## Section 2) as an exogenous variable in the VAR Equation (2).  Under the assumption thatz

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### Methodology and estimation approach
- Surprise series zt modeled as zt = α εmp,t + ηt with ηt orthogonal to all other variables; this consistently estimates impulse response functions (Paul (2020)).
- Contemporaneous reaction of factor j to a one-unit increase in Rt given by Aj/AR.
- zt identified only up to sign and scale; A normalized so a contractionary monetary policy shock corresponds to a median increase in the policy rate of 25 basis points (bps).
- Exogenous variable approach of Paul (2020) yields contemporaneous impulse responses identical to the external instrument approach of Stock and Watson (2018).
- FAVAR estimation strategy:
  - Two-step approach based on principal component analysis (Stock and Watson (2005), Korobilis (2013), Corsetti et al. (2022)).
  - First step: extract five principal components using the Bayesian information criterion (BIC) of Bai and Ng (2002).
  - Principal components obtained from standardized data; identification imposes Λ′F ΛF = Iq.
  - For IRFs, use demeaned but not fully standardized data.
  - Conditional on estimated principal components, observation Equation (1) collapses to N univariate regressions and transition Equation (2) is a standard VAR(X).
- Bayesian estimation details:
  - Parameters estimated via Bayesian MCMC with a Gibbs sampler.
  - Total of 10,000 draws with the first 5,000 draws dropped as ‘burn-in’.
  - Priors overall standard; somewhat tighter prior for Σ given short time dimension.
- Factor interpretability:
  - First five principal components shown alongside the monetary policy indicator (observed factor) in Figure C.1.
  - Suggested factor interpretations:
    - First factor: (mortgage) loan performance.
    - Second factor: homeownership rate.
    - Third factor: state-level rent price index.
    - Fourth factor: US prices and personal expenditures.
    - Fifth factor: state-level GDP deflator and personal bankruptcies.

### US aggregate evidence: response to a monetary policy tightening
- Monetary policy shock calibrated to increase the one-year treasury rate by 25bps on impact.
- Aggregate real activity:
  - Real GDP decreases by around 0.5 percent after two years.
  - Real GDP reaches a trough of around 0.8 percent after three to four years.
- Inflation:
  - Temporary rise in the one-year treasury rate (lasting about seven quarters) leads to a decline in CPI inflation over the medium term.
- Housing market variables:
  - House prices:
    - Fall on impact.
    - Decline by roughly 3 percent after two years.
    - Decline by 4 percent after five years.
  - Building permits:
    - Contract by almost 1 percent after two years.
    - Contract by 1.5-2 percent after five years.
- Comparison with Williams (2015) meta-analysis:
  - Williams (2015): 100bps shock → house prices decline between 1.7 percent and 10.8 percent after two years; this paper’s estimates: 12 percent.
  - Williams (2015): real activity falls between 0.3 percent and 9.3 percent after two years; this paper: 2 percent.
- Mortgage market structure:
  - Share of fixed-rate mortgages rose to 96.4% in 2023q2, up from 94.5% in 2019q4.
  - ARM mortgages uncommon: ARM share 5.5% of all outstanding mortgages nationally in 2019q4, with a standard deviation of 1.8 percentage points across states.
- Transmission margins:
  - Intensive margin: housing wealth effects transmit to consumption (Iacoviello 2005; Bhutta and Keys 2016; Aladangady 2017; Beraja et al. 2019; Cloyne et al. 2020; Garriga and Hedlund 2020).
  - Extensive margin: tighter credit conditions (SLOOS) reduce housing demand, lowering homeownership rates (Bhutta and Ringo 2021).
  - Reallocation to rentals evidenced by increases in home vacancy rate and falls in rental vacancy rate.

### Transmission to state-level housing markets: heterogeneity and tenure effects
- Main empirical findings for a 25bps increase in the one-year treasury rate:
  - Sizeable heterogeneity across US states in responses of economic activity, house prices, housing supply, and homeownership rate; all fall but magnitudes vary.
  - Real rents increase over the horizon while house prices fall—consistent with demand shifting from owner-occupied to rental segment.
  - Fall in the house price-to-rent ratio (HPI/rents) varies markedly across states, influencing buy-or-rent decisions.
  - Credit conditions tighten → contraction in mortgage debt and increase in mortgage delinquencies.
  - Heterogeneous vacancy and tenure responses:
    - Some states show declines in home vacancy rates and increases (decreases) in rental vacancy rates, deviating from median responses.
    - Persistent decline in rental vacancy rate in some states suggests high market segmentation; increasing rental demand not fully met by supply, explaining rising rents (Greenwald and Guren 2021).
- Distributional implications:
  - Combination of tighter credit, lower house prices, and higher rents could disproportionately affect mortgagors and renters—groups associated with larger MPCs (Cloyne et al. 2020).
  - Monetary policy may have differential distributional effects via housing wealth and consumption channels (Coibion et al. 2017; Holm et al. 2021; Amberg et al. 2022; Bonifacio et al. 2022; Amaral et al. 2024).
- Model caveat:
  - FAVAR assumes symmetry of monetary policy effects; possible regional asymmetries (Aastveit and Anundsen 2022) not analyzed here.

### Regional characteristics and channels explaining heterogeneity
- Empirical strategy:
  - Compare posterior distributions of average responses between states in top and bottom deciles of selected characteristics (Figures 5–8).
  - Complemented with conditional regression-based correlation analysis; Table B.2 reports state average characteristics and decile membership.
- Channels explored:
  - Housing supply elasticities (LRI).
  - Credit conditions and mortgage market characteristics (debt gap).
  - Housing wealth exposure and volatility.
  - State-specific characteristics account for a portion of regional variation in transmission.

### Housing supply channel (5.1)
- Concept and measure:
  - Land-use restriction index (LRI) of Herkenhoff et al. (2018) for 48 states (excluding Alaska and Hawaii) for decades 1950–2000 and 2014.
  - LRI divided by its standard deviation and sign changed so higher values reflect tighter land-use regulation.
  - Baseline choice motivated by state-level availability; Saiz (2010) elasticities are MSA-level.
- Key empirical findings:
  - States with tighter land-use regulation experience larger declines in house prices and permits after a 25bps tightening (Figure 5).
  - Shaded areas are 68% highest density interval (HDI) of average responses; HDI of group differences excludes zero for most variables.
  - Larger decline in housing wealth in inelastic states leads to greater fall in consumption and larger increase in unemployment (Figure C.15).
  - Mortgage debt falls more in inelastic states; mortgage delinquencies and foreclosures worsen (Figure 6).
- Mechanisms and interpretation:
  - Credit boom-bust dynamics, household overoptimism, financial-accelerator effects, and price-to-price feedback loops can amplify contractions in low-supply elasticity areas.
  - Inelastic states show larger fall in homeownership rates and smaller increase in rent prices—frictions/adjustment costs may inhibit conversion to rentals (Figure C.17).
  - Inelastic states are high-income with larger housing wealth and higher consumption/income per capita (Figures C.18–C.20); contractionary shocks may reduce regional consumption and housing wealth inequality.
- Caveats and robustness:
  - Housing supply constraints are not claimed as sole driver; other state differences may explain heterogeneity.
  - Results robust when using LRI reference year 2000 instead of 2014 and when exploring cross-sectional house value distributions (Figures C.12–C.14).

### Debt overhang channel (5.1)
- Concept and measure:
  - Debt overhang proxied by state-level debt gap: Hamilton (2018) filter on state mortgage debt-to-income ratio (quarterly, p=1, h=20).
  - States compared by top and bottom deciles of maximum debt gap over time.
- Key empirical findings:
  - States with larger debt gaps experience stronger transmission:
    - House prices, permits, mortgage debt, and consumption fall more in high-debt-gap states (Figure 7).
    - Financial stability risk increases more in these areas (Figure C.21).
  - Responses in high-debt-gap states qualitatively similar to low-supply-elasticity areas.
- Numeric note:
  - Correlation between supply constraints and household debt gaps described as “sizeable (around 0.6)”.
- Interpretation:
  - Higher borrowing costs bind households with larger debt imbalances more tightly, producing larger contractions in housing demand, prices, consumption, and activity.

### Housing wealth volatility and household balance sheet channel (5.1)
- Concept and measure:
  - Housing wealth volatility proxied by standard deviation of housing wealth over the sample.
  - Housing wealth computed as: (homeownership rate_{j,t} × total occupied housing units_{j,t}) × house price index_{j,t} × median house price in 2000_{j}.
- Key empirical findings:
  - States with larger housing wealth fluctuations react more strongly: larger house price falls and larger declines in consumption (Figure 8).
  - Correlations:
    - Housing wealth level and volatility highly correlated (around 0.9).
    - Consumption response correlates significantly and positively with housing wealth volatility but not with average housing wealth (Table C.2).
  - For most variables, correlation with housing wealth volatility stronger than with housing wealth level.
- Interpretation:
  - Higher housing wealth uncertainty may induce households to reduce real estate demand or postpone purchases, strengthening monetary transmission via weaker housing demand and consumption.

### Cross-sectional multivariate analysis (5.2)
- Methodology:
  - Cross-sectional regressions: IRF_y_h,i = α + X_i β + regions_i + η_i, η_i ∼ N(0, σ^2_η).
  - Focus on cumulative response after h = 12 quarters; similar for h = 8 and h = 20.
  - Regions: dummies for eight BEA divisions. Robust standard errors; significance ∗p<0.1, ∗∗p<0.05, ∗∗∗p<0.01.
- Variables and controls included:
  - LRI (Herkenhoff et al. (2018) 2014), Debt gap (average Hamilton-filtered 1999–2019), HW (avg.) = 100*log(Average housing wealth 1999–2019), HW (std.) = 100*log(Standard deviation of housing wealth 1999–2019), Sand state (AZ, CA, FL, NV), RTW, Manufacturing share, Small firms share, HPI growth (1999–2019).
- Dependent cumulative responses at h = 12: GDP, PCE, HPI, Rents, Permits, HOR.

### Table 1: Selected regression point estimates (h = 12) — key coefficients and statistics
- LRI:
  - GDP: -0.347 (0.200) ∗
  - PCE: -0.339 (0.091) ∗∗∗
  - HPI: -0.868 (0.335) ∗∗
  - Rents: -0.834 (0.418) ∗
  - Permits: -0.006 (0.089)
  - HOR: -0.021 (0.069)
- Debt Gap:
  - Permits: -0.013 (0.005) ∗∗
  - HOR: -0.005 (0.002) ∗
  - Other coefficients not significant at conventional levels.
- HW (avg.):
  - GDP: 0.012 (0.005) ∗∗
  - HPI: 0.022 (0.012) ∗
  - Rents: 0.018 (0.009) ∗
- Sand state:
  - GDP: -1.330 (0.482) ∗∗∗
  - HPI: -2.434 (1.001) ∗∗
- RTW:
  - GDP: -0.454 (0.220) ∗∗
  - PCE: -0.588 (0.138) ∗∗∗
  - Permits: 0.387 (0.113) ∗∗∗
- Small firms:
  - HPI: -0.055 (0.029) ∗
  - Permits: 0.017 (0.008) ∗
- HPI growth:
  - GDP: 0.072 (0.019) ∗∗∗
  - PCE: 0.035 (0.010) ∗∗∗
  - Permits: 0.016 (0.007) ∗∗
- Observations:
  - GDP: 48; PCE: 48; HPI: 48; Rents: 46; Permits: 48; HOR: 48.
- Adjusted R^2:
  - GDP: 0.657; PCE: 0.664; HPI: 0.861; Rents: 0.232; Permits: 0.720; HOR: 0.443.
- Main empirical interpretations:
  - A state with LRI one standard deviation higher exhibits a 0.9 percentage point larger house price drop after a 25bps tightening (HPI coefficient magnitude interpretation).
  - Debt gap significant for permits and HOR, indicating debt imbalances add explanatory power beyond supply constraints.
  - HW (avg.) explains heterogeneity in GDP, HPI, and Rents; HW (std.) not robustly significant once controls included.
  - Sand state and RTW dummies show notable associations with GDP, PCE, HPI, and permits.

### Robustness checks
- Alternative monetary policy surprise series (Swanson (2021); Jarociński and Karadi (2020)) yield qualitatively similar results.
- Alternative supply elasticity measures (Aastveit et al. (2023); Saiz (2010)) aggregated to state level produce comparable findings.
- Alternative state-level inflation series (Hazell et al. (2022)) yields comparable cross-state dispersion results; Hazell et al. (2022) ends in 2017q4 and is smoother for some states.

### Variable definitions and sample characteristics
- HW = (Homeownership rate × Housing units) × HPI × Median house price in 2000.
- HW (std.) = Standard deviation of housing wealth over 1999–2019.
- LRI = Land-use regulation index (2014) — Herkenhoff et al. (2018).
- Debt gap = Average of Hamilton-filtered mortgage debt-to-income ratio from 1999–2019 (maximum value over sample used for decile classification).
- Sample-average state characteristics (selected rows, preserved exactly):
  - AL: -1.61 | 0.03 | 4,575.3 | 2680.8 | 0 | 1 | 16.9 | 7.2 | 3.0
  - AK: –2 | 0.94 | 6,293.9 | 3970.5 | 0 | 0 | 2.9 | 7.2 | 10.7
  - AZ: -0.95 | 8.74 | 8,327.7 | 11721.2 | 1 | 1 | 10.0 | 6.1 | 17.7
  - CA: -0.37 | 6.79 | 5,388.2 | 23708.3 | 1 | 0 | 10.2 | 17.5 | 26.8
  - FL: -1.03 | 9.15 | 3,897.7 | 13862.7 | 1 | 1 | 5.4 | 7.4 | 21.4
  - NY: -0.9 | 14.68 | 4,779.7 | 12255.1 | 0 | 0 | 5.8 | 6.8 | 17.5
  - TX: -2.6 | 4.82 | 1,499.6 | 2044.7 | 0 | 1 | 13.9 | 7.2 | 17.9
  - WA: -0.63 | 4.69 | 7,000.7 | 15094.9 | 0 | 1 | 13.2 | 7.6 | 22.9

### Correlations and factor explanatory power
- Selected correlations (three-year responses) from Table C.2 (correlation (p-value)):
  - LRI — PCE: -0.42*** (0.00); HPI: -0.64*** (0.00); HPI/rents: 0.59*** (0.00).
  - Debt gap — GDP: -0.36*** (0.01); PCE: -0.55*** (0.00); HPI: -0.77*** (0.00); Mortgage debt: -0.76*** (0.00).
  - HW (avg.) — HPI: -0.54*** (0.00); Mortgage delinquency rate: -0.50*** (0.00).
  - HW (std.) — PCE: -0.33** (0.02); HPI: -0.78*** (0.00).
  - Sand state — GDP: -0.55*** (0.00); HPI: -0.65*** (0.00); Mortgage delinquency rate: -0.60*** (0.00).
  - RTW — GDP: -0.33** (0.02); HPI: 0.32** (0.02).
- Explanatory power (Table C.1): selected high R-squared examples:
  - Non performing loan share: Michigan — 0.9790.
  - New housing units started: US — 0.9789.
  - Mortgage delinquency rate: California — 0.9784.
  - One-year rate (observed factor) — FFR: 0.9728.

### Conclusions and policy implications
- Significant heterogeneity in transmission of contractionary monetary policy across US states.
- Key drivers of heterogeneity:
  - Housing supply elasticities (land-use regulation, LRI).
  - Household debt overhang (debt gap).
  - Housing wealth (HW (avg.)).
- Low-supply-elasticity areas with stringent land-use regulation experience larger falls in house prices, broader declines in economic activity, and greater deterioration in financial stability indicators.
- Monetary policy can affect housing tenure: higher rates → house price declines and rental price increases, with heterogeneity by state supply elasticity and market segmentation.
- Policy implications:
  - Financial supervision could tighten more in areas with inelastic housing supply to limit excessive house price volatility.
  - Strengthen macroprudential measures (limits on loan-to-income and/or debt-service ratios) before debt imbalances emerge.
  - Relaxation of land-use restrictions could reduce boom-bust cycles by allowing supply expansion during upswings, increasing resilience to contractionary shocks.
  - Monetary policy may have distributional effects: contractionary shocks can lead to larger declines in housing wealth and consumption in high-housing-wealth, high-income states, potentially decreasing consumption and housing wealth inequality across states.

*Source: wpiea2024023-print-pdf — The Housing Supply Channel of Monetary Policy — Working Paper No. WP/2024/023*

### Section 2) as an exogenous variable in the VAR Equation (2).  Under the assumption thatz

### wpiea2024023-print-pdf - Section 2) as an exogenous variable in the VAR Equation (2).  Under the assumption thatz

### Methodology and estimation approach
- The surprise series zt is treated as a noisy measure of the true monetary policy shock εmp,t, with zt = α εmp,t + ηt and ηt orthogonal to all other variables; this approach consistently estimates the relevant impulse response functions (Paul (2020)).
- The contemporaneous reaction of factor j to a one-unit increase in the policy rate Rt is given by Aj/AR.
- The surprise series zt is identified only up to sign and scale; the coefficient vector A is normalized such that a contractionary monetary policy shock corresponds to a median increase in the policy rate of 25 basis points (bps).
- The exogenous variable approach of Paul (2020) is analytically shown to yield contemporaneous impulse responses identical to the external instrument approach of Stock and Watson (2018).

- FAVAR estimation strategy:
  - Two-step approach based on principal component analysis (following Stock and Watson (2005), Korobilis (2013), Corsetti et al. (2022)).
  - First step: extract five principal components from the set of state-level and aggregate US variables using the Bayesian information criterion (BIC) of Bai and Ng (2002).
    - Principal components obtained from standardized data (subtract mean, divide by standard deviation).
    - Identification of principal component representation addressed by imposing Λ′F ΛF = Iq.
  - For subsequent estimation and IRFs, use demeaned but not fully standardized data to allow direct interpretation of impulse responses.
  - Conditional on estimated principal components (proxying F), the observation Equation (1) collapses to N univariate regressions and the transition Equation (2) is a standard VAR(X).

- Bayesian estimation details:
  - Parameters estimated using Bayesian MCMC methods with a Gibbs sampling algorithm.
  - Total of 10,000 draws with the first 5,000 draws dropped as ‘burn-in’.
  - Priors are overall standard, except for a somewhat tighter prior for the covariance matrix of the VAR innovations, Σ, given the relatively short time dimension of the sample.

- Factor interpretability:
  - Figure C.1 (Appendix C) shows the first five principal components together with the monetary policy indicator (observed factor).
  - Each variable is regressed on six factors—both one factor at a time and all factors jointly—to obtain R-squared values; Table C.1 lists the top five variables best explained by each factor.
  - Suggested interpretations:
    - First factor: relates closely to (mortgage) loan performance.
    - Second factor: homeownership rate.
    - Third factor: state-level rent price index.
    - Fourth factor: US prices and personal expenditures.
    - Fifth factor: state-level GDP deflator and personal bankruptcies.

### US aggregate evidence: response to a monetary policy tightening
- Monetary policy shock calibrated to increase the one-year treasury rate by 25bps on impact.
- Aggregate real activity:
  - Real GDP decreases by around 0.5 percent after two years.
  - Real GDP reaches a trough of around 0.8 percent after three to four years.
- Inflation:
  - The temporary rise in the one-year treasury rate (lasting about seven quarters) leads to a decline in inflation over the medium term as measured by the consumer price index (CPI).
- Housing market variables:
  - House prices:
    - Fall on impact.
    - Decline by roughly 3 percent after two years.
    - Decline by 4 percent after five years.
  - Building permits (housing supply):
    - Contract by almost 1 percent after two years.
    - Contract by 1.5-2 percent after five years.
- Comparison with meta-analysis (Williams (2015)):
  - Williams (2015) finds that a 100bps monetary policy shock leads average house prices to decline between 1.7 percent and 10.8 percent after two years; this compares with 12 percent in our estimates.
  - Williams (2015) finds that real activity falls between 0.3 percent and 9.3 percent after two years; this compares with 2 percent in our analysis.
- Possible reasons for large house price responsiveness:
  - Decline in housing supply elasticities since the GFC (Albuquerque et al. 2020, Aastveit et al. 2023).
  - Long-term increase in investor share of home purchases.
  - Prolonged period of ultra-low interest rates (Chudik and Kumar 2023).
- Mortgage market structure note:
  - Share of fixed-rate mortgages rose to 96.4% in 2023q2, up from 94.5% in 2019q4.
  - Higher interest rates therefore directly affect new mortgages; little variation in the share of fixed-rate mortgages across states.

- Intensive and extensive margins of housing transmission:
  - Intensive margin: homeowners’ housing wealth effects transmit to consumption (Iacoviello 2005; Bhutta and Keys 2016; Aladangady 2017; Beraja et al. 2019; Cloyne et al. 2020; Garriga and Hedlund 2020).
  - Extensive margin: tighter credit conditions reduce housing demand from prospective homeowners, measured by the net percentage share of banks reporting tightening standards for mortgage loans (SLOOS), leading to declines in the homeownership rate (Bhutta and Ringo 2021).
  - Reallocation toward rental market evidenced by increases in home vacancy rate and falls in rental vacancy rate.

### Transmission to state-level housing markets: heterogeneity and tenure effects
- Main empirical findings on state-level responses to a contractionary monetary policy shock (25bps on the one-year treasury rate):
  - Sizeable heterogeneity across US states in responses of economic activity, house prices, housing supply, and homeownership rate; all fall across the board but magnitudes vary widely.
  - Real rents increase over the horizon, contrasting with falling house prices—consistent with housing demand shifting from owner-occupied to rental segment.
  - Magnitude of the fall in the house price-to-rent ratio (HPI/rents) varies markedly across states, likely influencing household buy-or-rent decisions differently across states.
  - Credit conditions:
    - Tightening in credit conditions leads to contraction in mortgage debt and an increase in mortgage delinquencies.
  - Heterogeneous tenure and vacancy responses:
    - Some states experience declines in home (rental) vacancy rates and increases (decreases) in rental vacancy rates, deviating from median responses and US aggregate evidence.
    - Persistence in decline of rental vacancy rate in some states suggests a high degree of segmentation in US housing markets; increasing rental demand may not be fully met by supply, explaining rising rents (Greenwald and Guren 2021).
- Distributional and policy-relevant implications:
  - Combination of tighter credit conditions, lower house prices, and higher rent prices could disproportionately affect mortgagors and renters—groups associated with larger marginal propensities to consume (MPC) (Cloyne et al. 2020).
  - Monetary policy may therefore have important differential distributional effects via housing wealth and consumption channels (Coibion et al. 2017; Holm et al. 2021; Amberg et al. 2022; Bonifacio et al. 2022; Amaral et al. 2024).
- Model assumption and caveat on symmetry:
  - The FAVAR model assumes symmetry of monetary policy effects: contractionary and expansionary shocks give rise to effects of the same magnitude but opposite signs.
  - Recent literature finds possible asymmetries in regional responses (Aastveit and Anundsen 2022), which are not analyzed in this paper and are left for future work.

### Regional characteristics and channels explaining heterogeneity
- Empirical strategy:
  - Compare posterior distributions of average responses between states in the top and bottom deciles of selected state-specific characteristics (Figures 5–8).
  - Posterior distributions of group differences, individual IRFs, and average quintiles are presented in Appendix C (Figures C.3–C.11).
  - Complemented with conditional regression-based correlation analysis.
  - Table B.2 (appendix) contains average values of selected characteristics for each state and highlights top/bottom decile membership.

- Suggested channels explored:
  - Housing supply elasticities.
  - Credit conditions and mortgage market characteristics.
  - Housing wealth exposure.
  - These state-specific characteristics may account for a portion of the observed regional variation in monetary policy transmission to housing markets.

*Source: wpiea2024023-print-pdf - Section 2) as an exogenous variable in the VAR Equation (2).  Under the assumption thatz*

### 5.1    Transmission channels

### 5.1    Transmission channels

### Housing supply channel
- Concept and measure
  - Uses the land-use restriction index (LRI) constructed by Herkenhoff et al. (2018) as the measure of housing supply constraints.
  - LRI is available for 48 states (excluding Alaska and Hawaii) for each decade since 1950: 1950, 1960,..., 2000, and 2014.
  - The LRI is divided by its standard deviation and its sign changed so that higher values reflect states with tighter land-use regulation (terms “stringent land-use regulation”, “low housing supply elasticities”, and “inelastic housing supply” are used interchangeably).
  - Baseline choice motivated by state-level availability and to capture prevailing stringency during the estimation sample; Saiz (2010) elasticities are at the MSA level and estimated over 1970-2000.
- Key empirical findings
  - States with tighter land-use regulation experience a larger decline in house prices and permits after a contractionary monetary policy shock compared to states with less stringent regulation (Figure 5).
  - Posterior distributions presented are average (cumulative) IRFs across US states after a monetary policy tightening that increases the one-year treasury rate by 25bps.
  - Shaded areas reflect the 68% highest density interval (HDI) of the average responses; the HDI of the differences between the average IRFs across groups excludes zero for most variables.
  - Larger decline in housing wealth in inelastic states leads to a greater fall in consumption and a more substantial increase in the unemployment rate (Figure C.15 in Appendix C).
  - Mortgage debt falls more strongly in inelastic states; mortgage delinquencies rise more sharply; foreclosures and other bank-health indicators deteriorate more considerably (Figure 6).
  - ARM mortgages are uncommon in the US: ARM share stood at 5.5% of all outstanding mortgages nationally in 2019q4, with a standard deviation of 1.8 percentage points across all states.
- Mechanisms and interpretation
  - Reconciling stronger declines in house prices in inelastic states:
    - Credit boom-bust dynamics: inelastic areas relied more on credit (e.g., subprime mortgages) during the 2000s boom, producing larger busts when the credit crunch hit.
    - Household overoptimism/diagnostic expectations produced larger booms and thus larger corrections in high-growth price (low-supply elasticity) areas.
    - Financial-accelerator effects and price-to-price feedback loops can amplify contractions in low-supply elasticity areas.
  - Market segmentation and tenure responses:
    - Inelastic states show larger fall in homeownership rates and a smaller increase in rent prices, possibly due to frictions/adjustment costs converting owner-occupied units to rentals and relatively unchanged rental vacancy rates (Figure C.17).
    - High initial rent levels and local rent-control policies (noted for California and Maryland) may also mute rent responses.
  - Distributional implications:
    - Inelastic states are high-income, with larger housing wealth and higher consumption/income per capita (Figures C.18–C.20).
    - Contractionary monetary policy shocks may reduce regional consumption and housing wealth inequality; higher interest rates can decrease dispersion/inequality in house prices across US cities (cited literature).
- Caveats
  - The exercise does not imply housing supply constraints are the sole driver nor proves causality; other state differences (industry composition, demography, income, institutions) may also explain heterogeneity.
  - Results are consistent with established literature on constraints on housing supply and regional house price responses to demand shocks.
  - Robustness: results remain robust when using LRI reference year 2000 instead of 2014 and when exploring cross-sectional distributions of house values and house price-to-rent ratios (Figures C.12–C.14).

### Debt overhang channel
- Concept and measure
  - Debt overhang proxied by a state-level debt gap, computed with the Hamilton (2018) filter on the state-level mortgage debt-to-income ratio (quarterly frequency, p=1 and h=20).
  - States are compared by top and bottom deciles of the debt gap distribution, using the maximum debt gap value over time for each state.
- Key empirical findings
  - Contractionary monetary policy shocks transmit more strongly to states with larger debt gaps:
    - House prices, housing supply (permits), mortgage debt, and consumption fall by considerably more than in states with smaller debt imbalances (Figure 7).
    - Financial stability risk may increase more in areas with larger household debt imbalances (Figure C.21).
  - Responses of high-debt gap states are qualitatively similar to low-supply elasticity areas.
  - Positive correlation between supply constraints and household debt gaps (correlation magnitude described below), reinforcing interconnected amplification.
- Numeric/statistical notes
  - Correlation between supply constraints and household debt gaps is described as “sizeable (around 0.6)” with only partial overlap of states in high/low bins (California in top LRI and debt gap; North Dakota and Oklahoma in bottom bins).
- Interpretation
  - Results align with theory that higher borrowing costs bind households with larger debt imbalances more tightly, producing larger contractions in housing demand, house prices, consumption, and economic activity.

### Housing wealth volatility and household balance sheet channel
- Concept and measure
  - Uses standard deviation of housing wealth over the sample period as a proxy for housing wealth volatility.
  - Housing wealth for state j and quarter t computed as: (homeownership rate_{j,t} × total occupied housing units_{j,t}) × house price index_{j,t} × median house price in 2000_{j}.
- Key empirical findings
  - States with larger fluctuations in housing wealth react more strongly to monetary policy: house prices fall by more than in states with lower housing wealth volatility, accompanied by a larger fall in consumption expenditures (Figure 8).
  - Correlations:
    - Housing wealth level and its volatility are highly correlated (around 0.9).
    - Despite the high correlation, the consumption response correlates significantly and positively with housing wealth volatility but not with average housing wealth (Table C.2).
  - For most remaining variables, the correlation between response strength and housing wealth volatility appears stronger than that with housing wealth level.
- Interpretation
  - Higher uncertainty/volatility of housing wealth may induce households to reduce demand for real estate services or postpone house purchases, strengthening the transmission of monetary policy through weaker housing demand and consumption.

*Source: wpiea2024023-print-pdf — 5.1 Transmission channels*

### 5.2    Cross-sectional multivariate analysis

### 5.2    Cross-sectional multivariate analysis

### Methodology
- Cross-sectional regressions following Mumtaz et al. (2018) estimate:
  IRF_y_h,i = α + X_i β + regions_i + η_i, η_i ∼ N(0, σ^2_η),
  where IRF_y_h,i denotes the cumulative response of variable y in state i after h quarters; X_i is a 1×K vector of state-specific characteristics; β is K×1; regions_i are dummies for the eight BEA divisions.
- Results focus on the medium-term cumulative response after h = 12 quarters, with qualitative similarity for h = 8 and h = 20.
- Caution: relatively small cross section of US states; regressions capture average relationships across states.

### Variables and controls
- State-level characteristics included beyond Section 5.1:
  - Land-use regulation index (LRI) of Herkenhoff et al. (2018) for 2014.
  - Debt gap: Average of Hamilton-filtered mortgage debt-to-income ratio from 1999–2019.
  - HW (avg.) = 100*log(Average housing wealth over 1999–2019).
  - HW (std.) = 100*log(Standard deviation of housing wealth over 1999–2019).
  - Sand state = dummy for Arizona, California, Florida, Nevada.
  - RTW = dummy for right-to-work states (proxy for labor market flexibility).
  - Manufacturing = Share of manufacturing in state-level GDP.
  - Small firms = Share of small firms employment in total employment.
  - HPI growth = Growth rate of house prices over 1999–2019.
- Dependent cumulative responses after h = 12 quarters: GDP, PCE, HPI, Rents, Permits, HOR (homeownership rate).
- All regressions include regional dummies. Robust standard errors reported. Significance: ∗p<0.1, ∗∗p<0.05, ∗∗∗p<0.01.

### Table 1: Cross-sectional regression point estimates and standard errors (h = 12)
- Dependent variables (columns): GDP | PCE | HPI | Rents | Permits | HOR
- Coefficients (standard errors in parentheses):

  - LRI:
    - GDP: -0.347 (0.200) ∗
    - PCE: -0.339 (0.091) ∗∗∗
    - HPI: -0.868 (0.335) ∗∗
    - Rents: -0.834 (0.418) ∗
    - Permits: -0.006 (0.089)
    - HOR: -0.021 (0.069)

  - Debt Gap:
    - GDP: -0.002 (0.011)
    - PCE: -0.004 (0.005)
    - HPI: -0.022 (0.020)
    - Rents: 0.000 (0.024)
    - Permits: -0.013 (0.005) ∗∗
    - HOR: -0.005 (0.002) ∗

  - HW (avg.):
    - GDP: 0.012 (0.005) ∗∗
    - PCE: 0.000 (0.003)
    - HPI: 0.022 (0.012) ∗
    - Rents: 0.018 (0.009) ∗
    - Permits: 0.003 (0.003)
    - HOR: 0.001 (0.002)

  - HW (std.):
    - GDP: -0.006 (0.004)
    - PCE: 0.001 (0.003)
    - HPI: -0.013 (0.008)
    - Rents: 0.000 (0.007)
    - Permits: -0.001 (0.002)
    - HOR: -0.000 (0.001)

  - Sand state:
    - GDP: -1.330 (0.482) ∗∗∗
    - PCE: -0.496 (0.243) ∗∗
    - HPI: -2.434 (1.001) ∗∗
    - Rents: -0.759 (1.020)
    - Permits: -0.409 (0.255)
    - HOR: -0.003 (0.083)

  - RTW (right-to-work):
    - GDP: -0.454 (0.220) ∗∗
    - PCE: -0.588 (0.138) ∗∗∗
    - HPI: -0.736 (0.477)
    - Rents: -0.522 (0.644)
    - Permits: 0.387 (0.113) ∗∗∗
    - HOR: -0.008 (0.068)

  - Manufacturing:
    - GDP: -0.039 (0.021) ∗
    - PCE: 0.017 (0.010) ∗
    - HPI: 0.098 (0.036) ∗∗
    - Rents: 0.070 (0.043)
    - Permits: 0.002 (0.011)
    - HOR: 0.004 (0.006)

  - Small firms:
    - GDP: -0.024 (0.020)
    - PCE: -0.012 (0.010)
    - HPI: -0.055 (0.029) ∗
    - Rents: -0.014 (0.044)
    - Permits: 0.017 (0.008) ∗
    - HOR: 0.002 (0.004)

  - HPI growth:
    - GDP: 0.072 (0.019) ∗∗∗
    - PCE: 0.035 (0.010) ∗∗∗
    - HPI: 0.051 (0.030) ∗
    - Rents: 0.006 (0.031)
    - Permits: 0.016 (0.007) ∗∗
    - HOR: 0.008 (0.005)

  - Observations:
    - GDP: 48
    - PCE: 48
    - HPI: 48
    - Rents: 46
    - Permits: 48
    - HOR: 48

  - Adjusted R^2:
    - GDP: 0.657
    - PCE: 0.664
    - HPI: 0.861
    - Rents: 0.232
    - Permits: 0.720
    - HOR: 0.443

- Note: Table shows point estimates and robust standard errors. Definitions: GDP = Real GDP. PCE = Real personal consumption expenditure. HPI = Real house price index. HOR = Homeownership rate. Debt gap = Average of Hamilton-filtered mortgage debt-to-income ratio from 1999–2019. HW (avg.) and HW (std.) defined above. Sand state = Arizona, California, Florida, Nevada. RTW = right-to-work states. Manufacturing = share in state GDP. Small firms = share of small firms employment. HPI growth = cumulative growth of real house price index over 1999–2019.

### Main empirical findings
- Land-use regulation (LRI) is an important driver of heterogeneous transmission:
  - A state with land-use regulation one standard deviation higher exhibits a 0.9 percentage point larger house price drop following a surprise tightening of 25bps (interpretation based on coefficient magnitudes in the HPI column).
  - LRI coefficients are negative and often significant across GDP, PCE, and HPI.
  - This larger house price decline translates into lower economic activity and consumption; real rents increase by 0.8 percentage points less after three years in less flexible areas (reported in narrative).
- Debt overhang (Debt Gap) shows expected signs but limited significance:
  - Significant only for permits (Permits: -0.013 (0.005) ∗∗) and homeownership rate (HOR: -0.005 (0.002) ∗).
  - Suggests household debt imbalances add explanatory power for differential housing-market effects after accounting for supply constraints.
- Housing wealth channel:
  - HW (avg.) helps explain heterogeneity (GDP: 0.012 (0.005) ∗∗; HPI: 0.022 (0.012) ∗; Rents: 0.018 (0.009) ∗), while HW (std.) does not show robust significance once other controls included.
- Sand states and RTW:
  - Sand state dummy shows large negative coefficients for GDP and HPI (GDP: -1.330 (0.482) ∗∗∗; HPI: -2.434 (1.001) ∗∗).
  - RTW states show negative GDP and PCE effects (GDP: -0.454 (0.220) ∗∗; PCE: -0.588 (0.138) ∗∗∗) and a positive effect on permits (0.387 (0.113) ∗∗∗).
- Small firms share associated with stronger declines in economic activity, consumption and house prices (HPI: -0.055 (0.029) ∗).
- Manufacturing share results mixed: GDP reacts stronger (GDP: -0.039 (0.021) ∗) while consumption and house prices react weaker in some specifications.

### Robustness checks
- Alternative monetary policy surprise series:
  - Forward guidance shocks from Swanson (2021) and Jarociński and Karadi (2020) produce qualitatively similar results (Figures in Appendix C referenced).
- Alternative housing supply elasticity measures:
  - Replaced LRI with housing supply elasticity series from Aastveit et al. (2023) and Saiz (2010), aggregated to state level with population weights (similar results; comparable when using income weights).
  - Aastveit et al. (2023) elasticities averaged over 1996–2006 and 2012–2019 produce broadly comparable findings.
- Alternative inflation series:
  - Replacing state GDP deflator with Hazell et al. (2022) state-level inflation yields comparable cross-state dispersion results for IRFs of inflation and output; Hazell et al. (2022) series ends in 2017q4 and is smoother for some states.

### Conclusions and policy implications
- Significant heterogeneity exists in transmission of contractionary monetary policy across US states.
- Key drivers of heterogeneity include differences in housing supply elasticities (land-use regulation), household debt overhang, and housing wealth (average).
- Low-supply elasticity areas with stringent land-use regulation experience larger falls in house prices and broader economic activity, and greater deterioration in financial stability indicators (mortgage delinquencies, foreclosures, bank health proxies).
- Monetary policy can affect housing tenure: higher interest rates lead to house price declines and rental price increases, with heterogeneous effects across states depending on supply elasticity and market segmentation.
- Policy implications:
  - Financial supervision could tighten more in areas with inelastic housing supply to limit excessive house price volatility.
  - Strengthening macroprudential measures (limits on loan-to-income and/or debt-service ratios) before debt imbalances emerge.
  - Relaxation of land-use restrictions could reduce boom-bust cycles by allowing supply expansion during upswings, increasing resilience to contractionary shocks.
  - Monetary policy may have distributional effects: contractionary shocks can lead to larger declines in housing wealth and consumption in high-housing-wealth, high-income states, potentially decreasing consumption and housing wealth inequality across states.

*Source: 5.2 Cross-sectional multivariate analysis, wpiea2024023-print-pdf*

### 2019.  HW = (Homeownership rate x

### wpiea2024023-print-pdf - 2019.  HW = (Homeownership rate x

### Variable definitions and computed measures
- HW = (Homeownership rate x Housing units) x HPI x Median house price in 2000
- HW (std.) = Standard deviation of housing wealth over 1999–2019
- LRI = Land-use regulation index (in 2014) — Herkenhoff et al. (2018)
- Manufacturing = Share of manufacturing in state-level GDP
- RTW = Dummy variable for states with right-to-work legislation
- Sand state = Dummy variable for Arizona, California, Florida, and Nevada
- Small firms = Share of employees in firms with less than 250 employees divided by total number of employees in that state (average over 1999–2019)
- HPI growth = Cumulative real growth rate over the sample period (1999–2019)
- Note: Debt gap is the maximum value over the sample period. HW (avg.) = Average housing wealth over 1999–2019.

### Table B.2 — Sample-average state characteristics (selected rows and values)
- Format: State | LRI | Debt gap | HW (avg.) | HW (std.) | Sand state | RTW | Manufacturing | Small firms | HPI growth
- AL: -1.61 | 0.03 | 4,575.3 | 2680.8 | 0 | 1 | 16.9 | 7.2 | 3.0
- AK: –2 | 0.94 | 6,293.9 | 3970.5 | 0 | 0 | 2.9 | 7.2 | 10.7
- AZ: -0.95 | 8.74 | 8,327.7 | 11721.2 | 1 | 1 | 10.0 | 6.1 | 17.7
- CA: -0.37 | 6.79 | 5,388.2 | 23708.3 | 1 | 0 | 10.2 | 17.5 | 26.8
- FL: -1.03 | 9.15 | 3,897.7 | 13862.7 | 1 | 1 | 5.4 | 7.4 | 21.4
- NY: -0.9 | 14.68 | 4,779.7 | 12255.1 | 0 | 0 | 5.8 | 6.8 | 17.5
- TX: -2.6 | 4.82 | 1,499.6 | 2044.7 | 0 | 1 | 13.9 | 7.2 | 17.9
- WA: -0.63 | 4.69 | 7,000.7 | 15094.9 | 0 | 1 | 13.2 | 7.6 | 22.9
- Note: Values in table include many more states; above are illustrative selected rows preserved exactly as in source.

### Explanatory power of factors (Table C.1)
- R-squared values (selected series best explained by factors):
  - Non performing loan share: Michigan — 0.9790
  - New housing units started: US — 0.9789
  - Mortgage delinquency rate: California — 0.9784
  - Non performing loan share: Montana — 0.9761
  - New permits issued: US — 0.9756
  - Non performing loan share: Minnesota — 0.9406
  - Mortgage delinquency ratio: California — 0.9359
  - Factor 1 examples:
    - Non performing loan share: Florida — 0.9340
    - Homeownership rate: Nevada — 0.7876
    - Homeownership rate: US — 0.7763
  - Factor 2 examples:
    - Homeownership rate: California — 0.7066
    - Rents: Washington — 0.6124
    - Rents: Oregon — 0.5002
  - Factor 3 examples:
    - Rents: California — 0.4986
    - Consumer price index: US — 0.6005
    - Personal expenditures: US — 0.5690
  - Factor 4 examples:
    - Personal expenditures: Ohio — 0.5348
    - GDP deflator: New Hampshire — 0.4529
  - Factor 5 examples:
    - Non business bankruptcies: Texas — 0.4190
    - GDP deflator: Vermont — 0.4174
  - One-year rate (observed factor) — FFR: 0.9728

### Pairwise correlations with state-level responses after three years (Table C.2)
- Correlations (with p-values in parentheses) between state characteristics and responses after three years. Selected entries:
  - LRI correlations:
    - GD P: -0.11 (0.47)
    - PCE: -0.42*** (0.00)
    - HPI: -0.64*** (0.00)
    - HPI/rents: 0.59*** (0.00)
  - Debt gap correlations:
    - GDP: -0.36*** (0.01)
    - PCE: -0.55*** (0.00)
    - HPI: -0.77*** (0.00)
    - Mortgage debt: -0.76*** (0.00)
  - HW (avg.) correlations:
    - GDP: 0.16 (0.27)
    - HPI: -0.54*** (0.00)
    - Mortgage delinquency rate: -0.50*** (0.00)
    - Mortgage debt: -0.51*** (0.00)
  - HW (std.) correlations:
    - PCE: -0.33** (0.02)
    - HPI: -0.78*** (0.00)
    - Mortgage delinquency rate: -0.73*** (0.00)
    - Mortgage debt: -0.67*** (0.00)
  - Sand state correlations:
    - GDP: -0.55*** (0.00)
    - PCE: -0.55*** (0.00)
    - HPI: -0.65*** (0.00)
    - Mortgage delinquency rate: -0.60*** (0.00)
    - Mortgage debt: -0.59*** (0.00)
  - RTW correlations:
    - GDP: -0.33** (0.02)
    - HPI: 0.32** (0.02)
    - Mortgage debt: 0.28* (0.05)
  - Manufacturing correlations:
    - PCE: 0.31** (0.03)
    - HPI: 0.55*** (0.00)
    - Mortgage debt: 0.45*** (0.00)
  - Small firms correlations:
    - HPI/rents: 0.49*** (0.00)
    - Mortgage delinquency rate: 0.37*** (0.01)
    - Mortgage debt: 0.26* (0.07)
  - HPI growth correlations:
    - PCE: -0.27* (0.06)
    - HPI: -0.53*** (0.00)
    - Mortgage debt: -0.45*** (0.00)
- Note: GDP = Real GDP. PCE = Real personal consumption expenditure. HPI = Real house price index. HOR = Homeownership rate. MDR = Mortgage delinquency rate. LRI = Land-use regulation index of Herkenhoff et al. (2018) for the year 2014. Debt gap = Average of Hamilton-filtered mortgage debt-to-income ratio over 1999-2019. Standard errors in parentheses. ∗p<0.1, ∗∗p<0.05, ∗∗∗p<0.01.

### Figures and impulse-response summaries (Appendix C figures)
- Factor structure and monetary policy:
  - Five unobserved factors (Factor 1 to Factor 5) obtained from normalized data and an observed one-year treasury rate are displayed (Figure C.1).
- Dispersion and state-level IRFs:
  - Dispersion of variables across US states shown for GDP log growth, PCE log growth, GDP deflator log growth, Mortgage debt-to-income ratio, HPI log growth, Rent prices log growth, Building permits, Homeownership rate (percent), Home vacancy rate (percent), Rental vacancy rate (percent), HPI/rents ratio, Mortgage delinquency rate (percent) (Figure B.1).
  - Dispersion of additional state-level impulse response functions for Unemployment rate, Nonfarm payrolls, Nominal rents (Figure C.2).
- Differences in IRFs across state characteristics (decile and quintile averages):
  - Differences in IRFs shown across Herkenhoff et al. (2018) LRI, the debt gap distribution, housing wealth volatility, home values in 2000, and house price-to-rent ratio (Figures C.3–C.15, C.27).
  - Median (cumulative) IRFs after a monetary policy tightening that increases the one-year treasury rate by 25bps are presented, with comparisons between top and bottom deciles/quintiles of state characteristics (Figures C.6–C.14, C.16–C.21).
- Additional diagnostics and alternatives:
  - Correlations between LRI (2014) and housing wealth per capita (avg. 1999–2019), consumption per capita (avg. 1999–2019), personal disposable income per capita (avg. 1999–2019), and the debt gap (Figures C.18–C.22).
  - Banks’ indicators (Banks’ ROA, Banks’ NPLs, Foreclosure rate) impulse responses across the debt gap distribution: decile averages (Figure C.21).
  - Alternative monetary policy surprise specifications (Swanson (2021) forward guidance; Jarociński and Karadi (2020)) with PCE, HPI, Permits responses (Figures C.23–C.24).
  - Impulse responses across alternative supply elasticity measures (Aastveit et al. (2023) for 1996-2006 and 2012-19; Saiz (2010)) (Figures C.25–C.27).
  - Alternative state-level inflation series (Hazell et al. (2022)) compared to IRFs (Figure C.28).

*Source: wpiea2024023-print-pdf - 2019.  HW = (Homeownership rate x Housing units) x HPI x Median house price in 2000 (IMF working paper content provided).*

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*The Housing Supply Channel of Monetary Policy — Working Paper No. WP/2024/023*

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_Source: https://www.imf.org/-/media/files/publications/wp/2024/english/wpiea2024023-print-pdf.pdf_