56***, 1.37***, 1.34*** in first-stage specifications (Table 2).
- Higher local house price volatility (instrumented by supply inelasticity) is associated with increases in loan-to-income ratios and acceptance rates, with effects materially larger for local banks than for national banks:
  - Local bank HP Vol. effect on Δln(LTI): 5.31*** (0.96) (Table 3).
  - Interaction with local concentration (CR) typically offsets or reverses the HP Vol effect (e.g., HP Vol. × CR = -7.51*** (1.66) in Table 3 for local banks).
- Robustness checks (Herfindahl index, alternative loan-risk measures, realized volatility) broadly confirm:
  - Positive HP Vol coefficients and negative HP Vol × concentration interaction coefficients across specifications (Tables 6 and 7).
- Local competition and bank-level concentration influence banks’ loan-to-income responses and portfolio reallocation:
  - Bank-average local concentration effects and interactions with elasticity reported in Table 8 and Table 9.
- Local HP volatility adversely affected local employment outcomes during the crisis, especially in tradable sectors and for smaller establishments in some specifications:
  - Negative HP Vol coefficients on percentage change in employment (Tables 10 and 11), with heterogeneous effects by firm size and by local concentration (HP Vol × CR).

*Source: wp18157 - APPENDIX 1. PROOFS OF PROPOSITIONS (selected figures and tables reproduced from source content).*

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*Source: wp18157 - REFERENCES*

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_Source: https://www.imf.org/-/media/files/publications/wp/2018/wp18157.pdf_