David A. Rosenberg, Chief Economist & Strategist at Gluskin Sheff (Formerly of Merrill Lynch) recently reported that the Canadian Housing Market Could be in a Bubble. This article will provide an economic response to this accusation, provide the true economic metrics that must be considered in the Canadian Real Estate Market, and provide a copy of David Rosenbergs report so you can clearly reference his argument. I will attempt to remove the jargon from the economics so non-economics graduates (the general populous) can participate.
The whole idea about bubbles in Housing markets whether the Canadian Market or U.S. Market have been actively discussed over the past decades. Almost every argument will provide 3 ratios to throw up on a chart to ow and aw the crowd into believing. These 3 ratios are a Price to Income Ratio, a Price to Rent Ratio, and a Price Change Ratio. David Rosenbergs article is not different and provides these 3 ratios to form his conclusion.
Do I think David Rosenbergs argument is idiotic and based on Pure Rubbish? No, much of David’s supporting evidence is based on fundamental facts about the housing market in Canada; however, what it does lack is a realistic tool to estimate the bubbliness (a new word) of the Real Estate Market.
So you think you have a tool for assessing whether or not there is a bubble in the housing market? Yes….let me explain.
Have you ever heard of the USER COST APPROACH?
Back in 2005 there was an economic paper written by Charles Himmelberg Christopher Mayer and Todd Sinai that presented a much more accurate tool to estimate housing bubbles: Assessing High House Prices: Bubbles, Fundamentals and Misperceptions.
Now, I’m no genius, but I am familiar with this article. During my Urban Economics (Real Estate for economists) studies I adapted and applied the USER COST APPROACH developed by Mayer and Sinai to the Canadian Housing Market to determine whether there was or was not a bubble back in 2007. My findings were that no bubble existed, which I found surprising because during my research I was so sure a bubble did exist.
The basic problem with all other approaches to determining whether or not a real estate bubble exists is that no one considers the costs to the end user which includes opportunity costs lost when owning versus renting as well.
Now let me get all technical on you so you know exactly what the USER COST in Canada is and exactly how to calculate it. For those of you that dislike economics you may fall asleep hear, but I assure you this approach is solid gold. Otherwise scroll on and I will provide my results from the past.
The User Cost of Housing
The reasons and method for applying the User Cost Approach were best described in the recent paper Assessing High House Prices: Bubbles, Fundamentals and Misperceptions by Charles Himmelberg Christopher Mayer and Todd Sinai (2005). The reason they applied the User Cost Approach is that conventional measures, Real Price, Price-to-Rent and Price-to-Income ratios, make a key mistake when assessing overheating in housing markets because they erroneously equate the annual cost of owning a house to the purchase price of a house. They suggest instead, the owner occupied property should be assessed based on the financial return associated with the property by comparing the value of living in the home for one year with the opportunity cost of the capital invested in the home. Such a comparison should account for differences in risk, tax benefits, property taxes, maintenance expenses and any expected capital gains from owning the property.
This will establish a basis for an economically justified method to evaluate whether housing prices are unsustainably, too high or too low. The following analysis will incorporated the User Cost Method developed by Himmelberg et al., but will adapt the evaluation method to better suite the Canadian Market place.
A Formula
The formula for the annual cost of homeownership or “imputed rent” developed for the Canadian market place is similar to the formula used in the United States. The difference is that two variables that are present in the formula applied in the United States are not present in the formula applied to the Canadian market place because of tax differences. These variables are the income tax rate and the mortgage rate and they are not applied to the Canadian market place because both property tax and mortgage interest costs are not deducted from annual income tax in Canada. Thus, instead of six components representing both costs and offsetting benefits like in the Himmelberg paper, there are only 5. The first component is an opportunity cost—the cost of foregone interest that the homeowner could have earned by investing the capital in something other than a home. This one year cost was calculated as the risk free interest rate (RF) times the price of housing (Pt). The second component is the one year cost of property taxes and is calculated as the property tax rate (Wt) times the price of housing. The third component represents the maintenance cost expressed as a fraction of the home value (Dc) times the price of housing. The fourth term is the expected capital gain or loss on the property during the year; like the others it is the price of housing times the expected capital gain (gt + 1). Finally, the fifth term (Yt) represents an additional risk premium to compensate for the higher risk involved with owning a home versus renting; this is calculated by multiplying (Yt) by the cost of housing. The sum of these five components produces the total annual cost of homeownership:
Annual Cost of Ownership = Pt*RF + Pt*Wt + Pt*Mc – Pt*(gt +1) + Pt*Yt
For the housing market to be in equilibrium the annual cost of owning a house should not exceed the annual cost of renting. Under this scenario, if the annual cost of ownership increases without a corresponding increase in rents then potential home buyers will require a decrease in house price to encourage them to buy instead of rent. The converse will occur when annual ownership costs decrease. This implies a no arbitrage and following the same logic as applied in the Himmelberg paper the one year rent must equate to the annual cost of ownership.
Rt = Pt*Ut
Where the fraction Ut is know as the user cost of housing, defined as
Ut = RF + Wt + Mc – (gt + 1) + Yt
This is the user cost (Ut) and is a restatement of the annual cost of ownership in terms of cost per dollar of home value. Expressing the user cost this ways makes expressing the equilibrium situation much easier:
Pt/Rt = 1/Ut
Simply put, the equilibrium price-to-rent ration should equal the inverse of the user cost. From this equilibrium is should be noted that fluctuations in the user cost should lead to predictable changes in the price-to-rent ratio that reflect fundamentals, not bubbles.
The Himmelberg paper also discovered two key occurrences when illustrating how the user cost approach works: when interest rates are already low, house prices are more sensitive to changes in real interest rates, and in high appreciation rate cities home prices are more sensitive to real interest rate changes.
Calculating the User Cost
To examine the user cost within Canada we computed the user cost for 8 metropolitan areas in our sample. As is often true with theoretical constructs and was true in applying the user cost in the United States, there are a number of difficult challenges when apply theory to practice. The method used to generate all variables will be discussed followed by some problems with the data.
First, we calculated the risk-free rate (RF). This variable was generated specific to each metropolitan area by taking the 10 year bond yield on government of Canada bonds from January each year and subtracted the metropolitan area specific inflation determined by the CMA for the first quarter of each year. Since the actual inflation in each region was applied to the formula instead of an estimated inflation there are a number of periods that actually have a negative risk free rate.
Second, we produced a dummy variable of 1.5% to use for property tax and applied that in each city for each year. We decided to apply a dummy variable that would be somewhat similar to actual property tax rates because of the complexity of property tax assessment in each separate municipal region in Canada. As Kenneth J Klassen, stated in The Taxation of Residential Property in Canada (2001, March), “due to the differences in property tax assessment practices, there can be considerable variation in the applicability of the statutory property tax rates across cities, even within a given province (for example, the capping of adjustments in Toronto is not true in all Ontario cities).”[1] The other problem with collecting property tax information from a number of cities is that the data is collected by specific municipalities and the way many of these municipalities calculate property taxes has change over the past 20 years and detailed numbers are not offered via email in most cases.
Third, the maintenance cost (Mc) or depreciation cost was calculated. A straight 2.5% was applied throughout all calculations and was taken as an estimate from the Himmelberg paper.
Forth, the expected capital gain/loss was calculated. This was determined by taking the average of real price growth for the period that data was available for each specific metropolitan area. In this was we were able to account for differences in expected appreciation rates in each metropolitan area. For example, expected price appreciation rates are much higher in a city like Vancouver at 4.4% versus a city like Winnipeg at 1.4%.
Finally fifth, the added risk associated with homeownership versus renting the same property was produced to complete the user cost formula. The number applied across all years and cities was 2%. This was taken as an estimate from the Himmelberg paper. They suggested that this risk premium may be too high because it ignores factors such as insurance value from owning a home to hedge risk associated with future changes in rents; however, choosing alternate values would have minimal effect on the time series behaviour of user costs.
Here are my results Below – Bear with me because I am just cutting and pasting from my research paper (looks like my tables have failed to convert in Wordpress).
User Cost Results
Table 2 shows how the user cost can vary over time across cities and within cities. The average user cost is higher in the cities that did not experience any major peaks compared to cities that experienced peaks and troughs. For example, compare Edmonton, which has an average user cost of 4.89% and is one of the highest price growth cities recently with Montreal, which has an average user cost of 7.90% and is one of the lower growth cities. This range of user cost implies that average price-to-rent ratios ranging from 20.45 to 12.66 should be present in the major Canadian metropolitan areas. The last few years have seen falling user cost in all the cities analyzed and this is displayed in Table 2 as well. The only city that remains near its average 34 year average user cost is Toronto; the average in Toronto was 6.6% while in 2007 the city experience a user cost of 6.00%. Also noteworthy are the drops in user cost from their respective averages in Calgary and Edmonton. In Calgary, the drop from 6.35% to 0.92% implies that average price-to-rent ratios could have increased from 15.75 to 108.7. In Edmonton, the drop from 4.89% to 1.35% implies that average price-to-rent ratios could have increased from 20.45 to 74.1.
Table 2 also highlights the change in user costs for the cities since their prior peaks and troughs. The city that stands out the most on this basis is Vancouver. There is no coincidence here. The user cost experience at the peak of the Vancouver housing bubble in 1981 shows a dramatic 1065.29% decline since. What is very interesting to note is that user costs in all cities have declined even when compared to their previous troughs; these results are consistent with the affects in the United States that were described in the Himmelberg paper about the user costs in American cities.
Table 2
Are Current House Prices Too High?
So far we have assessed this question strictly by applying the conventional measures earlier in the paper and our findings indicated that housing not unsustainable high in any of the cities currently except for Edmonton. The following assessment will determine if housing prices are unsustainable too high or low in the all the Canadian cities discussed so far by comparing imputed rents to actual rents available in the market and should provide clarity with regard to the housing market situation in Edmonton currently.
To do this we create an index of imputed-to-actual-rent ratio for 1980 to 2007. This was done by first calculating the imputed rent in each city by multiplying the user cost (Ut) by the real price (Pt) within each city. Then the imputed rent (Pt*Ut) was normalized so that a value of 1 would correspond to the 27 year average imputed rent in each area. Finally, the normalized imputed rents were divided by the normalized real rental growth rates from each city. The imputed-to-actual-rent ratio was then compared to the Price-to-Rent ratio by graphing each of these variables on the same chart for each city to establish how they move in relation to one another.
At the same time we decided to calculate the imputed-to-actual-rent ratio for 1980 to 2007 as an alternative measure of housing valuations. This was done by taking the normalized imputed rent from each city and dividing that by the normalized real income growth calculated earlier. This measure was graphed with the Price-to-Rent, and the imputed-to-actual-rent ratios to visually asses how incomes have moved in relation to imputed rent. Figure 10 displays the results of the graphing exercise.
Graphs of Imputed-to-Actual-Rent, Imputed-Rent-to-Income, and Price-to-Rent ratios
Similar to the graphs of the conventional measures presented earlier in this paper, the cities can be divided into three trend groups. The first trend group has experience a “U” price and imputed rent and income trend and includes Halifax, Ottawa, and Winnipeg. The second group follows more of an “n” shaped pattern occurring within the variables and includes Montreal, and Vancouver. Finally, the third is a much more volatile looking group currently and includes Edmonton, and Calgary.
There are three important results to highlight that have been illustrated in the graphs in Figure 10. The first is that for 6 of the 8 cities analyzed, the imputed-to-actual-rent ratio does not suggest any widespread or historically large mispricing of owner-occupied housing in 2007. Taking in to account for the changes in imputed rent since previous peaks, troughs, and the 27 year average, the 2007 imputed rent in all cities has actually decreased.
The second key observation is that the three variables made dramatic deviations from their normalized averages in the Vancouver market during the 1981 bubble formation and collapse. The unique thing displayed was the Price-to-Rent ratio deviating strongly to the upside of its normalized average while the Imputed-to-Actual-Rent and
INCERT Figure 10 (Graphs of imputed ratios)
Imputed-to-Income ratios both deviated strongly in the opposing direction. This suggests that the imputed ratios may be good predictors of mispricing in property markets because they were able to predict such occurrences in the past in the Vancouver market.
The third significant observation made is that there are two cities that are experiencing dramatic deviations in all three variables similar to those experienced during the bubble in the Vancouver housing market in the year 1981, Calgary and Edmonton. The three indicators made significant movements in Calgary in 2006 with the Price-to-Rent ratio moving sharply higher and the two imputed variables sinking downwards. In 2007, the Price-to-Rent ratio seems to have corrected slightly in Calgary with a downward move. In Edmonton, in 2007 there has been a significant divergence with the Price-to-Rent ratio shooting upwards and the imputed ratios declining sharply. This does not necessarily signify a bubble forming in these markets; however, it does increase the likelihood of unsustainable property prices presently existing in Edmonton, and/or Calgary.
What Might Be Misleading in these Calculations?
There are a number of things that are potentially misleading within the calculations we made. First, the actual inflation experienced in each city as reported by the CMA was subtracted from the 10 year bond yield to derive a risk free rate for each year in each metropolitan area. The problem here is that the inflation experienced was greater than the yield on the 10 year bond during some time periods so a negative risk free rate was applied in a few instances. This actually led to a negative user cost for a few years. Under this scenario it may have been better to apply the rate of a real interest 10 year government of Canada bond rate. Second, because of the complexity of collecting data for property taxes a dummy variable was applied. The user cost for each city could have varied significantly depending on the size of property taxes each year. Third, we only focused on residential owner occupied housing when referring to the user cost; however, if we had included income properties our analysis would have needed some alterations to account for income tax deductions with regard to mortgage interest expenses, deprecation allowances, etc. Fourth, the expected growth rate applied was derived from the average real price increase over the period from 1978 to 2007 for most cities and this average may over or under represent the actual expected appreciation in each market.[2] Fifth, our analysis of imputed rent assumes that there is low-cost arbitrage between owning and renting; however, we know this to be untrue as there are significant expenditures attached to moving including mortgage fees, broker commissions, moving costs, etc; although, this would justify minor deviations of the imputed rent from actual rents. Finally, our valuation ratios may be biased due to the tendencies in unmeasured quality differences between rental properties and owner-occupied units.
Conclusion
We have discussed how to apply the User Cost Approach to the Canadian property market to aide the conventional ratios in producing better analysis of the sustainability of property markets in the major Canadian metropolitan areas.
[1] Kenneth J. Klassen, Stanley N. Larken. The taxation of Residential Property in Canada. March 2001. CMHC. 3.6.8 Comparison of Property Taxes.
[2] In the Himmelberg paper they applied a 60 year average appreciation.
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