## 1. Estimation Result for the Panel Regression

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### Econometric specification and synchronization measure
- Model decomposition:
  - Quarterly growth of real house prices for country i in period t, Δp_{i,t}, decomposed into:
    - time-varying loading on the global factor g_t,
    - time-varying loading on a regional factor r_{k,t} (region k ∈ {Europe, Asia, America}),
    - country-specific idiosyncratic component ε_{i,t}.
  - Global factor extracted first; regional factor extracted from residuals after removing global factor.
  - Each global (regional) factor modeled jointly with global (regional) output, inflation, and interest rate via a VAR with time-varying parameters Θ_{t}.
- Estimation approach:
  - Two-step procedure:
    1. Extract principal component of house price growth, output, inflation and short-term interest rates to estimate time-varying factor loadings, variance-covariance matrix, and VAR parameters.
    2. Extract the global (or regional) factor by the Kalman smoother given step-1 estimates.
  - Two-step approach yields almost identical results to Bayesian simultaneous estimation in most cases.
- Synchronization measure:
  - S_{i,t,L} is the share of variance explained by the global (and regional) factor over the window [t-L, t].
  - Higher S_{i,t,L} can arise from larger time-varying factor loadings or from smaller relative variance of the country-specific component.

### Data
- Datasets:
  - Long dataset: starts at 1971: Q1; covers 19 countries (AUS, BEL, CAN, CHE, DEU, DNK, ESP, FIN, FRA, GBR, IRL, ITA, JPN, NLD, NOR, NZL, SWE, USA, ZAF); used for time developments and panel regressions.
  - Short dataset: starts at 2002: Q1; covers 27 countries and area (includes Euro Area as one unit); used to identify cross-sectional heterogeneity and include emerging economies.
  - City-level dataset: starts at 2002: Q1; covers 224 cities; caveats on cross-country comparability due to varying city counts and sizes.
- House prices: residential property prices (seasonally adjusted) deflated by CPI inflation; compiled from multiple sources (BIS; CEIC; Emerging Markets Economic Data Ltd; Global Financial Data Solutions; Global Property Guide; Haver Analytics; IMF Research Department house price data set; OECD; Thomson Reuters Datastream; IMF staff calculation).

### Time-series developments in synchronization (main empirical patterns)
- Upward trend in global-factor synchronization (S_{i,t,L}) using rolling windows L = 60, 80, 100 (15, 20, 25 years).
- Example statistics:
  - Median of the 15-year window synchronization: just around 10 percent in the mid-1980s; around 35 percent in 2016.
  - Interpretation: around 35 percent of variance in house price growth across countries can on average be accounted for by one common global factor in 2016.
- Global factor robustness:
  - Global factors estimated from the long dataset (from 1970: Q1) and the short dataset (from 2002: Q1) are almost identical.

### Cross-country heterogeneity and regional patterns
- Large heterogeneity across countries (long dataset, whole-sample measures):
  - DEU and ITA: importance of the global factor is almost zero percent.
  - GBR: importance of the global factor around 60 percent.
  - AUS and CAN: substantial idiosyncratic components.
  - ZAF and NLD: slightly influenced by the global cycle but mostly driven by country-specific factors.
- Short dataset (whole-sample average synchronization S_i):
  - Advanced economies: 30-40 percent.
  - Emerging economies: less than 10 percent.
  - Regional averages (global factor contribution):
    - Europe: around 20 percent.
    - North and South America: around 20 percent.
    - Asia: around 10 percent.

### City-level versus country-level synchronization
- City-level house price growth modeled as: global factor (g_t) + country factor (f_{c,t}) + city-specific idiosyncratic component (u_{i,t}).
- Global and country factors from city-level data closely track those from country-level data (Figure 7).
- Findings for selected large cities (Figure 8):
  - Global factor explains substantial portion of house price variations in Seoul, Vancouver (and Montreal), New York, Los Angeles, and Chicago.
  - Global factor has much smaller effects in Dallas.
  - Beijing and Shanghai show house prices barely exposed to the global factor.
  - Country factor has considerable influence in almost all cities.
- Interpretation and caveats:
  - Rise in international synchronization may be driven by connectivity among large international cities where global investors concentrate.
  - Large gaps in city-level data across countries limit generalization; aggregate country-level results may be weighted toward large cities or reflect idiosyncratic factors that wash out at the country level.

### Drivers of synchronization — empirical strategy
- Objectives:
  - Explain upward trend in aggregate synchronization since the 1970s.
  - Explain cross-country heterogeneity in synchronization.
- Empirical approaches:
  - Panel regression using the long dataset (dynamic factor model estimated from 1971: Q1).
  - Cross-sectional regression using the short dataset (dynamic factor model estimated from 2002: Q1).
- Key regressors:
  - Financial openness: Chinn-Ito index (de-jure capital account openness), Chinn-Ito_{c,t}.
  - Trade openness: gross trade volume (imports + exports) to GDP, trade_{c,t}.
  - Controls: country fixed effects (alpha_c), time dummies (gamma_t), X_{c,t} (including log real GDP and CPI inflation).
  - For panel windows [t-L, t], financial and trade openness summarized by a weighted average placing more weight on periods close to the beginning of the window.

### Panel regression findings (19 countries, 1971:Q1 to 2016:Q4)
- Main conclusion: degree of house price synchronization is significantly influenced by financial and trade openness; financial openness remains relevant after controlling for gross trade volume.
- Coefficients (selected specifications; robust standard errors in parentheses; significance notation: *** p<0.01, ** p<0.05, * p<0.1):
  - Financial Openness:
    - (1) 0.06691** (0.02387)
    - (2) 0.02904 (0.02321)
    - (3) 0.06220*** (0.01585)
    - (4) 0.04354*** (0.01477)
    - (5) 0.07481** (0.01578)
    - (6) 0.06670*** (0.01289)
  - Trade Openness:
    - (1) 0.00911** (0.00394)
    - (2) 0.00658** (0.00312)
    - (3) 0.01096*** (0.00351)
    - (4) 0.00891** (0.00334)
    - (5) 0.00779*** (0.00141)
    - (6) 0.00699*** (0.00184)
  - Log(Output):
    - (1) 0.22121 (0.13475)
    - (2) 0.39513** (0.15312)
    - (3) 0.27416** (0.11590)
    - (4) 0.40820*** (0.14007)
    - (5) 0.23717* (0.11904)
    - (6) 0.32661** (0.09859)
  - Inflation:
    - (1) 0.02439 (0.02069)
    - (2) 0.02159 (0.02898)
    - (3) 0.00052 (0.00643)
    - (4) 0.00253 (0.00962)
    - (5) ‐0.00340 (0.00324)
    - (6) ‐0.00260 (0.00393)
  - Variance of idiosyncratic factor (in some specs):
    - ‐0.16292* (0.08650)
    - ‐0.11162 (0.08338)
    - ‐0.05319 (0.06079)
  - Constants:
    - (1) ‐1.31628** (0.51871)
    - (2) ‐1.68169*** (0.54940)
    - (3) ‐1.53109*** (0.43175)
    - (4) ‐1.84651*** (0.52551)
    - (5) ‐1.23922** (0.48204)
    - (6) ‐1.51223*** (0.37440)
  - Observations:
    - (1) 1,861
    - (2) 1,861
    - (3) 1,645
    - (4) 1,645
    - (5) 1,357
    - (6) 1,357
  - R-squared:
    - (1) 0.38823
    - (2) 0.46960
    - (3) 0.47414
    - (4) 0.51310
    - (5) 0.59165
    - (6) 0.60401
  - Number of countries: 19
- Robustness nuance:
  - Adding the variance of the country-specific factor u_{c,t}:
    - Financial and trade openness remain positive and statistically significant for L = 80 and L = 100 (20 and 25 years).
    - For L = 60 (15 years), financial openness loses significance while variance of the country-specific factor has negative and statistically significant effects, indicating short-term synchronization driven by changes in country-specific variance.

### Cross-sectional regression findings (25 countries, 2002: Q1 to 2016: Q4)
- Purpose: assess financial openness effect in broader sample including emerging economies.
- Results highlights (standard errors in parentheses; significance notation: *** p<0.01, ** p<0.05):
  - Financial Openness:
    - (1) 0.0803** (0.0319)
    - (2) 0.0077 (0.0393)
    - (3) ‐0.0190 (0.0458)
    - (4) 0.1153*** (0.0261)
    - (5) 0.0786** (0.0353)
    - (6) 0.0611 (0.0431)
  - Trade Openness (all specifications):
    - (1) ‐0.0010 (0.0005)
    - (2) ‐0.0010 (0.0005)
    - (3) ‐0.0006 (0.0005)
    - (4) ‐0.0005 (0.0004)
    - (5) ‐0.0004 (0.0004)
    - (6) ‐0.0002 (0.0005)
  - Dummy for AE (Advanced Economy):
    - (1) 0.2614** (0.0985)
    - (2) 0.2662** (0.1045)
    - (3) 0.1321 (0.0883)
    - (4) 0.1224 (0.0985)
  - dLog(Output) and Inflation (specs 5–6):
    - (5) dLog(Output): ‐0.1578 (0.1119); Inflation: 0.0685 (0.0880)
    - (6) dLog(Output): ‐0.0881 (0.1054); Inflation: 0.0071 (0.0829)
  - Constants:
    - (1) 0.1945** (0.0710)
    - (2) 0.1589** (0.0643)
    - (3) 0.2419 (0.1621)
    - (4) 0.2247*** (0.0579)
    - (5) 0.2067*** (0.0576)
    - (6) 0.2857 (0.1527)
  - R-squared:
    - (1) 0.2178
    - (2) 0.3862
    - (3) 0.4083
    - (4) 0.4249
    - (5) 0.4555
    - (6) 0.4202
  - Number of countries: 25
- Interpretations:
  - Scatter plots (Figure 9) show a clear positive relationship between synchronization and financial openness for some measures.
  - Trade openness not significant in cross-section; when an advanced-economy dummy is added, financial openness sometimes loses significance (financial openness correlated with advanced economy status).
  - Adding output growth and inflation as controls can remove statistical significance due to multicollinearity and limited sample size.

### Key empirical conclusions
- Degree of synchronization of house prices has been rising since the 1970s.
- Large heterogeneity across countries in the degree of synchronization.
- City-level analysis suggests international synchronization may be driven by connectivity among large, international cities; limited by data coverage.
- Financial openness is a robust correlate of higher house price synchronization in both panel and cross-sectional analyses; trade openness significant in panel regressions but not consistently in cross-section.
- Evidence points to financial factors (investment flows by global investors) influencing synchronization separately from trade-driven real economic connectivity.

### Policy implications and research directions
- Policy and monitoring:
  - House prices should be monitored with a global perspective; incorporate global housing cycles and their drivers in domestic assessments of macro-financial stability.
  - Continued financial liberalization and greater financial openness among countries are likely to increase future house price synchronization and associated cross-border spillover risks to financial stability.
- Research avenues:
  - Distinguish whether increases in synchronization are driven by increases in factor loadings (greater sensitivity) or by reductions in idiosyncratic variance.
  - Develop a structural macroeconomic model to explain why greater financial and trade openness is associated with higher house price synchronization.
  - Investigate effects of house price synchronization on real economic activity and tail risks to growth.
  - Examine interactions between macroprudential policies and house price synchronization.
  - Collect more comprehensive and comparable city-level data across countries to quantify city-level synchronization dynamics and reconcile city- and country-level results.

*Source: wp18209 - 1. Estimation Result for the Panel Regression; PDF chapter/section; canonical URL: https://www.imf.org/-/media/files/publications/wp/2018/wp18209.pdf*

### 1. Estimation Result for the Panel Regression ____________________________________27

### 1. Estimation Result for the Panel Regression ____________________________________27

### Section scope
- Title of the content unit: "1. Estimation Result for the Panel Regression"
- Page location: 27

### Associated figures referenced elsewhere in the document
- Figure 1: Individual House Price Growth and the Global Factor ____________________________21
- Figure 2: Developments in Synchronization of House Prices ______________________________21
- Figure 3: Synchronization of House Prices by Country (1971: Q1-) _________________________22
- Figure 4: Contribution of Global Factor in House Price Growth ____________________________22
- Figure 5: Synchronization of House Prices by Country (2002: Q1-) _________________________23
- Figure 6: Contribution of Global and Regional Factors in Asian House Price Growth ___________23
- Figure 7: Global Factor for the City-Level Data and the Country-Level Data _________________24
- Figure 8: Contribution of Global and Regional Factors in Selected Cities ____________________25
- Figure 9: House Price Synchronization and Financial Openness ____________________________26

### Related document sections and appendix
- Section 2: Estimation Results for the Cross Sectional Regression ___________________________28
- Appendix 1: Data Sources and Country Coverage _________________________________________20

*Source: wp18209 - 1. Estimation Result for the Panel Regression; PDF chapter/section; canonical URL: https://www.imf.org/-/media/files/publications/wp/2018/wp18209.pdf*

### References ________________________________________________________________18

### wp18209 - References ________________________________________________________________18

### I. Introduction — motivation and main empirical findings
- Purpose: investigate cross-country synchronization of house prices and its drivers using a dynamic factor model that decomposes house price growth into a global factor, a regional factor, and an idiosyncratic country-specific factor.
- Methodological outline:
  - Global factor is common across all countries; regional factor is common only within a region and is orthogonal to the global factor.
  - The share of variance explained by the common global factor is used as a proxy for the degree of house price synchronization for each country.
  - Rolling-window estimation provides time variation in synchronization for panel regressions linking synchronization to country-specific variables (e.g., financial openness, trade openness).
- Theoretical channels for synchronization:
  - Real economic synchronization (consumption, income, output) via trade linkages.
  - Financial channels: global financial conditions, investor expectations, and global investors’ access to housing markets.
  - Consequence: financial openness may independently influence synchronization, separate from trade-induced synchronization.
- Key empirical findings (summary):
  - Using house price data for 19 countries with long time series, the share of variance explained by the common global factor rose from around 10 percent in the 1980s to around 40 percent in 2016.
  - Cross-sectional and panel regressions indicate statistically significant effects of financial openness (proxied by the Chinn-Ito index) on the degree of house price synchronization, even after controlling for gross trade volume to GDP ratios.
  - City-level analysis: the global factor is significant mainly in large and international cities in some countries, implying city-level connectivity between large international cities may drive international synchronization more than country-level connectivity.
- Policy implications:
  - House prices should be monitored with a global perspective; domestic monitoring should incorporate global housing cycles and their drivers.
  - Increased financial openness among more countries, including emerging economies, is likely to increase future house price synchronization and associated spillover risks to financial stability.

### II. Econometric specification and synchronization measure
- Model specification:
  - Quarterly growth of real house prices for country i in period t, Δp_{i,t}, is assumed to decompose as:
    - time-varying loading on the global factor g_t,
    - time-varying loading on a regional factor r_{k,t} (region k ∈ {Europe, Asia, America}),
    - country-specific idiosyncratic component ε_{i,t}.
  - Global and regional factors are extracted sequentially: global factor first; regional factor extracted from residuals after removing the global factor.
  - Each global (regional) factor is modeled jointly with global (regional) output, inflation, and interest rate via a VAR with time-varying parameters Θ_{t}.
- Estimation approach:
  - Two-step approach:
    1. Extract the principal component of house price growth, output, inflation and short-term interest rates to estimate time-varying factor loadings and variance-covariance matrix, and VAR parameters.
    2. Extract the global (or regional) factor by the Kalman smoother given step-1 estimates.
  - Note: the two-step approach is less rigorous than a Bayesian simultaneous estimation but is more tractable and yields almost identical results in most cases.
- Synchronization measure:
  - Synchronization for country i at time t, S_{i,t,L}, is measured as the share of variance explained by the global (and regional) factor over the window [t-L, t]:
    - S_{i,t,L} = Var_component_share calculated from realized variances over period t-L to t.
  - Interpretation:
    - Higher S_{i,t,L} can arise from larger time-varying factor loadings (greater sensitivity to the global factor) or from a smaller relative variance of the country-specific component (less idiosyncratic volatility).
  - Distinguishing these two drivers is important for interpreting changes in synchronization.

### III. Data
- Country-level datasets:
  - Short dataset:
    - Starts at 2002: Q1, contains around 60 periods.
    - Covers 27 countries, including many emerging economies.
    - Used mainly to identify cross-sectional heterogeneity among countries.
  - Long dataset:
    - Starts at 1971: Q1.
    - Covers 19 countries, most of which are advanced economies.
    - Used to analyze developments in synchronization over time and for panel regression analysis.
- City-level dataset:
  - Starts at 2002: Q1 and covers 224 cities in advanced and emerging economies.
  - Caveat: number and size of cities vary across countries (e.g., China: >30 cities including rural ones; France: 8 cities mainly around Paris), so city-level data are better used for within-country city comparisons rather than cross-country city-sample comparisons.

### IV. Estimation results — developments, heterogeneity, and drivers
- Global factor existence and robustness:
  - The estimated global factor captures a smooth cyclical common component despite volatile idiosyncratic country series.
  - Global factors estimated from the long dataset (from 1970: Q1) and the short dataset (from 2002: Q1) are almost identical, indicating robustness to sample period and country coverage.
- Time-series developments in synchronization:
  - Synchronization measure S_{i,t,L} (using the global factor only) exhibits a clear upward trend for rolling windows of 15, 20, and 25 years (L = 60, 80, 100 for quarterly data).
  - Example statistics:
    - Median of the 15-year window synchronization was just around 10 percent in the mid-1980s and increased to around 35 percent in 2016.
    - Interpreted: around 35 percent of variance in house price growth across countries can on average be accounted for by one common global factor in 2016.
- Cross-country heterogeneity:
  - Large heterogeneity exists in the importance of the global factor across countries.
  - Examples from the long dataset (1971: Q1 to end of sample):
    - DEU and ITA: importance of the global factor is almost zero percent.
    - GBR: importance of the global factor around 60 percent.
    - AUS and CAN: substantial idiosyncratic components.
    - ZAF and NLD: slightly influenced by the global cycle but mostly driven by country-specific factors.
- Advanced vs. emerging economies and regional differences (short dataset results, whole-sample measure):
  - Average synchronization S_i for advanced economies: 30-40 percent.
  - Average synchronization S_i for emerging economies: less than 10 percent.
  - Regional averages (global factor contribution):
    - Europe: around 20 percent.
    - North and South America: around 20 percent.
    - Asia: around 10 percent.
  - Note: regional decomposition shows global factor (dark blue bar) and regional factor contributions (light blue = Europe, green = Asia, yellow = North and South America).
- Drivers of heterogeneity — financial openness:
  - Cross-sectional and panel regressions indicate financial openness (proxied by the Chinn-Ito index) is a statistically significant driver of higher house price synchronization, even after controlling for real economic connectivity captured by gross trade volume to GDP ratios.
- City-level findings:
  - In some countries, the global factor significantly affects house prices mainly in large and international cities, suggesting that international synchronization may be driven by city-level connectivity among major international cities rather than by country-level linkages alone.

### V. Implications and next steps
- Monitoring and policy:
  - Policymakers should incorporate global house price cycles and their drivers when assessing domestic house prices and macro-financial stability risks.
  - Continued financial liberalization and greater financial openness among countries are likely to increase house price synchronization and the potential for cross-border spillovers to financial stability.
- Research avenues:
  - Distinguish whether increases in synchronization are driven by increases in factor loadings (greater sensitivity) or by reductions in idiosyncratic variance.
  - Further analysis at the city level to assess the role of large international cities in driving global synchronization.

*Source: wp18209 - References ________________________________________________________________18*

### conclusion is, however, almost unchanged even if we use individual country’s data rather than the Euro area

### wp18209 - conclusion is, however, almost unchanged even if we use individual country’s data rather than the Euro area

### City-level versus country-level synchronization
- City-level house price growth is modeled as the sum of: the global factor (g_t), the country factor for the country to which city i belongs (f_{c,t}), and a city-specific idiosyncratic component (u_{i,t}).
- Global and country factors extracted from city-level data closely track the factors extracted from country-level data (Figure 7), suggesting that country- and city-level datasets are driven by almost the same common factor in the dynamic factor model.
- Findings from selected large cities (Figure 8):
  - Global factor explains a substantial portion of house price variations in Seoul, Vancouver (and Montreal), New York, Los Angeles, and Chicago.
  - Global factor has much smaller effects in Dallas.
  - Beijing and Shanghai show house prices barely exposed to the global factor.
  - Country factor, orthogonal to the global factor, has a considerable influence in almost all cities across all countries.
- Interpretation:
  - The rise in international synchronization of house prices may be driven by city-level connectivity among large and international cities (e.g., where global investors concentrate) rather than by country-level connectivity.
- Caveats / data limitations:
  - Large gaps in availability of city-level data across countries make it difficult to generalize city-level findings globally.
  - Reconciling city-level results (global factor negligible in most small cities) with country-level results (substantial portion of country-level variance explained by global factor) requires more granular and comparable city-level data for more countries.
  - Possible reconciliation mechanisms noted: independent city-specific idiosyncratic factors washing out in aggregate; country-level aggregates possibly weighted toward large cities.

### What drives synchronization of house prices? (empirical strategy)
- Objective: explain (i) the upward trend in aggregate house price synchronization, and (ii) the cross-country heterogeneity in synchronization.
- Empirical approaches:
  - Panel regression using the long dataset (dynamic factor model estimated from 1971Q1).
  - Cross-sectional regression using the short dataset (dynamic factor model estimated from 2002Q1, covering 27 countries including emerging economies).
- Synchronization measure: share of variance of house price growth explained by the global factor (computed via the dynamic factor model).
- Panel regression specification notes:
  - Synchronization measure y_{c,t} computed using moving fixed windows of length L = 60, 80, and 100 (i.e., 15 years, 20 years, and 25 years).
  - Financial openness proxied by the Chinn-Ito index (de-jure capital account openness), denoted Chinn-Ito_{c,t}.
  - Trade openness measured by gross trade volume (imports + exports) to GDP, denoted trade_{c,t}.
  - For each window [t-L, t], financial and trade openness are summarized by a weighted average that puts more weight on periods close to the beginning of the window.
  - Country fixed effects (alpha_c), time dummies (gamma_t), and control vector X_{c,t} (including log real GDP and CPI inflation) are included.
  - Panel regression equation referenced as (3) in the text.

### Panel regression findings
- Main result: degree of house price synchronization is significantly influenced by financial and trade openness.
- For all window lengths (L = 60, 80, 100), coefficients on financial openness and trade openness are positive and statistically significant.
- Interpretation:
  - Heterogeneity across countries in rises (or declines) in synchronization since the 1970s is partly explained by differences in the progress of financial and trade openness.
  - Financial openness remains a relevant factor after controlling for real economic connectivity captured by gross trade volume, implying financial factors (e.g., investment flows by global investors) play an important role separate from trade linkages.
- Robustness checks:
  - Adding the variance of the country-specific factor (u_{c,t}) as a control:
    - Financial and trade openness remain positive and statistically significant for L = 80 and L = 100 (20 and 25 years), indicating long-term synchronization increases operate mainly through a rise in sensitivity of house prices to the global factor.
    - For the short window (L = 60; 15 years), financial openness loses significance; the variance of the country-specific factor has negative and statistically significant effects on synchronization. This suggests short-term synchronization within short windows is driven by changes in country-specific variance that can mask long-term financial openness effects.

### Cross-sectional regression findings (broader sample)
- Purpose: assess whether the financial openness effect holds in a broader sample including emerging economies.
- Setup:
  - Synchronization measure y_c computed from the short dataset covering 2002Q1 onward for 27 countries.
  - Simple averages of financial openness (Chinn-Ito) and trade openness over the sample period used as regressors.
  - Cross-sectional regression equation referenced as (4) in the text.
- Results:
  - Scatter plots (Figure 9) show a clear positive relationship between synchronization and financial openness.
  - Table 2 results: financial openness has positive and statistically significant effects on synchronization for both synchronization measures (global factor only; global plus regional factor).
  - Trade openness does not have a significant effect in the cross-sectional regressions.
  - When a dummy for advanced economies is added, the coefficient on financial openness loses statistical significance (financially open countries tend to be advanced economies), but financial openness remains statistically significant when using the synchronization measure that includes both global and regional factors.
- Robustness caveat noted in footnote:
  - When output growth and inflation are added as controls, statistical significance is lost for both cases of y_c—likely because financial openness is highly correlated with economic developments and the cross-sectional regression cannot separately identify financial openness effects given the limited sample size.

### Key empirical conclusions
- The degree of synchronization of house prices has been rising since the 1970s.
- There is large heterogeneity across countries in the degree of synchronization.
- City-level analysis suggests international synchronization may be driven by connectivity among large, international cities, but this finding is complementary and limited by data coverage.
- Financial openness is a robust correlate of higher house price synchronization in both panel and cross-sectional analyses; trade openness is significant in panel regressions but not consistently in cross-section.
- Evidence points to financial factors (investment flows by global investors) influencing synchronization separately from trade-driven real economic connectivity.

### Policy and research implications / future directions
- Need for a structural macroeconomic model to explain why greater financial and trade openness is associated with higher house price synchronization (theoretical prediction is not straightforward; openness could dampen synchronization via substitution across countries).
- Investigate effects of house price synchronization on real economic activity and whether higher synchronization implies greater tail risk for economic growth.
- Examine interactions between macroprudential policies and house price synchronization—whether effectiveness of macroprudential tools depends on the prevailing degree of synchronization.
- More comprehensive and comparable city-level data across countries are required to quantify city-level synchronization dynamics and reconcile city- and country-level results.

*Italic: Source — wp18209 (conclusion and related sections) from the supplied IMF PDF content.*

### Appendix 1. Data Sources and Country Coverage

### Appendix 1. Data Sources and Country Coverage

### Data sources
- House prices: residential property prices (seasonally adjusted) at country level (also at city level) deflated by CPI inflation in each country.
- Compiled from multiple sources: Bank for International Settlements; CEIC Data Co. Ltd; Emerging Markets Economic Data Ltd; Global Financial Data Solutions; Global Property Guide; Haver Analytics; IMF, Research Department house price data set; Organisation for Economic Co-operation and Development; Thomson Reuters Datastream; IMF staff calculation.

### Country coverage
- Long dataset (from 1971Q1) covers 19 countries: AUS, BEL, CAN, CHE, DEU, DNK, ESP, FIN, FRA, GBR, IRL, ITA, JPN, NLD, NOR, NZL, SWE, USA, ZAF.
- Short dataset (from 2002Q1) covers 27 countries and area: AUS, CAN, CHE, CHL, CHN, COL, CZE, DNK, Euro Area, GBR, HKG, HUN, IDN, ISR, JPN, KOR, MYS, NOR, NZL, RUS, SGP, SRB, SWE, THA, TWN, USA, ZAF.
- Note: The short dataset treats European countries in the euro area as one country (Euro Area) rather than using individual country data.

### Figures (summarized content and notes)
- Figure 1: Individual Q/Q real house price growth (black thin lines) by country; global factor extracted from long dataset (light blue line) and short dataset (dashed red line).
- Figure 2: Developments in synchronization of house prices — charts show the 25-percentile, median, and 75-percentile of synchronization measures (defined in equation (3)) using only the global factor for 15-year, 20-year, and 25-year windows.
- Figure 3: Synchronization of house prices by country (1971: Q1-) — synchronization measure defined in equation (3) computed over the whole sample period by country.
- Figure 4: Contribution of global factor in house price growth — charts show the global factor multiplied by the factor loading (i.e., ߣ௚,௜,௧݃௧; red lines) along with developments in house prices for selected countries (GBR, FRA, USA, ESP, AUS, NZL, FIN, SWE, CAN, DNK, CHE, BEL, ZAF, JPN, NOR, IRL, NLD, ITA, DEU).
- Figure 5: Synchronization by country (2002: Q1-) — ݄ܿ݊ݕݏ௜ from equation (3) for each country by region; contribution of global factor shown as dark blue bar; contribution of regional factor shown as light blue bar (Europe), green bar (Asia), yellow bar (North and South America).
- Figure 6: Contribution of global and regional factors in Asian house price growth — house prices for selected Asian countries with global and regional factor multiplied by factor loadings (i.e., ߣ௚,௜,௧݃௧ and ߣ௞,௜,௧ݎ௞,௧; red and green lines).
- Figure 7: Global factor for city-level and country-level data — global factor from city-level data (blue solid line) and country-level data (red dashed line); charts include 10- and 90-percentile.
- Figure 8: Contribution of global and regional factors in selected cities — developments in house prices for large cities in KOR, CAN, USA, and CHN with global and country factor multiplied by factor loadings (ߣ௚,௜,௧݃௧ and ߣ௞,௜,௧ݎ௞,௧; red and green solid lines).
- Figure 9: House price synchronization and financial openness — scatter plots of ݄ܿ݊ݕݏ௜ against financial openness; left chart uses only global factor, right chart uses both global and regional factor.

### Key statistics and estimation findings (from tables)
- Panel regression (19 countries, 1971:Q1 to 2016:Q4). Dependent variable: House Price Synchronization (rolling windows of 15 years, 20 years, 25 years). Robust standard errors in parentheses. Country fixed effect and year dummies included.
  - Financial Openness coefficients:
    - (1) 0.06691** (0.02387)
    - (2) 0.02904 (0.02321)
    - (3) 0.06220*** (0.01585)
    - (4) 0.04354*** (0.01477)
    - (5) 0.07481** (0.01578)
    - (6) 0.06670*** (0.01289)
  - Trade Openness coefficients:
    - (1) 0.00911** (0.00394)
    - (2) 0.00658** (0.00312)
    - (3) 0.01096*** (0.00351)
    - (4) 0.00891** (0.00334)
    - (5) 0.00779*** (0.00141)
    - (6) 0.00699*** (0.00184)
  - Log(Output) coefficients:
    - (1) 0.22121 (0.13475)
    - (2) 0.39513** (0.15312)
    - (3) 0.27416** (0.11590)
    - (4) 0.40820*** (0.14007)
    - (5) 0.23717* (0.11904)
    - (6) 0.32661** (0.09859)
  - Inflation coefficients:
    - (1) 0.02439 (0.02069)
    - (2) 0.02159 (0.02898)
    - (3) 0.00052 (0.00643)
    - (4) 0.00253 (0.00962)
    - (5) ‐0.00340 (0.00324)
    - (6) ‐0.00260 (0.00393)
  - Variance of idiosyncratic factor coefficients (reported in some specifications):
    - ‐0.16292* (0.08650)
    - ‐0.11162 (0.08338)
    - ‐0.05319 (0.06079)
  - Constant terms:
    - (1) ‐1.31628** (0.51871)
    - (2) ‐1.68169*** (0.54940)
    - (3) ‐1.53109*** (0.43175)
    - (4) ‐1.84651*** (0.52551)
    - (5) ‐1.23922** (0.48204)
    - (6) ‐1.51223*** (0.37440)
  - Observations:
    - (1) 1,861
    - (2) 1,861
    - (3) 1,645
    - (4) 1,645
    - (5) 1,357
    - (6) 1,357
  - R-squared:
    - (1) 0.38823
    - (2) 0.46960
    - (3) 0.47414
    - (4) 0.51310
    - (5) 0.59165
    - (6) 0.60401
  - Number of countries: 19
  - Significance notation: *** p<0.01, ** p<0.05, * p<0.1

- Cross-sectional regression (25 countries, 2002: Q1 to 2016: Q4). Dependent variable: two types of synchronization measure computed by whole sample — one based only on global factor; the other based on both global and regional factor. Standard errors in parentheses.
  - Financial Openness coefficients:
    - (1) 0.0803** (0.0319)
    - (2) 0.0077 (0.0393)
    - (3) ‐0.0190 (0.0458)
    - (4) 0.1153*** (0.0261)
    - (5) 0.0786** (0.0353)
    - (6) 0.0611 (0.0431)
  - Trade Openness coefficients (all specifications):
    - (1) ‐0.0010 (0.0005)
    - (2) ‐0.0010 (0.0005)
    - (3) ‐0.0006 (0.0005)
    - (4) ‐0.0005 (0.0004)
    - (5) ‐0.0004 (0.0004)
    - (6) ‐0.0002 (0.0005)
  - Dummy for AE (Advanced Economy) coefficients:
    - (1) 0.2614** (0.0985)
    - (2) 0.2662** (0.1045)
    - (3) 0.1321 (0.0883)
    - (4) 0.1224 (0.0985)
  - dLog(Output) coefficients:
    - (5) ‐0.1578 (0.1119)
    - (6) ‐0.0881 (0.1054)
  - Inflation coefficients:
    - (5) 0.0685 (0.0880)
    - (6) 0.0071 (0.0829)
  - Constant terms:
    - (1) 0.1945** (0.0710)
    - (2) 0.1589** (0.0643)
    - (3) 0.2419 (0.1621)
    - (4) 0.2247*** (0.0579)
    - (5) 0.2067*** (0.0576)
    - (6) 0.2857 (0.1527)
  - R-squared:
    - (1) 0.2178
    - (2) 0.3862
    - (3) 0.4083
    - (4) 0.4249
    - (5) 0.4555
    - (6) 0.4202
  - Number of countries: 25
  - Significance notation: *** p<0.01, ** p<0.05

### Analytical highlights (as presented)
- Financial Openness is generally associated with higher house price synchronization across specifications in both panel and cross-sectional analyses, with several coefficients statistically significant at conventional levels (examples: 0.06691**, 0.06220***, 0.07481**, 0.0803**, 0.1153***).
- Trade Openness shows small positive coefficients in the panel regressions (e.g., 0.00911**, 0.01096***) and near-zero or negative coefficients in the cross-sectional regressions (e.g., ‐0.0010).
- Larger output (Log(Output)) is positively associated with synchronization in multiple panel specifications (e.g., 0.39513**, 0.40820***).
- The variance of the idiosyncratic factor enters with negative coefficients in some panel specifications (e.g., ‐0.16292*), suggesting higher idiosyncratic volatility is associated with lower synchronization in those specifications.
- Advanced economy dummy (Dummy for AE) is positive and significant in some cross-sectional specifications (e.g., 0.2614**, 0.2662**).

*Source: Appendix 1. Data Sources and Country Coverage (wp18209 - Appendix 1. Data Sources and Country Coverage).*

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_Source: https://www.imf.org/-/media/files/publications/wp/2018/wp18209.pdf_