## 2. Estimation Results

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---

### I. Introduction
- Canadian real house prices almost doubled since early 2000s (largest increase among advanced economies over the period, OECD, 2012).
- Residential investment returned to pre-recession level in about a year and a half after the Great Recession (Bank of Canada, 2011); historically it took 3 to 4 years.
- When residential investment-to-GDP ratio previously reached the 7 percent threshold, the Canadian housing sector experienced a long subsequent period of stagnation.
- Paper objective:
  - Estimate Canada’s housing stock to determine whether there is excess supply of housing units by (i) constructing yearly provincial series of housing stock and household formation and (ii) estimating an equilibrium housing stock using a panel error-correction specification (pooled mean-group estimator) for the ten provinces over 1982-2013.
- Key empirical preview:
  - Some excess supply in housing units, particularly during the build-up to the Great Recession, when there were about 120,000 housing units in excess, or slightly above 1 percent of the total housing stock.

### II. Reconstructing Canada’s Housing Stock and Household Series
- Data limitations and sources:
  - StatCan housing stock series discontinued in 2000; CENSUS provides five-year household and private dwelling estimates but is subject to under-counting bias (Gabay, 2011).
  - Table 1 data sources used:
    - Stock: Statistics Canada: Table 030-0001.
    - Completions: Canada Mortgage and Housing Corporation: Table 027-0009.
    - Conversions: Statistics Canada: Table 026-0001.
    - Demolition: Statistics Canada: Table 026-0012 (provincial demolition data from StatCan).
- Stock model and reconstruction method:
  - Housing stock R_t = occupied units O_t + vacant units V_t.
  - Occupancy evolves by adding net household formation; vacant units evolve via completions, conversions/additions, and demolitions.
  - Starting from StatCan latest available stock (2000), stock in year t = stock in t-1 + completions + additions - demolitions.
  - Assumed conversions occur within one year.
- Validation and computed growth:
  - Backward testing from 1971 yields generally good results; computed estimates are generally lower than StatCan series (downward bias in excess supply estimates).
  - Canada’s housing stock almost doubled over last three decades.
  - Between 1980 and 2013, Canada’s housing stock grew at a yearly average rate of 1.7 percent.
  - Alberta and British Columbia grew at an average yearly 2 percent.
  - Ontario and Quebec shares of national stock stagnated at around ⅓ and ¼ respectively.
- Household formation:
  - Driven by population growth, aging, headship rates, household size, income, social benefits, and financial conditions.
  - Immigration (international and interprovincial) important over last two decades.
  - Interpolated annually using CMHC, StatCan, and CENSUS; used StatCan population data and extrapolated headship rates (primary household maintainers / population in age segment).
  - Cumulative supply of new housing units outpaced household formation by about 10 percent when comparing 2011 with 2001 (updating Lewis, 2008).
- Vacancy ratio:
  - Vacancy ratio (unoccupied units / housing stock) reached historical highs in 2008.
  - Demographic-only measure suggests an excess supply of about 1½ percent of the total housing stock as of end 2013.
  - Provincial contributions roughly align with stock sizes; Quebec’s excess supply appears relatively high.
  - Caveat: demographic-only approach omits other determinants of construction activity; model-based analysis follows.

### III. Modeling Housing Units’ Supply
- Model framework and variables:
  - Stock-adjustment model in the spirit of Ball et al. (2010) with an arbitrage relationship: imputed rent R is function of housing stock, occupied units (households), and real income; adjustments include expected capital gain and cost factors.
  - Adjustment equation: net completions depend on real house price growth and the size of the stock; construction cost proxy added.
  - Variables (entered in logs where indicated):
    - Housing stock and households (logs).
    - Household average after-tax income (logs).
    - House prices: CREA average prices deflated by CPI excluding shelter (provincial indices).
    - Construction cost proxy: share of construction workers in good-producing industries (evolves with weekly average earnings of construction sector workers).
    - Mortgage rate included.
- Estimation sample and method:
  - Yearly data, ten provinces, 1982-2013 (T = 31, N = 10).
  - Error-correction specification using pooled mean-group estimator (long-run coefficients constrained equal across panels; short-run and adjustment coefficients allowed to vary by group).
  - Dynamic panel autoregressive distributed lag reparameterized to error-correction form.

### IV. Estimation Results (pooled mean-group long-run and short-run findings)
- Long-run (normalized cointegration relationship; pooled mean-group estimates):
  - Households: 0.8783 (significant at 1 percent level; labeled "a" in source).
  - Income (household disposable income): 0.1297 (significant at 1 percent level).
  - Interest rate: -0.4339 (significant at 1 percent level).
  - House prices: -0.0211 (significant at 5 percent level; labeled "b" in source).
  - Construction cost: 0.0072 (not reported as significant in the pooled mean-group column).
- Short-run and adjustment:
  - Error-correction term (speed of adjustment): -0.2041 (significant at 1 percent level).
  - Lagged house price growth positively impacts changes in housing stock (short-run), consistent with profitability expectations driving residential investment.
  - Coefficients vary across provinces in dynamic fixed-effects and province-specific columns (province-level heterogeneity reported in Table 2).
- Model interpretation:
  - Demographic component (household formation) is the largest and primary determinant of housing stock.
  - Household income positively and significantly related to housing stock.
  - Interest rates negatively related to housing stock.
  - Construction cost negatively linked to stock (not significant in pooled mean-group).
  - Negative long-run house price coefficient implies higher prices lower demand for housing stock (consistent with model formulation).
  - Disequilibrium arises because stock cannot adjust instantaneously to changes in fundamentals.

### V. Disequilibrium Estimates and Key Quantitative Findings
- Peak disequilibrium:
  - At its peak during the late 2000s build-up to the Great Recession, the disequilibrium represented about 120,000 units (slightly above 1 percent of the housing stock).
- Sample-end and comparative measures:
  - Model-based lower-bound estimate: Canadian housing market in excess supply by about 0.5 percent of the total housing stock by end 2013.
  - At the highs of the 2009 Great Recession, excess supply found to have reached almost 1 percent.
  - After the early 1990s housing crisis, excess supply reached about 0.6 percent of total stock and house prices subsequently experienced a decade-long stagnation.
- Note on bias and robustness:
  - Reconstructed housing stock estimates are generally lower than StatCan series, so disequilibrium estimates are biased downwards and represent lower bounds.
  - Running the model on StatCan series prior to 2000 produced an excess supply estimate closer to 1½ percent of total supply.
  - Estimated disequilibrium is stationary and a good and robust predictor of house prices.

### VI. Conclusions
- Contributions:
  - Provided yearly estimates of housing stock and household formation for the 10 Canadian provinces over 1980-2013.
  - Estimated excess supply in housing units for the ten provinces using a panel error-correction approach.
- Main empirical conclusions:
  - Demographics (household formation) are the dominant long-run determinant of housing stock.
  - Model suggests excess supply around 0.5 percent of total housing stock by end 2013 (lower-bound), with a peak near 120,000 units (about 1 percent) during the late 2000s.
  - Historical episodes: excess supply near 1 percent in 2009; about 0.6 percent after early 1990s crisis, associated with prolonged house price stagnation.
- Robustness:
  - Disequilibrium estimates are stationary and robust predictors of house prices.

*Source: _wp15128 - 2. Estimation Results (excerpt from the supplied IMF PDF content).*

### References.................................................................................................16

### _wp15128 - References.................................................................................................16

### References
- References.................................................................................................16

### Appendix
- Appendix. Data Sources.................................................................................17

### Figures
- 1. Reconstructing Net Completions Series by Province before 2000.............................7
- 2. Computed Housing Stock by Province............................................................8
- 3. Computed Households by Province................................................................9
- 4. Computed Excess Vacancy.........................................................................10
- 5. Computed Vacant Units by Province..............................................................10
- 6. Estimated Housing Disequilibrium: Contribution by Province...............................14

### Tables
- 1. Reconstructing the Housing Stock: Data Sources................................................6

*https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2015/_wp15128.pdf*

### 2. Estimation Results...................................................................................13

### 2. Estimation Results

### I. Introduction
- Canadian real house prices almost doubled since early 2000s (largest increase among advanced economies over the period, OECD, 2012).
- Residential investment returned to pre-recession level in about a year and a half after the Great Recession (Bank of Canada, 2011); historically it took 3 to 4 years.
- When residential investment-to-GDP ratio previously reached the 7 percent threshold, the Canadian housing sector experienced a long subsequent period of stagnation.
- Paper objective: estimate Canada’s housing stock to determine whether there is excess supply of housing units by (i) constructing yearly provincial series of housing stock and household formation and (ii) estimating an equilibrium housing stock using a panel error-correction specification (pooled mean-group estimator) for the ten provinces over 1982-2013.
- Key empirical result preview: some excess supply in housing units, particularly during the build-up to the Great Recession, when there were about 120,000 housing units in excess, or slightly above 1 percent of the total housing stock.

### II. Reconstructing Canada’s Housing Stock and Household Series
A. Housing stock: data, model, and reconstruction
- Data limitations:
  - StatCan housing stock series discontinued in 2000; CENSUS provides five-year household and private dwelling estimates but is subject to under-counting bias (Gabay, 2011).
- Stock model (as used):
  - Housing stock R_t = occupied units O_t + vacant units V_t (equation (1) in source).
  - Occupancy evolves by adding net household formation; vacant units evolve via completions, conversions/additions, and demolitions (equations (2)–(4) in source).
  - Excess supply defined as difference between current stock and equilibrium stock (equation (5) in source).
- Data sources used to reconstruct stock (Table 1 in source):
  - Stock: Statistics Canada: Table 030-0001.
  - Completions: Canada Mortgage and Housing Corporation: Table 027-0009.
  - Conversions: Statistics Canada: Table 026-0001.
  - Demolition: Statistics Canada: Table 026-0012 (provincial demolition data from StatCan).
- Method:
  - Starting from StatCan latest available stock (2000), stock in year t = stock in t-1 + completions + additions - demolitions.
  - Assumed conversions occur within one year (note from source).
- Validation:
  - Backward testing from 1971 yields generally good results; computed estimates are generally lower than StatCan series (downward bias in excess supply estimates).
- Computed long-run growth:
  - Canada’s housing stock almost doubled over last three decades.
  - Between 1980 and 2013, Canada’s housing stock grew at a yearly average rate of 1.7 percent.
  - Alberta and British Columbia grew at an average yearly 2 percent.
  - Ontario and Quebec shares of national stock stagnated at around ⅓ and ¼ respectively.

B. Household formation
- Household formation driven by population growth, aging, headship rates, household size, income, social benefits, and financial conditions.
- Immigration (international and interprovincial) important over last two decades.
- Method:
  - Interpolated household formation annually using CMHC, StatCan, and CENSUS; used StatCan population data (per Gabay, 2011) and extrapolated headship rates (primary household maintainers / population in age segment).
- Finding:
  - Cumulative supply of new housing units outpaced household formation by about 10 percent when comparing 2011 with 2001 (updating Lewis, 2008).

C. Vacancy ratio
- Vacancy ratio (unoccupied units / housing stock) reached historical highs in 2008.
- Assuming a relatively small and constant share of natural unoccupied units, the difference between the vacancy ratio and its historical average measures disequilibrium.
- Demographic-only measure suggests an excess supply of about 1½ percent of the total housing stock as of end 2013.
- Provincial contributions roughly align with stock sizes; Quebec’s excess supply appears relatively high.
- Caveat: demographic-only approach omits other determinants of construction activity; model-based analysis follows.

### III. Modeling Housing Units’ Supply
- Model framework:
  - Stock-adjustment model in the spirit of Ball et al. (2010).
  - Arbitrage relationship: imputed rent R is function of housing stock, occupied units (households), and real income; adjustments include expected capital gain and cost factors.
  - Adjustment equation: net completions depend on real house price growth and the size of the stock; construction cost proxy added.
- Variables and data:
  - Housing stock and households enter in logarithms.
  - Household average after-tax income in logs.
  - House prices: Canadian Real Estate Association average prices deflated by CPI excluding shelter (provincial indices).
  - Construction cost proxy: share of construction workers in good-producing industries (evolves with weekly average earnings of construction sector workers).
  - Mortgage rate included.
  - Model estimated on yearly data, ten provinces, 1982-2013 (T = 31, N = 10).
- Estimation method:
  - Error-correction specification using pooled mean-group estimator (long-run coefficients constrained equal across panels; short-run and adjustment coefficients allowed to vary by group).
  - Dynamic panel autoregressive distributed lag reparameterized to error-correction form (equations (6)–(9) in source).

### IV. Estimation Results (summary of Table 2: Pooled mean-group)
Long-run (normalized cointegration relationship; pooled mean-group estimates):
- Households: 0.8783 (significant at 1 percent level; labeled "a" in source).
- Income (household disposable income): 0.1297 (significant at 1 percent level).
- Interest rate: -0.4339 (significant at 1 percent level).
- House prices: -0.0211 (significant at 5 percent level; labeled "b" in source).
- Construction cost: 0.0072 (not reported as significant in the pooled mean-group column).

Short-run and adjustment:
- Error-correction term (speed of adjustment): -0.2041 (significant at 1 percent level).
- Lagged house price growth positively impacts changes in housing stock (short-run), consistent with profitability expectations driving residential investment.
- Coefficients vary across provinces in dynamic fixed-effects and province-specific columns (Table 2 provides province-level heterogeneity).

Model interpretation and fit:
- Demographic component (household formation) is the largest and primary determinant of housing stock.
- Household income positively and significantly related to housing stock.
- Interest rates negatively related to housing stock.
- Construction cost negatively linked to stock (not significant in pooled mean-group).
- Negative long-run house price coefficient implies higher prices lower demand for housing stock (consistent with model formulation).
- Disequilibrium arises because stock cannot adjust instantaneously to changes in fundamentals.

### V. Disequilibrium Estimates and Key Quantitative Findings
- Peak disequilibrium captured by the model:
  - At its peak during the late 2000s build-up to the Great Recession, the disequilibrium represented about 120,000 units (slightly above 1 percent of the housing stock).
- Sample-end and comparative disequilibrium measures:
  - Model-based lower-bound estimate: Canadian housing market in excess supply by about 0.5 percent of the total housing stock by end 2013.
  - At the highs of the 2009 Great Recession, excess supply found to have reached almost 1 percent.
  - After the early 1990s housing crisis, excess supply reached about 0.6 percent of total stock and house prices subsequently experienced a decade-long stagnation.
- Note on bias:
  - Because reconstructed housing stock estimates are generally lower than StatCan series, the paper’s disequilibrium estimates are biased downwards and represent lower bounds.
  - Running the model on StatCan series prior to 2000 produced an excess supply estimate closer to 1½ percent of total supply (as noted in source footnotes and discussion).

### VI. Conclusions (author’s summary)
- Contributions:
  - Provided yearly estimates of housing stock and household formation for the 10 Canadian provinces over 1980-2013.
  - Estimated excess supply in housing units for the ten provinces using a panel error-correction approach.
- Main empirical conclusions:
  - Demographics (household formation) are the dominant long-run determinant of housing stock.
  - Model suggests excess supply around 0.5 percent of total housing stock by end 2013 (lower-bound), with a peak near 120,000 units (about 1 percent) during the late 2000s.
  - Historical episodes: excess supply near 1 percent in 2009; about 0.6 percent after early 1990s crisis, associated with prolonged house price stagnation.
- Robustness:
  - Estimated disequilibrium is stationary and a good and robust predictor of house prices (as reported in source).

*Source: _wp15128 - 2. Estimation Results (excerpt from the supplied IMF PDF content).*

### REFERENCES

### REFERENCES

### Bibliographic references
- Allen, Jason , Robert Amano, David Byrne and Allan Gregory, 2006. “Canadian City Housing Prices and Urban Market Segmentation”.
- Ball, Michael, Geoffrey Meen and Christian Nygaard, 2010. “Housing supply price elasticities revisited: Evidence from international, national, local and company data”. Journal of Housing Economics 19, pp. 255–268.
- Bank of Canada, 2011. “Housing in Canada”. Remarks by Mark Carney, Governor of the Bank of Canada, Vancouver Board of Trade, 15 June 2011
- Bank of Canada, 2013. Monetary Policy Report, April 2013.
- Congressional Budget Office, 2008. “The Outlook for Housing Starts, 2009 to 2012”, Background Paper, Pub. No. 3183.
- Demers, Frederick, 2005. “Modelling and Forecasting Housing Investment: The Case of Canada”. Bank of Canada, Working Paper No. 2005–41.
- Dupuis, David, and Yi Zheng, 2010. “A Model of Housing Stock for Canada”. Bank of Canada, Working Paper No. 2010–19.
- Egebo, Thomas, Pete Richardson and Ian Lienert, 1990. “A model of housing investment for the major OECD economies”. OECD, Economic Studies No. 14 (Spring 1990).
- Gabay, Richard, 2011. “Long-term household projections—2011 update”. Canadian Mortgage and Housing Corporation, Socio-economic Series 11-008.
- International Monetary Fund, 2012. United States Selected Issues, IMF Country Report No. 12/214.
- International Monetary Fund, 2013. Canada Selected Issues, IMF Country Report No. 13/41.
- Lewis, Roger, 2008. “2006 Census Housing Series: Issue 1—Demographics and Housing Construction”. Canadian Mortgage and Housing Corporation, Socio-economic Series 08-004.
- Organization for Economic Co-operation and Development, 2012. OECD Economic Outlook No. 92 (database).
- Tomura, Hajime, 2008. “A Model of Housing Boom and Bust in a Small Open Economy”. Bank of Canada, Working Paper 2008-9.

### APPENDIX. DATA SOURCES
- Sources of the data used for the regression model:
  - Variable: Housing stock
    - Source: StatCan and author’s calculations (as describe above)
  - Variable: Household formation
    - Source: CENSUS, StatCan and author’s calculations (as describe above)
  - Variable: Real household average after-tax income
    - Source: Haver
  - Variable: Construction cost
    - Source: Haver
  - Variable: Mortgage rate
    - Source: Haver
  - Variable: CPI excluding shelter
    - Source: Haver
  - Variable: House prices
    - Source: CREA (average house prices) and shelter CPI for MN, NB, NL, NS, PEI and SK from 1980 to 1986.

*Source: _wp15128 - REFERENCES*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2015/_wp15128.pdf_