Canada: Selected Issues Paper

International Monetary Fund. Western Hemisphere Dept.

doi:10.5089/9781498321037.002.A001

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Canada: Selected Issues Paper

Author: International Monetary Fund. Western Hemisphere Dept.

Publication Date:: 24 Jun 2019

ISBN:: 9781498321037

Language:: English

Keywords:: ISCR; CR; house price; household income; price development; price correction; attainable price; house price fundamentals; Housing; Credit

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Selected Issues

Abstract

Selected Issues

Assessing House Prices in Canada¹

This chapter uses a “borrowing capacity” approach to evaluate Canadian house prices. The approach uses household income, interest rates, and leverage requirements to determine households’ borrowing capacity. The results show that house prices respond rapidly to households’ ability to borrow, suggesting that policy measures that facilitate greater access to credit would likely increase house prices and household debt. In most Canadian metropolitan areas, house prices are broadly aligned with households’ borrowing capacity. However, house prices are significantly higher than “attainable” levels in Hamilton, Toronto, and Vancouver.

A. Introduction

1. House prices in eleven Canadian census metropolitan areas (CMAs) are assessed using a static borrowing-capacity (SBC) approach.² The approach uses household income, mortgage interest rates, and leverage requirements to determine households’ borrowing capacity. Estimates of “attainable” house prices are compared with actual prices to determine whether they are aligned, where it is implicitly assumed that house prices ultimately reflect households’ ability to borrow.

2. Why the SBC approach? While other approaches are available, ranging from simple detrended price-to-income indicators and regression analysis to more complicated structural dynamic economic models, the SBC approach has several attractive features:

The approach is intuitive, simple to implement, and available in real time. It incorporates few variables and a handful of structural parameters. Unlike normalized price-to-income ratios, it has clear units of interpretation. Standard regression analysis is often used to estimate measures of house price fundamentals, but these measures impose the restriction that house prices are in line with fundamentals on average over the sample—a strong assumption, especially in short samples. Unlike time-series regression models, the SBC approach also does not require historical data.
The approach can readily be used to assess the impact of monetary and macroprudential policy on borrowing capacity. Because interest rates explicitly enter the model, the impact of monetary policy can easily be assessed. The impact of macroprudential policy can also be evaluated through changes to the debt-service-to-income (DSTI) ratio, the loan-to-value (LTV) ratio, and the loan-to-income (LTI) ratio.
The approach appears to match the observed behavior of Canadian households. According to the 2018 Canadian Mortgage and Housing Corporation’s (CMHC) Mortgage Survey³, 85 percent of first-time buyers spent as much as they could afford when purchasing their home.

3. The chapter proceeds as follows. Section B outlines the SBC approach and its implications for households’ borrowing capacity. Section C describes the data and assumptions used in the analysis and sections D and E discuss the results and other findings. Section F concludes with a summary of the findings and a policy discussion.

B. Static Borrowing-Capacity Approach

Model

4. The static borrowing-capacity approach (SBC) determines how much housing a household can afford given its income, the prevailing mortgage rate, and leverage requirements.⁴ A household can allocate a portion α of its income Y_t (at origination) to service its mortgage payment, A_t:

\begin{matrix} A_{t} = α Y_{t} & (1) \end{matrix}

Given the monthly mortgage payment, A_t, the mortgage interest rate, $i_{t}^{m}$ (per month), and the maturity of the mortgage loan in months, $N_{t}^{m}$ , the bank determines the mortgage loan amount available, L_t, using standard mortgage-contract calculations:

\begin{matrix} L_{t} = [\frac{(1 + i_{t}^{m})^{\land N_{t - 1}^{m}}}{i_{t}^{m} (1 + i_{t}^{m})^{\land N_{t}^{m}}}] \times α Y_{t} \equiv f (i_{t}^{m}, N_{t}^{M}) \times α Y_{t} . & (2) \end{matrix}

Household’s mortgage loan, L_t, and its savings for the down payment, D_t, add up to the “housing”, PH_t, it can attain:

\begin{matrix} P H_{t} \equiv p_{t}^{h} H_{t} = L_{t} + D_{t}, & (3) \end{matrix}

where the value of the house is a combination of price per quantity of housing and the quantity of housing.

5. Assumptions about each household’s down payment are crucial for estimates of “attainable” house prices. One possible assumption is to consider the down payment as a constant share of income, or household wealth. Another option is to let households choose their down payment as implied by a stable loan-to-value (LTV) ratio (for example, a down payment of 20 percent of the property price). Given that a stable LTV is observed for the marginal buyer, it is used in the baseline model, resulting in a closed-form solution for attainable housing:

\begin{matrix} P H_{t} = \frac{1}{L T V} f (i_{t}^{m}, N_{t}^{m}) \times α Y_{y} . & (4) \end{matrix}

Model Implications

6. The house pricing formula (4) is the key relationship used to assess house prices.⁵ It estimates “attainable” house prices, conditioned on the households’ borrowing-capacity. The pricing formula has several important implications, discussed below.

Nominal house prices grow in line with nominal income in the long run. With constant loan-to-value ratios, debt-service-to-income ratios, and mortgage interest rates, (4) implies that house prices will grow with households’ income, $\dot{P H_{t}} = {\dot{Y}}_{t}$ .
A permanent decrease in mortgage rates will permanently increase debt-to-income ratios. If a household keeps its debt-service-to-income ratio, a, constant (at origination), a permanent decline in nominal interest rates will lead to a permanently higher loan-to-income ratio. This follows from (2), which shows that the loan-to-income ratio, L_t/ Y_t, is a function of DSTI (a), the interest rate, and the amortization period: $L_{t} / Y_{t} = f (i_{t}^{m}, N_{t}^{m}) \times α$ . Lower interest rates quickly increase LTI ratios for new home-owners and gradually increase overall household debt relative to income. Figure 1 demonstrates the non-linear relationship between LTI ratios and interest rates for different maturities.
A permanent decrease in mortgage rates will permanently increase price-to-income ratios. Often, the price-to-income ratio is used to assess if house prices are overvalued, under an implicit or explicit assumption that the ratio is mean-reverting. Under the SBC hypothesis, however, it is the DSTI that is considered stable, and permanent changes in interest rates also permanently change the price-to-income ratio: from (4) it follows that ${P H}_{t} / Y_{t} = f (i_{t}^{m}, N_{t}^{m}) \times α / L T V$ . The fact that price-to-income ratio depends on the nominal level of the mortgage rate, which has been declining, may limit the usefulness of comparing price-to-income ratios to historical levels for house price assessments.
A decline in mortgage rates increases the down payment as a share of income. This is because lower mortgage rates increase the price-to-income ratio when the LTV is assumed to be constant, increasing the time required to save for the down payment Thus, declining interest rates worsen housing affordability for many households.⁶
It is the flow of credit, not the stock of credit, that is the relevant variable for house price assessments. The borrowing-capacity model makes it clear why focusing on the newly-issued credit for the marginal buyers is relevant for house prices. The stock of mortgage credit is a combination of new and historical vintages of credit, complicating the interpretation of the credit stance for assessing house prices, and distorting real-time information about credit developments.⁷

7. In the long term, house price deviations from fundamentals will adjust through changes in price, changes in borrowing capacity, or both. Deviations from fundamentals can be caused by supply-side constraints and a number of other factors (e.g. speculation). The bigger the deviation, the higher the risk of a sharp correction in prices. This is because house prices can adjust more quickly than housing supply and income.

C. Data and Assumptions

8. The analysis uses data from a variety of sources. Detailed descriptions and data references can be found in the appendix.

9. Median-income households are assumed to take on mortgage loans for 25 years with interest rates fixed for 5-year intervals. Correspondingly, “conventional mortgage lending rate” for the five-year term from CMHC is used in all computations. Unless otherwise noted, the baseline loan-to-value (LTV) ratio is 80 percent. The fixed LTV affects estimated house price levels but not their dynamics. Median-income households are assumed to be the prospective buyers of median-priced housing. House prices are sourced from Real Property Solutions and Teranet, expressed in nominal Canadian dollars.

10. The share of income allocated to DSTI at origination, a, is a crucial assumption. An obvious option is to set a to an identical value across all CMAs, say 30 percent of after-tax median household income. This choice, however, ignores the fact that there may be good reasons for a to vary across regions. Even under an assumption of perfect regional mobility and households equalizing utility across regions, outlays on housing as a share of income can differ, as indicated by the literature on spatial equilibrium (see Roback, 1982, for example). Regions differ in their amenities, productivity, local taxes, price of services, etc. But even with the same amenities, the share of income allocated for housing expenses may vary with income. For instance, earning C$100,000 a year and paying 50 percent of your income on housing may still be preferable to earning C$70,000, allocating “only” 30 percent of your income to housing, and having lower “ex-housing residual income”.⁸

11. For transparency, both the region-specific housing share of income, a, and the common share are used in the analysis. To estimate the region-specific a_ut, SBC formula (4) is used with available income, mortgage rate, and observed regional house prices. An average for 2004—2006 is then used for the whole sample of 2000Q1—2018Q4. The normalization aims to avoid the sample around the dot-com and financial crisis episodes.

D. Results

12. House prices in most CMAs can be explained by households’ borrowing capacity. Figure 2 displays observed house prices and the estimate of “attainable” house prices using the SBC. These baseline calculations assume region-specific DSTI ratios, α_ut. From 2000 to 2018, house prices in most CMAs grew in line with rising nominal incomes and declining mortgage interest rates.⁹

13. However, house prices in Hamilton, Toronto, and Vancouver are significantly higher than estimated attainable levels. The pricing gaps in 2018 are around 50 percent for Toronto and Vancouver, and almost 60 percent for Hamilton.¹⁰ Additional factors beyond borrowing capacity are needed to explain the evolution of house prices in these CMAs, such as supply-side factors.¹¹ Such large pricing gaps are not without precedent in Canada, with developments in Calgary and Edmonton over 2006 to 2012 being examples.

14. Declining mortgage rates have contributed significantly to rising house prices. The SBC formula (4) can be decomposed into contributions from income and interest rates. Figure 3 illustrates such a decomposition for Edmonton. The contributions from interest rates reflect changes in mortgage rates since 2001Q1. In 2017 when mortgage rates were at their lowest point, they could have added C$100,000 to the median house price of C$400,000. On the other hand, the recent increase in mortgage rates has put downward pressure on house prices.

15. The experience of Calgary and Edmonton metropolitan areas are examples of a “soft landing”. In Edmonton, the median house price exceeded the attainable level by 60 percent at its peak in 2007Q3 (figure 3). By 2012Q1, the median price became more aligned with fundamentals due to a moderate decline in house prices, income growth, and sizable declines in mortgage interest rates. Their experience suggest that market exuberance and supply constraints may widen the price deviation from fundamentals only temporarily. In this context, Calgary and Edmonton offer credence to the magnitude of the price deviations in Hamilton, Toronto, and Vancouver and reassurance that the gaps will eventually close. However, the adjustment path will be different because such a large decline in mortgage rates is unlikely in the future.

16. Real estate transactions occurring at very elevated prices suggest a rising share of purchases by households with high income. For example, in 2016, households in Toronto with 1.7 times median income could comfortably afford to devote 30 percent of their income to mortgage debt servicing. There were at least 20 percent of such households in the Toronto CMA, but this share has shrunk as house prices have continued to climb since 2016. As a result, housing affordability has deteriorated.

E. Other Findings

17. There are sizable differences in DSTI ratios across CMAs. Figure 4 displays the estimates for all the CMAs.¹² The share of income needed to service the mortgage loan to afford housing at a prevailing price depends on the definition of income (household income vs. family income) but the relative differences are stable. In Toronto, Vancouver, or Victoria median-income households would need to devote more than 50 percent of their after-tax income to housing. The share is considerably lower in other CMAs, averaging around 30 percent. In Hamilton, the share was around 30 percent up until 2016, and then a sharp increase in house prices pushed the required DSTI for the median household towards 45 percent.

18. As mortgage rates increase, house prices need not decline if income growth compensates for rising interest costs. If mortgage interest rates continue to increase, they will put house prices under pressure. Without additional policy measures, income growth will be the decisive factor for keeping attainable house prices stable or even increasing in the future.

19. Staff Report (SR) projections for income growth and interest rates suggest that attainable house prices could decline slightly over the next five years. Expected income growth will support attainable prices, while an expected increase in interest rates will reduce attainable prices. As shown in figure 5, the balance of these two offsetting effects suggests a slight decline in attainable prices over the forecast horizon. Assuming staff’s interest rate projections, levels of income growth required to raise attainable prices enough to close pricing gaps over the next 5 years in Toronto and Vancouver are very high (cumulative annual growth rates CAGRs needed are 9.3 and 8 percent, respectively). In other CMAs, with house prices better aligned with estimated attainable prices, closing pricing gaps through borrowing capacity alone would require income CAGRs below 3 percent. The results suggest that without very strong income growth in Hamilton, Toronto, and Vancouver there is a risk of further price corrections in these markets.¹³

F. Summary and Policy Implications

20. House prices in most Canadian regions can be explained by economic fundamentals, but prices in Hamilton, Toronto, and Vancouver are currently well-above estimated attainable levels. Since 2000, house price developments in most metropolitan regions can be explained by robust income growth and a decline in mortgage interest rates. House prices have broadly increased in line with households’ borrowing capacity. However, since 2015, prices in Hamilton, Toronto, and Vancouver have deviated significantly from fundamentals. By the end of 2018, pricing gaps stood at around 50 percent for Toronto and Vancouver, and almost 60 percent for Hamilton.

21. The overvaluations currently observed in Hamilton, Toronto, and Vancouver are not unprecedented. In 2006, house prices in Calgary and Edmonton increased sharply above estimates of borrowing capacity. Pricing gaps normalized by 2012 due to a combination of moderate declines in house prices, strong household income growth, and a decline in interest rates. Looking ahead, housing markets in Hamilton, Toronto, and Vancouver are not likely to benefit from such significant declines in interest rates. This suggests that without very strong income growth, there is a risk of further price corrections in these markets.

22. Nationwide increases in price-to-income ratios have significantly lowered housing affordability. Declines in mortgage rates have generally been rapidly priced in by housing markets, increasing price-to-income and loan-to-income ratios. With rising price-to-income ratios, down payments have become larger, increasing the time it takes to save for a house, and adversely impacting housing affordability. While housing affordability has deteriorated in all of the regions examined, the deterioration has been most marked in Hamilton, Toronto, and Vancouver.

23. If house prices rapidly reflect households’ ability to borrow, even well-intentioned policies that improve access to credit are likely to increase house prices and adversely impact affordability. Policy measures that increase households’ capacity to borrow—such as increasing the mortgage loan amortization period or subsidizing loans—will likely put additional upward pressure on prices. Indeed, for such measures to work, the supply of housing would need to be exceptionally (and unrealistically) elastic, even in the short run. As such, policy measures focused on increasing housing supply are needed to durably improve housing affordability over the long term.

References

Adalid, R. and M. Falagiarda (2018): “How Repayments Manipulate Our Perceptions about Loan Dynamics after Boom”, European Central Bank WP No. 2211/2019, December 2018 https://www.ecb.europa.eu/pub/pdf/scpwps/ecb.wp2211.en.pdf
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Andrle, M. and M. Plašil (2019): “Assessing House Prices with Prudential and Valuaftion Measures”, IMF Working Paper IMF WP/19/59, March 2019. https://www.imf.org/~/media/Files/Publications/WP/2019/WPIEA2019059.ashx
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IMF (2018): “How to improve housing affordability in Canada’s dynamic regions?” by Zsofia Arvai, Canada Selected Issues, IMF Country Report No. 18/222, pp. 53–63, https://www.imf.org/~/media/Files/Publications/CR/2018/cr18222.ashx
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Roback, J. (1982): “Wages, Rents, and the Quality of Life”, Journal of Political Economy, Vol. 90, No. 6, pp. 1257–1278. https://www.jstor.org/stable/1830947?seq=1#metadata_info_tab_contents
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Real Property Solutions (2017): RPS – House Prices Index (HPI) Product & Methodology Information, https://www.rpsrealsolutions.com/documents/en/the-rps-hpi-product-and-methodology-overview-aug-14-2017.pdf
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Teranet (2019): The Teranet-National Bank House Price Index ™, https://housepriceindex.ca/wp-content/uploads/2017/08/Teranet-National-Bank-House-Price-Index-Methodology-Overview.pdf
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Appendix I. Data and Additional Results

A. Data Sources and Transformations

House Prices Data

1. Multiple data sources are used to analyze house prices in selected Census Metropolitan Areas (CMAs) in Canada, but the main resource is the Real Property Solutions, LLC, (RPS) database¹ with house prices in Canadian dollars. This database is at monthly frequency, available back to 2005M1, see RPS (2017) for details of the methodology of estimating the median house prices. The RPS dataset is extend as far back to 2000M1 using the dynamics of house price indices from the Teranet database. The RPS and Teranet database dynamics in the overlapping sample are similar, however, with the dollar values of the Teranet indices not available.

Income, Population, and Other Data

2. Income data for the assessment of house prices should match well the information about the dwelling concerned (aggregate, house, condo), its size, and the likely demographics demanding the dwelling. For the aggregates and houses, the analysis works with the pre-tax median income of a family for which annual estimates are available. To work with household median income, the levels of the family income are scaled to household income levels from the 2016 Consensus for each CMA. The annual numbers are interpolated to quarterly frequency in 2000— 2016 and extrapolated to the end of 2018 using the disposable income dynamics for the province as an auxiliary series. The results are rather robust to use of alternative measures of household income.

3. The choice of the demand unit is mainly relevant to the level of income, less so for its dynamics. The median family income is higher than the median household income in Canada. The composition matters – in 2016 the median pre-tax income of a “couple family with or without children” was $89,610. This is 58 percent higher than the “all family units” income and higher than “lone-parent” families. The dynamics of median family income are converted to median “household” income using the income levels from 2016 Census.

4. Population data are sourced from Statistics Canada via Haver Analytics database. For 2018, the annual series were extended by the monthly three-month averages of population estimates from Labor Force Survey, via Haver Analytics. The average size of the household is based on 2016 Census (Statistics Canada, Census Profile).

B. Additional Results

Prepared by Michal Andrle (RES). The author would like to thank Cheng Hoon Lim, Ivo Krznar, Troy Matheson (all WHD), and Ben Hunt (RES) for comments and Miroslav-Kleki Plašil (Czech National Bank) for collaboration on the house-prices assessment methods. Dan Pan provided excellent research assistance.

See Andrle and Plašil (2019).

https://www.cmhc-schl.gc.ca/en/data-and-research/consumer-surveys/mortgage-consumer-survey/homebuyers-data

Andrle and Plašil (2019) also develop the concept of “dynamic borrowing capacity”, where the future path of income and interest rates are reflected in household capacity to borrow, with emphasis on the financial stability.

The formula is labeled as “pricing”, rather than “valuation” due to differences between the static borrowing-capacity approach and the investment approach, see Andrle and Plašil (2019) for more details.

Should one assume that the down payment is, for simplicity, a constant fraction of income D_t = κY_t the resulting estimate of the price of housing would be $P H_{t} = [f (i_{t}^{m}) \times α + κ] Y_{t}$ . Under this assumption, the estimated house price would be less elastic with respect to the mortgage rate and the estimated a would differ. Also, assuming each household saves a portion of its current income for R years results in a similar expression. Loan-to-income ceilings would have even larger effect, with PH_t = LTI_max × Y_t + D_t when LTI limit is binding. With binding LTI limit, a reduction in interest rate would lead to decline in DSTI.

Adalid and Falagiarda (2018) illustrate in detail the delayed effects of new loan origination and loan repayment on the stock of credit.

This would be a natural result with non-homothetic preferences. For instance, with Stone-Geary utility over housing, H, and other goods, C, a minimum necessary consumption of other goods, C_min, the share of housing services on total income will increase with the income, Ph*H = alpha * (Y – Pc*C_min). It will be a constant share of the “after-necessities residual income”, (Y – Pc*Qc).

The attainable house prices estimate with uniform 30 percent DSTI assumption are in Figure 2 in the Appendix.

Hamilton house prices seemed aligned with borrowing capacity of households until very recently. The recent misalignment likely reflects the commuting distance to Toronto, and a tight housing market in Toronto CMA.

The analysis of supply-side factors in Canada is detailed in the 2018 Staff Report (IMF 2018).

Figure 2 in the Appendix presents the estimated “attainable” house prices from the SBC model under the common assumption of 30 % of after-tax median household income going to mortgage payments (at origination).

It is worthwhile noting here that exactly how house-price gaps ultimately adjust is highly uncertain, and can occur through changes in prices, changes in attainable prices, or some combination of both.

RPS Real Property Solutions provided the database free of charge for this analysis. Terms of Use and Disclaimer: All rights reserved. Any reproduction or distribution with respect to the content of the RPS House Price Index is prohibited. The information provided herein is for informational purposes on matters of general interest, and is not intended to provide the basis for investment, financial, real estate, tax or other professional advice or services. The information is derived from sources believed reliable; however, no warranties or representations are being made with respect to the information, and RPS Real Property Solutions, along with its parent companies, subsidiaries and affiliates, disclaims all liability with respect to the accuracy of the information. The information is not a substitute for the advice of a qualified professional.

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