Measuring House Price Bubbles Steven C. Bourassa School of Urban and Regional Planning and School of Public Administration, Florida Atlantic University, 777 Glades Road, Boca Raton, FL 33431, USA, email: [email protected] Martin Hoesli Geneva Finance Research Institute and Swiss Finance Institute, University of Geneva, 40 boulevard du Pont‐d’Arve, CH‐1211 Geneva 4, Switzerland; University of Aberdeen Business School, Scotland; and Kedge Business School, France, email: [email protected] Elias Oikarinen School of Economics, University of Turku, Rehtorinpellonkatu 3, FI‐2500 Turku, Finland, email: [email protected] January 28, 2016 Keywords: Housing; Bubble; Overvaluation; Asset Pricing; Price‐Rent Ratio; Policy Measures JEL Codes: R31; G12; E58 1 Measuring House Price Bubbles Abstract Using data for six metropolitan housing markets in three countries, this paper provides a comparison of methods used to measure house price bubbles. We use an asset pricing approach to identify bubble periods retrospectively and then compare those results with results produced by six other methods. We also apply the various methods recursively to assess their ability to identify bubbles as they form. In view of the complexity of the asset pricing approach, we conclude that a simple price‐rent ratio measure is a reliable method both ex post and in real time. Our results have important policy implications because a reliable signal that a bubble is forming could be used to avoid further house price increases. Introduction Several countries experienced soaring house prices in the early 2000s, with severe price declines during the latter part of the decade. Rapid price increases also occurred in the late 1980s in some other countries. When prices rise rapidly, commentators often refer to this as a housing bubble, which is then hypothesized to have collapsed when house prices drop. A bubble refers to house price levels that depart markedly from “fundamental” values (Stiglitz 1990). There is, however, a lack of consensus in the literature as to what method should be used to measure fundamental house values and hence any discrepancy between such values and actual house prices. This issue applies with respect to both ex post and real time measurement of bubbles. It has been suggested that problems in specifying house price fundamentals imply that bubbles should instead be defined as dramatic increases in prices followed by rapid falls in prices (Lind 2009). Of course, this definition begs the question of how much and how rapidly nominal or real prices must rise and fall to constitute a bubble. 2 In spite of the woolly nature of the concept of a bubble, there seems to be some consensus about when they have occurred in the past and the negative effects they have had on the economy. For example, there is widespread agreement that there was a bubble in the U.S. (or, at least, parts of the U.S.) in the 2000s. Moreover, the U.S. bubble has generally been seen as a major factor contributing to the recent financial and economic crises (Shiller 2008, Brunnermeier 2009, Martin 2010). In addition to contributing to a general decline in the economy, this has also caused substantial harm to households and neighborhoods in many parts of the U.S. House price volatility has had similar effects in other countries, most notably in Spain and Ireland. In hindsight, it appears that efforts to avoid the formation of bubbles would be sound public policy (Crowe et al. 2013). The methods that have been used in the literature to identify housing bubbles may be categorized as: (1) analyses of various ratios that typically compare house prices to either rents or incomes (Himmelberg, Mayer and Sinai 2005); (2) regression analyses of various sorts, including models based on either housing supply and demand theory or asset pricing (present value) concepts as well as cointegration and unit root tests (Abraham and Hendershott 1996, Black, Fraser and Hoesli 2006, Oikarinen 2009b, Yiu, Yu and Jin 2013); and (3) a method drawn from physics that focuses on the rate of growth in prices (Zhou and Sornette 2006). The first two of these categories are usually consistent with the “Stiglitz” bubble definition as in most cases the aim is to compare house prices with fundamentals, such as income, rent, and other variables. The third category seems consistent with the “Lind” bubble definition in that the focus is solely on how fast prices grow. This paper is the first to provide a comparison of a broad subset of these methods. We apply the methods to a set of metropolitan areas representing a range of circumstances, including variations in the occurrence and timing of bubbles as well as contextual differences across locations both within and across countries. We use an asset pricing model to retrospectively identify bubble periods given that the value of an asset is the sum of the present values of future earnings. Although other methods are less firmly based on theory, they are generally simpler to implement. Initially, we compare findings from retrospective or 3 “ex post” analyses of each location. Then we apply the methods recursively to determine which is the most effective in capturing the formation and dissolution of bubbles in “real” time. We also undertake a number of variations on our analysis to check the robustness of our conclusions. The empirical analysis is based on six metropolitan areas in three countries: Helsinki (Finland), Geneva and Zurich (Switzerland), and Chicago, Miami, and San Francisco (U.S.). Some of these cities have experienced what are generally considered to be significant price bubbles in recent decades (Figure 1). The U.S. is widely thought to have experienced a substantial bubble in the mid‐2000s, although this occurred, with some exceptions, mainly in coastal supply‐
constrained cities such as Miami. A large house price overreaction took place in Finland after financial market liberalization in the late 1980s. The overreaction was followed by a drastic drop in housing prices and eventually by an overreaction downwards. Large price increases also occurred in Switzerland at that time, and it may be that a bubble began to form in Geneva at the end of our sample period. Our results show that it is possible to identify bubbles as they are developing and that a simple price‐rent ratio method is reliable in detecting bubble and non‐bubble periods. Applying the price‐rent ratio across our six cities, the average of sensitivity (percentage of bubble quarters identified correctly) and specificity (percentage of non‐bubble quarters identified correctly) is 88.6 percent ex post and 84.1 percent recursively. The worst‐performing methods ex post are the imputed‐actual rent ratio (63.6 percent accuracy) and multivariate regression (65.7 percent). The worst‐performing methods recursively are multivariate regression and the growth rate measure from physics (both 66.7 percent). The robustness checks all confirm the superiority of the price‐rent method. The next section presents alternative approaches to measuring house price bubbles. Our empirical strategy is outlined in the following section. The empirical results are then discussed. A final section concludes. 4 Alternative Approaches to Measuring Bubbles The methods that have been employed to measure house price bubbles typically aim to compare actual price levels with some indicator of fundamental or equilibrium levels. Fundamental price levels are consistent with a long‐run relationship between house prices and determinants of the supply and demand for housing. For example, prices might be compared to per capita or household incomes, given the importance of income as a driver of house values. Alternatively, prices can be related to rents in an asset pricing model. Approaches to measuring bubbles include simple comparison of ratios (such as price‐
rent or price‐income ratios) to their long‐term averages. More complicated approaches in most cases involve some type of regression analysis to identify the long‐term relationships among variables. In some cases, price levels or changes have been regressed against various supply and demand variables, with fitted values interpreted as equilibrium levels or changes. In other cases, regression models have been based on present value concepts, emphasizing the relationship between discounted expected rents and current prices. Other regression approaches involve unit root tests of house prices, price‐rent ratios, or price‐income ratios. One final strand of research has focused on identifying rates of growth in house prices that are by definition considered to be unsustainable.1 Given the heterogeneity of housing markets within a country, we focus here on applications of these methods that use metropolitan or regional rather than national data. Ratio measures include: rent‐price, price‐rent, imputed rent (or user cost)‐actual rent, imputed rent‐price, price‐income, and imputed rent‐income ratios. For example, Case and Shiller (2003) calculate price‐income ratios for U.S. states for 1985 to 2002 and find that, at their peaks in the late 1980s or early 1990s, the price‐income ratios exceeded their long‐term average by at least 20 percent. Ambrose, Eichholtz and Lindenthal (2013) calculate rent‐price ratios for Amsterdam over the lengthy period from 1650 to 2005; they report several extended 1
Another approach, which we do not pursue here, involves creating an index based on multiple measures and observing how the index varies from its long‐term average. UBS (2014) has a set of national and regional house price bubble indexes for Switzerland that combine six measures, including price‐rent and price‐income ratios. 5 deviations from the average. Other ratio studies focus on imputed rent measures that are based on the user cost of housing. Himmelberg, Mayer and Sinai (2005) compare imputed‐
actual rent ratios with price‐rent ratios and imputed rent‐income ratios with price‐income ratios for U.S. MSAs. While their results based on imputed rent do not find evidence of bubbles as of the end of the 1980‐2004 period, the price‐rent and price‐income ratios lead to different conclusions for many of the MSAs. Using data for Finnish cities, Oikarinen (2010) focuses on how house price growth expectations affect user cost measures. He calculates user cost‐rent ratios using different assumptions about house price appreciation and concludes that the evidence for bubbles is highly dependent on the appreciation assumption. Regression methods can be grouped broadly into three types. Regardless of the type, the dependent variable is specified as either the price or a ratio relating price to rent or income (in levels or in changes). The first type models price or a price ratio as a function of supply and demand fundamentals. In some variations, the fundamentals are supplemented with disequilibrium variables designed to capture bubble building, on one hand, and the tendency to revert to equilibrium, on the other hand. These models are sometimes based directly on urban economic theory, while in other cases the choice of explanatory variables is more ad hoc. The second type of model derives from the financial economics literature and is based on the fact that prices are the present value of future rents. The final type relies on time series techniques to test for unit roots. Studies based on supply and demand fundamentals find evidence of a bubble (or at least overvaluation) in some U.S. locations in the early 2000s (Case and Shiller 2003, Goodman and Thibodeau 2008, Wheaton and Nechayev 2008). A series of papers by Hendershott and his colleagues incorporate disequilibrium variables into supply and demand models and find evidence of bubbles in U.S. coastal cities and some Australian and New Zealand locations (Abraham and Hendershott 1996, Bourassa and Hendershott 1995, Bourassa, Hendershott and Murphy 2001). Bourassa, Hendershott and Murphy (2001) also apply cointegration techniques to their data, finding results similar to those of their primary method. Oikarinen (2009a) estimates a cointegrating relationship for Helsinki, Finland, finding substantial over‐valuation in 6 the late 1980s. Using a present value model, Campbell et al. (2009) find evidence of bubbles in some U.S. MSAs in the 2000s. Ambrose, Eichholtz and Lindenthal (2013) apply a present value model to their Amsterdam rent‐price ratio series, finding several bubble periods.2 The third regression approach, which uses unit root tests to identify bubbles, has been applied by Taipalus (2006), who studies five countries, including the U.S., and six urban areas in the U.S. She finds, for example, that there was a bubble in San Francisco starting in 2003 and in Chicago starting in 2000. Applying a method developed by Phillips, Wu and Yu (2011), Yiu, Yu and Jin (2013) apply unit root tests to Hong Kong, identifying 10 short‐lived “bubbles” during an 18‐year period. The exponential growth rate (EGR) method posits that a faster than exponential rate of growth in house prices is unsustainable and evidence of a bubble. Sornette and his colleagues apply this method in several studies, including Zhou and Sornette (2006), who find that 22 U.S. states had bubbles at the end of the 1993‐2005 period. Evaluating alternative methods for measuring house price bubbles, the present value approach is soundest from a theoretical point of view as asset prices are the present values of expected earnings. Assuming a constant relationship between gross rents and after‐tax cash flows, house prices can be modeled as a function of the present value of expected gross rents. The price‐rent ratio measure is closely related to the present value method; however, it assumes constant risk premia and rental growth expectations. Although imputed rent (or user cost) measures do not assume constant risk premia, they are highly sensitive to price growth expectations, which are difficult to quantify. Price‐income ratios assume a constant relationship between prices and per capita incomes, which ignores the independent effect of population change on prices. The specification of regression models based on the supply and demand for housing depends on the definition of fundamentals. Some variables included in such models may not 2
Smith and Smith (2006) apply a simple present value approach to data for single‐family homes that were purchased or rented. Their aim was to collect data that were as comparable as possible for the two types of tenure. Out of 10 urban markets, only one (San Mateo County) was over‐valued as of 2005.
7 actually be fundamentals determining the long‐term equilibrium price level because they tend to be mean‐reverting. Although such variables can lead to significant improvements in model fit, they may track disequilibrium prices rather than equilibrium prices. An alternative is to specify a parsimonious model, which could, for example, include only aggregate personal income as an explanatory variable. Such a model could be viewed as an improvement over the price‐income ratio approach in that it takes population into account rather than just per capita income. As there are good theoretical reasons to expect that the long‐term coefficient on income can take values other than one (implicitly assumed by the price‐income ratio) and can vary substantially across regions, another advantage of the regression method over the price‐
income ratio is that the long‐term coefficient on income is not restricted to equal one. The unit root test method is based on the time series properties of the data only, meaning that it does not give any indication of the magnitude of a bubble. In recent applications of this technique to national housing markets (Engsted, Hviid and Pedersen 2015, Pavlidis et al. 2016), it identifies a bubble as it is forming but generally does not capture disequilibria beyond the peak of the bubble. Also, in some cases, the method seems oversensitive to departures from equilibrium (such as in Taipalus 2006 or Yiu, Yu and Jin 2013). Finally, the EGR method is unappealing from a theoretical perspective, as it does not relate house prices to fundamentals and hence could lead to incorrect bubble signals. This comment also applies to the unit root approach when applied to a house price index without consideration of rents or incomes. One criterion for evaluating different approaches to measuring price bubbles is ease of implementation. Although the present value method is appealing from a theoretical point of view, it is relatively difficult to apply in practice due to computational complexity. Most of the other methods are relatively simple to implement. The price‐rent and price income ratio methods are particularly easy to apply. 8 Empirical Strategy The first step of our empirical approach is to identify bubbles ex post using the present value method. We then compare various other ex post measures to the present value benchmark, using over 30 years of quarterly data for each location. Then we assess the usefulness of these other methods in identifying bubbles in real time. To achieve this, we apply each of the methods recursively, progressively adding one quarter of data to the analysis. We focus on the last 10 years of the sample period in each of our cities, so that at least 20 years of data are available prior to that period to identify long‐term equilibria. Our strategy for identifying bubbles involves comparing measures with their long‐term averages (for ratios), estimated equilibrium levels (for regression methods), or log‐linear trend (for EGR) and observing when the discrepancy exceeds 20 percent.3 That rule is based on our judgment about the criteria that could be viewed as strongly indicating the presence of a bubble. We next discuss each of the methods, starting with the benchmark present value model. The section concludes with an overview of the data. Present Value Method It has been long acknowledged that the value of an asset should reflect the discounted present value of its expected future cash flows, the discount rate being possibly time‐varying: 

Pt    1
i 1 

i
 1     E  R  t j
j 1

t
t i
(1) where Pt is the real asset (house) price in period t, stands for the real discount rate, Et denotes the rational expectation as of period t, and R is the real cash flow (rent) provided by the asset. Our empirical application of the present value model is based on the work of Campbell and Shiller (1988a, 1988b) and on that of Black, Fraser and Hoesli (2006), who apply the model 3
We also perform robustness checks by setting the threshold to 10 and 30 percent, respectively. 9 to the housing market. The latter authors show that the equilibrium log price‐rent ratio, pt - rt , with lower case letters representing the natural logarithms of their upper case counterparts, can be defined as:4 

j 0
j 0
pt  rt      j 1Etc  rt  j 1      j 1Etc  t2 j 1  (2) c
where Et   is a conditional expectations operator. While α represents a time‐invariant constant term, the other two components determining the equilibrium price‐rent ratio are time‐varying. The second component caters for the time variation in the expected rental growth  r  . Obviously, greater expected rental growth causes lower required current yield. The last constituent of the ratio incorporates the influence of a time‐varying risk premium on the required yield: the greater the expected volatility in returns, the greater the risk premium and hence the lower the equilibrium price level relative to rents. Following the work of Merton (1973, 1980) on the inter‐temporal CAPM, the time‐varying risk premium component is modeled as the product of the coefficient of relative risk aversion, b , and the expected 2
variance of housing returns, s . The constant term  is defined as  k  f  1    , where f is the constant real risk‐free component of real required returns measured as the average real 10‐year government bond yield in the respective country over the sample period. The terms k and m are linearization 

constants with k   ln   1    r  p  and   1 1  exp  r  p  , where  r  p  is the 1 (in practice close to 1 in each city). sample mean of the log rent‐price ratio and 0
To estimate the expected returns, we adopt the vector autoregressive (VAR) methodology introduced by Campbell and Shiller (1988a, 1988b). Following Black, Fraser and Hoesli (2006), the rental growth is forecast using a three‐variable VAR model, 4
Black, Fraser and Hoesli (2006) substitute income for rent because rent data were not available, while Hott and Monnin (2008) substitute imputed rent for rent. 10 zt   pt  rt , rt ,  t2  , while housing return variance is forecast using an ARMA‐GARCH(1,1) model.5 All variables in the VAR model are demeaned thus avoiding the need to include a deterministic constant in the equations. The inclusion of the log price‐rent ratio in the VAR helps the model to summarize the market’s relevant information (Campbell and Shiller 1988a). 

Finally, as in Black, Fraser and Hoesli (2006),  is computed as r e   2 2   2 where r e is the mean total return for housing over the risk‐free interest rate during the sample period and  2 the variance of these excess returns. After estimating each period’s equilibrium price‐rent ratio,  pt  rt  * , for each time period based on (2), we define the disequilibrium, , as:  t    pt  rt   pt  rt  *
 p  r   p
t
t
t
 rt  * . (3) That is, the disequilibrium in period t is computed by taking the ratio of the actual and fundamental log price‐rent relations and “normalizing” this ratio by the sample mean of the actual to fundamental price‐rent ratio. Hence, it is implicitly assumed that the mean disequilibrium over the sample period is zero. Ratio Measures We focus on price‐rent, price‐income, and imputed‐actual rent ratios because they are the main types of ratios that have been used to measure bubbles. The price‐rent ratio is specified as Pmt Rmt , where Pmt and Rmt are the real median house price and annual rent for metropolitan area m at time t for Switzerland and the U.S. For Finland, Pmt and Rmt are the average price and rent per square meter, respectively. The price‐income ratio is Pmt Ymt , where Y is real per capita income.6 Imputed rents are defined as the expected user cost per dollar of 5 The ARMA specifications are selected based on the Schwartz Information Criterion together with the Lagrange Multiplier test for residual autocorrelations at lag length two. The specifications vary across cities. 6
Household income is probably more relevant than per capita income as a housing affordability measure; however, time series of household income are generally not available for metropolitan areas. 11 owner‐occupied housing for a typical household multiplied by the real price level: *
Rmt
 Pmt E  umt  , where R* is annual imputed rent, E   is the expectations operator, and u is the annual user cost. As discussed in Bourassa et al. (2015), user costs vary across countries depending on factors such as the taxation of imputed rents and capital gains and tax deductibility of mortgage interest and other costs. For Finland, the user cost per dollar of investment in owner‐occupied housing is: E  umt   1   mt  imt   m  E  gmt  (4) where t is the marginal income tax rate for the median household until 1992 and the capital gains tax rate since 1993 (due to a change in the tax rules), i is the nominal mortgage interest rate, d is a set of costs not itemized separately (in this case, property tax, depreciation and maintenance, hazard insurance, and annualized transaction cost rates), and g is nominal house price appreciation. Note that this assumes that the cost of equity and debt financing are the same (i), avoiding the need to make any assumptions about debt ratios. The costs of equity and debt financing are both after‐tax, because returns on alternative investments of the equity would be taxed and mortgage interest is deductible from income for tax purposes.7 Capital gains are not taxed. The U.S. user cost is quite similar to the Finnish one, with the notable exception that property taxes,  , are generally deductible in the U.S.: E  umt   1   mt  imt  m    m  E  gmt  (5) where d in this case excludes the property tax rate. As in the Finnish case, this equation assumes that the cost of both equity and debt is equal to the mortgage interest rate and both costs are after‐tax. The cost of debt financing is after‐tax if the typical household itemizes deductions (rather than taking the standard deduction). The U.S. marginal tax rates include 7
Starting from 2012, the deductibility of mortgage interest payments has declined. The computations for Helsinki adjust for this change in the rules. 12 both federal and state income tax rates where appropriate. This equation also assumes that capital gains on a typical owner‐occupied house would generally be exempt from taxation in the U.S. The Swiss user cost is somewhat more complicated mainly due to the taxation of imputed rent as defined by the tax authorities (  ) and capital gains (at the annualized capital g
gains rate, t ): g
E  umt   1  mt  imt  m  m   m  mtm  1  mt
 E  gmt  (6) This equation also differs from the Finnish and U.S. cases in that both property taxes (  ) and maintenance ( ) are deductible (here d refers to depreciation and annualized transaction costs). The Swiss marginal tax rates include both federal and cantonal rates. The imputed rent and maintenance figures are drawn from Bourassa and Hoesli (2010). The house price growth rate is the most problematic assumption in the user cost calculations. As noted above, Oikarinen (2010) reaches varying conclusions about the existence of bubbles depending on assumptions about house price growth expectations. We focus here on the Himmelberg, Mayer and Sinai (2005) approach, which bases expectations on a long‐term average nominal price growth rate as rents on average tend to grow at the same long‐term rate as house prices.8 Regression Methods Attempts to identify bubbles using regression methods raise questions regarding model specification, estimation techniques, and interpretation of results. One issue with respect to 8
In contrast, survey data suggest that experts’ and consumers’ actual expectations about house price growth reflect recent experience to some extent, suggesting that some function of recent years’ growth rates might more closely approximate household behavior. This is based on comparison of the Federal Housing Finance Agency’s U.S. house price index (http://www.fhfa.gov) with house price expectations data from Thomson Reuters University of Michigan Surveys of Consumers (http://www.sca.isr.umich.edu) and the Wall Street Journal Economic Forecasting Survey of economists (http://online.wsj.com/public/page/economic‐forecasting.html). Of course, during periods of rapid price growth, expectations themselves could explain that growth, making it impossible to observe a bubble. 13 specification of housing supply and demand models concerns the choice between parsimony and a larger set of variables. Theory suggests that a number of variables are relevant to the demand and supply sides of the housing market. These include, but are not limited to, aggregate income and interest rates on the demand side and construction costs, regulatory constraints, and topography (land constraints) on the supply side. One issue with a “fully” specified model is that it might explain too much in the sense that it explains the formation of bubbles rather than just long‐term equilibrium price levels. For example, interest rates have themselves been identified as a factor contributing to the recent U.S. bubble (Allen and Carletti 2010, McDonald and Stokes 2013). Moreover, in the long run, interest rates tend to be mean‐
reverting, implying that they cannot explain long‐run changes in house prices. This suggests a parsimonious modeling strategy that would focus on aggregate income, with separate models for each metropolitan area so that the estimated income elasticities reflect each location’s supply constraints. We estimate both multivariate and parsimonious (univariate) models. The multivariate models have real house prices on the left‐hand side and a range of variables that have been used in the literature on the right‐hand side, including real aggregate income, population, unemployment rates, real interest rates, real construction costs, rate spreads between 10‐year and 3‐month government securities, and consumer sentiment indexes: a
pmt  Ymt
, N mt , u mt , mt , bmt , smt ,  mt  (7) a
where p is the natural logarithm of house price, Y is real aggregate income, N is population, u is the unemployment rate,  m t is the real mortgage interest rate, b is an index of construction costs, s is the term spread, and  is a measure of consumer sentiment. For each metropolitan area we select the variables that maximize adjusted R‐squared and for which the estimates have the correct signs. Then we also estimate models with only real aggregate income on the right‐hand side. In every case, the models are estimated using the Fully Modified Ordinary Least Squares (FMOLS) estimator developed by Phillips and Hansen (1990), which is 14 asymptotically efficient when using non‐stationary variables and adjusts for serial correlation and for the possible endogeneity of regressors (unlike the conventional “static” OLS).9 EGR Approach The EGR approach focuses on identifying and modeling rates of growth that are, by definition, considered to be unsustainable. The basic idea is that asset markets are subject to positive feedback that can cause price growth to accelerate to unsustainable rates. This phenomenon is characterized by what is referred to as a power‐law singularity in which prices increase to infinity in finite time: pt  A  B t c  t  m
(8) where p is the natural logarithm of house price as defined above, t c is an estimate of the critical point (i.e., the peak of the bubble), and A, B, and m are coefficients. A bubble is identified whenever Pt increases at a rate faster than exponential. For example, if pt is graphed against time, then faster than exponential growth would be diagnosed whenever pt curves upwards, departing from a straight line. We modify the EGR approach to require actual prices to exceed the log‐linear trend by at least 20 percent.10 Data We have attempted to define the data as consistently as possible across countries. The main data sources are summarized in the Appendix. In some cases, the data were not available on a quarterly basis and it was necessary to interpolate. To retain degrees of freedom, interpolations were based on quarterly percentage changes in another closely related series.11 For example, U.S. aggregate income data for metropolitan areas are available on an annual 9
The long‐run variance calculations are based on the Bartlett Kernel and a bandwidth selected by the automated procedure described in Andrews (1991).
10
In logarithmic terms, this means that actual prices must exceed the trend by at least ln 1.2. 11
In a few cases, such as when the two series were moving in opposite directions, it was necessary to resort to straight‐line interpolation. 15 basis. The annual data were assigned to the second quarter of each year and the remaining quarters were interpolated based on national GDP statistics. Similarly, missing U.S. rent data were interpolated based on movements in the national all urban consumers’ CPI shelter costs component and missing U.S. metropolitan area construction cost data were interpolated based on a combination of more frequent national construction cost index numbers and the national all urban consumers’ CPI shelter costs component. Similar rules were used for the conversion of Swiss and Helsinki data. In all but one case, the interpolation was undertaken using quarterly percentage changes in another series. The only exception is for Zurich and Geneva population data where we apply a linear interpolation because national population data were also unavailable on a quarterly basis. Regarding Helsinki data, some variables were interpolated only during the early sample period, as there are readily available quarterly series for the late sample period. As a robustness check on the effects of interpolation on our results, we also undertake the analysis using annual data. The U.S. FHFA house price data are metropolitan area all transactions indexes. The all transactions indexes are repeat sales‐type indexes based on single‐family homes with mortgages securitized by the government enterprises Fannie Mae and Freddie Mac. These agencies focus on the middle of the price range, as they are prohibited from purchasing mortgages for expensive houses and other agencies are responsible for financing low‐income homeownership. The indexes are based on both appraisal‐based refinancing transactions as well as sales, so they may tend to lag the market somewhat (due to appraisal lag). These, the rental indexes, and the construction cost indexes were converted to real terms using the national all urban consumers’ CPI net of shelter costs. Nominal aggregate incomes were converted to real incomes using the national all urban consumers’ CPI (all costs). The Helsinki housing price index is the hedonic index depicting the price development of privately financed (non‐subsidized) condominium apartments provided by Statistics Finland. Some three‐quarters of all dwellings in the area are apartments, and rental units are almost solely apartments. The index is based on all condominium sales in each quarter. 16 The Swiss house price indexes are the IAZI/CIFI hedonic indexes based on transactions data for properties where debt financing has been used (Bourassa, Hoesli, and Scognamiglio, 2010). The indexes encompass transactions for both houses and condominiums and a large number of attributes are used to control for the quality of properties. The house price, rent, and construction cost indexes were converted to real indexes using the CPI net of rent. Nominal aggregate incomes were converted to real incomes using the Swiss CPI. Empirical Results Ex Post Analysis The aims of the ex post analysis are, first, to identify bubble periods using the present value approach and, second, to compare those results with results based on alternative methods. Initially we discuss the present value estimations followed by a discussion of the parsimonious and multivariate regressions. Table 1 presents summary statistics regarding the key variables in the present value analysis and in the VAR models estimated to forecast the rental growth rate. All the variables, including the estimated coefficients of relative risk aversion and the discount factors, exhibit notable variation across cities. Similar to Black, Fraser and Hoesli (2006), the VAR model fits are better for the price‐rent ratio and conditional variance than for the rental growth. Nevertheless, rental growth rate too shows predictability in all the cities. Table 2 provides descriptive statistics for the ratio measures and for the variables included in the regression analyses. The average ratios tend to be high in the Swiss cities and low in Chicago and Miami. Table 3 contains the FMOLS regression results for both the multivariate and parsimonious models. In line with theory, house prices are positively related to aggregate income and construction costs. Depending on the city, the multivariate model also includes one or more additional variables: the unemployment rate, the mortgage interest rate, and the 17 term spread are all negatively related to house price changes. The adjusted R‐squared statistics are generally high, with the notable exception of Zurich. When aggregate income is the only explanatory variable, the adjusted R‐squared statistics are markedly lower, except for Chicago and San Francisco. Income is highly significantly related to house prices; Zurich again constitutes the exception with no statistically significant impact of income on house prices.12 Figure 2 compares the ex post normalized disequilibria for the various methods for one of the European cities, Helsinki, and one U.S. city, Miami.13 Helsinki experienced bubbles in the late 1970s and mid to late 1980s, while Miami had a bubble in the mid to late 2000s. With the exception of Helsinki in the late 1970s, after each of the identified bubble periods in all six of our cities even nominal prices decreased notably over a relatively short period of time.14 Further, there are no substantial nominal price drops in periods that are not preceded by bubble signals in any of the cities. In cities where a bubble is identified, the price‐rent ratio disequilibria generally track the benchmark disequilibria. For Miami in the 2000s, none of the methods shows disequilibria as large as that of the benchmark. In Miami, every method identifies a bubble, which is not the case for Chicago or San Francisco. Across all cities, the imputed‐actual rent ratio method is least consistent with the benchmark, and sometimes shows implausible results. Table 4 reports the average percentage of quarters that each measure is in agreement with the benchmark with respect to the existence of a bubble (using the 20 percent threshold). The percentages are averages of sensitivity (the percentage of bubble periods correctly identified) and specificity (the percentage of non‐bubble periods correctly identified).15 Table 5 contains the Mean Relative Absolute Errors (MRAEs) between the normalized disequilibria for the present value and each of the other measures. Both tables show that the price‐rent ratio is 12
We have been unable to find a convincing explanation for this. By “normalized” we mean that for each measure each period’s value is divided by the long‐term equilibrium value for that measure. To conserve space, our graphical analysis focuses on two cities. 14
Helsinki in the late 1970s was an exception largely due to high general inflation rates that allowed real prices to drop while nominal prices remained stable. 15
Because bubbles occur relatively infrequently, taking the average of sensitivity and specificity avoids bias in favor of methods that tend not to find bubbles. 13
18 on average the best ex post alternative to the benchmark. With respect to identifying bubbles, the price‐rent ratio is best in all but the two Swiss cities; with respect to MRAEs, it is best in all cities except Geneva (where it performs poorly) and Miami. The least effective method by both criteria is the imputed‐actual rent ratio. It is interesting to note that parsimonious regression performs somewhat better than multivariate regression, consistent with our expectation that the latter would explain too much of the movement in house prices. Recursive Analysis The recursive analysis focuses on the data that are available at each time period. The analysis is updated each quarter as new data become available. The aim is to assess which method would be most effective in highlighting a house price bubble contemporaneously, using the ex post present value measure as a benchmark. As noted above, we focus on the last ten years of data for each city. Figure 3 compares the recursive measures with the ex post benchmark for Helsinki and Miami. There is a bubble in Miami, but not in Helsinki. In both cities, the recursive price‐rent ratio clearly tracks the benchmark most closely. In Helsinki, one recursive method (EGR) suggests a bubble. The imputed‐actual rent ratio is an outlier in both locations, as is multivariate regression in Miami. Table 4 provides the average correct recursive identification of bubble and non‐bubble periods. The price‐rent ratio is the best method for four of the six cities and is best overall, while multivariate regression and the EGR methods are the least effective. The disequilibrium MRAEs shown in Table 5 also indicate that the price‐rent ratio is preferred. As for the ex post comparisons, it is notable that the recursive parsimonious regression method performs better than the multivariate regression method. Robustness Tests Table 6 reports the results of several robustness tests. The first line of the table repeats the last line from Table 4 for comparison purposes. The robustness tests include: modifying the 19 bubble threshold from 20 percent down to 10 percent and up to 30 percent; deleting the first five years of data; deleting the last five years of data; and using annual rather than quarterly data (to avoid potential problems with interpolation of some of the quarterly data). In all cases, the price‐rent ratio performs best overall both ex post and recursively as an alternative to the ex post present value benchmark. The worst performers ex post are the imputed‐actual rent ratio and multivariate regression. The worst performers recursively are multivariate regression and the EGR method. Notably, the results based on annual data provide even stronger support for the price‐rent ratio than the results based on quarterly data. Conclusions The marked periods of boom and bust in many housing markets over the past decade have led to the need to assess which methods, if any, are effective in identifying large price overvaluations. If such methods are effective not only ex post but also as the bubble is forming, policy measures could be taken to avoid further house price increases and the resulting detrimental effects on the economy. This paper has sought to identify which of a wide array of methods that have been used to identify house price bubbles is most effective in identifying bubbles not only ex post but also recursively. We focus on a sample of six cities that have experienced varying housing market circumstances over the past 30 or more years, including variations in the occurrence and timing of bubbles as well as contextual differences across locations both within and across countries. Bubble periods in each city are identified using an asset pricing approach. The best method both ex post and recursively is the price‐rent ratio approach; it identifies bubble and non‐bubble periods correctly in 88.6 percent of cases ex post and 84.1 percent of cases recursively and yields the lowest MRAEs relative to the ex post present value benchmark. The method also acts as an early warning signal when applied recursively as the bubble signal is triggered from 3 to 6 months prior to house prices being 20 percent above their 20 fundamental values. Hence, a simple method is shown to be very effective in identifying bubbles. We thank John Clapp, Martijn Dröes, Mika Kortelainen, and Song Shi for helpful comments. Financial support from the Academy of Finland, the OP‐Pohjola Group Research Foundation, the Kluuvi Foundation, and the Emil Aaltonen Foundation is gratefully acknowledged. References Abraham, J. and P. Hendershott. 1996. Bubbles in Metropolitan Housing Markets. Journal of Housing Research 7(2): 191‐207. Allen, F. and E. Carletti. 2010. An Overview of the Crisis: Causes, Consequences, and Solutions. International Review of Finance 10(1): 1‐26. Ambrose, B.W., P. Eichholtz and T. Lindenthal. 2013. House Prices and Fundamentals: 355 Years of Evidence. Journal of Money, Credit and Banking 45(2‐3): 477‐491. Andrews, D.W.K. 1991. Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation. Econometrica 59(3): 817‐858. Black, A., P. Fraser and M. Hoesli. 2006. House Prices, Fundamentals and Bubbles. Journal of Business Finance and Accounting 33(9): 1535‐1155. Bourassa, S.C., D.H. Haurin, P.H. Hendershott and M. Hoesli. 2015. Determinants of the Homeownership Rate: An International Perspective, Journal of Housing Research 24(2): 193‐
210. Bourassa, S.C. and P.H. Hendershott. 1995. Australian Capital City Real House Prices, 1979‐
1993. Australian Economic Review 28(3): 16‐26. 21 Bourassa, S.C., P.H. Hendershott and J. Murphy. 2001. Further Evidence on the Existence of Housing Market Bubbles. Journal of Property Research 18(1): 1‐19. Bourassa, S.C. and M. Hoesli. 2010. Why Do the Swiss Rent? Journal of Real Estate Finance and Economics 40(3): 286‐309. Bourassa, S.C., M. Hoesli and D. Scognamiglio. 2010. Housing Finance, Prices, and Tenure in Switzerland. Journal of Real Estate Literature 18(2): 263‐282. Brunnermeier, M.K. 2009. Deciphering the Liquidity and Credit Crunch 2007‐2008. Journal of Economic Perspectives 23(1): 77‐100. Campbell, J. and R. Shiller. 1988a. The Dividend‐Price Ratio and Expectations of Future Dividends and Discount Factors. Review of Financial Studies 1(3): 195‐227. Campbell, J. and R. Shiller. 1988b. Stock Prices, Earnings and Expected Dividends. Journal of Finance 43(3): 661‐676. Campbell, S.D., M.A. Davis, J. Gallin and R.F. Martin. 2009. What Moves Housing Markets: A Variance Decomposition of the Rent‐Price Ratio. Journal of Urban Economics 66(2): 90‐102. Case, K. and R. Shiller. 2003. Is There a Bubble in the Housing Market? Brookings Papers on Economic Activity (2): 299‐342. Crowe, C., G. Dell’Ariccia, D. Igan and P. Rabanal. 2013. How to Deal with Real Estate Booms: Lessons from Country Experiences. Journal of Financial Stability 9(3): 300‐319. Engsted, T., S.J. Hviid and T.Q. Pedersen. 2015. Explosive Bubbles in House Prices? Evidence from the OECD Countries, CREATES Research Paper 2015‐1. Aarhus University: Aarhus, Denmark. Goodman, A. and T. Thibodeau. 2008. Where Are the Speculative Bubbles in US Housing Markets? Journal of Housing Economics 17(2): 117‐137. 22 Harding, J.P., S.S. Rosenthal and C.F. Sirmans. 2007. Depreciation of Housing Capital, Maintenance, and House Price Inflation: Estimates from a Repeat Sales Model. Journal of Urban Economics 61(2): 193‐217. Himmelberg, C., C. Mayer and T. Sinai. 2005. Assessing High House Prices: Bubbles, Fundamentals and Misperceptions. Journal of Economic Perspectives 19(4): 67‐92. Hott, C. and P. Monnin. 2008. Fundamental Real Estate Prices: An Empirical Estimation with International Data. Journal of Real Estate Finance and Economics 36(4): 427‐451. Lind, H. 2009. Price Bubbles in Housing Markets: Concept, Theory and Indicators. International Journal of Housing Markets and Analysis 2(1): 78‐90. Martin, R. 2010. The Local Geographies of the Financial Crisis: From the Housing Bubble to Economic Recession and Beyond. Journal of Economic Geography 10(6): 1‐32. McDonald, J.F. and H.H. Stokes. 2013. Monetary Policy and the Housing Bubble. Journal of Real Estate Finance and Economics 46(3): 437‐451. Merton, R. 1973. An Intertemporal Capital Asset Pricing Model. Econometrica 41(5): 867‐888. Merton, R. 1980. On Estimating the Expected Return on the Market: An Exploratory Investigation. Journal of Financial Economics 8(4): 323‐361. Oikarinen, E. 2009a. Household Borrowing and Metropolitan Housing Price Dynamics – Empirical Evidence from Helsinki. Journal of Housing Economics 18(2): 126‐139. Oikarinen, E. 2009b. Interaction between Housing Prices and Household Borrowing: The Finnish Case. Journal of Banking and Finance 33(4): 747‐756. Oikarinen, E. 2010. Empirical Application of the Housing Market No‐Arbitrage Condition: Problems, Solutions and a Finnish Case Study. Nordic Journal of Surveying and Real Estate Research 7(2): 7‐33. 23 Pavlidis, E., A. Yusupova, I. Paya, D. Peel, E. Martínez‐García, A. Mack and V. Grossman. 2016. Episodes of Exuberance in Housing Markets: In Search of the Smoking Gun. Journal of Real Estate Finance and Economics, forthcoming. Phillips, P.C.B. and B.E. Hansen. 1990. Statistical Inference in Instrumental Variables Regressions with I(1) Processes. Review of Economic Studies 57(1): 99‐125. Phillips, P.C.B., Y. Wu and J. Yu. 2011. Explosive Behavior in the 1990s NASDAQ: When Did Exuberance Escalate Asset Values? International Economic Review 52(1): 201‐226. Shiller, R.J. 2008. The Subprime Solution: How Today’s Financial Crisis Happened and What to Do About It. Princeton University Press: Princeton, NJ. Smith, M. and G. Smith. 2006. Bubble, Bubble, Where’s the Housing Bubble? Brookings Papers on Economic Activity (1): 1‐50. Stiglitz, J.E. 1990. Symposium on Bubbles. Journal of Economic Perspectives 4(2): 13‐18. Taipalus, K. 2006. A Global House Price Bubble? Evaluation Based on a New Rent‐Price Approach, Research Discussion Papers No. 29‐2006. Bank of Finland: Helsinki. UBS. 2014. Swiss Real Estate Market: UBS Swiss Real Estate Bubble Index ‒ 2Q2014. Available at http://www.ubs.com/global/en/wealth_management/wealth_management_research/ bubble_index.html. Wheaton, W. and G. Nechayev. 2008. The 1998‐2005 Housing “Bubble” and the Current “Correction”: What’s Different this Time? Journal of Real Estate Research 30(1): 1‐26. Yiu, M.S., J. Yu and L. Jin. 2013. Detecting Bubbles in Hong Kong Residential Property Market. Journal of Asian Economics 28(October): 115‐124. Zhou, W. and D. Sornette. 2006. Is There a Real Estate Bubble in the US? Physica A 361(1): 297‐
308. 24 1980
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
1975
1976
1977
1978
1980
1981
1982
1983
1985
1986
1987
1988
1990
1991
1992
1993
1995
1996
1997
1998
2000
2001
2002
2003
2005
2006
2007
2008
2010
2011
2012
400
350
300
250
200
150
100
50
0
Helsinki
Chicago
Geneva
Miami
25 Zurich
a. European cities (1981Q1 = 100) San Francisco
b. U.S. cities (1980Q1 = 100) Figure 1. Real price indexes 350
300
250
200
150
100
50
0
2.3
2.1
1.9
1.7
1.5
1.3
1.1
0.9
0.7
0.5
0.3
0.1
1975
1976
1978
1979
1980
1981
1983
1984
1985
1986
1988
1989
1990
1991
1993
1994
1995
1996
1998
1999
2000
2001
2003
2004
2005
2006
2008
2009
2010
2011
‐0.1
Bubble period
Bubble criterion
Price‐rent ratio
Price‐income ratio
Imputed‐actual rent ratio
Parsimonious regression
Multivariate regression
EGR method
Present value method
a. Helsinki 2.1
1.9
1.7
1.5
1.3
1.1
0.9
0.7
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
0.5
Bubble period
Bubble criterion
Price‐rent ratio
Price‐income ratio
Imputed‐actual rent ratio
Parsimonious regression
Multivariate regression
EGR method
Present value method
b. Miami Figure 2. Comparison of ex post disequilibria 26 1.3
1.1
0.9
0.7
0.5
0.3
0.1
‐0.1
Bubble period
Bubble criterion
Price‐rent ratio
Price‐income ratio
Imputed‐actual rent ratio
Parsimonious regression
Multivariate regression
EGR method
Ex post PV benchmark
a. Helsinki 2.1
1.9
1.7
1.5
1.3
1.1
0.9
0.7
0.5
Bubble period
Bubble criterion
Price‐rent ratio
Price‐income ratio
Imputed‐actual rent ratio
Parsimonious regression
Multivariate regression
EGR method
Ex post PV benchmark
b. Miami Figure 3. Comparison of recursive disequilibria 27 Table 1. Statistics for the variables and VAR models in the present value analysis City Mean (standard deviation) VAR model R2 Lineariza‐
Coeffi‐
tion cient of relative constant risk () aversion () Log Log price‐
real rent rent growth ratio (pt – rate rt) (rt) VAR lag length Log Log Log price‐
real real rent rent house price growth ratio (pt – rate growth rate rt) (rt) (pt) Condi‐
tional variance of total real housing returns (2) Helsinki .0053 .0046 2.97 (.0351) (.0209) (.243) .0007
(.0006) 1.73
.988
.123
.984 .557 2
Geneva .0069 .0047 3.56 (.0221) (.0114) (.158) .0005
(.0005) 4.71
.993
.218
.985 .412 4
Zurich .0029 .0027 3.44 (.0370) (.0166) (.138) .0012
(.0008) 1.46
.992
.647
.967 .965 8
Chicago .0015 .0018 2.77 (.0191) (.0124) (.153) .0003
(.0004) 12.3
.985
.589
.998 .958 11
Miami .0011 –.0001 2.81 (.0310) (.0098) (.235) .0006
(.0008) 4.55
.986
.203
.993 .800 4
San .0058 .0040 3.18 Francisco (.0257) (.0198) (.243) .0004
(.0003) 5.00
.990
.307
.994 .674 3
Condi‐
tional variance of total real housing returns (2) Note: The sample period is 1980Q1‐2011Q2 for the U.S. cities, 1980Q1‐2011Q4 for Zurich, 1981Q1‐2011Q4 for Geneva, and 1975Q1‐2012Q4 for Helsinki. All variables are quarterly except for the annual price‐rent ratio. The VAR model lag length is selected based on the Schwartz Bayesian Information Criterion. However, more lags are included if necessary to be able to accept the null of no autocorrelation in the Lagrange Multiplier test at lags 1‐2. 28 Table 2. Descriptive statistics for ex post ratios and supply‐demand regression analyses City Price‐
rent ratio Price‐
income ratio Imputed‐
actual rent ratio Log change real house prices (pt) Log change real aggregate income (yt) Log change real constr. costs (ct) Unem‐
Term Real ployment mortgage spread rate (ut) (st) interest rate (it) Helsinki 20.1 (5.41) .147
(.0221) .618 (.387) .0053
(.0351) .0079
(.0186) –.0001
(.0073) .0709
(.0509) –.0047 (.0421) —
Geneva 37.0 (6.08) 15.4
(3.59) .959 (.441) .0069
(.0221) .0021
(.0010) .0002
(.0145) .0442
(.0262) .0271 (.0124) .0052
(.0149) Zurich 31.3 (4.64) 8.94
(1.37) 1.36 (.529) .0029
(.0370) .0048
(.0093) .0003
(.0144) .0236
(.0167) .0263 (.0130) .0048
(.0149) Chicago 16.1 (2.64) 5.22
(.545) 1.15 (.241) .0015
(.0191) .0039
(.0087) .0020
(.0089) —
.0486 (.0254) .0185
(.0126) Miami 17.1 (4.83) 6.36
(1.77) 1.09 (.277) .0010
(.0310) .0067
(.0103) .0007
(.0103) —
.0486 (.0254) .0185
(.0126) San 24.9 Francisco (6.35) 11.3
(1.94) .767 (.360) .0058
(.0257) .0058
(.0103) .0010
(.0093) —
.0486 (.0254) .0185
(.0126) Note: The table reports the means and standard deviations (in parentheses) of the variables. For the U.S. and Swiss cities, the price‐income ratio is computed as the median house price divided by the median annual income, and the price‐rent relationship is that between the median house price and the annualized median rent. For Helsinki, the price‐income ratio is the average per square meter price divided by average annual income, and the price‐rent ratio is computed as the average per square meter price divided by the annualized average rent per square meter. This means that the price‐income ratio for Helsinki, in particular, is not comparable to that for the other cities. The sample period is 1980Q1‐2011Q2 for the U.S. cities, 1980Q1‐2011Q4 for Zurich, 1981Q1‐2011Q4 for Geneva, and 1975Q1‐2012Q4 for Helsinki. 29 Table 3. Supply and demand regression results Variable Helsinki Geneva
Zurich
Chicago Miami
San Francisco
Multivariate model
Constant ‐.974 Aggregate income
.910 *** ‐5.384 ***
1.817 ***
‐.668
.440 **
Unemployment rate ‐2.822 *** —
—
Mortgage interest rate — —
—
Term spread
— —
Construction costs
Adjusted R
2
.283 .926 1.330 ***
.596
‐.378 .892 ***
— ‐.040
‐5.393 ***
.712 ***
—
‐.010 ***
‐.012 **
‐.009 **
‐.048 ***
.724
.197 ***
.241
.884 1.485 ***
.738
‐4.352 **
1.105 ***
—
‐.025 **
—
.0928 **
.889
Parsimonious model
Constant 1.103 ** Aggregate income
Adjusted R
2
n Time period
.722 *** .737 152 1975Q1‐2012Q4 ‐5.170 **
2.110 ***
.478
124
1981Q1‐2011Q4
4.257 ***
.108
.039
‐.257 **
.927
1.036 ***
.747 ***
.870 128
126 1980Q1‐2011Q4
1980Q1‐2011Q2
Note: ***, **, and * indicate significance at the 1, 5, and 10 percent levels, respectively. 30 .528
126
1980Q1‐2011Q2
‐1.248 ***
1.318 ***
.843
126
1980Q1‐2011Q2
Table 4. Agreement of ex post and recursive measures with present value benchmark measure (%) Price‐rent ratio Price‐income ratio Imputed‐
actual rent ratio Parsimonious regression Multivariate regression Exponential growth rate Ex post Recur‐ Ex post Recur‐ Ex post Recur‐ Ex post Recur‐ Ex post Recur‐ Ex post Recur‐
sive sive sive sive sive sive Helsinki 74.9 100.0 61.9 100.0 74.5 100.0 63.1 100.0 58.3 100.0 63.8 77.5 Geneva 89.0 60.0 82.2 40.0 65.3 100.0 89.0 55.0 94.1 55.0 88.1 45.0 Zurich 94.4 100.0 98.6 100.0 94.9 100.0 94.9 100.0 53.2 100.0 99.1 100.0 Chicago 97.0 90.0 75.0 82.5 46.3 50.0 50.0 50.0 50.0 50.0 50.0 50.0 Miami 97.7 81.1 77.3 86.4 65.7 72.7 78.8 68.7 81.6 45.5 83.8 68.7 San Francisco 78.6 73.7 68.6 71.0 35.3 50.0 59.7 54.8 57.1 50.0 67.2 59.0 Average 88.6 84.1 77.3 80.0 63.6 78.8 72.6 71.4 65.7 66.7 75.3 66.7 Note: These figures give equal weight to sensitivity (percentage of bubble periods identified by the measure) and specificity (percentage of non‐bubble periods identified by the measure) except if there are no bubble periods, then the percentages are based solely on specificity. The percentages are based on the 20 percent criterion for identifying a bubble. Table 5. Mean relative absolute errors of ex post and recursive measures compared with present value benchmark (%) Price‐rent ratio Price‐income ratio Imputed‐
actual rent ratio Parsimonious regression Multivariate regression Exponential growth rate Ex post Recur‐ Ex post Recur‐ Ex post Recur‐ Ex post Recur‐ Ex post Recur‐ Ex post Recur‐
sive sive sive sive sive sive Helsinki 9.3 3.7 16.8 17.3 49.4 81.1 15.2 27.6 23.2 11.7 15.6 29.7 Geneva 17.3 13.8 13.7 27.8 44.8 50.9 11.4 13.4 9.6 11.4 14.0 15.1 Zurich 2.4 1.8 4.1 5.8 22.0 35.1 5.1 9.4 6.9 7.7 5.1 9.6 Chicago 3.7 6.9 6.0 4.1 20.7 24.8 12.2 8.7 12.6 17.5 10.9 14.3 Miami 3.5 7.8 17.8 18.2 27.1 29.8 15.6 17.8 19.6 31.2 15.7 19.9 San Francisco 11.1 7.9 23.9 23.5 57.1 59.6 23.5 22.4 26.6 36.0 26.6 26.9 Average 7.9 7.0 13.7 16.1 36.8 46.9 13.9 16.6 16.4 19.2 14.7 19.2 Note: These are the averages of the absolute values of the percentage differences between each ex post and recursive measure and the ex post benchmark. 31 Table 6. Robustness checks for agreement of ex post and recursive measures with present value benchmark measure (%) Price‐rent ratio Price‐income ratio Imputed‐
actual rent ratio Parsimonious regression Multivariate regression Exponential growth rate Ex post Recur‐ Ex post Recur‐ Ex post Recur‐ Ex post Recur‐ Ex post Recur‐ Ex post Recur‐
sive sive sive sive sive sive 20% bubble threshold 88.6 84.1 77.3 80.0 63.6 78.8 72.6 71.4 65.7 66.7 75.3 66.7 10% bubble threshold 91.5 82.8 81.5 80.2 59.4 71.0 78.0 59.6 75.6 69.5 79.3 55.4 30% bubble threshold 92.3 91.6 71.8 71.8 64.0 78.9 72.6 75.4 59.8 71.0 76.7 73.3 Without first 5 years 91.7 82.9 77.8 81.8 75.9 80.9 69.0 79.5 63.0 67.5 72.5 64.5 Without last 5 years 91.0 98.3 74.9 88.6 66.1 76.8 76.9 93.1 59.1 76.4 76.8 79.3 Annual 94.7 88.6 83.5 86.8 59.5 69.0 79.0 75.7 67.2 68.6 80.7 76.9 Note: These figures are averages across the six cities of the correct identification of bubble and non‐bubble periods. The 20% bubble threshold averages are from the last row of Table 4 and are listed here for comparison purposes. 32 Appendix: Data sources, frequency, and available date ranges Variable Finland Switzerland
United States House price indexes Statistics Finland: quarterly from 1975 IAZI/CIFI: quarterly from 1980 for Zurich and annual from 1981 to 1997 then quarterly for Geneva (www.iazicifi.ch); quarterly values for 1981‐1997 estimated using Wüest & Partner indices of list prices of houses and condominiums in Switzerland Federal Housing Finance Agency (FHFA): quarterly from 1975 or 1976 for Metropolitan Statistical Areas (MSAs) (www.fhfa.gov) Rent indexes City of Helsinki Urban Facts: annual 1975‐
1984; Statistics Finland: annual from 1985 to 2002 and then quarterly; quarterly variation in 1975‐1999 estimated based on the “Living, heating and light” part and in 2000‐
2002 based on the “rental cost” part of the nationwide cost of living index Zurich Statistical Office: monthly from 1939 (www.statistik.zh.ch); Geneva Statistical Office: annual from 1977 (www.ge.ch/statistique); quarterly values estimated from the Swiss CPI REIS: annual from 1980 to 1998 and then quarterly for MSAs (custom file) (www.reis.com); quarterly data estimated from the all urban consumers’ CPI shelter costs component Consumer price indexes (CPIs) Statistics Finland: quarterly from 1975 (www.stat.fi) Swiss Statistical Office: monthly from 1977 for Switzerland (www.statistics.admin.ch) Bureau of Labor Statistics (BLS): monthly from 1970 for U.S. (www.bls.gov) Aggregate and per capita Statistics Finland: income annual from 1975, quarterly variation computed based on the quarterly nationwide earnings index Swiss Statistical Office: annual from 1965 for Zurich and Geneva (www.statistics.admin.ch); quarterly values calculated based on the Swiss GDP Bureau of Economic Analysis (BEA): annual from 1969 for MSAs (www.bea.gov); quarterly figures estimated based on U.S. GDP Gross domestic product (national) N/A State Secretariat for Economic Affairs: quarterly from 1980 (www.seco.admin.ch) BEA: quarterly from 1947
Population Statistics Finland: quarterly from 1975 Zurich Statistical Office: annual since 1960 (www.statistik.zh.ch); Geneva Statistical Office: annual from 1900 (www.ge.ch/statistique); quarterly values calculated by linear interpolation BEA: annual from 1969 for MSAs; quarterly figures based on U.S. GDP 33 Unemployment rates Ministry of employment and the economy: annual from 1975 to 1990 and then quarterly; quarterly variation for 1975‐1990 is estimated based on the nationwide quarterly values Swiss Statistical Office: monthly from 1975 for Zurich and Geneva (www.statistics.admin.ch) Not used (available only from 1990 for MSAs) Mortgage interest rates Bank of Finland: Swiss National Bank: quarterly from 1989Q3; monthly from 1976 for for 1975Q1‐1989Q2 Switzerland (www.snb.ch) the average lending interest rate concerning the whole outstanding loan stock is used to estimate the evolution of the mortgage rate Freddie Mac: quarterly from 1971 for U.S. (www.freddiemac.com) Government security yields Bank of Finland: quarterly from 1975 Swiss National Bank: monthly from 1974 for Switzerland (www.snb.ch) Board of Governors of the Federal Reserve System: quarterly from 1962 (10‐
year notes) or 1934 (3‐
month bills) (www.federalreserve.gov) Consumer sentiment indexes N/A State Secretariat for Economic Affairs: quarterly since 1972 for Switzerland (www.seco.admin.ch) Reuters Thomson University of Michigan Surveys of Consumers: quarterly from 1978 for U.S. (www.sca.isr.unmich.edu) Marginal income tax rates Salo (1990): annual from 1975 to 1976; Finnish Ministry of Finance: annual from 1977; tax rates assumed constant within a year Eidgenössische Steuerverwaltung (ESTV) (www.estv.admin.ch): annual; tax rates assumed constant within a year National Bureau of Economic Research (NBER) TAXSIM (www.nber.org/taxsim): annual; tax rates assumed constant within a year Capital income tax rate Finnish Ministry of Finance: annual from 1993; tax rates assumed constant within a year Eidgenössische Steuerverwaltung (ESTV) (www.estv.admin.ch): annual; tax rates assumed constant within a year Property tax rates Included in the maintenance costs Negligible
Metro area average rates calculated from American Housing Survey data 34 Maintenance costs Statistics Finland: quarterly: the average per square meter maintenance cost of free‐market flats used as the base value in 2012Q4, quarterly values back‐casted until 1975 by the flat section of property maintenance cost indices Bourassa and Hoesli (2010) Harding, Rosenthal, and Sirmans (2007) Construction cost indexes Statistics Finland: quarterly from 1975 (www.stat.fi) Stadt Zürich Präsidialdepartement: bi‐
annual from 1914 to 1998 then annual (www.stadt‐
zuerich.ch); quarterly figures computed from producer price index for Switzerland RS Means Construction Cost Indexes, 39(1), January 2013: every five years from 1940 through 1990, then annual from 1993; quarterly figures calculated from a combination of national construction cost index numbers and the national all urban consumers’ CPI shelter costs component 35