## 2.1    Data and measurements; 2.3    Within-lender tests

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### Data sources and sample construction
- Primary data: loan-level sample of mortgage applications and originations from the Home Mortgage Disclosure Act (HMDA).
- HMDA coverage: close to 95 percent of mortgage originations in the US.
- Institutional reporting scope: regulated financial institutions with more than $30 million in assets.
- Exclusions and restrictions:
  - Exclude loans guaranteed by the Federal Housing Administration, Veterans Administration, Farm Service Agency, or Rural Housing Service (restrict to conventional loans).
  - Restrict to loans for single-family home purchase; exclude refinancing and home improvement loans.
- Geographic market definition: 3-digit zip code level; final dataset covers 880 local markets out of 882 3-digit U.S. zip codes.
- Lender-level data: HMDA merged with the Report of Condition and Income (“Call Reports”) by linking Call Report identification number with the HMDA identification number.
- Housing prices: quarterly house price index from the Federal Housing Finance Agency (FHFA) measured in 3-digit zip codes.

### Sample sizes and summary statistics
- Raw HMDA sample size: 485 million applications over the 1995–2017 period.
- Final sample after exclusions: 362 million mortgage applications.
- Conforming segment:
  - 20.9 percent of applicants are women.
  - 3.6 percent of applicants are members of minority groups.
  - Average acceptance rate: 87 percent by loan number and 88.2 percent by loan volume.
  - Lenders on average originate $190 million of loans per year and keep 45 percent of them on their balance sheets.
- Jumbo segment:
  - 9.6 percent of applicants are women.
  - 2.1 percent of applicants are members of minority groups.
  - Acceptance rate: 90.3 percent by loan number and 90.4 by loan volume.
  - Lenders on average originate $79.4 million mortgages and keep 80 percent of them on their balance sheets.
- Lender size in sample:
  - Mean lender size: $2.4 billion.
  - Median lender size: $206 million.
- Average exposure to high-growth areas: 10.5 (6.2) percent of total loans (Sand States (constrained areas)).

### Definition and identification of high-growth markets
- Two alternative definitions:
  - Sand States: Arizona, California, Florida, and Nevada.
  - Geographically constrained areas: bottom decile of Lutz and Sand (2019) land-availability index for 3-digit zip codes (index extends Saiz (2010) measure).
- Notes on land-availability indices:
  - Saiz (2010) index used for 269 MSAs with population of 50,000 or more.
  - Lutz and Sand (2019) extend index to all 3-digit zip codes; methodological differences noted but high correlation (correlation of 0.8 and R^2 of 0.7).

### Housing cycle patterns in high-growth markets
- Mortgage volume trends:
  - Share of mortgages originated in Sand States increased from 31 percent in 1995 to 40 percent in 2005, falling to 25 percent in 2010 before recovery.
  - Share of loans to constrained areas followed a similar trend with smaller magnitude.
- House price growth and collapse:
  - 2001–2005 house price growth: Sand States 103 percent; constrained areas 51 percent; national average 44 percent.
  - 2008–2010 house price collapse: Sand States −27.8 percent; constrained areas −10.5 percent; national average −8.7 percent.
  - 2011–2017 house price growth: Sand States 6.3 percent; constrained areas 3.1 percent; national average 2.6 percent.

### Acceptance-rate regressions and empirical specifications
- Baseline regression (equation (1)):
  - Yijt = α + β HighGrowthShareijt−1 + λ Xijt−1 + μt + εijt
  - Y is acceptance rate (accepted applications as share of total applications), calculated by number of applications or loan volume.
  - HighGrowthShare is lending to high-growth markets as a share of total lending.
  - Controls (X): lender size (log of total assets), Tier 1 capital ratio, deposit-to-total assets ratio, lender diversification, average income of applicants, percentage of applicants who are women, percentage of applicants who are minority, and year fixed effects.
  - Lender diversification index: 1 − sum of squared shares of mortgages across markets; ranges from 0 (single-market lender) to nearly 1 (highly diversified lender).
- Extended specification (equation (2)):
  - Yijt = α + β HighGrowthShareijt−1 + γ HighGrowthLenderijt−1 + δ HighGrowthShareijt−1 × HighGrowthLenderijt−1 + λ Xijt−1 + μt + εijt
  - HighGrowthLender = 1 if a lender’s mortgage loans to high-growth markets exceeds 25 percent of total mortgage loans (robustness to thresholds of 20, 33.3, or 50 percent noted).

### Key empirical findings on acceptance rates (cross-lender)
- Main patterns:
  - Lenders more exposed to high-growth markets have significantly lower acceptance rates (β < 0).
  - Results robust to acceptance defined by number of loans or loan volume and to high-growth definition (Sand States or constrained areas).
  - Borrower characteristics do not drive the difference; estimates without and with borrower controls are very similar.
- Economic magnitudes:
  - Conforming segment: a 1 standard deviation increase in a lender’s lending share to Sand States (28.4 percent) increases likelihood of loan rejection by 10 percent (from 13 to 14.4 percentage points) (Panel A column 3).
  - Jumbo segment: a 1 standard deviation increase in lending share to Sand States (28.4 percent) increases likelihood of loan rejection by 17 percent (from 9.7 to 11.3 percentage points) (Panel B column 3).
- Cross-lender heterogeneity (local versus nonlocal, Table 3a/3b):
  - For conforming loans: negative relationship between exposure and acceptance holds for nonlocal lenders; interaction term positive and offsets standalone exposure term for local lenders (negligible effect for local lenders).
  - For jumbo loans: larger magnitudes. Effects reported as 212 percent and 131 percent for high-growth market defined as Sand States and constrained areas, respectively. Example: if a lender’s lending share to Sand States increases by 1 standard deviation (28.4 percent), the model (Table 3b column 3) suggests the likelihood of loan rejection increases by 58 percent (from 13 to 20.6 percentage points).
  - Interpretation: credit rationing in high-growth areas is concentrated among nonlocal lenders serving these areas as peripheral markets.

### Summary table coefficients and sample sizes (selected, preserved exactly)
- Table 1 highlights:
  - Conforming Loans Panel A: No. of accepted application: N = 83088, Mean = 144820.
  - Acceptance rate by number (Panel A): Mean = 25.8, Std = 7.1.
  - Jumbo Loans Panel B: Acceptance rate by number: Mean = 6.90, Std = 3.18.
  - Lender characteristics Panel C: Total assets (millions) Mean = 2,394,342, Std = 1,058.9206; Tier 1 ratio Mean = 9.15, Std = 5.07.
- Table 2 (Acceptance Rate and Exposure to High-growth Markets):
  - Panel A (Conforming Loans) Exposure to High-Growth Markets (sand states) coefficients: -0.044*** (col 1), -0.051*** (col 2). Exposure to High-Growth Markets (constrained areas): -0.021***, -0.024***.
  - Panel B (Jumbo Loans) Exposure to High-Growth Markets (sand states): -0.052***, -0.056***. Exposure to High-Growth Markets (constrained areas): -0.032***, -0.034***.
  - Sample sizes: Panel A N = 69,580 (cols 1-2) and 68,723 (cols 3-4); Panel B N = 57,426 and 51,103.
- Table 3a (Conforming) and Table 3b (Jumbo) key coefficients:
  - Conforming, sand states: Exposure to High-Growth Markets = -0.129*** (col 1); Local Lender = -0.037**, Exposure to HGM * Local Lender = 0.122***.
  - Jumbo, sand states: Exposure to High-Growth Markets = -0.237***; Local Lender = -0.066***; Exposure to HGM * Local Lender = 0.251***.

### Within-lender regression specification and identification (section 2.3)
- Regression:
  Yijkt = α + βPrimaryMarketikt + γJumboj + δHighGrowthMarketk + θPrimaryMarketikt × HighGrowtheMarketk + φJumboj × PrimaryMarketikt + ψJumboj × HighGrowthMarketk + λXijkt + μit + εijkt
  - i, j, k, t index lender, loan segment, (3-digit zip code) market, and year.
  - Y is acceptance rate.
  - PrimaryMarket = 1 for a lender’s primary market (market with highest lending volume).
  - HighGrowthMarket = dummy for Sand States or constrained areas.
  - Jumbo = dummy for jumbo loans.
  - Includes lender×year fixed effects and market fixed effects.
- Identification: variation across loans in different loan segments and in different markets for the same lender in the same year, controlling for time-varying lender-specific shocks and local market demand-side factors.

### Main within-lender findings on acceptance rates (Table 4a)
- Peripheral versus primary markets:
  - Lenders accept significantly fewer applications in peripheral markets than in primary markets.
  - Column 1 (by number of applications): average acceptance rate is 1 percentage point lower for peripheral markets in nonhigh-growth areas, compared to 2 percentage points lower for peripheral markets in Sand States.
  - Column 2 (by number of applications, constrained areas): average acceptance rate is 1.9 percentage points lower for peripheral markets in constrained areas.
  - These differences are economically meaningful given the average likelihood of the rejections of a loan is 12 percent.
  - Results based on loan volume (columns 3 and 4) are very similar.
- Jumbo versus conforming within-lender:
  - Lenders accept significantly fewer applications in the jumbo segment than in the conforming segment.
  - Column 1: average acceptance rate for jumbo loans is 1.5 percentage points lower than conforming loans in non-Sand states.
  - Jumbo acceptance is 2.8 percentage points lower than conforming loans in Sand States.
- Interpretation: consistent with lenders investing less in private information to screen applicants in peripheral nonhigh-growth areas and in the jumbo segment.

### Local versus nonlocal lenders within-lender (Table 4b)
- Reestimating without market fixed effects allows estimation of average acceptance rates and change for nonlocal lenders expanding to high-growth markets.
- Both local and nonlocal lenders accept fewer applications when they expand to high-growth markets.
  - Example (column 4, measured by loan volume):
    - Difference for a nonlocal lender expanding to a constrained area: 1.6 percentage points in the conforming segment and 4.3 percentage points in the jumbo segment.
    - Difference for a constrained-area lender expanding to another constrained area: 2.3 percentage points in the conforming segment and 4.5 percentage points in the jumbo segment.
- Conclusion: Table 4a results are driven by both local and nonlocal lenders; both groups similarly reduce acceptance rates when expanding to high-growth markets.

### Robustness to market definition and sample periods
- Primary analyses use 3-digit zip codes to define local markets.
- Alternative definitions tested: counties and MSAs.
- Results are very similar when using counties and MSAs (Appendix Tables A1 and A2).
- Sample periods:
  - Main analyses cover 1995-2017.
  - Systemic risk measures use 2000-2017.
  - Several robustness and subperiod analyses cover 2010-2017.

### Evidence on lender profitability and risk (Tables 5, 6, Appendix A6–A7)
- Profitability (ROE):
  - Exposure to Sand States is not significantly associated with ROE for local or nonlocal lenders (column 1).
  - Exposure to constrained areas is negatively correlated with ROE for nonlocal lenders but positively associated with ROE for local lenders (column 2).
- Stock return volatility and excess return volatility:
  - Exposure to high-growth markets is positively correlated with volatility for nonlocal lenders (columns 3 to 6). Effects are statistically significant and economically large.
    - A 1 standard deviation increase (28.4 percent) in exposure to Sand States is associated with a 0.67 increase in stock return volatility (column 3).
    - For constrained areas, a 1 standard deviation increase (19 percent) in exposure is associated with a 0.43 increase in stock return volatility (column 4).
    - Results for excess return volatility are quantitatively very similar (columns 5 and 6).
  - For local lenders, the interaction term is negative and offsets the standalone positive term, so the overall effect of high-growth exposure on risk for local lenders is not statistically different from zero.
  - Interpretation: increased volatility associated with high-growth exposure is unique to nonlocal lenders expanding to high-growth markets.
- SRISK and systemic risk (Table 6):
  - SRISK calculation limited to large lenders trading on stock exchange; sample reduced to 67 lenders over 2000-2017.
  - Exposure to Sand States is associated with higher MES for nonlocal lenders and lower MES for local lenders (column 1).
  - Exposure to constrained areas shows similar patterns and is statistically significant for SRISK (column 4) but not for MES (column 2).
  - Exposure to Sand States on SRISK is not statistically significant (column 3).
  - Overall evidence on systemic risk is inconclusive, and small sample size limits representativeness.

### Mortgage portfolio performance and risk (Tables 7, 8, A8)
- Portfolio summary statistics (Table 7, lender-year level, N = 82,062):
  - Mortgage portfolio return: Mean = .0593, Std = .0358, p10 = .0237, p50 = .0488, p90 = .105.
  - Mortgage portfolio risk: Mean = .0576, Std = .0242, p10 = .0344, p50 = .052, p90 = .0916.
  - Return loss: Mean = .0217, Std = .0143, p10 = .00829, p50 = .0189, p90 = .0384.
  - Relative Sharpe ratio loss: Mean = .301, Std = .189, p10 = .0908, p50 = .262, p90 = .579.
- Portfolio regressions (Table 8, 1995-2017, N = 77,263):
  - Log Risk: Exposure to High-Growth Markets = 0.924*** (col 1, sand states), Local Lender = 0.117***, Exposure to HGM * Local Lender = -0.255***.
  - Log Return Loss: Exposure to High-Growth Markets = -3.803***, Local Lender = -1.068***, Exposure to HGM * Local Lender = 5.254***.
  - Log Relative Sharpe Ratio Loss: Exposure to High-Growth Markets = -4.727***, Local Lender = -1.185***, Exposure to HGM * Local Lender = 5.509***.
- Interpretation from portfolio evidence:
  - A 1 standard deviation increase in exposure is associated with a 0.26 (0.11) increase in the log of portfolio risk for nonlocal lenders in Sand States (constrained areas).
  - A 1 standard deviation increase in lending share to Sand States (constrained areas) is associated with a 1.1 (0.2) decrease in the log of return loss for nonlocal lenders.
  - Exposure to high-growth markets is negatively associated with relative Sharpe ratio loss for nonlocal lenders; effects for local lenders are negligible.
  - Overall: exposure increases portfolio risk for nonlocal lenders while improving portfolio efficiency and return—consistent with a risk–return tradeoff tied to less-informed investments.

### Overall interpretation and implications
- Lenders expanding to high-growth markets accept fewer loan applications, especially in peripheral markets and in the jumbo segment; this pattern holds for both local and nonlocal lenders.
- Credit rationing in high-growth areas is concentrated among nonlocal lenders serving these areas as peripheral markets.
- Nonlocal lenders’ exposure to high-growth markets is associated with higher stock return volatility and higher portfolio risk, while also being associated with higher portfolio return and efficiency—consistent with a risk–return tradeoff where nonlocal lenders may accept higher risk in exchange for higher return and higher portfolio efficiency.
- Evidence on systemic risk (SRISK) is inconclusive due to small sample size for publicly traded large lenders.
- Robustness checks (alternative market definitions and postcrisis period analyses) show findings continue to hold.

*Source: IMF working paper chapter "2.1    Data and measurements" and "2.3    Within-lender tests" (wpiea2021151-print-pdf).*

### 2.1    Data and measurements

### 2.1    Data and measurements

### Data sources and sample construction
- Primary data: loan-level sample of mortgage applications and originations from the Home Mortgage Disclosure Act (HMDA).
- HMDA coverage: close to 95 percent of mortgage originations in the US.
- Institutional reporting scope: regulated financial institutions with more than $30 million in assets.
- Restrictions on sample:
  - Exclude loans guaranteed by the Federal Housing Administration, Veterans Administration, Farm Service Agency, or Rural Housing Service (restrict to conventional loans).
  - Restrict to loans for single-family home purchase; exclude refinancing and home improvement loans.
- Geographic market definition: 3-digit zip code level; final dataset covers 880 local markets out of 882 3-digit U.S. zip codes.
- Lender-level data: HMDA merged with the Report of Condition and Income (“Call Reports”) by linking Call Report identification number with the HMDA identification number.
- Housing prices: quarterly house price index from the Federal Housing Finance Agency (FHFA) measured in 3-digit zip codes.

### Sample sizes and summary statistics
- Raw HMDA sample size: 485 million applications over the 1995–2017 period.
- Final sample after exclusions: 362 million mortgage applications.
- Conforming segment:
  - 20.9 percent of applicants are women.
  - 3.6 percent of applicants are members of minority groups.
  - Average acceptance rate: 87 percent by loan number and 88.2 percent by loan volume.
  - Lenders on average originate $190 million of loans per year and keep 45 percent of them on their balance sheets.
- Jumbo segment:
  - 9.6 percent of applicants are women.
  - 2.1 percent of applicants are members of minority groups.
  - Acceptance rate: 90.3 percent by loan number and 90.4 by loan volume.
  - Lenders on average originate $79.4 million mortgages and keep 80 percent of them on their balance sheets.
- Lender size in sample:
  - Mean lender size: $2.4 billion.
  - Median lender size: $206 million.
- Average exposure to high-growth areas: 10.5 (6.2) percent of total loans (Sand States (constrained areas)).

### Definition and identification of high-growth markets
- Two alternative definitions:
  - Sand States: Arizona, California, Florida, and Nevada.
  - Geographically constrained areas: bottom decile of Lutz and Sand (2019) land-availability index for 3-digit zip codes (index extends Saiz (2010) measure).
- Notes on land-availability indices:
  - Saiz (2010) index used for 269 MSAs with population of 50,000 or more.
  - Lutz and Sand (2019) extend index to all 3-digit zip codes; methodological differences noted but high correlation (correlation of 0.8 and R^2 of 0.7).

### Housing cycle patterns in high-growth markets
- Mortgage volume trends:
  - Share of mortgages originated in Sand States increased from 31 percent in 1995 to 40 percent in 2005, falling to 25 percent in 2010 before recovery.
  - Share of loans to constrained areas followed a similar trend with smaller magnitude.
- House price growth and collapse:
  - 2001–2005 house price growth: Sand States 103 percent; constrained areas 51 percent; national average 44 percent.
  - 2008–2010 house price collapse: Sand States −27.8 percent; constrained areas −10.5 percent; national average −8.7 percent.
  - 2011–2017 house price growth: Sand States 6.3 percent; constrained areas 3.1 percent; national average 2.6 percent.

### Acceptance-rate regressions and empirical specifications
- Baseline regression (equation (1)):
  - Yijt = α + β HighGrowthShareijt−1 + λ Xijt−1 + μt + εijt
  - Y is acceptance rate (accepted applications as share of total applications), calculated by number of applications or loan volume.
  - HighGrowthShare is lending to high-growth markets as a share of total lending.
  - Controls (X): lender size (log of total assets), Tier 1 capital ratio, deposit-to-total assets ratio, lender diversification, average income of applicants, percentage of applicants who are women, percentage of applicants who are minority, and year fixed effects.
  - Lender diversification index: 1 − sum of squared shares of mortgages across markets; ranges from 0 (single-market lender) to nearly 1 (highly diversified lender).
- Extended specification (equation (2)):
  - Yijt = α + β HighGrowthShareijt−1 + γ HighGrowthLenderijt−1 + δ HighGrowthShareijt−1 × HighGrowthLenderijt−1 + λ Xijt−1 + μt + εijt
  - HighGrowthLender = 1 if a lender’s mortgage loans to high-growth markets exceeds 25 percent of total mortgage loans (robustness to thresholds of 20, 33.3, or 50 percent noted).

### Key empirical findings on acceptance rates
- Table 2 (equation (1)) findings:
  - Lenders more exposed to high-growth markets have significantly lower acceptance rates (β < 0).
  - Results robust to acceptance defined by number of loans or loan volume and to high-growth definition (Sand States or constrained areas).
  - Borrower characteristics do not drive the difference; estimates without and with borrower controls are very similar.
  - Economic magnitudes:
    - Conforming segment: a 1 standard deviation increase in a lender’s lending share to Sand States (28.4 percent) increases likelihood of loan rejection by 10 percent (from 13 to 14.4 percentage points) (Panel A column 3).
    - Jumbo segment: a 1 standard deviation increase in lending share to Sand States (28.4 percent) increases likelihood of loan rejection by 17 percent (from 9.7 to 11.3 percentage points) (Panel B column 3).
  - Negative effect stronger for jumbo loans than conforming loans; possible explanation: GSE purchase willingness for conforming mortgages reduces lenders’ incentive to invest in private information for conforming loans.

- Table 3a and 3b (equation (2)) findings:
  - Distinguishing local (HighGrowthLender = 1) vs nonlocal lenders:
    - For conforming loans (Table 3a): negative relationship between exposure to high-growth markets and acceptance rate holds for nonlocal lenders; interaction term positive and offsets standalone high-growth exposure term for local lenders, implying negligible effect for local lenders.
    - For jumbo loans (Table 3b): results hold with larger magnitudes:
      - Effects reported as 212 percent and 131 percent for high-growth market defined as Sand States and constrained areas, respectively.
      - Example: if a lender’s lending share to Sand States increases by 1 standard deviation (28.4 percent), the model (Table 3b column 3) suggests the likelihood of loan rejection increases by 58 percent (from 13 to 20.6 percentage points).
  - Interpretation:
    - Credit rationing in high-growth areas is concentrated among nonlocal lenders serving these areas as peripheral markets.
    - Lenders behave differently in peripheral markets than in their primary markets; local lenders do not show the same decrease in acceptance rates with greater exposure to high-growth areas.

*Source: IMF working paper chapter "2.1    Data and measurements" (wpiea2021151-print-pdf).*

### 2.3    Within-lender tests

### 2.3    Within-lender tests

### Regression specification and identification
- Regression estimated:
  Yijkt = α + βPrimaryMarketikt + γJumboj + δHighGrowthMarketk + θPrimaryMarketikt × HighGrowtheMarketk + φJumboj × PrimaryMarketikt + ψJumboj × HighGrowthMarketk + λXijkt + μit + εijkt
  - i, j, k, t index lender, loan segment, (3-digit zip code) market, and year.
  - Y is acceptance rate.
  - PrimaryMarket = 1 for a lender’s primary market (market with highest lending volume).
  - HighGrowthMarket = dummy for Sand States or constrained areas.
  - Jumbo = dummy for jumbo loans.
  - Includes lender×year fixed effects and market fixed effects.
- Identification comes from variation across loans in different loan segments and in different markets for the same lender in the same year, controlling for time-varying lender-specific shocks and local market demand-side factors.

### Main findings on acceptance rates (Table 4a)
- Lenders accept significantly fewer loan applications in peripheral markets than in primary markets; credit rationing is more pronounced for peripheral markets in high-growth areas.
  - Column 1 (by number of applications): average acceptance rate is 1 percentage point lower for peripheral markets in nonhigh-growth areas, compared to 2 percentage points lower for peripheral markets in Sand States.
  - Column 2 (by number of applications, constrained areas): average acceptance rate is 1.9 percentage points lower for peripheral markets in constrained areas.
  - These differences are economically meaningful given the average likelihood of the rejections of a loan is 12 percent.
  - Results based on loan volume (columns 3 and 4) are very similar.
- Lenders accept significantly fewer applications in the jumbo segment than in the conforming segment; rationing of jumbo loans is more pronounced in high-growth areas.
  - Column 1: average acceptance rate for jumbo loans is 1.5 percentage points lower than conforming loans in non-Sand states.
  - Jumbo acceptance is 2.8 percentage points lower than conforming loans in Sand States.
- Interpretation: evidence consistent with lenders investing less in private information to screen applicants in peripheral nonhigh-growth areas and in the jumbo segment (loans not eligible for GSE subsidies).

### Local versus nonlocal lenders (Table 4b)
- Reestimating equation (3) without market fixed effects allows estimation of average acceptance rates in high-growth markets and the change for nonlocal lenders expanding to those markets.
- Both local and nonlocal lenders accept fewer applications when they expand to high-growth markets.
  - Example (column 4, measured by loan volume):
    - Difference for a nonlocal lender expanding to a constrained area: 1.6 percentage points in the conforming segment and 4.3 percentage points in the jumbo segment.
    - Difference for a constrained-area lender expanding to another constrained area: 2.3 percentage points in the conforming segment and 4.5 percentage points in the jumbo segment.
- Conclusion: results in Table 4a are driven by both local and nonlocal lenders; both groups similarly reduce acceptance rates when expanding to high-growth markets.

### Robustness to market definition
- Primary analyses use 3-digit zip codes to define local markets.
- Alternative definitions tested: counties and MSAs.
- Results are very similar when using counties and MSAs (Appendix Tables A1 and A2).

### Transition to evidence on lender performance and risk
- Question posed: Are lower acceptance rates in high-growth markets due to greater selectivity (leading to better performance and lower risk) or due to less investment in private information (leading to poorer performance and higher risk)?
- Approach: estimate regressions of lender profitability and risk measures (ROE, daily stock return volatility, excess stock return volatility) on exposure to high-growth markets, including interaction with local-lender indicator and lender controls, with year fixed effects.

### Evidence from lender profitability and risk (Table 5 and SRISK results)
- Profitability (ROE):
  - Exposure to Sand States is not significantly associated with ROE for local or nonlocal lenders (column 1).
  - Exposure to constrained areas is negatively correlated with ROE for nonlocal lenders but positively associated with ROE for local lenders (column 2).
- Risk (stock return volatility and excess return volatility):
  - Exposure to high-growth markets is positively correlated with volatility for nonlocal lenders (columns 3 to 6). Effects are statistically significant and economically large.
    - A 1 standard deviation increase (28.4 percent) in exposure to Sand States is associated with a 0.67 increase in stock return volatility (column 3).
    - For constrained areas, a 1 standard deviation increase (19 percent) in exposure is associated with a 0.43 increase in stock return volatility (column 4).
    - Results for excess return volatility are quantitatively very similar (columns 5 and 6).
  - For local lenders, the interaction term is negative and offsets the standalone positive term, so the overall effect of high-growth exposure on risk for local lenders is not statistically different from zero.
  - Interpretation: effect of high-growth market exposure on increased volatility is unique to nonlocal lenders expanding to high-growth markets.
- SRISK and systemic risk (Table 6):
  - SRISK calculation limited to large lenders trading on stock exchange; sample reduced to 67 lenders over 2000-2017.
  - Exposure to Sand States is associated with higher MES for nonlocal lenders and lower MES for local lenders (column 1).
  - Exposure to constrained areas shows similar patterns and is statistically significant for SRISK (column 4) but not for MES (column 2).
  - Exposure to Sand States on SRISK is not statistically significant (column 3).
  - Overall evidence on systemic risk is inconclusive, and small sample size limits representativeness.

### Key statistics and moments (portfolio preview from later sections)
- Sample for SRISK analyses: 67 lenders over a sample period of 2000-2017.
- Average mortgage portfolio return: 5.93 percent with a standard deviation of 3.58 percent (Table 7).
- Average risk (portfolio risk measure reported): about 5.76 percent.
- Portfolio-level regression results (Table 8, summary):
  - A 1 standard deviation increase in exposure is associated with a 0.26 (0.11) increase in the log of portfolio risk for nonlocal lenders in Sand States (constrained areas).
  - A 1 standard deviation increase in lending share to Sand States (constrained areas) is associated with a 1.1 (0.2) decrease in the log of return loss for nonlocal lenders.
  - Exposure to high-growth markets is negatively associated with relative Sharpe ratio loss for nonlocal lenders; effects for local lenders are negligible.
- Overall interpretation from portfolio evidence: exposure to high-growth markets increases portfolio risk for nonlocal lenders while improving portfolio efficiency and return, consistent with a tradeoff where nonlocal lenders may accept higher risk in exchange for higher return and higher portfolio efficiency.

### Overall interpretation and implications
- Lenders expanding to high-growth markets accept fewer loan applications, especially in peripheral markets and in the jumbo segment; this pattern holds for both local and nonlocal lenders.
- Nonlocal lenders’ exposure to high-growth markets is associated with higher stock return volatility and higher portfolio risk, while also being associated with higher portfolio return and efficiency—consistent with a risk–return tradeoff tied to less-informed investments in these markets.
- Evidence on systemic risk (SRISK) is inconclusive due to small sample size for publicly traded large lenders.
- Robustness checks (alternative market definitions and postcrisis period analyses) show findings continue to hold.

*Source: 2.3 Within-lender tests — excerpt from wpiea2021151-print-pdf*

### References

### wpiea2021151-print-pdf - References

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### Figure captions (selected)
- Figure 1: Mortgage origination by Local Lenders. Local lender defined as those with 50 percent or more of total lending in a single local market.
- Figure 2: Mortgage Lending in High-Growth Markets. High-growth markets measured by Sand States (Arizona, California, Florida, and Nevada) or constrained areas (land availability in the bottom decile according to Lutz and Sand (2019)).
- Figure 3: Nonlocal Lender Share in High-Growth Markets. Nonlocal lender defined as those with less than 50 percent of total lending in a single local market.
- Figure 4: House Price Index in High-Growth Markets. House price data from Federal Housing Finance Agency. House prices in 1994 normalized to 100.
- Figure 5: Mortgage Portfolio Return and Risk. Lender-level mortgage portfolio return and risk in 2017 estimated with CAPM. The national portfolio is denoted by a black diamond.
- Figure A1: Linkage Between 3-digit Zip Code and County. Examples for zip = 222 (Arlington county, Virginia) and zip = 326 (overlaps with Dixie county, Gilchrist county, Alachua county, Levy county in Florida; MSA Gainesville-Lake City, FL).
- Figure A2: Distribution of Lending to High-Growth Markets. Histogram of share of lending to high-growth markets (Sand States or constrained areas per Lutz and Sand (2019)).

### Key empirical findings and statistics (from tables)
- Summary statistics (Table 1, Panel A: Conforming Loans):
  - No. of accepted application: N = 83088, Mean = 144820, p10 = 20964, p50 = 1106830.
  - Acceptance rate by number: Mean = 25.8, Std = 7.1, p10 = 2.7, p50 = 3.89, p90 = 6.99.
  - Acceptance rate by volume: Mean = 25.8, Std = 82.1, p10 = 23.7, p50 = 42.9, p90 = 131.
  - Average income (thousand): Mean = 99.1, Std = 17.1, p10 = 31.05, p50 = 303.09, p90 = 24.193.
- Summary statistics (Table 1, Panel B: Jumbo Loans):
  - No. of accepted application: N = 83088, Mean = 114229, p10 = 90337.
  - Acceptance rate by number: Mean = 6.90, Std = 3.18, p10 = 6.69, p50 = 6, p90 = 11.
  - Acceptance rate by volume: Mean = 6.90, Std = 4.19, p10 = 2.69, p50 = 6, p90 = 11.
- Lender characteristics (Table 1, Panel C):
  - Total assets (millions): Mean = 2,394,342, Std = 1,058.9206, p10 = 1,235.
  - Tier 1 ratio: Mean = 9.15, Std = 5.07, p10 = 7.09, p50 = 6.11, p90 = 31.22.
  - Diversification: Mean = 0.554, Std = 0.249, p10 = 0.157, p50 = 0.598, p90 = 0.845.
  - Share of lending in sand states: Mean = 0.091, Std = 0.128, p50 = 0.338.
  - Share of lending in constrained areas: Mean = 0.0616, Std = 0.192, p50 = 0.142.
- Acceptance Rate and Exposure to High-growth Markets (Table 2):
  - Panel A (Conforming Loans): Exposure to High-Growth Markets (sand states) coefficients: -0.044*** (col 1), -0.051*** (col 2). Exposure to High-Growth Markets (constrained areas): -0.021***, -0.024***.
  - Panel B (Jumbo Loans): Exposure to High-Growth Markets (sand states): -0.052***, -0.056***. Exposure to High-Growth Markets (constrained areas): -0.032***, -0.034***.
  - Sample sizes: Panel A N = 69,580 (cols 1-2) and 68,723 (cols 3-4); Panel B N = 57,426 and 51,103.
- Acceptance Rate of Local and Nonlocal Lenders (Tables 3a, 3b):
  - Conforming loans (Table 3a): Measure using sand states: Exposure to High-Growth Markets = -0.129*** (col 1), -0.126*** (col 2); Local Lender = -0.037**, -0.030**; Exposure to HGM * Local Lender = 0.122***, 0.104**.
  - Jumbo loans (Table 3b): Measure using sand states: Exposure to High-Growth Markets = -0.237***, -0.267***; Local Lender = -0.066***, -0.072***; Exposure to HGM * Local Lender = 0.251***, 0.285***.
  - Measure using constrained areas shows larger negative Exposure coefficients and positive interactions for Local Lender * Exposure in both conforming and jumbo segments (coefficients listed in tables).
- Within-Lender Tests (Tables 4a, 4b and Appendix A1–A5):
  - Primary Market coefficient consistently positive and significant: 0.010*** to 0.015*** across specifications (Table 4a and 4b).
  - Jumbo coefficient consistently negative and significant: values such as -0.015***, -0.018***, -0.025***, -0.027*** (Table 4a).
  - Primary Market * Jumbo interaction positive and significant: values around 0.020*** to 0.027***.
  - High-Growth Market * Primary market positive and significant in sand states and constrained area measures (e.g., 0.010***, 0.009***).
- Lender Profitability and Stock Return Volatility (Tables 5 and A6):
  - Using sand states (Table 5): Exposure to High-Growth Markets: Return on Equity coefficient -0.271 (not significant); Stock Return Volatility coefficients 1.877*** and 1.857*** (cols 2-3). Exposure to HGM * Local Lender: Stock Return Volatility interaction -2.361***, -2.339***.
  - Using constrained areas: Exposure to High-Growth Markets: Return on Equity -1.081***; Stock Return Volatility 1.744*** and 1.718***. Exposure to HGM * Local Lender: Return on Equity 1.413***, interaction on volatility -2.214***, -2.186***.
  - Appendix A6 (2010-2017) shows similar patterns with coefficients such as Exposure to High-Growth Markets (sand states) Stock Return Volatility 1.621***, Excess Return Volatility 1.624***; Exposure to HGM * Local Lender interactions negative and significant for volatility (e.g., -2.189***, -2.192***).
- Lender Systemic Risk (Tables 6 and A7):
  - Table 6 (2000-2017): Marginal Expected Shortfall: Exposure to High-Growth Markets = 19.751*** (col 1). SRISK(%): Exposure to High-Growth Markets = -3.215 (col 2, not significant). Exposure to HGM * Local Lender for Marginal Expected Shortfall = -31.356***.
  - Appendix A7 (2010-2017): Exposure to High-Growth Markets coefficients vary (e.g., Marginal Expected Shortfall 8.445, SRISK -4.859), and Local Lender shows 6.033** for Marginal Expected Shortfall.
- Mortgage Portfolio Performance (Tables 7, 8, and A8):
  - Table 7 summary statistics (lender-year level, N = 82,062):
    - Mortgage portfolio return: Mean = .0593, Std = .0358, p10 = .0237, p50 = .0488, p90 = .105.
    - Mortgage portfolio risk: Mean = .0576, Std = .0242, p10 = .0344, p50 = .052, p90 = .0916.
    - Return loss: Mean = .0217, Std = .0143, p10 = .00829, p50 = .0189, p90 = .0384.
    - Relative Sharpe ratio loss: Mean = .301, Std = .189, p10 = .0908, p50 = .262, p90 = .579.
  - Table 8 (1995-2017 regressions, N = 77,263):
    - Log Risk: Exposure to High-Growth Markets = 0.924*** (col 1, sand states), Local Lender = 0.117***, Exposure to HGM * Local Lender = -0.255***.
    - Log Return Loss: Exposure to High-Growth Markets = -3.803***, Local Lender = -1.068***, Exposure to HGM * Local Lender = 5.254***.
    - Log Relative Sharpe Ratio Loss: Exposure to High-Growth Markets = -4.727***, Local Lender = -1.185***, Exposure to HGM * Local Lender = 5.509***.
  - Appendix A8 (2010-2017) shows consistent patterns: Log Risk Exposure to High-Growth Markets = 0.965***, Log Return Loss = -3.472***, Log Relative Sharpe Ratio Loss = -4.437***; Local Lender and interaction coefficients are similar and significant.

### Appendix notes (selected)
- Market definitions used throughout:
  - High-growth markets measured by Sand States (Arizona, California, Florida, and Nevada) or constrained areas (areas with land availability in the bottom decile according to Lutz and Sand (2019)).
  - Local lender definitions vary by specification: 50 percent or more of total lending in a single local market (figures) or 25 percent or more of total lending in high-growth markets (tables).
- Fixed effects and controls:
  - Many regressions include applicant controls (share of loans with full documentation, share of women applicants, share of minority applicants), lender controls (log of total assets, Tier 1 capital ratio, deposit to asset ratio), year fixed effects, market fixed effects, and lender×year fixed effects depending on the specification.
- Sample periods:
  - Main analyses cover 1995-2017; systemic risk measures use 2000-2017; several robustness and subperiod analyses cover 2010-2017.

*Italic: Source — wpiea2021151-print-pdf - References*

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_Source: https://www.imf.org/-/media/files/publications/wp/2021/english/wpiea2021151-print-pdf.pdf_