## _wp08247

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---

### Introduction
- Objective: Estimate the elasticity of residential housing prices with respect to the short-term interest rate using two different cross-country datasets and multiple econometric techniques.
- Motivation: Short-term interest rate is a key policy instrument influencing housing prices; existing empirical literature shows wide variation in estimated elasticities.
- Structure: Section II reviews theory and empirical literature; Section III presents regression analysis; Section IV draws conclusions.

### Literature overview
- Theoretical foundations:
  - Residential housing is a durable good producing service streams and serving as a store of purchasing power (Zhu, 2003; Barker, 2005).
  - Households choose between owning and renting; in equilibrium they are indifferent between owning and renting and between housing services and consumption goods (Poterba, 1984; Iacoviello, 2005).
  - User cost of housing equals “the sum of after-tax depreciation, repair costs, property taxes, mortgage interest payments, and the opportunity cost of housing equity, minus the capital gain...on the housing structure” (Poterba, 1984, p. 732).
  - External financing, credit rationing, tax treatment, and mortgage market constraints are central determinants of housing demand.
  - Supply-side: under perfect competition, price determined by real construction costs and real price of land (Hilbers, Lei, and Zacho, 2001; Himmelberg, Mayer, and Sinai, 2005); supply rigidities and local market features (Zhu, 2003) imply demand-driven short-run price dynamics.
  - Market imperfections and expectations can generate housing price bubbles (Stiglitz, 1990; Hilbers, Lei, and Zacho, 2001).

- Empirical evidence and gaps:
  - Fundamental determinants consistently identified: aggregate household income and wealth, unemployment, short- and long-term interest rates, inflation, returns on other assets, mortgage availability and terms, tax incentives, demographics.
  - Reported elasticities of housing prices to short-term interest rates vary widely—roughly from zero to minus 8 (Appendix I).
  - Two potential sources of variance:
    - Use of unsuitable estimation techniques (pooled and within-group OLS with residual autocorrelation; Arellano-Bond on small N datasets).
    - Comparability issues in cross-country panel datasets: country-specific housing price indices with non-comparable bases are ill-suited to estimate level elasticities.
  - Pattern observed: panel data studies often report elasticities smaller (in absolute value) than one; single-country studies often report elasticities from minus 3 to minus 8.

- Contribution of this study:
  - Apply 3SLS with country-specific intercepts and cross-equation coefficient restrictions to a commonly used cross-country panel dataset to address endogeneity and lagged dependent variables.
  - Complement with cross-section analysis of residential property prices in US$ per square meter for 89 countries (Global Property Guide, mid-2007) to gather further evidence on interest rate elasticity.

### Regression analysis — data and methodology
- Datasets:
  - Panel: 20 advanced countries; quarterly residential property price indices; time span 1980–2007 (many countries only since 1988). Countries listed in source.
  - Cross-section: residential property prices in US dollars per square meter in 2005–06 for 89 countries from Global Property Guide (mid-2007). Original availability: 118 countries; starting sample 93 due to lack of explanatory variables; dropped Ecuador, India, The Gambia and Paraguay based on outlier analysis.

- Caveats on data:
  - Global Property Guide data for many countries compiled in-house and are not official; quality checks on familiar markets provided some assurance.
  - Cross-country panel indices have non-comparable bases—better suited for growth-rate analysis than level-elasticity estimation.

- Choice of explanatory variables (expected sign; variable names as used in regressions):
  - [+] ln_pcrgdppp (panel) / ln_pcgdpusd (cross-section): Scale variable proxying life-cycle wealth.
  - [–] srate (nominal) and r_srate (real): Short-term interest rate.
  - [–] slpyc: Slope of the yield curve.
  - [+] infl: Rate of inflation.
  - [–] unemplr: Unemployment rate.
  - [+] ln_r_m2 (panel) / crd_gdp (cross-section): Measures of financial deepening.
  - [+] shpopa (panel) / shpopurb (cross-section): Demographic variables.
  - [+] govbal: Primary government balance as a ratio to GDP.
  - [–] curracc: Current account balance as a ratio to GDP.

- Panel functional form and estimator:
  - Semi-loglinear; dependent variable ln_r_housprc (log of the real residential property price index).
  - Estimation: 3SLS with country-specific intercepts and cross-equation restrictions to make coefficients equal across countries; address endogeneity and dynamic panel concerns.

### 3SLS estimation strategy and diagnostics
- Exploratory stage:
  - Residential housing price equation estimated in first-differences as a partial adjustment model with country-specific intercepts.
  - Main determinants included: real per capita PPP GDP, real broad money, nominal short-term interest rate (in level), rates of inflation and unemployment, ratio of the government balance to GDP.

- Limitations of Arellano-Bond GMM for this dataset:
  - Arellano-Bond GMM estimators require large cross-sectional dimension relative to time dimension; not met here.
  - GMM-DIF, GMM-SYS, and Anderson-Hsiao IV estimators break down for Model 6 (Appendix Table 4).
  - Empirical studies using Arellano-Bond often fail consistency conditions, questioning their validity.

- Alternative: 2SLS and 3SLS with system estimation:
  - 3SLS preferred for efficiency (uses covariance structure across equations).
  - Implementation notes:
    - reg3 STATA procedure drops missing observations across all equations; Belgium, France, Germany dropped due to missing observations.
    - Instrument strategy: for each explanatory variable extract first five principal components from country realizations; use second lags of the first five principal components of all explanatory variables as instruments (lagged by two periods).
    - For Model 6 (seven explanatory variables) this yields 35 instruments used in all equations.
    - Time dimension for each country: 1990:4 to 2006:Q4.

- Model reduction and selection:
  - Model 6 reduced by dropping variables insignificant at 90% to form Model 7; dropping ln_pcrgdppp made unemployment insignificant, leading to Model 8.
  - Model 8 is the preferred specification in first-differences.
  - Median R-squared of country equations in first-differences: 0.33.
  - In the system, first-order residual autocorrelations close to –0.5 (informal test for lack of serial correlation beyond theoretical value).

### Key 3SLS coefficient estimates (selected)
- Estimated coefficient of the lagged dependent variable: 0.45.
- Selected coefficients from Table 1 (columns labeled (6)(7)(8)); standard errors in parentheses:
  - d1_ln_r_housprc_: 0.432** (0.034) ; 0.460** (0.034) ; 0.453** (0.037)
  - d1_ln_pcrgdppp: -0.065 (0.079)
  - srate (untransformed variable): -0.124** (0.018) ; -0.117** (0.018) ; -0.131** (0.018)
  - d1_infl: -0.152** (0.017) ; -0.159** (0.017) ; -0.173** (0.018)
  - d1_unemplr: -0.428* (0.195) ; -0.317 (0.198)
  - d1_govbal: 0.228** (0.073) ; 0.242** (0.080) ; 0.385** (0.086)
  - d1_ln_r_m20: 0.087** (0.029) ; 0.092** (0.030) ; 0.076* (0.032)
  - Observations per country: 65 65 65
  - Number of countries: 17 17 17
  - Median R-squared: 0.32 0.34 0.33
  - Significant first-order residual autocorrelation coefficients: -0.45** -0.46** -0.46** ; additional values: -0.37* -0.39* -0.38* ; and: 0.36* 0.35*

- Notes:
  - Standard errors in parentheses.
  - + significant at 10%; * significant at 5%; ** significant at 1%.
  - All variables in first-differences unless otherwise specified.
  - Country-specific intercepts not shown.

### Long-run elasticities (derived from Model 8)
- Long-run elasticities obtained by dividing 3SLS coefficient estimates (excluding lagged dependent variable) by one minus the coefficient of the lagged dependent variable (lagged dependent variable coefficient = 0.45).
- Reported long-run elasticities for quarter-on-quarter growth rate of real residential housing prices:
  - A 1 percentage point increase in the nominal short-term interest rates from one quarter to the next is associated with a 0.24 percentage point decline in the quarter-on-quarter growth rate of real residential housing prices.
  - A 1 percentage point increase in the quarter-on-quarter inflation is associated with a 0.31 percentage point decline in the quarter-on-quarter growth rate of real residential housing prices.
  - A 1 percentage point increase in the ratio of the primary government balance to GDP from one quarter to the next is associated with a 0.8 percentage point increase in the quarter-on-quarter growth rate of real residential housing prices.
  - A 1 percentage point increase in the quarter-on-quarter growth rate of real broad money is associated with a 0.14 percentage point increase in the quarter-on-quarter growth rate of real residential housing prices.

### Interpretation and inertia
- The lagged dependent variable coefficient (0.45) implies:
  - Approximately 55 percent of any gap between actual growth and the fundamentals-consistent growth is closed in each subsequent quarter.
  - Significant inertia in quarter-on-quarter growth rates of real residential housing prices in the short run.
- The estimated interest rate elasticity from the cross-country panel dataset is relatively low and falls within the range reported by studies on similar datasets.
- Better-suited econometric techniques cannot bridge the gap between interest rate elasticity estimates from single-country datasets and cross-country panel datasets.

### Cross-Section Regression Analysis (overview and findings)
- Question: Does a large interest-rate elasticity of housing prices (in excess of minus 3) found in single-country datasets extend to a larger set of countries?
- Approach:
  - Cross-section semi-loglinear model; dependent variable ln_housprcusd (log of residential property prices in US dollars per square meter).
  - Exploratory OLS with heteroskedasticity-adjusted standard errors; explanatory variables entered as five-year averages to mitigate endogeneity.
- Exploratory OLS results:
  - Main determinants: per capita GDP in US$, real short-term interest rate, availability of credit measured by crd_gdp (Table 2, Model 19).
- Preferred cross-section specification:
  - Model 20 is the preferred regression specification of the residential housing price equation in levels.
  - Model 20 fits the data well, with a R-squared of 0.63.
- Selected cross-section coefficient results (Table 2; standard errors in parentheses):
  - ln_pcgdpusd 0.374 ** 0.275 **  
    - (0.057)(0.070)
  - r_srate -4.324 ** -3.605 *  
    - (1.566)(1.803)
  - crd_gdp 0.398 * 0.436 *  
    - (0.191)(0.207)
  - Regional dummy variables:
    - Asia and Pacific -0.158  (0.218)
    - North America -0.134  (0.351)
    - Central and Latin America -0.369 +  (0.193)
    - Africa -0.627 **  (0.195)
  - Intercept 4.392 ** 5.425 **  (0.415)(0.578)
  - Number of countries 89 89
  - Overall R2 0.59 0.63
  - Note: Robust standard errors consistent in the presence of heteroskedasticity.
  - Significance notation: + significant at 10%; * significant at 5%; ** significant at 1%

- Additional cross-section findings (selected, preserved):
  - A 3.61 percentage points decline in residential housing prices.  
  - A 1 percentage point increase in per capita GDP in US$ is associated with a 0.28 percentage point increase in residential housing prices.  
  - A 1 percentage point increase in the ratio of credit to private sector to GDP is associated with a 0.44 percentage point increase in residential housing prices.
  - Regional differences (after controlling for GDP per capita and credit market conditions):
    - On average housing prices (in US$ per square meter) in Africa are 63 percent lower than in Europe.
    - In Central and Latin America housing prices are 37 percent lower than in Europe.
    - No statistically significant differences between average housing prices in Europe and North America and Asia and Pacific after controlling for macroeconomic fundamentals.

### Preferred estimate and conclusion
- Preferred estimate of the interest-rate elasticity of housing prices: –3.6 (value from Model 20).
- Comparison and interpretation:
  - Using residential housing prices expressed in comparable units across countries yields a much larger estimate of the interest-rate elasticity, within the range of single-country studies.
  - Better-suited econometric techniques applied to cross-country panel data cannot bridge the gap between estimates derived from single-country datasets and cross-country panel datasets, attributed to inherent weaknesses of cross-country panel data on country-specific housing price indices.
- Conclusion:
  - Best estimate of the elasticity of residential housing prices with respect to the short-run real interest rate: –3.6.
  - This estimate corroborates and extends single-country findings that the interest-rate elasticity of housing prices is greater than –3.

### Appendix: Variable definitions and data sources (selected)
- ln_r_housprc: Real residential property price index (log). Index of nominal residential property prices (in domestic currency units) 2000 =100. Deflated by CPI.
- ln_pcrgdppp: Real per capita PPP GDP (log). Gross Domestic Product, Volume, 2000 Constant PPP. Unit: Thousand 2000 PPP USD. Source: OECD (2008).
- srate: Short-term interest rate. Series/Unit: Short-term interest rate; Fraction. Source: OECD (2008).
- infl: Inflation rate. Series: Consumer price index (CPI) 2000 =100. Unit: Annualized quarter-on-quarter growth rate. Source: OECD (2008).
- ln_r_m2: Real broad money (M2) (log). Broad money Billion dom. currency units. Deflated by CPI. Source: OECD (2008).
- Cross-section variables:
  - ln_housprcusd: Average price per square meter of an apartment located in the centre of the most important city of each country; US dollars per square meter; Source: www.globalpropertyguide.com (data as published mid-2007).
  - ln_pcgdpusd: Per capita nominal GDP in US dollars (log); Average value over 2000–2005; Source: IMF (2007).
  - srate (cross-section): Rate of return on 91 day T-bills; Fraction; Average value over 2000–2005; Source: IMF (2007).
  - crd_gdp: Domestic credit to private sector in ratio to GDP; Fraction; Average value over 2000–2005; Source: World Bank (2007).

*Source: _wp08247 (Appendix III and accompanying tables and notes).*

### References..............................................................................................................

### _wp08247 - References..............................................................................................................

### Introduction
- Objective: Estimate the elasticity of residential housing prices with respect to the short-term interest rate using two different cross-country datasets and multiple econometric techniques.
- Motivation: Short-term interest rate is a key policy instrument influencing housing prices; existing empirical literature shows wide variation in estimated elasticities.
- Structure: Section II reviews theory and empirical literature; Section III presents regression analysis; Section IV draws conclusions.

### Literature overview
- Theoretical foundations:
  - Residential housing is a durable good producing service streams and serving as a store of purchasing power (Zhu, 2003; Barker, 2005).
  - Households choose between owning and renting; in equilibrium they are indifferent between owning and renting and between housing services and consumption goods (Poterba, 1984; Iacoviello, 2005).
  - User cost of housing equals “the sum of after-tax depreciation, repair costs, property taxes, mortgage interest payments, and the opportunity cost of housing equity, minus the capital gain...on the housing structure” (Poterba, 1984, p. 732).
  - External financing, credit rationing, tax treatment, and mortgage market constraints are central determinants of housing demand.
  - Supply-side: under perfect competition, price determined by real construction costs and real price of land (Hilbers, Lei, and Zacho, 2001; Himmelberg, Mayer, and Sinai, 2005); supply rigidities and local market features (Zhu, 2003) imply demand-driven short-run price dynamics.
  - Market imperfections and expectations can generate housing price bubbles (Stiglitz, 1990; Hilbers, Lei, and Zacho, 2001).

- Empirical evidence and gaps:
  - Fundamental determinants consistently identified: aggregate household income and wealth, unemployment, short- and long-term interest rates, inflation, returns on other assets, mortgage availability and terms, tax incentives, demographics.
  - Reported elasticities of housing prices to short-term interest rates vary widely—roughly from zero to minus 8 (Appendix I).
  - Two potential sources of variance:
    - Use of unsuitable estimation techniques (pooled and within-group OLS with residual autocorrelation; Arellano-Bond on small N datasets).
    - Comparability issues in cross-country panel datasets: country-specific housing price indices with non-comparable bases are ill-suited to estimate level elasticities.
  - Pattern observed: panel data studies often report elasticities smaller (in absolute value) than one; single-country studies often report elasticities from minus 3 to minus 8.

- Contribution of this study:
  - Apply 3SLS with country-specific intercepts and cross-equation coefficient restrictions to a commonly used cross-country panel dataset to address endogeneity and lagged dependent variables.
  - Complement with cross-section analysis of residential property prices in US$ per square meter for 89 countries (Global Property Guide, mid-2007) to gather further evidence on interest rate elasticity.

### Regression analysis — data and methodology
- Datasets:
  - Panel: commonly analyzed set of 20 advanced countries with quarterly residential property price indices; time span 1980–2007 (many countries only since 1988). Countries: Australia, Austria, Belgium, Canada, Denmark, Finland, France, Germany, Ireland, Italy, Japan, Netherlands, New Zealand, Norway, Portugal, Spain, Sweden, Switzerland, United Kingdom, United States.
  - Cross-section: residential property prices in US dollars per square meter in 2005–06 for 89 countries from Global Property Guide (mid-2007). Original availability: 118 countries; starting sample 93 due to lack of explanatory variables; dropped Ecuador, India, The Gambia and Paraguay based on outlier analysis.

- Caveats on data:
  - Global Property Guide data for many countries compiled in-house and are not official; quality checks on familiar markets provided some assurance.
  - Cross-country panel indices have non-comparable bases—better suited for growth-rate analysis than level-elasticity estimation.

A. Choice of explanatory variables (expected sign in square brackets; variable names as used in regressions)
- [+] Scale variable proxying life-cycle wealth — log of real per capita purchasing power parity (PPP) gross domestic product (ln_pcrgdppp) in panel regressions and log of per capita GDP in US dollars (ln_pcgdpusd) in cross-section regressions.
- [–] Short-term interest rate (srate in nominal terms and r_srate —in real) — proxy for the opportunity cost of investments in owner-occupied housing.
- [–] Slope of the yield curve (slpyc) — spread between long- and short-term rates; proxy for direction of future short-term rates and potential capital gains/losses.
- [+] Rate of inflation (infl) — proxy for the repayment burden of mortgage debt; higher inflation likely associated with higher housing prices.
- [–] Unemployment rate (unemplr) — reduces pool of home buyers.
- [+] Measures of financial deepening — log of real broad money M2 (ln_r_m2) in panel regressions; domestic credit to the private sector as a ratio to GDP (crd_gdp) in cross-section regressions.
- [+] Demographic variables — share of active population in total population (shpopa) in panel regressions; share of urban population (shpopurb) in cross-section regressions.
- [+] Primary government balance as a ratio to GDP (govbal) — potential crowding-out effect on mortgage financing; may co-move with housing prices.
- [–] Current account balance as a ratio to GDP (curracc) — wealth effects and foreign-buyer dynamics can link current account and housing prices.

B. Panel data regression analysis
- Functional form: semi-loglinear; dependent variable is log of the real residential property price index (ln_r_housprc).
- Estimation approach highlighted: 3SLS with country-specific intercepts and cross-equation restrictions to make coefficients equal across countries, to address endogeneity and dynamic panel concerns.

### Appendices, tables, and figures (listed in source)
- Appendices:
  - I. Survey of Studies of Determinants of Housing Prices
  - II. Variables Definitions and Data Sources
  - III. Additional Regression Output
- Tables:
  - 1. 3SLS Estimates of the Residential Housing Price Equation in First-Differences
  - 2. OLS Estimates of the Housing Price Equation Using Cross-Country Data
- Appendix Tables:
  - 1. Variables Definitions and Data Sources
  - 2. Within (Fixed Effects) Estimates of the Residential Housing Price Equation
  - 3. OLS and Within Estimates of Unrestricted Residential Housing Price Equation
  - 4. IV and GMM Panel Data Estimates of the Residential Housing Price Equation in First-Differences
  - 5. OLS Estimates of the Effect of Fundamentals on Residential Housing Prices in Cross-Country Data
- Appendix Figures:
  - 1. Real Residential Housing Price Indices, 1980–2007
  - 2. Scatter Plots of Residential Housing Prices on Fundamental Determinants

*Content derived from the document _wp08247 - References..............................................................................................................*

### Appendix III summarizes the

### Appendix III: Summary of Regression Analysis (Excerpt)

### Exploratory Stage: specification and variables
- Residential housing price equation can be reasonably estimated in first-differences as a simple partial adjustment model with country-specific intercepts.
- Main determinants included:
  - real per capita PPP GDP
  - real broad money
  - nominal short-term interest rate (in level)
  - rates of inflation and unemployment
  - ratio of the government balance to GDP (Appendix Table 2)
- Pooled OLS and within-group estimators are inconsistent in the presence of a lagged dependent variable (Hsiao, 2003, p. 72–4), prompting use of more sophisticated techniques.

### Dynamic-panel GMM (Arellano-Bond) — limitations for this dataset
- Arellano-Bond dynamic-panel GMM estimators are only well defined when the time dimension of the sample is smaller than the cross-sectional unit dimension (Arellano, 2003, p. 90).
- Asymptotic properties require a very large cross-sectional unit dimension; estimators are asymptotically biased when the ratio of the time and cross-sectional unit dimensions tends to a nonzero constant (Arellano, 2003, p. 170).
- To avoid finite sample bias, the number of instruments must be less than or equal to the number of cross-sectional units (Roodman, 2003).
- Because these conditions are not met for the dataset, estimation of Model 6 by GMM-DIF, GMM-SYS, and Anderson and Hsiao instrumental variables (A-H IV) estimators breaks down (Appendix III, Appendix Table 4).
- Empirical studies of housing prices employing Arellano-Bond dynamic-panel GMM often do not meet at least two of the three consistency conditions, raising questions about the validity of their findings.

### Alternative approach: 2SLS and 3SLS with system estimation
- 2SLS or 3SLS with country-specific intercepts and cross-equation restrictions (coefficients equal across countries) are consistent with endogenous explanatory variables and a lagged dependent variable (Greene, 1997, Chapter 16; Hayashi, 1992, p. 15; Arellano, 2003, p. 133).
- 3SLS is more efficient than 2SLS because it uses the covariance structure of errors across equations.
- Implementation steps:
  - Construct housing price equation for each country with time-indexed observations.
  - Form system of simultaneous equations from country equations, restrict coefficients to be equal across countries except country-specific intercepts.
  - Treat all explanatory variables as endogenous.
- reg3 STATA procedure issues:
  - Drops missing observations across all equations rather than individually; Belgium, France, and Germany are dropped due to large number of missing observations.
  - Applies the same set of instruments to all equations; number of potential instruments greatly exceeds degrees of freedom.
- Instrument strategy used:
  - For each explanatory variable in Model 6, extract first five principal components from country realizations.
  - Use second lags of the first five principal components of all explanatory variables as instruments (lagged by two periods to ensure exogeneity).
  - For Model 6 (seven explanatory variables) this yields 35 instruments for use in all equations of the system.
- Time dimension for each country: from 1990:4 to 2006:Q4.

### 3SLS estimates (Table 1) and model selection
- 3SLS estimates of Model 6 and refinements are consistent with pooled and within-group OLS signs for statistically significant coefficients.
- Statistical significance and relative magnitudes:
  - Short-term interest rate and quarter-to-quarter growth rate of inflation and real broad money: statistically significant at the 99 percent level of confidence; point estimates higher (in absolute values) than within-group OLS counterparts.
  - Other explanatory variables: point estimates lower (in absolute values) than within-group OLS counterparts; quarter-to-quarter growth rate of real per capita PPP GDP statistically insignificant at the 90 percent level of confidence.
- Model reduction process:
  - Model 6 contains several low-significance variables; drop variables statistically insignificant at 90 percent to form Model 7.
  - Dropping real per capita PPP GDP makes rate of unemployment statistically insignificant; drop unemployment to form Model 8.
- Model 8 is the preferred specification in first-differences:
  - Median R-squared of the country residential housing price equations in first-differences: 0.33.
  - In the system of equations all but one first-order residual autocorrelations, statistically significant at the 95 percent level of confidence, are close to –0.5 (informal test for lack of first-order serial correlation in excess of the theoretically predicted value of –0.5).

### Key 3SLS coefficient estimates (selected, from Table 1 and text)
- Estimated coefficient of the lagged dependent variable: 0.45.
- Table 1 (columns labeled (6)(7)(8)) coefficients and statistics (standard errors in parentheses):
  - d1_ln_r_housprc_: 0.432** (0.034) ; 0.460** (0.034) ; 0.453** (0.037)
  - d1_ln_pcrgdppp: -0.065 (0.079)
  - srate (untransformed variable): -0.124** (0.018) ; -0.117** (0.018) ; -0.131** (0.018)
  - d1_infl: -0.152** (0.017) ; -0.159** (0.017) ; -0.173** (0.018)
  - d1_unemplr: -0.428* (0.195) ; -0.317 (0.198)
  - d1_govbal: 0.228** (0.073) ; 0.242** (0.080) ; 0.385** (0.086)
  - d1_ln_r_m20: 0.087** (0.029) ; 0.092** (0.030) ; 0.076* (0.032)
  - Observations per country: 65 65 65
  - Number of countries: 17 17 17
  - Median R-squared: 0.32 0.34 0.33
  - Significant first-order residual autocorrelation coefficients: -0.45** -0.46** -0.46**
    - additional values: -0.37* -0.39* -0.38*
    - and: 0.36* 0.35*
- Notes:
  - Standard errors in parentheses.
  - + significant at 10%; * significant at 5%; ** significant at 1%.
  - All variables in first-differences unless otherwise specified.
  - Country-specific intercepts not shown.

### Long-run elasticities (derived from Model 8 3SLS estimates)
- Long-run elasticities obtained by dividing the 3SLS coefficient estimates (excluding the lagged dependent variable) by one minus the coefficient of the lagged dependent variable (note: lagged dependent variable coefficient = 0.45).
- Reported long-run elasticities for quarter-on-quarter growth rate of real residential housing prices:
  - A 1 percentage point increase in the nominal short-term interest rates from one quarter to the next is associated with a 0.24 percentage point decline in the quarter-on-quarter growth rate of real residential housing prices.
  - A 1 percentage point increase in the quarter-on-quarter inflation is associated with a 0.31 percentage point decline in the quarter-on-quarter growth rate of real residential housing prices.
  - A 1 percentage point increase in the ratio of the primary government balance to GDP from one quarter to the next is associated with a 0.8 percentage point increase in the quarter-on-quarter growth rate of real residential housing prices.
  - A 1 percentage point increase in the quarter-on-quarter growth rate of real broad money is associated with a 0.14 percentage point increase in the quarter-on-quarter growth rate of real residential housing prices.

### Interpretation and inertia
- The lagged dependent variable coefficient (0.45) implies:
  - Approximately 55 percent of any gap between actual growth and the fundamentals-consistent growth is closed in each subsequent quarter.
  - A significant degree of inertia in quarter-on-quarter growth rates of real residential housing prices in the short run.
- The estimated interest rate elasticity of housing prices from the cross-country panel dataset is relatively low and falls within the range reported by studies on similar datasets.
- Better-suited econometric techniques cannot bridge the gap between interest rate elasticity estimates from single-country datasets and cross-country panel datasets.

### Cross-Section Regression Analysis (overview)
- Question: Does a large interest-rate elasticity of housing prices (in excess of minus 3) found in single-country datasets extend to a larger set of countries?
- Approach:
  - First analysis of determinants of residential housing prices in a cross-section of countries; housing price equation estimated in semi-loglinear form.
  - Dependent variable: ln_housprcusd (log of residential property prices in US dollars per square meter index).
  - Exploratory stage: OLS with heteroskedasticity-adjusted standard errors; explanatory variables entered as five-year averages to mitigate endogeneity from business-cycle shocks (Appendix III).
- Exploratory OLS results:
  - Main determinants identified: per capita GDP in US$, real short-term interest rate, availability of credit measured by ratio of domestic credit to the private sector to GDP (Table 2, Model 19).
- Controls and robustness:
  - Sequentially add control variables to account for time-invariant unobserved heterogeneity and measurement errors; retain statistically significant controls.
  - Controls tested include regional dummies (Europe omitted) and World Bank institutional quality indicators: business rank, corruption rank, governance rank.
  - Results show only regional dummies capture some unobserved heterogeneity (Appendix Table 5).
- Preferred cross-section specification:
  - Model 20 is the preferred regression specification of the residential housing price equation in levels.
  - Model 20 fits the data well, with a R-squared of 0.63.
- From OLS estimates in the cross-section (Model 20), long-run elasticities indicate:
  - "A 1 percentage point increase in the real short-term interest rate is associated with a" (text truncates at source).

*Source: Appendix III, _wp08247 - Appendix III summarizes the (PDF chapter/section).*

### 3.61 percentage points decline in residential housing prices.

### _wp08247 - 3.61 percentage points decline in residential housing prices.

### Key empirical findings
- A 3.61 percentage points decline in residential housing prices.  
- A 1 percentage point increase in per capita GDP in US$ is associated with a 0.28 percentage point increase in residential housing prices.  
- A 1 percentage point increase in the ratio of credit to private sector to GDP is associated with a 0.44 percentage point increase in residential housing prices.  
- Regional differences (after controlling for GDP per capita and credit market conditions):  
  - On average housing prices (in US$ per square meter) in Africa are 63 percent lower than in Europe.  
  - In Central and Latin America housing prices are 37 percent lower than in Europe.  
  - There are no statistically significant differences between average housing prices in Europe and North America and Asia and Pacific after controlling for macroeconomic fundamentals.

### Table 2: OLS estimates of the housing price equation (cross-country)
- Coefficients reported (two columns shown):
  - ln_pcgdpusd 0.374 ** 0.275 **  
    - (0.057)(0.070)
  - r_srate -4.324 ** -3.605 *  
    - (1.566)(1.803)
  - crd_gdp 0.398 * 0.436 *  
    - (0.191)(0.207)
- Regional dummy variables:
  - Asia and Pacific -0.158  
    - (0.218)
  - North America -0.134  
    - (0.351)
  - Central and Latin America -0.369 +  
    - (0.193)
  - Africa -0.627 **  
    - (0.195)
- Intercept 4.392 ** 5.425 **  
  - (0.415)(0.578)
- Number of countries 8989
- Overall R2 0.590.63
- Note: Robust standard errors consistent in the presence of heteroskedasticity.  
- Significance notation: + significant at 10%; * significant at 5%; ** significant at 1%

### Preferred estimate of the interest-rate elasticity of housing prices
- Comparison of Model 8 (Table 1) and Model 20 (Table 2) shows that using residential housing prices expressed in comparable units across countries yields a much larger estimate of the interest-rate elasticity of housing prices, within the range of single-country studies.  
- The authors pick the value (–3.6) from Model 20 as their best estimate of the interest-rate elasticity of housing prices.  
- This best estimate corroborates and extends single-country findings that the interest-rate elasticity of housing prices is greater than –3.

### Conclusion
- Best estimate of the elasticity of residential housing prices with respect to the short-run real interest rate: –3.6.  
- This estimate falls within the range of estimates reported by single-country studies and corroborates those findings across a much wider cross-section of countries.  
- The authors show that better suited econometric techniques applied to cross-country panel data cannot bridge the gap between estimates derived from single-country datasets and cross-country panel datasets, attributing the gap to inherent weaknesses of cross-country panel data on country-specific housing price indices.

*Source: _wp08247 - 3.61 percentage points decline in residential housing prices.*

### Appendix Table 1. Definitions and Data Sources of Variables

### Appendix Table 1. Definitions and Data Sources of Variables

### Variable definitions and data sources
- ln_r_housprc
  - Real residential property price index (log)
  - Series: Index of nominal residential property prices (in domestic currency units) 2000 =100
  - Unit: Deflated by CPI.
  - Sources/Notes: 1, 2, 3 (see Appendix footnotes for country-level series and splicing details)
- ln_pcrgdppp
  - Real per capita PPP GDP (log)
  - Series: Gross Domestic Product, Volume, 2000 Constant PPP
  - Unit: Thousand 2000 PPP USD
  - Source: OECD (2008). Note: For the 12 Euro area countries, data in monetary units are expressed in euros; pre-1999 data converted using irrevocable conversion euro rates.
- srate
  - Short-term interest rate
  - Series/Unit: Short-term interest rate; Fraction
  - Source: OECD (2008)
- infl
  - Inflation rate
  - Series: Consumer price index (CPI) 2000 =100
  - Unit: Annualized quarter-on-quarter growth rate.
  - Source: OECD (2008)
- slpyc
  - Slope of yield curve (difference between long and short-term rates)
  - Series/Unit: Short-term interest rate; Fraction
  - Source: OECD (2008)
- unemplr
  - Unemployment rate
  - Series/Unit: Unemployment rate; Fraction
  - Source: OECD (2008)
- govbal
  - Primary government balance as a ratio to GDP
  - Series: Primary government balance as a percentage of GDP
  - Unit: Fraction
  - Source: OECD (2008)
- curracc
  - Current account balance as a ratio to GDP
  - Series: Current account balance as a percentage of GDP
  - Unit: Fraction
  - Source: OECD (2008)
- ln_r_m2
  - Real broad money (M2) (log)
  - Series: Broad money Billion dom. currency units
  - Unit: Deflated by CPI.
  - Source: OECD (2008)
- shpopa
  - Share of active population in total population
  - Series/Unit: Active population (aged 15 to 64) Fraction
  - Source: OECD (2008)

- Cross-section variables (selected)
  - ln_housprcusd: Average price per square meter of an apartment located in the centre of the most important city of each country; US dollars per square meter; Source: www.globalpropertyguide.com (data as published mid-2007; scatter plot updated mid-2008). Note: average apartment sizes vary across regions, ranging from 100 to 300 square meters.
  - ln_pcgdpusd: Per capita nominal GDP in US dollars (log); US dollars; Average value over 2000–2005; Source: IMF (2007).
  - srate (cross-section): Rate of return on 91 day T-bills; Fraction; Average value over 2000–2005; Source: IMF (2007). (Missing observations filled by World Bank (2007) lending rates where applicable.)
  - crd_gdp: Domestic credit to private sector in ratio to GDP; Fraction; Average value over 2000–2005; Source: World Bank (2007).
  - shpopurb: Percent of urban population; Fraction; Average value over 2000–2005; Source: UN Population Division (2007).
  - curracc (cross-section): Current account balance Billion US dollars and as a ratio to GDP; Average value over 2000–2005; Source: IMF (2007).

Notes on notation:
- Lags denoted by suffix “_#” where “#” is number of quarters.
- First-differences denoted by prefix “d1_”.

*For country-level historic housing price series and splicing notes see Appendix footnotes 1–6 in the source.*

### Panel regression framework and estimation strategy
- Dependent variable
  - The dependent variable in panel regressions is ln_r_housprc (log of the real residential property price index).
- Modeling steps and specifications
  - Benchmark (Model 1): All variables entered in contemporaneous levels. Result: All demand-side fundamentals except the short-term interest rate, the slope of the yield curve, and the rate of inflation enter significantly with theoretically consistent signs.
  - Serial correlation: Wooldridge test for autocorrelation in panel data signals strong residual serial correlation in levels (sign of possible “spurious regression”).
  - General autoregressive distributed lag (Model 2): Estimated in levels with initial lag-length of six for all variables (chosen based on serial correlation tests). Extremely high goodness-of-fit suggests potential overfitting.
  - Parsimonious reduction (Model 3): Drop lags 2 through 6 of all explanatory variables except the lagged dependent variable. Coefficients of contemporaneous level and first-lag often have opposite signs and similar magnitudes.
  - First-difference representation (Model 4): Enter all variables except the short-term interest rate in first differences (Model 4) as a parsimonious representation of Model 3. Rationale:
    - Within-group OLS estimation of the ECM representation yields an equilibrium-correction coefficient implying "2 percent" of misalignment corrected each quarter.
    - Indices with non-comparable bases across countries make first-differences preferable to level elasticities.
  - Further reductions:
    - Model 5: Drop statistically insignificant first-difference explanatory variables at the 95 percent level (slpyc, curracc, shpopa). Keep ln_pcrgdppp for theoretical importance.
    - Model 6: Drop second through fifth lags of the dependent variable. Wooldridge test then fails to detect serial correlation in excess of the theoretically predicted value of –0.5 at the 95 percent level.

### Key panel-regression findings and diagnostics
- Preferred panel specification: Model 6 (first-differences, reduced lags) — described as the preferred interim regression specification.
- Statistical and inference highlights for Model 6:
  - Number of countries: 20
  - Observations (as reported in table columns for various specifications): values shown include 1,814; 1,722; 1,722; 1,750; 1,818 (see Appendix Table 2 and Table 3 for specification-specific counts).
  - Within adjusted R-squared reported across models (column headers correspond to models): 0.61; 0.99; 0.39; 0.38; 0.12 (preserve as reported in table).
  - In Model 6 all coefficients have signs consistent with theoretical predictions and all except real per capita PPP GDP (ln_pcrgdppp) are statistically significant at the 99 percent level of confidence.
  - The F-test of the joint significance of all fixed effects rejects the hypothesis of a common intercept across countries (supports longitudinal estimation).
  - Equilibrium-correction coefficient (from ECM representation of Model 3, not the preferred Model 4) was reported as "2 percent" (2 percent of misalignment corrected each quarter).
- Estimation methods and robustness checks
  - GMM and IV estimators:
    - GMM-DIF and GMM-SYS (two-step) estimators return markedly different coefficient estimates and larger standard errors than their one-step counterparts, contrary to theoretical efficiency expectations.
    - One-step GMM-SYS estimates are very close to pooled OLS estimates, signaling likely overfitting.
    - Sargan tests of overidentifying restrictions are noted as unreliable due to small cross-sectional sample dimension; thus instrument validity cannot be concluded from these tests.
    - Anderson and Hsiao (A-H IV) estimators performed poorly: biased coefficient estimates and very large standard errors.
  - Serial correlation diagnostics:
    - Wooldridge test used for autocorrelation in panel data; presence of serial correlation in levels, acceptable residual autocorrelation after Model 6 reductions (test fails to detect serial correlation in excess of –0.5 at 95 percent level for Model 6).

### Selected reported coefficient magnitudes (examples preserved exactly as in tables)
- From Appendix Table 2 / Appendix Table 3 (within / OLS estimates of unrestricted specifications; standard errors in parentheses; significance markers preserved):
  - ln_r_housprc_1: 1.204** (0.024) in one reported column; other columns show 0.240** (0.024), 0.242** (0.024), 0.168** (0.023)
  - ln_r_housprc_2: -0.237** (0.033); -0.015 (0.020)
  - ln_r_housprc_4: 0.562** (0.029); 0.529** (0.019); 0.515** (0.019)
  - ln_pcrgdppp (contemporaneous): 0.703** (0.057) in one specification; other specifications show 0.023 (0.065), 0.077 (0.064), 0.073 (0.065), 0.118 (0.077)
  - srate (untransformed in some specs): 0.420+ (0.231) and untransformed negative entries such as -0.072** (0.016)
  - infl: 0.082 (0.166) and in other specs -0.143** (0.026), -0.089** (0.018), -0.102** (0.021)
  - unemplr: -3.801** (0.275) in one spec; other specs -0.535* (0.210), -0.668** (0.204), -1.325** (0.237)
  - govbal: 0.607** (0.174) in one spec; other specs 0.298** (0.083), 0.302** (0.081), 0.328** (0.098)
  - ln_r_m2: 0.143** (0.026) and other specs 0.059* (0.023), 0.078** (0.023), 0.072** (0.027)
- Notes on significance notation in tables: + significant at 10%; * significant at 5%; ** significant at 1%.

### Cross-section regression approach and findings
- Dataset and dependent variable
  - Cross-country regressions use ln_housprcusd (log of residential property price in US$ per square meter) as dependent variable.
  - Sample sizes and aggregation: number of countries in cross-section regressions generally reported as 89 (varies slightly by specification due to data availability).
- Key cross-section coefficient findings (selected, preserved exactly as reported)
  - ln_pcgdpusd (coefficient estimates across multiple specifications): 0.487**; 0.509**; 0.465**; 0.474**; 0.463**; 0.387**; 0.491**; 0.488**; 0.546**; 0.489**; 0.374**; 0.275**; 0.402**; 0.381**; 0.480** (standard errors reported in parentheses in the source).
  - infl: reported entries include 0.935 and 4.966** (with standard errors shown).
  - srate: reported entries include -0.801 and -4.498**.
  - r_srate (real short-term rate): -4.616**; -4.324**; -3.605*; -4.612**; -4.387**; -4.395** (standard errors in parentheses).
  - crd_gdp: 0.445*; 0.398*; 0.436*; 0.418*; 0.327; 0.477* (standard errors in parentheses).
  - govbal: -0.435 (2.156) in one reported column.
  - unemplr: 0.06 (0.615) in one reported column.
  - shpopurb: -0.585 (0.444) in one reported column.
  - curracc: -0.095 (0.815) in one reported column.
  - Regional dummy examples: Central and Latin America: -0.369+ (0.193); Africa: -0.627** (0.195).
  - Institutions (rank variables) reported with small coefficients and standard errors (e.g., Governance rank 0.001 (0.003)).
- Goodness-of-fit across cross-section specifications
  - Overall R-squared values reported across specifications range from 0.52 to 0.63 (preserve as reported per column).
  - Number of countries: 89 across many specifications; some specifications show slightly fewer due to data availability (e.g., columns with 88, 87, 82 as noted in the table).
- Estimation notes
  - Robust standard errors used (consistent in presence of heteroskedasticity).
  - Significance markers: + significant at 10%; * significant at 5%; ** significant at 1%.

*Source: Appendix Table 1 and accompanying Appendix III tables and notes in the provided IMF document.*

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