## _wp15276

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---

### Introduction and Executive Findings
- Main finding: the large role of the value of housing collateral in driving the secular trend in household debt since financial liberalization in the mid 1980s.
- Housing prices:
  - In October 2015, house price gains reached 18 percent y/y led by apartment price rises in Stockholm and Gothenburg of over 20 percent.
  - House price trends are "well explained by fundamentals" in the long run; credit growth plays a significant role in short-run dynamics.
- Household debt:
  - Household debt reached 176 percent of disposable income in September 2015 (195 percent including housing associations).
  - Net wealth of Swedish households rose to 490 percent of disposable income in mid-2015, up from 200 percent at the end of the crisis in the 1990s.
  - Aggregate loan-to-value ratio proxied by debt-to-housing-assets is "close to a historic low at less than 50 percent."
- Interaction summary:
  - Two-way short-run interaction: housing prices raise collateral value, easing borrowing and increasing household debt; credit increases feed back into housing price momentum.
  - Long run: debt is not a long-run driver of housing price equilibrium (life-cycle model property).

### Housing and Mortgage Market Analysis (Sweden)
- Demand and supply drivers:
  - Rising incomes and demographics increased housing demand.
  - Housing supply shaped by changes in government support for construction and the mid-1980s boom-bust cycle.
  - Rent controls have limited availability of rental housing and encouraged conversion of rental apartments to tenant ownership.
- Construction and completions:
  - By 1991, dwelling completions were "more than double their average level in mid-1980s."
  - Completions in 1995 were only 19 percent of the peak 4 years earlier.
  - 1985–1991: stock rose by less than 182,000 new homes while total completions were almost 309,000.
- Metropolitan imbalance and tenure:
  - 85 percent of the 290 municipalities reported a shortage of rented accommodation in 2013.
  - Between 1991 and 2011, three rented dwellings were converted for each new rented dwelling built in Stockholm.
  - Home ownership share rose by 8 percentage points between 1990 and 2014.
- Tax and policy environment:
  - Mortgage interest deductibility: 58 percent in 1980; 54 percent by 1987; 40 percent in 1988; cut to 30 percent in 1991.
  - Swedish property tax virtually abolished in 2008; mortgage interest deductibility of 30 percent encourages home buying and reduces incentive to amortize.
  - European Commission’s 2014 index: fiscal environment supports home ownership in Sweden more than in other European countries.

### Modeling Framework and Key Equations
- System overview: three-equation model with endogenous residential investment capturing:
  - Housing prices (p), real household debt per capita (d), residential investment scaled by GDP (inv).
- Long-run housing price (cointegrating) equation:
  - p* = f(hs, X) where X includes di, RR, fa, dem.
  - Expected signs: di, fa, dem positive; hs and RR negative.
- Short-run housing price dynamics (ECM):
  - Includes lagged ECM, lags of Δp, Δd, Δdi, and R; allows momentum and credit-driven amplification.
- Long-run household debt equation:
  - d* driven mainly by hv (housing value per capita) and RR.
  - hv incorporates housing prices, stock, and home tenure effects.
- Short-run debt dynamics:
  - ECM with lagged Δd, Δp, and ΔR.
- Residential investment (supply) equation:
  - inv = function(Tobin’s Q, time trend t).
  - hs_t = hs_{t-1} + completions (completions assumed proportional to inv based on past-decade average).
- Identification:
  - Long run: housing prices not affected by debt.
  - Short run: mutual feedbacks allowed.

### Data, Estimation, and Statistical Properties
- Sample: quarterly data over 1980q1-2015q2.
- Estimation methods:
  - Long-run: Dynamic Ordinary Least Squares (DOLS) with one lead and one lag of differences.
  - Short-run: Error Correction Models (ECM) via general-to-specific approach.
  - Robustness: FMOLS and CCR also considered.
- Variable construction and transforms:
  - p: composite real housing price index (Valueguard from 2005q1 backdated to 1986q1 using Statistics Sweden and to 1980q1 using OECD). Seasonally adjusted; rebased to 1980q1.
  - hs, di, fa, dem, d, hv per capita; p, inv, GDP seasonally adjusted.
  - Real variables deflated by CPIFX.
  - Lower-case variables in logs; RR and R in percent.
- Time-series properties:
  - Unit root tests indicate variables are I(1); first differences stationary.
- Implementation:
  - DOLS residuals used to build ECM terms; cointegration residuals reject unit root.

### Empirical Findings — Long Run and Short Run
- Long-run drivers of housing prices (Table 5; standard errors in parentheses):
  - di: 1.295 (0.041)*** 
  - hs: -1.524 (0.295)*** 
  - RR: -0.040 (0.002)*** 
  - fa: 0.076 (0.009)*** 
  - dem: 0.071 (0.005)*** 
  - Constant: 4.161 (1.149)***
  - Observations: 139; Adjusted R-squared: 0.967; S.E. of regression: 0.061.
- Interpretation:
  - Income elasticity of housing: 1.295.
  - Housing stock semi-elasticity: -1.524.
  - Interest rate semi-elasticity: -0.040 (implies a 4 percent increase in real housing prices from a 1 percentage point decrease in interest rates).
  - Long-run standard error is 2%; model explains 97% of variance in level real housing prices.
- Decomposition:
  - Real disposable income growth predominant driver of housing prices, especially since 2000.
  - As of 2015q2, prices estimated some 5.5 percent above long-run equilibrium.
- Cointegration and stability:
  - Engle-Granger tau-statistic: -6.35; Phillips-Ouliaris tau-statistic: -6.54; probabilities 0.00.
  - Hansen Instability Lc-statistic: 0.49 (Probability: >0.2).

- Short-run housing price dynamics (Table 7; standard errors in parentheses):
  - ecm-p-1: -0.083 (0.018)*** (implies ~30 percent correction over 1 year; ~65 percent over 3 years).
  - Δp-1: 0.241 (0.079)***.
  - Δp-4: 0.262 (0.083)***.
  - Δd-2: 0.214 (0.098)**.
  - Δd-3: 0.154 (0.085)*.
  - Δdi: 0.262 (0.088)***.
  - ΔR-1: -0.010 (0.004)**.
  - Observations: 137; Adjusted R-squared: 0.480; S.E. of regression: 0.018.
  - Sum of lagged persistence > 0.5.
  - Debt growth effect: sum of Δd-2 and Δd-3 implies a 1 percentage point acceleration in lending has a first-round impact of just under 0.4 percent on housing prices.

- Long-run drivers of household debt (Table 8):
  - hv: 0.470 (0.036)***.
  - RR: -0.030 (0.012)**.
  - Constant: 0.792 (0.416)*.
  - Observations: 139; Adjusted R-squared: 0.950; S.E. of regression: 0.084.
  - Interpretation: 1 percent increase in housing valuation raises household debt by just under 0.5 percent in the long run.
  - Semi-elasticity to RR: 1 percentage point cut in rates associated with 3 percent increase in household debt in equilibrium.
  - Indirect effect via prices leads system to imply a 1 percentage point interest rate change results in a long-run decline in household debt of almost 5 percent (before housing supply response).
  - Housing loans ≈ 82 percent of total lending to households as of August 2015.

- Short-run debt dynamics (Table 9):
  - ecm-d-1: -0.027 (0.013)** (≈10 percent of disequilibria corrected over one year).
  - Δd-2: 0.125 (0.074)*.
  - Δd-4: 0.632 (0.105)***.
  - Δp-1: 0.096 (0.045)**.
  - ΔR: -0.009 (0.004)**.
  - Observations: 137; Adjusted R-squared: 0.579; S.E. of regression: 0.011.
  - Persistence in debt growth high; lag sum = 0.76.
  - Real household debt deviation from trend: 6.3 percent (historical peak 18.5 percent before 1990s crisis).

### Housing Supply Responsiveness and Residential Investment
- Residential investment regression (Table 10):
  - Q coefficient: 0.017 (0.002)***.
  - Time trend t: -0.016 (0.001)***.
  - Constant: 2.396 (0.098)***.
  - Observations: 142; Adjusted R-squared: 0.766; S.E. of regression: 0.2056.
- Interpretation:
  - A 10 percent increase in house prices relative to costs results in a 17 percent rise in residential investment to GDP.
  - Housing stock responds sluggishly; time trend may proxy for omitted variables (land prices, planning, rent controls, reduced state support).

### Housing Supply and Rent Controls (Box 1 summary)
- Housing shortages described as "large and rising, especially in urban areas."
- Estimates of shortage:
  - Swedish National Board of Housing, Building and Planning: between 90,000 and 160,000 homes (≈ one-third concentrated in Stockholm).
  - Stockholm Chamber of Commerce: deficit around 120,000 homes in Stockholm region.
  - Housing Crisis Committee (2014): up to 156,000 dwellings; more than half in Stockholm, Goteborg, and Malmo.
  - Housing Europe (2015): up to 276,000 dwellings needed for 2008–2013 population increase; projects shortage to reach 436,000 dwellings by 2020.
  - Housing Ministry: more than 350,000 young adults without a home; increase of 18 percent in two years (Svenska Dagbladet, July 29, 2015).
- Structural features and mechanisms:
  - Rent controls keep rent below market, produce market rigidity, skew demand toward older/attractive urban dwellings, and create lock-in effects that impede mobility.
  - Municipal housing companies own almost half of rental stock; public housing ≈ 20 percent of total housing stock; "every seventh Swede lives in public housing."
  - Swedish model characterized as "universalistic" with no social housing; rent controls substitute for targeted social housing.

### Policy Simulations and Quantitative Impacts
- Government housing completion plan:
  - Target: cumulative dwelling completions ≈ 250,000 by 2020.
  - Simulation: additions raised by 20,000 units each year from 2017 to 2019 → 1.3 percent addition to housing stock → reduces real housing prices by 1.4 percent by 2020.
- Mortgage interest deductibility:
  - Current: deductibility of 30 percent on mortgage interest costs up to 100,000 krona; amounts over that deducted at 21 percent.
  - Cost: deductibility currently costs about ½ percent of GDP annually.
- Simulation 1 (immediate reduction 30 → 20 percent over 1 year):
  - Max decrease in real housing prices relative to baseline: 1.4 percent after 4 years.
  - Max decrease in real household debt relative to baseline: 2 percent after 7 years.
- Simulation 2 (phasing-out deductibility by 5 ppts p.a. over 6 years):
  - Max decrease in real housing prices relative to baseline: 4 percent after 8 years.
  - Max decrease in real household debt relative to baseline: 5.5 percent after 11 years.
  - Modest impacts partly due to current low interest rates.
- Simulation 3 (prolonged low interest rates):
  - Baseline: low rates for 2 years before normalizing; shock: low rates persist for 5 years.
  - Real housing prices and real household debt increase by 8 and 7 percent more over 3 years before normalization.
  - Max increase relative to baseline: housing prices 8 percent after 3 years; household debt 7 percent after 3 years.
  - Implication: larger misalignment increases likelihood of more difficult adjustment at normalization; supports arguments for unconventional policies to raise inflation and for macroprudential measures.

### Outlook and Model Projections (2015–2020 assumptions and results)
- Model assumptions for 2015–2020:
  - Real disposable income per capita: increase 1.8 percent p.a.
  - Financial assets per capita: rise 7 percent p.a.
  - Net migration: rise 5 percent p.a.
  - Construction costs: rise 2.5 percent p.a.
  - Population projection: Statistics Sweden; GDP growth path: NIER.
- Under assumptions:
  - Real housing price growth slows from 12.3 percent in 2015q2 to about 3.5 percent.
  - Growth in household debt little changed at about 3 percent in real per capita terms (vs. 3.5 percent in 2015q2).
  - Debt-to-disposable-income ratio expected to exceed 190 percent by 2020.
  - Model-implied debt-to-income trajectory rises more slowly than Sveriges Riksbank forecasts (September 2015 Monetary Policy Report).

### Conclusions and Policy Implications
- Reassessment emphasizes collateral channel as key to household debt trends.
- Main conclusions:
  - Modest housing price overvaluation (model-specific); more likely a price deceleration than a decline.
  - Adjustment to equilibrium is gradual, especially for household debt, permitting significant divergences from equilibrium.
  - Historical 1990s bust occurred when prices and debt were both significantly above estimated equilibrium levels.
- Policy-relevant recommendations:
  - Government policies to gradually increase housing stock by 2020 are helpful with limited downside to prices.
  - Phasing out mortgage interest deductibility eases demand pressures with manageable impact on prices and modest decline in household debt.
  - A prolonged period of low real mortgage rates increases the risk of a difficult adjustment at normalization; strengthen case for:
    - Returning inflation to target more quickly (including unconventional policies to raise inflation if needed).
    - Considering macroprudential tools such as amortization requirements and debt-to-income ceilings.

*Source: _wp15276 - References*

### REFERENCES ___________________________________________________________37

### _wp15276 - REFERENCES ___________________________________________________________37

### BOX
- 1. Housing Supply and Rent Controls in Sweden  _________________________________41

### FIGURES
- 1. Real Housing Prices, Household Debt, and Disposable Income  _____________________4
- 2. Growth in Real Housing Prices and Real Household Debt Per Capita_________________5
- 3. Housing Completions and Change in Population _________________________________7
- 4. Residential Investment _____________________________________________________8
- 5. Housing Supply: Sweden vs. Urban cities  ______________________________________8
- 6. Type of Dwellings_________________________________________________________9
- 7. Tenure of Apartments ______________________________________________________9
- 8. Household Debt to Disposable Income ________________________________________10
- 9. Household Debt Ratios ____________________________________________________11
- 10. Household Debt  ________________________________________________________11
- 11. Tax Incentives for Home Ownership  ________________________________________12
- 12. Conceptual Overview:3-Equation Model   ____________________________________20
- 13. Real Housing Prices: Actual vs. Long Run Fitted    _____________________________24
- 14. Housing Price Model Predictability  _________________________________________24
- 15. Contribution of Fundamentals to Housing Prices   ______________________________26
- 16. Housing Price Deviation from Fundamentals    ________________________________27
- 17. Real Household Debt: Actual vs. Long Run Fitted  _____________________________30
- 18. Contribution of Fundamentals to Household Debt   _____________________________30
- 19. Household Debt Deviation from Fundamentals     ______________________________30
- 20. Dynamics: Growth in Real Housing Prices and Real Household Debt    _____________32
- 21. Outlook for the Debt-to-Income Ration   _____________________________________32
- 22. Impact of Increasing Housing Supply on Real Housing Prices    ___________________34
- 23. Simulation 1: Mortgage Deductibility Reduction from 30 to 20 percent over 1 year  ___35
- 24. Simulation 2: Phasing-Out Mortgage Deductibility by 5 ppts p.a. over 6 years    ______35
- 25. Simulation 3: Normalization after a Prolonged Period of Low Interest   _____________36

### TABLES
- 1. Brief Summary of the Literature _____________________________________________14
- 2. Variables Definition and Data Sources ________________________________________21
- 3. Summary Statistics _______________________________________________________22
- 4. Unit Root Tests __________________________________________________________22
- 5. LR Cointengrating Relationship: Real Housing Prices  ___________________________23
- 6. Selected Findings from the Literature _________________________________________25
- 7. Short-Run Dynamics: Real Housing Prices  ____________________________________27
- 8. LR Cointegrating Relationship: Real Household Debt ____________________________29
- 9. Short-Run Dynamics: Real Household Debt  ___________________________________31
- 10. Residential Investment ___________________________________________________33

### ANNEX
- I. Robustness Checks  _______________________________________________________42

*Source: _wp15276 - REFERENCES ___________________________________________________________37*

### ANNEX TABLES

### ANNEX TABLES

### Introduction and Executive Findings
- Main finding: "the large role of the value of housing collateral in driving the secular trend in household debt since financial liberalization in the mid 1980s."
- Housing prices:
  - In October 2015, house price gains reached 18 percent y/y led by apartment price rises in Stockholm and Gothenburg of over 20 percent.
  - House price trends are "well explained by fundamentals" in the long run, though credit growth plays a significant role in the short-run dynamics of housing prices.
- Household debt:
  - Household debt reached 176 percent of disposable income in September 2015 (195 percent including housing associations).
  - Net wealth of Swedish households rose to 490 percent of disposable income in mid-2015, up from 200 percent at the end of the crisis in the 1990s.
  - Aggregate loan-to-value ratio proxied by debt-to-housing-assets is "close to a historic low at less than 50 percent."
- Interaction summary:
  - Two-way short-run interaction is allowed: housing prices raise collateral value which eases borrowing and increases household debt; increases in credit feed back into housing price momentum.
  - Long-run structure preserves life-cycle model property: debt is not a long-run driver of housing price equilibrium.

### Housing and Mortgage Market Analysis (Sweden)
- Supply and demand drivers:
  - Rising incomes and demographics increased housing demand over past decades.
  - Housing supply growth shaped by changes in government support for construction and the mid-1980s boom-bust cycle.
  - Rent controls have limited availability of rental housing and encouraged conversion of rental apartments to tenant ownership.
- Construction and completions:
  - By 1991, dwelling completions were "more than double their average level in mid-1980s."
  - Completions in 1995 were only 19 percent of the peak 4 years earlier.
  - The 1980s/early 1990s boom produced excess completions: stock rose by less than 182,000 new homes between 1985 and 1991 while total completions were almost 309,000.
- Metropolitan imbalance and tenure:
  - The shortage of beds in major cities is "substantial" despite accounting for past surpluses.
  - 85 percent of the 290 municipalities in Sweden reported a shortage of rented accommodation in their area in 2013.
  - Between 1991 and 2011, a large-scale conversion occurred: "three rented dwellings were converted for each new rented dwelling built in Stockholm."
  - Home ownership (share of rentals declined) rose by 8 percentage points between 1990 and 2014.
- Tax and policy environment:
  - Mortgage interest deductibility was reduced to 30 percent in 1991, down from 58 percent in 1980, leading to a substantial rise in after-tax mortgage rates at that time.
  - The Swedish property tax was virtually abolished in 2008; mortgage interest deductibility of 30 percent encourages home buying and reduces incentive to amortize principal.
  - According to the European Commission’s 2014 index, the fiscal environment supports home ownership in Sweden more than in other European countries.

### Empirical Evidence and Literature Context
- Comparative and prior findings:
  - Studies for Sweden report varied semi-elasticities of housing prices with respect to interest rates, ranging from close to 0 percent to as high as 6 percent in Claussen (2013).
  - Cross-country and country studies (Finland, Norway, Spain, Ireland) document two-way interactions between housing prices and mortgage credit; this paper provides similar evidence for Sweden.
- Collateral channel:
  - Literature (Kiyotaki and Moore, 1997; Iacoviello, 2004; Aoki et al., 2004) shows collateral value amplifies borrowing and can generate financial accelerator effects; this paper assesses importance of collateral via the value of the housing stock per capita.
- Supply feedback:
  - Rising prices increase profitability of construction and, over time, expand housing stock; slow supply response (due to planning, zoning, regulations) allows persistent price misalignments.

### Modeling Framework and Key Equations
- Model overview: three-equation system with endogenous residential investment, capturing:
  - Housing prices (p)
  - Real household debt per capita (d)
  - Residential investment scaled by GDP (inv)
- Long-run housing price equation (cointegrating relationship):
  - Long-run real housing price p* is a function of housing stock hs and demand shifters X (real household disposable income per capita di, real after-tax mortgage interest rate RR, real household financial assets net of liabilities per capita fa, net migration inflows per capita dem).
  - Expected signs: income, financial wealth, demographics positive; hs and RR negative.
- Short-run housing price dynamics (ECM specification):
  - Includes lagged ECM term, lags of changes in p, changes in real debt per capita d, di, and after-tax nominal mortgage rate R.
  - Allows momentum/expectation effects and credit-driven short-run amplification.
- Long-run household debt equation:
  - Long-run equilibrium real household debt per capita d* is driven mainly by value of housing per capita hv (in logs) and RR.
  - hv accounts for both housing prices and the housing stock and incorporates rising home ownership effects.
- Short-run household debt dynamics:
  - Include lagged ECM term, lagged changes in debt, changes in housing prices, and after-tax mortgage rate R.
- Residential investment (supply) equation:
  - inv = function of Tobin’s Q (ratio of housing prices to construction costs) and time trend t.
  - Housing stock identity: hs_t = hs_{t-1} + completions (completions assumed multiple of residential investment based on past-decade average).
- Identification of interactions:
  - Long run: housing prices not affected by debt (consistent with life-cycle framework).
  - Short run: mutual feedbacks allowed—debt growth affects prices and prices affect debt.

### Data, Estimation, and Statistical Properties
- Sample and frequency:
  - Quarterly data over 1980q1-2015q2.
- Estimation methods:
  - Long-run (cointegrating) regressions estimated by Dynamic Ordinary Least Squares (DOLS) including one lead and one lag of differences.
  - Short-run dynamics estimated via Error Correction Models (ECM) using a general-to-specific approach for parsimonious specification.
- Variable definitions and transformations:
  - Composite real housing price index p includes both houses and apartments; based on Valueguard data back to 2005 and backdated using Statistics Sweden and OECD.
  - hs, di, fa, dem, d, and hs considered on a per capita basis; p, residential investment, and GDP are seasonally adjusted.
  - Real variables deflated by CPIFX (consumer price index at fixed interest costs and excluding energy).
  - Lower-case variables are in logs; RR and R are in percent.
- Time series properties:
  - Unit root tests indicate variables are I(1); first differences are stationary.
- Implementation notes:
  - DOLS residuals used to construct ECM terms; presence of unit root rejected for residuals.
  - The model allows simulation of shocks (e.g., negative interest rate shock raises p via RR and R, increases hv, eases collateral constraint, raises d, feeds back into p; expanded inv eventually damps prices).

*Source: _wp15276 - ANNEX TABLES*

### Annex I provides a number of robustness checks, including sensitivity of the results to the estimation method.

### _wp15276 - Annex I provides a number of robustness checks, including sensitivity of the results to the estimation method.

### Robustness checks
- Robustness checks allow for additional leads and lags in the estimation.
- Alternative estimation methods considered include fully modified ordinary least squares (FMOLS) and canonical correlation (CCR).

### Data sources and variable definitions (selected)
- Housing Price, p — Valueguard. From 2005q1, 2004=100. Backdated to 1986q1 using Statistics Sweden data and to 1980q1 using OECD data. Seasonally adjusted; rebased to 1980q1.
- Household Disposable Income, di — Haver. From 1980q1. Seasonally adjusted, real, per capita, in logs.
- Household Debt, d — Haver; Riksbank. From 1996q1 backdated to 1980q1 using Riksbank series; adjusted for jump in 2001q1. Seasonally adjusted, real, per capita, in logs.
- Housing Value, hv — Riksbank; Statistics Sweden. From 1980q1. Cross product of value of household real assets and home tenure. Seasonally adjusted, per capita, in logs.
- Household Financial Assets Net of Liabilities, fa — Haver. From 1996q1, backdated to 1980q1 using Riksbank series with liabilities adjusted for 2001q1 jump. Seasonally adjusted, real, per capita, in logs.
- After-Tax Mortgage Rate, real RR and nominal R — Riksbank. Since 1980q1. In percent.
- Housing Stock, hs — Statistics Sweden. From 1980q1. Annual number of dwellings for 1980, 1985, and annual data since 1990. Backdated using quadratic match average and interpolated to quarterly frequency using Statistics Sweden quarterly completions. Per capita, in logs.
- Tobin’s Q — Statistics Sweden. From 1980q1. Ratio of housing price to construction costs (1968=100, rebased to 1980q1).
- Investment to GDP, inv — OECD; Statistics Sweden. From 1980q1. Ratio of residential investment to GDP. Seasonally adjusted, in logs.
- CPIFX — Statistics Sweden. From 1987q1. Consumer prices at fixed interest costs and excluding energy, backdated to 1980q1. In percent.
- Population — Statistics Sweden. From 1980q1. Annual data interpolated to quarterly frequency until 2005, with quarterly data until 2015q1. In thousands.
- Net migration, dem — Haver. From 1980q1. Difference between immigration and emigration flows. Annual data interpolated to quarterly frequency. Per capita, in logs.

### Summary statistics (selected)
- First difference in real housing prices (Δp): Obs 141, Mean 0.010, Max 0.01, Min -0.08, Std. Dev. 0.02, Jarque-Bera Prob. 0.01, 1st order autocorr 0.51 *
- First difference in real disposable income pc (Δdi): Obs 141, Mean 0.000, Max 0.05, Min -0.05, Std. Dev. 0.02, Jarque-Bera Prob. 0.00, 1st order autocorr -0.33 *
- First difference in real debt pc (Δd): Obs 141, Mean 0.010, Max 0.07, Min -0.07, Std. Dev. 0.02, Jarque-Bera Prob. 0.000, 1st order autocorr 0.22 *
- First difference in after-tax mortgage rate (ΔR): Obs 141, Mean -0.04, Max 1.94, Min -1.17, Std. Dev. 0.44, Jarque-Bera Prob. 0.000, 1st order autocorr 0.11
- Note: * Significant at the 1 percent level. “D” refers to first difference; pc refers to “per capita”.

### Unit root tests (selected results)
- ADF, PP, and KPSS tests reported for levels and first differences for variables p, di, hs, RR, fa, dem, d, hv.
- In levels some t-ADF statistics are above critical values shown (e.g., p: t-ADF -1.66; di: -2.14; fa: -3.10).
- In first differences variables largely show stationarity by ADF/PP (e.g., di first difference t-ADF -3.93; d first difference t-ADF -3.16).
- The null hypothesis for the ADF and PP tests is non-stationarity; KPSS null is stationarity.

### Empirical findings — long-run drivers of housing prices
- Estimated coefficients for long-run drivers have signs consistent with priors and are statistically significant (table 5).
- Key long-run coefficient estimates (LR Cointegrating Relationship: Real Housing Prices; standard errors in parentheses):
  - di: 1.295 (0.041)*** 
  - hs: -1.524 (0.295)*** 
  - RR: -0.040 (0.002)*** 
  - fa: 0.076 (0.009)*** 
  - dem: 0.071 (0.005)*** 
  - Constant: 4.161 (1.149)***
- Observations: 139
- Adjusted R-squared: 0.967
- S.E. of regression: 0.061
- Standard errors in parentheses. *** p<0.01, ** p<0.05, * p<0.1

### Cointegration and stability tests
- Engle-Granger / Phillips-Ouliaris:
  - tau-statistic: -6.35 (Engle-Granger), -6.54 (Phillips-Ouliaris)
  - Probability: 0.00 (Engle-Granger tau), 0.00 (Phillips-Ouliaris tau)
  - z-statistic: -46.87 (Engle-Granger), -52.31 (Phillips-Ouliaris)
  - Probability: 0.01 (Engle-Granger z), 0.00 (Phillips-Ouliaris z)
- Hansen Instability:
  - Lc-statistic: 0.49
  - Probability: >0.2

### Interpretation of coefficients and comparisons
- Income elasticity of housing is 1.295 (above unity), similar to Claussen (2013).
- Housing stock semi-elasticity: -1.524 — lies between Barot and Yang (2002) (-0.3) and Caldera Sánchez and Johansson (2011) (-3).
- Interest rate semi-elasticity: -0.040 — implies a 4 percent increase in real housing prices from a 1 percentage point decrease in interest rates.
- Long-run standard error is 2% and 97% of the variance in the level in real housing prices is explained by the model.

### Literature comparison (selected entries from Table 6)
- Hort (1998), Sweden, Real after-tax mortgage rate, 1967-1994: LR effect of a 1% decrease in interest rates = 2.9%.
- Barot (2001), Sweden, Real after-tax LR govt interest rate, 1970h1-1997h2: LR effect 1.4%, SR effect 3.3%, ECM coefficient -0.32, Yearly adjustment 32%.
- Claussen (2013), Sweden, Real after-tax mortgage rate, 1986q1-2011q2: LR effect 6.0%, SR effect 0.5%, ECM coefficient -0.08, Yearly adjustment 32%.
- Turk (2015), Sweden, Real after-tax mortgage rate, 1980q1-2015q2: LR effect 4.0%, SR effect 1.0%, ECM coefficient -0.08, Yearly adjustment 32%.
- Andrews (2010), OECD panel, Real LR interest rate, 1975q1-2007q2: LR effect 0.9%, ECM coefficient -0.04, Yearly adjustment 16%.

### Decomposition of drivers and recent assessment
- Decomposition shows real disposable income growth is the predominant driver of housing prices, especially since the turn of the century.
- The sharp increase in the real after-tax mortgage rate in the early 1990s accounts for the largest part of the house price bust in that period.
- As of 2015q2, housing prices are estimated to be some 5.5 percent above the long-run equilibrium implied by estimates of equation 1, described as a relatively modest deviation compared to a historical peak.

*Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2015/_wp15276.pdf*

### 14.3 percent prior to the 1990s bust.

### _wp15276 - 14.3 percent prior to the 1990s bust.

### Housing valuation and overvaluation assessment
- Real interest rates are currently "1.5 percentage points below their average since 2000".
- A full reversal of real interest rates would lower housing prices by "6 percent in equilibrium" based on the semi-elasticity on RR of "-0.04" from table 5.
- Combining estimates suggests an overvaluation in the housing market of "up to 12 percent".
- Recursive regressions of different window length (not reported) show stability in estimated residuals, suggesting valuation assessment is not unduly sensitive to the sample period.

### Short-run dynamics of housing prices
- Error correction coefficient (ecm-p-1) from Table 7: "-0.083" (standard error (0.018)***).
  - Implies correction of around "30 percent of disequilibria over 1 year" and about "65 percent over 3 years".
- Lagged dynamics and estimated coefficients from Table 7 (Δ denotes first difference):
  - Δp-1: "0.241" (0.079)***.
  - Δp-4: "0.262" (0.083)***.
  - Δd-2: "0.214" (0.098)**.
  - Δd-3: "0.154" (0.085)*.
  - Δdi: "0.262" (0.088)***.
  - ΔR-1: "-0.010" (0.004)**.
  - Constant: "0.001" (0.002).
  - Observations: "137". Adjusted R-squared: "0.480". S.E. of regression: "0.018".
- Housing price growth shows significant persistence; lagged coefficients sum to more than "0.5".
- Disposable income impacts price dynamics contemporaneously and via the error correction term.
- The second lag of the change in the after-tax mortgage rate accelerates the impact of interest rates on housing prices via the error correction term.
- Debt growth leads housing price adjustments:
  - Sum of coefficients on Δd-2 and Δd-3 implies a "1 percentage point acceleration in lending to households has a first round impact of just under 0.4 percent on housing prices".
  - Persistence in housing prices and debt growth means dynamic effects may persist for some years.

### Long-run relationship and drivers of household debt
- Table 8 (LR cointegrating relationship: Real Household Debt) estimates:
  - HH housing value pc: "0.470" (0.036)***.
  - Real after-tax rate: "-0.030" (0.012)**.
  - Constant: "0.792" (0.416)*.
  - Observations: "139". Adjusted R-squared: "0.950". S.E. of regression: "0.084".
- A "1 percent increase in the valuation of housing that is owned by households raises household debt by just under 0.5 percent in the long run".
- Semi-elasticity of borrowing to the real after-tax interest rate: a "1 percentage point cut in rates is associated with 3 percent increase in household debt in equilibrium".
- Allowing for the indirect impact via house prices, the system implies a "1 percentage point change in interest rates results in a long-run decline in household debt of almost 5 percent" (before accounting for housing supply response).
- Swedish household debt composition: housing loans represent "around 82 percent of total lending to households as of August 2015".
- Cointegration test statistics reported: Engle-Granger / Phillips-Ouliaris tau-statistic "-3.83" and "-3.55" with probabilities "0.05" and "0.09"; z-statistic "-17.78" and "-14.10" with probabilities "0.18" and "0.34". Hansen instability Lc-statistic "0.01" with Probability ">0.2".

### Debt dynamics and deviations from fundamentals
- Real household debt deviation from long-term trend stands at "6.3 percent".
  - Historical peak deviation was "18.5 percent" in the run-up to the 1990s crisis; current misalignment is about one-third of that peak.
- Short-run dynamics of real household debt (Table 9):
  - Error correction term (ecm-d-1): "-0.027" (0.013)**.
    - Implies around "10 percent of debt disequilibria are corrected over one year".
  - Δd-2: "0.125" (0.074)*.
  - Δd-4: "0.632" (0.105)***.
  - Δp-1: "0.096" (0.045)**.
  - ΔR: "-0.009" (0.004)**.
  - Constant: "0.001" (0.001).
  - Observations: "137". Adjusted R-squared: "0.579". S.E. of regression: "0.011".
- Persistence in debt growth is high; coefficients on lagged dependents sum to "0.76".
- Housing collateral is the greatest contributor to trends in household debt; rising value of privately owned housing stock explains most increases in household debt.
- Real after-tax interest rate had largest effect on debt in the 1980s; recent decline in interest rates makes a modest direct contribution to debt increases.

### Housing supply responsiveness and residential investment
- Residential investment response (Table 10):
  - Q coefficient: "0.017" (0.002)***.
  - Time trend (t): "-0.016" (0.001)***.
  - Constant: "2.396" (0.098)***.
  - Observations: "142". Adjusted R-squared: "0.766". S.E. of regression: "0.2056".
- A "10 percent increase in house prices relative to costs results in a 17 percent rise in residential investment to GDP".
- Housing stock responds sluggishly; positive investment response requires increasingly high prices relative to construction costs over time.
- Time trend may proxy for omitted variables such as land prices, complex land and planning processes, rent controls, and reduced state support for financing construction.

### Policy simulations and quantitative impacts
- Government plan to raise cumulative dwelling completions to about "250,000 by 2020".
  - Simulation assumption: additions to housing stock raised by "20,000 units each year from 2017 to 2019".
  - Reaching the government's target implies a "1.3 percent addition to the housing stock" and is estimated to reduce real housing prices by only "1.4 percent by 2020".
- Mortgage interest deductibility context:
  - Current deductibility: borrowers can deduct "30 percent" on mortgage interest costs up to 100,000 krona (above capital income); amounts over that deducted at "21 percent".
  - Tax deductibility currently costs about "½ percent of GDP annually".
  - Historical deductibility: "58 percent in 1980", "54 percent by 1987", "40 percent in 1988", cut to "30 percent in 1991".
- Simulation 1: Immediate reduction of deductibility from "30 to 20 percent" over 1 year:
  - Maximum decrease in real housing prices relative to baseline: "1.4 percent" after 4 years.
  - Maximum decrease in real household debt relative to baseline: "2 percent" after 7 years.
- Simulation 2: Phasing-out deductibility by "5 ppts p.a. over 6 years":
  - Maximum decrease in real housing prices relative to baseline: "4 percent" after 8 years.
  - Maximum decrease in real household debt relative to baseline: "5.5 percent" after 11 years.
  - Modest estimated impacts partly due to current low level of interest rates.
- Simulation 3: Prolonged low interest rates scenario:
  - Baseline: interest rates remain low for "2 years before normalizing"; shock scenario: low rates persist for "5 years".
  - Real housing prices and real household debt would increase by "8 and 7 percent more over the 3 years before interest rates begin to normalize".
  - Maximum increase of housing prices relative to baseline: "8 percent" after 3 years.
  - Maximum increase of household debt relative to baseline: "7 percent" after 3 years.
  - Implication: larger misalignment increases likelihood of more difficult adjustment to interest normalization; arguments for unconventional policies to raise inflation more quickly and for considering macroprudential measures.

### Outlook and model-projected trajectories
- Model projection assumptions noted for 2015–2020 simulations:
  - Real disposable income per capita assumed to increase by "1.8 percent p.a.".
  - Financial assets per capita assumed to rise by "7 percent p.a.".
  - Net migration assumed to rise by "5 percent p.a.".
  - Construction costs assumed to rise by "2.5 percent p.a.".
  - Population projection from Statistics Sweden; growth path of GDP from NIER.
- Under model assumptions:
  - Real housing price rises would slow from "12.3 percent in 2015q2" to about "3.5 percent" to be more consistent with growth in incomes and financial assets.
  - With house price growth easing, growth in household debt would remain little changed at about "3 percent in real per capita terms", compared to "3.5 percent in 2015q2".
  - Ratio of debt to disposable income is expected to "exceed 190 percent by 2020".
  - Model-implied debt-to-income trajectory rises at a slower pace compared to Sveriges Riksbank forecasts in the September 2015 Monetary Policy Report.

### Conclusions and policy implications
- The paper revisits linkages between housing and household debt, emphasizing the collateral channel.
- Findings: modest housing price overvaluation (model-specific); projection suggests a housing price deceleration is more likely than a decline.
- Adjustment to equilibrium is gradual, especially for household debt, allowing scope for significant divergences from equilibrium.
- Historical note: the major housing bust in the early 1990s occurred when housing prices and debt were both significantly above estimated equilibrium levels.
- Policy-relevant conclusions:
  - Government policies to gradually increase housing stock by 2020 are helpful and not expected to produce significant downside to housing prices.
  - Phasing out mortgage interest deductibility helps ease demand pressures with manageable impact on housing prices and modest decline in household debt.
  - A more prolonged period of low real mortgage interest rates increases the potential for a more difficult adjustment to normalization, strengthening the case for:
    - Returning inflation to target more quickly (including unconventional policies to raise inflation if needed).
    - Considering macroprudential policy measures, such as amortization requirements and debt-to-income ceilings.

*Source: IMF staff estimates and model results from the content unit _wp15276 - 14.3 percent prior to the 1990s bust.*

### References

### _wp15276 - References

### References (selected citations)
- Adams, Z. and Füss, R. (2010). “Macroeconomic Determinants of International Housing Markets.” Journal of Housing Economics 19(1), pp. 38-50.
- Andrews, D. (2010). “Real House Prices in OECD Countries: The Role of Demand Shocks and Structural and Policy Factors”. OECD Economics Department, Working Papers No. 831, OECD Publishing.
- Andrews, D., Caldera Sánchez, A. and Johansson, Å. (2011). “Housing markets and structural policies in OECD countries”, OECD Economics Department, Working Paper No. 836. OECD Publishing.
- Aoki, K., Proudman, J., and Vlieghe, G. (2004). “House Prices, Consumption, and Monetary Policy: A Financial Accelerator Approach”, Journal of Financial Intermediation 13, pp. 414-35.
- Anundsen, A. and Jansen, E. (2013). “Self-Reinforcing Effects Between Housing Prices and Credit." Journal of Housing Economics, 22(3), pp.192-212.
- Barot, B. and Takala, K. (1998). “House prices and inflation: a cointegration analysis for Finland and Sweden.” Bank of Finland Discussion Papers 12/1998.
- Barot, B. (2001). “An Econometric Demand-Supply model for Swedish Housing”. European Journal of Housing Policy 1(3), pp.417-444.
- Barot, B. and Yang, Z. (2002). “House Prices and Housing Investment in Sweden and the UK. Econometric analysis for the period 1970-1998.” Review of Urban and Regional Development studies 14(2), pp. 189-216.
- Berg, L. and Bergström, R. (1995). “Housing and Financial Wealth, Financial Deregulation and Consumption: The Swedish Case”. The Scandinavian Journal of Economics 97(3), pp. 421-439.
- Bernanke, B. and Gertler, M. (1995). “Inside the Blackbox: the Credit Channel of Monetary Policy Transmission”, Journal of Economic Perspectives 9(4), pp. 27-48.
- Bårdsen, G., den Reijer, A., Jonasson, P., and Nymoen, R. (2012). MOSES: Model for studying the economy of Sweden, Economic Modelling 29, pp. 2566-2582.
- Borio, C and Lowe, P. (2002). “Assessing the risk of banking crises.” BIS Quarterly Review, December, pp. 43–54.
- Chaney, T., Sraer, D., and Thesmar, D. (2012). “The Collateral Channel: How Real Estate Shocks Affect Corporate Investment”. American Economic Review 102:6, 2381-2409.
- Caldera Sánchez, A. and Johansson, Å. (2011). “The Price Responsiveness of Housing Supply in OECD Countries”, OECD Economics Department, Working Papers No. 837, OECD Publishing.
- Claussen, C. A. (2013). “An Error-Correction Model of Swedish House Prices.” International Journal of Housing Markets and Analysis 6(2), pp. 180 - 196.
- Collyns, C. and Senhadji, A. (2002). “Lending booms, real estate bubbles, and the Asian crisis”. IMF Working Paper 02/20. (Washington, D.C.; International Monetary Fund).
- Davis, E.P. and Zhum, H. (2011). “Bank lending and commercial property cycles: Some International Evidence.” Journal of International Money and Finance 30, pp. 1-21.
- Dennis, J.G. (2006). CATS in RATS, Cointegration Analysis of Time Series, Version 2. Estima: Evanston, Illinois.
- Emanuelsson, R. (2015). “Supply of Housing in Sweden.” Sveriges Riksbank Economic Review, 2015:2, pp. 47-75, Sveriges Riksbank, Stockholm, Sweden.
- Englund, P., Hendershott, P., and Turner, B. (1995). “The Tax Reform and the Housing Market.” Swedish Economic Policy Review 2, pp. 319-356.
- Englund, P. and Ioannides, Y. (1997). “House Price Dynamics: An International Empirical Perspective.” Journal of Housing Economics 6(2), pp. 119-136.
- Englund, P. (2015). “The Swedish 1990s banking crisis: A revisit in the light of recent experience.” Paper presented at the Riksbank Macroprudential Conference, Stockholm 23-24 June, 2015.
- European Parliament (2013). “Social Housing in the EU”. Directorate General for Internal Policies, Policy Department A: Economic and Scientific Policy, IP/A/EMPL/NT/2012-07, PE 492.469, Brussels.
- Finansinspektionen (2013). “Memorandum 1 – Explanations for the Development in Household Debt since the Mid-1990s.” Sten Hansen, Finansinspektionen, Sweden.
- Finansinspektionen (2015). “The Swedish Mortgage Market Survey 2015.” April. Finansinspektionen, Sweden.
- Finansinspektionen, Riksgälden, and Sveriges Riksbank (2015). The Driving Forces Behind Household Indebtedness in Sweden. Memorandum.
- Gerlach, S. and Peng, W. (2005). “Bank lending and property prices in Hong Kong”. Journal of Banking and Finance 29, 461–481.
- Gimeno, R. and Martinez-Carrascal, C. (2010). “The Relationship Between House Prices and House Purchase Loans: The Spanish Case.” Journal of Banking and Finance, 34, pp. 1849-55.
- Greenspan, A., Kennedy, J. (2008). Sources and uses of equity extracted from homes. Oxford Review of Economic Policy 24(1), pp. 120–144.
- Ho, G. (2015). “Housing Supply Constraints in Sweden”. Selected issues, Sweden. International Monetary Fund, Washington, D.C.; International Monetary Fund.
- Hort, K. (1998). The Determinants of Urban House Price Fluctuations in Sweden 1968-1994. Journal of Housing Economics 7(2), pp. 93.120.
- Housing Crisis Committee (2014). “A Functioning Housing Market – A Reform Agenda.” Housing Crisis Committee (Bokriskommittén), Sweden.
- Housing Europe (2015). The State of Housing in the EU. The European Federation for Public Cooperative and Social Housing, Brussels.
- Hüfner, F. and Lundsgaard, J. (2007). The Swedish Housing Market – Better Allocation via Less Regulation. OECD Economics Department Working Papers, No. 559, OECD Publishing.
- Hurst, E. and Stafford, F. (2004). “Home Is Where the Equity Is: Mortgage Refinancing and Household Consumption.” Journal of Money, Credit, and Banking 36(6), pp. 985–1014.
- Iacoviello, M. (2004). “Consumption, House Prices and Collateral Constraints: A Structural Econometric Analysis”. Journal of Housing Economics 13, pp. 304–20.
- Iacoviello, M. (2005). “House Prices, Borrowing Constraints, and Monetary Policy in the Business Cycle”. American Economic Review 95, pp. 739–64.
- International Monetary Fund (2011). Global Financial Stability Report, International Monetary Fund (September), Washington, D.C.
- Juselius, K. (2006). The Cointegrated VAR Model: Methodology and Applications. Oxford University Press, Oxford.
- Kiyotaki, N. and Moore, J. (1997). “Credit Cycles”, Journal of Political Economy 105, pp. 211–248.
- Liang, Q., Cao, H. (2007). “Property prices and bank lending in China”. Journal of Asian Economics 18, pp. 63–75.
- Lind, H. (2003). “Rent Regulation and New Construction: With a Focus on Sweden 1995-2001.” Swedish Economic Policy Review 10, pp. 135-167.
- Lustig, H. and van Nieuwerburgh, S. (2005). “Housing Collateral, Consumption Insurance, and Risk Premia: An Empirical Perspective.” Journal of Finance 60(3), pp. 1167–1219.
- Lyons, R. and J. Muellbauer (2013). “Explaining the bubble: House prices, user-cost and credit conditions in Ireland, 1975-2012.” Trinity Economics Papers.
- Meen, G. (2002). “The Time-Series Behavior of House Prices: A Transatlantic Divide?” Journal of Housing Economics 11 (1), pp. 1-23.
- Mian, A., Sufi, A. (2011). House prices, home equity-based borrowing, and the US household leverage crisis. American Economic Review 101, pp. 2132–2156.
- Muellbauer, J., Murphy, A. (2008). “Housing markets and the Economy”. Oxford Review of Economic Policy 24(1), pp.1–33.
- Oikarinen (2009a). “Interaction Between Housing Prices and Household Borrowing: The Finnish Case.” Journal of Banking and Finance 33, pp. 747–756.
- Oikarinen (2009b). “Household Borrowing and Metropolitan Housing Price Dynamics: Empirical Evidence from Helsinki.” Journal of Housing Economics 18 (2), pp. 126–139.
- Poterba, J. (1984). “Tax Subsidies to Owner-Occupied Housing: An Asset Market Approach”. Quarterly Journal of Economics 99, pp. 729–752.
- Sørensen, P. (2013). The Swedish Housing Market: Trends and Risks. Finanspolitiska rådet.
- Walentin, K. (2014). “Housing Collateral and the Monetary Transmission Mechanism.” The Scandinavian Journal of Economics 116(3), pp. 635-668.

### Box 1 — Housing Supply and Rent Controls in Sweden (summary of findings)
- Housing supply shortages in Sweden are described as "large and rising, especially in urban areas."
- Estimates of housing shortage:
  - Swedish National Board of Housing, Building and Planning: between 90,000 and 160,000 homes, with around one-third concentrated in Stockholm (Emanuelsson, 2015).
  - Stockholm Chamber of Commerce: deficit around 120,000 homes in the Stockholm region (Emanuelsson, 2015).
  - Housing Crisis Committee (2014): up to 156,000 dwellings, more than half concentrated in Stockholm, Goteborg, and Malmo.
  - Housing Europe (2015): up to 276,000 dwellings would be needed to match population increase between 2008 and 2013; projects housing shortage to reach 436,000 dwellings by 2020.
  - Housing Ministry announcement: more than 350,000 young adults are without a home, an increase of 18 percent in two years (Svenska Dagbladet, July 29, 2015).
- Structural feature: rent controls and rejection of social housing as "segregating and stigmatizing."
  - Swedish model described as "universalistic" but with no social housing; instead a complex system of rent controls makes the private rental market "the most highly regulated among other OECD countries" (Andrews, Caldera Sanchez, and Johansson, 2011).
  - Housing Crisis Committee (2014) finds rent controls have led to "the same undesired outcomes as social housing."
- Mechanisms and effects of rent controls:
  - Rent controls keep rent below market levels and result in market rigidity.
  - Benchmark for all rent derives from municipal housing stock; municipal housing companies own almost half of the rental stock and set norms following the "tenant’s value system."
  - Rent setting traditionally occurs between municipal housing companies and the Swedish Union of Tenants; since 2011 private landlords were added to negotiations but tenant-union pressure has contained rent increases.
  - Effects include skewed property demand toward older and more attractive dwellings in urban areas and lock-in effects that impede mobility and efficient utilization.
- Additional factual notes:
  - Public housing in Sweden represents almost 20 percent of the total housing stock and "every seventh Swede lives in public housing."
  - Footnotes in the box:
    - Social housing elsewhere is targeted by income ceilings or vulnerability.
    - "A high number of unemployed people live in the suburbs of the big cities."

### ANNEX I — Robustness Checks (summary)
- Major structural reforms in Sweden since mid-1980s that may induce breaks:
  - Tax reform in 1983 and 1991 (Englund and Ioannides, 1997).
  - Credit market deregulation in 1984 (Berg and Bergström, 1995).
  - Change from a fixed to a floating exchange rate in 1992 and shift to explicit inflation targeting that became operational after 1995.
- Sample choice and sensitivity:
  - Paper starts sample from 1980 to capture decline before the 1990s boom/crisis.
  - Robustness: sample reduced to after 1987 and after 1996; results qualitatively unchanged (results not shown but available from the author).
  - Recursive and reverse-recursive estimations indicate the long-run relation holds (Dennis, 2006; Juselius, 2006).
- Estimation methods and checks:
  - Primary estimator: DOLS; alternative estimators used include FMOLS and CCR.
  - Table A1 and Table A2 present results from DOLS (with variations), FMOLS, and CCR; parameter estimates are sensitive to estimator but results broadly in line with main findings.
  - Additional checks:
    - Replacing housing price index with OECD indicator revised in 2015q2.
    - Including additional determinants of household debt such as disposable income.
    - Including home tenure separately in equation 3.
    - Lagging Tobin’s Q in equation 5.
  - Findings are reported as "qualitatively unaffected."
- Notes on estimators:
  - DOLS uses leads and lags of differenced regressors to soak up long-run correlations.
  - FMOLS and CCR use semiparametric corrections to eliminate cross-correlation problems.

### Key statistics from Table A1 — Cointegrating Relationship: Real Housing Prices, Robustness Tests
- Estimation methods displayed: DOLS (1 Lead/1 Lag; 2Leads/2Lags), FMOLS, CCR.
- Selected coefficient estimates (standard errors in parentheses; significance: *** p<0.01, ** p<0.05, * p<0.1):
  - Di:
    - Column (1): 1.592 (0.197)***
    - Column (2): 1.294 (0.051)***
    - Column (4): 1.141 (0.024)***
    - Column (6): 1.530 (0.202)***
    - Column (7): 1.690 (0.285)***
    - Column (8): 1.514 (0.207)***
    - Column (9): 1.701 (0.325)***
  - Hs:
    - Column (1): -1.096 (0.557)**
    - Column (2): 1.164 (0.397)***
    - Column (4): 0.965 (0.070)***
    - Column (6): -2.783 (1.523)*
    - Column (7): -2.880 (0.900)***
    - Column (8): -2.945 (1.544)*
    - Column (9): -2.859 (0.922)***
  - RR:
    - Column (1): -0.040 (0.003)***
    - Column (2): -0.058 (0.002)***
    - Column (4): -0.059 (0.000)***
    - Column (6): -0.031 (0.009)***
    - Column (7): -0.029 (0.005)***
    - Column (8): -0.031 (0.009)***
    - Column (9): -0.029 (0.005)***
  - Fa:
    - Column (1): 0.103 (0.022)***
    - Column (2): 0.031 (0.011)***
    - Column (4): 0.017 (0.003)***
    - Column (6): 0.044 (0.041)
    - Column (7): 0.066 (0.035)*
    - Column (8): 0.048 (0.043)
    - Column (9): 0.067 (0.039)*
  - Dem:
    - Column (1): 0.063 (0.009)***
    - Column (2): 0.073 (0.006)***
    - Column (4): 0.078 (0.001)***
    - Column (6): 0.046 (0.022)**
    - Column (7): 0.039 (0.013)***
    - Column (8): 0.049 (0.022)**
    - Column (9): 0.038 (0.014)***
  - Trend (where included):
    - Examples: -0.002 (0.001); 0.001 (0.000)***; -0.001 (0.002)
  - Constant examples:
    - 1.095; -5.888; -4.391; 8.076; 7.643; 8.759; 7.511
- Sample and fit:
  - Observations vary: 139, 137, 137, 141, 141, 141, 141.
  - Adj. R-sq. reported: 0.967, 0.975, 0.975, 0.862, 0.819, 0.856, 0.786.

### Key statistics from Table A2 — Cointegrating Relationship: Real Household Debt Per Capita, Robustness Tests
- Estimation methods displayed: DOLS (1 Lead/1 Lag; 2Leads/2Lags), FMOLS, CCR.
- Selected coefficient estimates (standard errors in parentheses; significance: *** p<0.01, ** p<0.05, * p<0.1):
  - Hv:
    - Column (1): 0.753 (0.171)***
    - Column (2): 0.472 (0.036)***
    - Column (4): 0.805 (0.164)***
    - Column (6): 0.484 (0.030)***
    - Column (7): 0.792 (0.152)***
    - Column (8): 0.483 (0.030)***
    - Column (9): 0.779 (0.143)***
  - RR:
    - Column (1): -0.023 (0.010)**
    - Column (2): -0.033 (0.013)**
    - Column (4): -0.025 (0.010)**
    - Column (6): -0.031 (0.009)***
    - Column (7): -0.025 (0.008)***
    - Column (8): -0.030 (0.009)***
    - Column (9): -0.025 (0.008)***
  - Trend (where included):
    - Examples: -0.006 (0.003)*; -0.007 (0.003)**; -0.006 (0.003)**; -0.006 (0.003)**
  - Constant examples:
    - -2.143 (1.775); 0.776 (0.428)*; -2.676 (1.707); 0.634 (0.349)*; -2.545 (1.578); 0.639 (0.347)*; -2.417 (1.486)
- Sample and fit:
  - Observations: 139, 137, 137, 141, 141, 141, 141.
  - Adj. R-sq. reported: 0.959, 0.952, 0.964, 0.905, 0.949, 0.904, 0.955.

*Italicized source attribution: Content derived from the PDF file titled "_wp15276 - References."*

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