Valuing homeownership

Valuing Homeownership K. Sekkat and A. Szafarz Housing tenure decision combines financial, economic and socio-psychological factors. This paper considers the global premium associated to homeownership. On the one hand, homeownership is associated to private benefits of being a landlord. On the other hand, overinvestment in housing is harmful to diversification and distorts portfolio management. This trade-off, similar to the one associated to corporate private benefits of control, is the cornerstone of our theoretical model. Furthermore, the empirical implementation of the model exhibits a homeownership premium for houses in the Brussels Region reaching at least 9% of the housing price. The findings are robust to several methodological refinements. JEL Classifications: R21, E21, G11 Keywords: Homeownership, tenure choice, housing, real-estate CEB Working Paper N° 09/006 February 2009 Université Libre de Bruxelles – Solvay Business School – Centre Emile Bernheim ULB CP 145/01 50, avenue F.D. Roosevelt 1050 Brussels – BELGIUM e-mail: ceb@admin.ulb.ac.be Tel. : +32 (0)2/650.48.64 Fax : +32 (0)2/650.41.88 Valuing Homeownership Khalid Sekkat and Ariane Szafarz Université Libre de Bruxelles DULBEA and Centre Emile Bernheim Av. F.D. Roosevelt, 50, CP 145/1 1050 Brussels, BELGIUM February 2009 Abstract Housing tenure decision combines financial, economic and socio-psychological factors. This paper considers the global premium associated to homeownership. On the one hand, homeownership is associated to private benefits of being a landlord. On the other hand, overinvestment in housing is harmful to diversification and distorts portfolio management. This trade-off, similar to the one associated to corporate private benefits of control, is the cornerstone of our theoretical model. Furthermore, the empirical implementation of the model exhibits a homeownership premium for houses in the Brussels Region reaching at least 9% of the housing price. The findings are robust to several methodological refinements. JEL Classification: R21, E21, G11 Keywords: Homeownership, tenure choice, housing, real-estate. 1 1. Introduction With perfect capital market, no externalities, divisible assets, homogeneous agents, etc., there should be no reason to prefer home owning over renting. The distribution of owners and renters should, therefore, be random. However, evidence shows that this not the case. For instance, Henessy (2003) reports that in Canada 64% of households own their home while in the US1 the percentage is 67%. In some European countries the percentages are much higher: Belgium 74%, Ireland 79%, and Spain 83% in 2000 (Raponi and Sak, 2002). Since the seminal paper by Shelton (1968); various explanations to such tenure choice have been investigated including housing taxation (Weiss, 1978; Englund,1985; Díaz and LuengoPrado, 2008), transaction costs (Linneman, 1985), borrowing constraints (Haurin et al., 1996) and rental externality (Henderson and Ioannides, 1983). The present paper contributes to this literature by considering a premium (including the socio-psychological benefits) associated to owning a house. In our setting, the agents associate tenure with private benefits of owning. This existence of such premium seems to fit with survey findings which show that 86% of adults in the USA prefer to own their house. Interviewees find it “more comfortable” both financially and psychologically to own instead of rent2 (Henessy, 2003). The paper offers a way to model and estimate the global premium associated to owning a house. It also conducts an empirical application to the Belgian housing market. The decision of owning combines a set of financial, economic and socio-psychological factors. From the financial perspective, the portfolio implications of homeownership have been widely discussed in the literature (Chiuri and Jappelli, 2003). Overinvestment in housing is obviously harmful to diversification and distorts portfolio management (Grossman and Laroque, 1990; Goetzmann, 1993; Flavin and Yamashita, 2002; Englund et al., 2002). Nevertheless, renting might also reveal risky as it increases the exposure to financial markets (Sinai and Souleles, 2005). The comparison sends back to the efficiency of the real-estate market (Case and Shiller, 1989; Hjalmarsson and Hjalmarsson, 2006). Coulson (1999) stresses that this proportion is lower among recent immigrants. The phenomenon has also been considered from the socio-psychological viewpoint. For instance, Dupuis and Thorns (2002) refer to the “ontological security” of homeownership. 2 1 2 Beside the financial view, a number of key economic variables, including taxes, externalities3 and life cycle aspects, affect the decision of owning. While in most countries tax laws tend to favor owning, taxation is far from being the only factor at stake in the “owning versus renting” decision-making (Megbolugbe and Cho, 1996; Linneman et al., 1997). Henderson and Ioannides (1993) stress that the marginal costs due to increased utilization of housing cannot be fully charged by the landlord to the tenant utilization, and therefore create an externality. Consequently, at equilibrium, owning is preferable to renting. However, portfolio considerations enter the picture as owner-occupiers may face a suboptimal portfolio composition due to the size of their real-estate investment (Brueckner, 1997). The final decision on renting versus owning thus depends heavily on the wealth and risk attitude of the agent at stake. This paper starts from the basic observation that tenure decision is linked to individual characteristics, which go far beyond the strictly economic characteristics. In that perspective, we place the agents of our model in a one-dimensional space reflecting their propensity to be an owner. In other terms, each agent benefits from a quantifiable private benefit of owning. Keeping to a simple formulation which entirely relies on the private benefit vs. portfolio management trade-off, we derive an equilibrium condition on the real-estate market allowing for identifying the premium associated to owner-occupiers. This premium reflects the minimal private benefit that is required to be an owner-occupier under given equilibrium conditions. This threshold value depends on a) the difference between the renting and owning costs (externality effect), and b) the interest rates and the real-estate volatility (portfolio effect). Most importantly, the premium may largely vary from one place to another, according to tax laws, cultural habits and social status associated to tenure. For instance, in Belgium being a landlord is more common than in the US and is heavily associated to a successful position. One might thus expect to find quite large private benefits of owning. The rest of the paper is organized as follows. Section 2 presents the theoretical model. Section 3 tests the empirical implications of the model in the context of the Brussels real-estate market. Specifically, the section presents the estimation of the pivotal agent’s private benefit of owning. Section 4 concludes. See, e.g, Green and White (1997) and. Aaronson (2000) on the impact of homeownership on school attainments. 3 3 2. The model We propose a simple one-period homeownership model4 based on the expected utility maximization. The originality of the model comes from its simplicity. Indeed, we intend to focus on the trade-off: ownership benefits versus risk management. For this reason, the tenure decision is modeled through a single quantitative household-specific factor, denoted α i , that aggregates the impacts of all reasons, whether objective or subjective, to prefer owning over renting. This factor, referred to as the “private benefit of homeownership”, is the only variable that differentiates households. We avoid incorporating any other differentiation (wealth, risk aversion, etc.) The market for housing is also kept very simple. All houses are supposed identical and the total number of houses is equal to the total number of households. The end-of-period price of houses is exogenous and random and the model predicts a relation between the current price and rent depending on the distribution of the α i ’s in the population. Indeed, in equilibrium a threshold value α * exists such that any household i with α i ≥ α * is a homeowner. The exercise thus consists in the identification of that threshold and, consequently, in the valuation of homeownership. Each household lives one period and has two possibilities at the beginning of the period: either buy or rent a house. The initial endowment W0 is the same for all households and is sufficient to pay cash the typical house. This allows avoiding financing costs and tax rebates frequently associated to such a transaction. Also no consumption is taken into account. At the beginning of the period, the wealth W0 is thus allocated by each household either to the purchase of the house, at the price P0 , and the remaining W0 − P0 to financial assets, or to the renting of the home, at the rental cost R0 , and the remaining W0 − R0 again to financial assets. The main difference between the two scenarios -buying or renting - comes from the fact that, besides being consumption good, housing is also a financial asset. In that respect, the renting This approach is in line with the analytical framework proposed by Henderson and Ioannides (1993) but contrasts with most existing papers that use dynamic models (see, for instance, Chambers et al., 2005). 4 4 households reach a more efficient financial risk management, notably by avoiding the loss of diversification possibilities implied by portfolio largely invested in a single real-estate asset. The tenure is, however, associated with a private benefit of owning, α i , specific to each household i. In a sense, the tenure decision is analogous to the decision of taking the control over a company leading to less diversification but more control. For landlords as for shareholders, the amplitude of the private benefits of control varies with the individual characteristics of the owner (Dyck and Zingales, 2004). In this basic setting, we assume that the financial asset is unique and not risky, with rate of % return r. In turn, the value of the house at time 1, denoted by P , is a normal random variable: 1 % P 1 N ( P ,σ1 ) . 1 At the end of the period, household i realizes its assets. If it is a homeowner, then its individual final stochastic wealth is equal to: % W1O ,i = (W0 − P0 )(1 + r ) + P + α i . 1 On the other hand, the final wealth of all renters is identical and deterministic: W1R = (W0 − R0 )(1 + r ) . Assuming a mean-variance expected utility with common risk-aversion parameter ρ , one gets the respective expected utilities of the household i in any situation, owner or renter: E0 (U O ,i ) = (W0 − P0 )(1 + r ) + P + α i − ρ σ 12 1 E0 (U R ) = (W0 − R0 )(1 + r ) . According to the maximization principle, household i chooses to buy the house if: (W0 − P0 )(1 + r ) + P1 + α i − ρ σ 12 > (W0 − R0 )(1 + r ) ⇔ ( R0 − P0 )(1 + r ) + P + α i − ρ σ 12 > 0 1 ⇔ α i > ( P0 − R0 )(1 + r ) − P + ρ σ 12 = α * 1 (1) Thus, all households with α i 's larger than α * are going to be homeowners while the other ones will be renters. Naturally, the threshold α * is linked to the equilibrium housing price P0* : P = * 0 α * + R0 (1 + r ) + P − ρ σ 12 1 1+ r P − ρ σ 12 + α * = R0 + 1 1+ r (2) 5 In equilibrium, the buying households are the ones with α i > α * . Logically, the equilibrium price depends positively on α * , on the rent R0 because of the substitution effect, and on the expected future house price. It depends negatively on the interest rate r, on the risk aversion coefficient ρ (tenure is the only risky option in this setting) and on the volatility σ 1 of the housing market. As a matter of fact, the rent and the housing price are linked. Under the no-bubble hypothesis5 (or equivalently, under the transversality condition on the real estate market), the fundamental value of the house may be viewed as the expected present value of perpetual renting (Adam and Szafarz, 1992): P0 = E0 ∑ i =1 ∞ (1 + r ) Rt t . ∞ If the rent is constant, then P0 = ∑ i =1 (1 + r ) R0 t = R0 ⇒ R0 = r P0 , and condition (1) becomes: r α i > ( P0 − r P0 )(1 + r ) − P + ρ σ 12 = P0 (1 − r 2 ) − P + ρ σ 12 , 1 1 The cut-off value α * is then: α * = P0 (1 − r 2 ) − P + ρ σ 12 . 1 and the equilibrium price P0* depends now positively on the interest rate because of its impact through the endogenous rent: P0* = α * + P − ρ σ 12 1 1− r2 This equilibrium price drives the equilibrium rent: * R0 = r (α * + P1 − ρ σ12 ) . 1− r2 (3) which depends positively on the interest rate since: * ∂R0 1+ r2 = (α * + P1 − ρ σ 12 ) . 2 2 ∂r (1 − r ) 5 See, e.g., Glaeser et al. (2008) on housing bubbles. 6 Equation (3) will serve as the starting point for an empirical exercise aiming at valuing α * , the threshold for the private benefit of owning that characterizes the landlords. Indeed, rewriting Equation (3) in the following way, makes α * appear as a regression coefficient: * R0 − r σ 12 r r P =α * +ρ . 1 1− r2 1− r2 1− r2 (4) Note that this equation has been derived without any assumption regarding the origin of the homeownership benefits. The individual α i ' s represent the monetary counterpart of all advantages associated to being a landlord for a specific household. Therefore, it can include purely financial advantages like tax cuts as well as purely psychological benefits provided they are valued in a proper way. Thanks to its global perspective, our model offers a rather simple way to investigate the empirics associated to the approach by Henderson and Ioannides (1993). 3. Empirical implementation Equation (4) allows for testing the main hypothesis, namely the existence of a private benefit of owning. Section 2 has shown that, in equilibrium, the landlords are the households i for which α i > α * . Let us rewrite Equation (4) in a stochastic form as: Yt = α * X 1t + ρ X 2t + ν t where: Yt = Rt −1 − rt Pt 1 − rt 2 (5) X 1t = rt 1 − rt 2 rt σ t2 2 1 − rt X 2t = − and υt is the error term. Provided the relevant statistical requirements for Yt , X 1t , X 2t , and υt are fulfilled, OLS method applied to Equation (5) gives estimates for α* and ρ. If the estimates of α* is found positive 7 and statistically different from zero, then we will conclude in favor of the existence of a private benefit of owning. Estimation of Equation (5) raises, however, three types of issues related to: variables measurement, statistical properties of the data, and theoretical assumptions. Since the real housing market is assumed to be composed of unique goods, measurement of housing prices and rents requires a kind of normalization (price per unit of surface/volume in a given neighborhood, for instance). Hedonic regression can be taken as a preliminary step in the procedure (Goodman, 1978) but besides requiring a large dataset for characteristics, such step introduces inevitably additional errors in variables. Another approach would consist in taking prices of traded real estate investment trusts (REIT) which are easily available but these are mainly related to the market for corporate real-estate (office spaces) and follow patterns that look like financial securities rather than like real house price series and exhibit high heterogeneity (Chan et al., 2003 ; Gyourko and Keim, 2003). The statistical properties of the data should be examined in order to use an adequate estimation methodology and get reliable estimates of the parameters in Equation (5). Since the variables in this equation are time-dependent, one should test whether they are stationary. If yes, the OLS method gives an unbiased estimates of α* and of ρ. Otherwise a more sophisticated method should be used. Lastly, the theoretical assumptions exposed in Section 2 are simplistic in at least three respects. First, the model is static and, therefore, excludes time spill-over that are certainly present on the housing market where transactions take time to settle and information is imperfectly transmitted to the agents. Second, the households’ saving possibilities are limited to housing and a riskless asset. Third, households are assumed to have enough liquidity to buy the house or, alternatively, they have easy access to credit. In practice, however, households may be liquidity constrained. As a robustness check, we consider potential interactions with risky financial assets and liquidity constraints in a subsequent step of the analysis. 8 3.1 Data Issues To estimate Equation (5) and the above discussed extensions, comparable house prices and rents are required. We will use data on the Brussels housing market coming from the Union des Géomètres Experts de Belgique (UGEB) and the Belgian Institut National de Statistique (INS). On, the one hand, UGEB (see Dekeuleneer, 2005) published series that allow computing the price of houses sold in Brussels, each year since 1972. Based on the observed prices and physical characteristics of single-household houses (surface, comfort, location, etc.), the UGEB computes the annual average price per square-meter (m2) of a representative house. On the other hand, INS6 uses a similar approach for deriving the yearly rent per m2 for a representative house in Brussels, each year since 1977. Merging the two dataset provides an assessment of the price and the rent per m2 for a similar representative house. So, regarding the housing market, we end up with a bivariate series of comparable prices and rents over the period 1979-20037 The assumptions underlying the theoretical model and the resulting condition insure the comparability of the yearly rent and price of the representative house. With regard to the remaining variables, we use the lending interest rate.8 The proxy for the housing price volatility is more problematic. Indeed, the price is available only on an annual basis. It is, therefore, impossible to derive a yearly value for σt from prices. Fortunately, the rent is observable on a monthly basis. Assuming that uncertainty over rent is correlated with uncertainty over price, we use the within-year standard deviation (i.e. the “realized volatility”) of the rent as a proxy of σt. 9Table 1 summarizes the main characteristics of the raw data over the sample period 1979-2003. The rent, price, and standard deviation are in Euros per m2. On average over the period, the rent for a representative house of 100 m2 is 4208 Euros per year with an average variation (standard deviation) of around 1212 euros over the year. http://www.nbb.be/belgostat/PublicatieSelectieLinker?LinkID=596000016|910000082&Lang=E 2003 is the last year for which the UGEB data are available. 8 Source: World Development Indicators CD-2005. 9 Measuring the volatility of the real-estate market remains a challenge which hampers any empirical study on real-estate investments. Actually, appraisal indices by private companies are the major source of time series data and, hence, for empirical studies. However, such indices are smoothed which induces the housing market’s volatility to be underestimated (Ross and Zisler, 1991, and Geltner, 1993). One advantage of our approach is that, being based on observations (not on appraisal), it circumvents the risk of underestimating volatility. 7 6 9 Table 1. Descriptive statistics of the raw data Mean Rent Price Standard deviation Interest rate 42.08 1131.13 0.32 10.72 Std Dev 12.12 422.46 0.09 3.28 Minimum Maximum 20.74 660.13 0.17 6.71 59.35 2086.71 0.53 18.00 3.2 Estimation results As discussed above, in order to use an adequate estimation methodology and get reliable estimates of the parameters of Equation (5), one should test for the stationary of Y, X1 and X2. Table 2 presents the results of the ADF stationarity tests. Due to degrees of freedom concerns, we limit the number of lags to 2. The results show that all the variables are stationary. Table 2. Stationarity tests Y Number of lags T-Statistics P-value 0 0.87 1 0.02 2 0.03 0 0.32 X1 1 0.00 2 0.07 0 0.72 X2 1 0.00 2 0.16 -1.38 -3.75 -3.57 -2.52 -4.97 -3.27 -1.76 -4.60 -2.92 Table 3 reports the estimation results of Equation (5) as it stands (Specification 1). The quality of the fit is good and all the coefficients have the expected sign and are significant. However, the Durbin-Watson statistics suggests that the residual are autocorrelated. Hence, while the estimates are unbiased, they are not efficient. To deal with this problem, we include the lagged dependent variable as an additional explanatory variable (Specification 2). The Pvalue of the Durbin’s h test does not reject the null of absence of autocorrelation, and the LM test result does not reject the hypothesis of homoskedasticity. So, one can interpret the estimates with confidence. They are unbiased and efficient. The adjusted R2 is very high (0.93) even for a time-series regression. The coefficient of the lagged dependent variable is significant. Moreover, the introduction of this variable seems to have cleaned the error term from any autocorrelation as shown by the h test. The coefficient of X2 has the expected positive sign and is significant. To catch the intuition behind this coefficient, one should 10 combine it with the explanatory variable. Such an exercise suggests that a 1% increase in the housing price uncertainty indicator pushes upward the difference between the rent and the price by 1.73%. Our main interest relates to the coefficient of variable X1. This coefficient is positive and significantly different form zero as expected. Hence, one cannot reject the hypothesis that there exists a private benefit of owning. Compared to the average price of a house (1131.13 euros per m2), the value taken by this coefficient suggests that the private benefit of owning amounts to around 20% (243/1131) of the price which may seem rather high. However, using the lower bound of the confidence interval, α* is equal to 9% of the price; which looks more reasonable. Therefore, one can conjecture that landlords in Brussels value the homeownership premium at least at 9% of the house price. Table 3. Estimation results of Equation (5) Explanatory variable C t-stat X1 t-stat X2 t-stat Y(-1) t-stat Adjusted R2 P-value: LM test for heteroskedasticity P-value: Durbin-Watson P-value: Durbin's h Specification 1 -46.59 -4.26 489.46 2.88 19.83 6.82 Specification 2 -17.66 -2.03 243.30 2.21 11.46 5.81 0.47 7.69 0.80 0.78 0.01 0.93 0.16 0.28 Standard Errors are heteroskedastic-consistent. Degree of freedom is 25. Equation (5) is derived from a very simplified model built to get a clear relationship between the rent and the price. In particular, the model does not embody the possibility for households’ liquidity constraints. It also considers a single risk-free financial asset (rate of return r) only. 11 To check for the robustness of the results with respect to these simplifying assumptions, we rerun the regressions in Table 3 adding the Belgian unemployment rate, the MSCI-Europe stock return index and the variance of this return. The unemployment rate is a common proxy for households’ liquidity constraints (see Flavin, 1985). The other two variables aim at capturing the impact of the presence of risky assets. Table 4 shows that while the stock return and its variance are stationary, the unemployment rate is integrated of order one, i.e. I(1). Therefore, the latter will be included in first difference. Table 4. Stationarity tests Unemployment Number of lags t-stat P-value 0 0.95 1 0.12 2 0.60 Δ unemployment 0 0.24 1 0.04 2 0.25 0 0.00 Return (MSCI, Europe) 1 0.06 2 0.08 Variance of return (MSCI, Europe) 0 0.01 1 0.00 2 0.24 -0.97 -3.06 -1.99 -2.68 -3.54 -2.67 -4.33 -3.37 -3.21 -4.08 -4.38 -2.70 The estimation results of Equation (5) augmented with the above additional variables are presented in Table 5. The coefficients of the MSCI-Europe return and of its variance are not significant and the corresponding adjusted R2 is unaffected. These variables add no explanatory power to Equation (5). In contrast, the coefficient of the first difference of the unemployment rate is positive and significant. The corresponding adjusted R2 is also higher than in Table 3. Following our interpretation, liquidity constraints play an important role in the choice between renting and owning. The sign of the coefficient suggests that the more severe is the liquidity constraint the higher the rent with respect to the price (taken in a comparable measure). Liquidity constraints making owning more difficult, households will move from buying to renting. As a consequence, rent increases and/or price decreases. Now, the coefficient of X1 is equal to 198.88. Compared to the average price of a house (1131.13 euros per m2), the value taken by this coefficient suggests that the private benefit of owning amounts to around 17% (199/1131). The link between liquidity constraints and house prices has been investigated in the literature, mainly as a mean to explain how house prices affect consumption. According to Iacoviello (2004, p. 307) “changes in the market value of houses affect the borrowing capacity of indebted households and, therefore, the availability of loans. Therefore an increase in 12 residential property prices permits households to borrow and to spend more.” In the same line of though, Benito and Mumtaz (2006) emphasize the collateral role of housing for indebted households. Our results confirm the existence of a link between liquidity constraints and house prices but reveal a link in the opposite direction i.e. liquidity constraints influence housing possibilities and subsequently house pricing. Table 5. Robustness check Explanatory variable C t-stat X1 t-stat X2 t-stat Y(-1) T-Statistics ΔUnemployment rate t-stat Return (MSCI, Europe) t-stat Variance of return (MSCI, Europe) t-stat Adjusted R2 P-value: LM test for heteroskedasticity P-value: Durbin's h Specification 1 -13.37 -1.84 198.88 2.41 9.66 5.52 0.58 9.55 6.14 3.80 Specification 2 -17.61 -1.99 246.20 2.21 11.52 5.44 0.47 7.08 Specification 3 -17.35 -1.79 242.89 2.18 11.46 5.73 0.47 7.30 -0.14 -0.09 -0.01 -0.06 0.95 0.23 0.20 0.93 0.18 0.28 0.93 0.15 0.25 Standard Errors are heteroskedastic-consistent. Degree of freedom is 25. 13 4. Conclusion This paper proposes a simple model that allows for investigating the value of homeownership. The model summarizes in a single term the monetary counterpart of all benefits from being a landlord and differentiates the households on the basis of this sole characteristic. By definition, the latter represents the value the pivotal household attributes to homeownership. The empirical exercise on the Brussels real-estate market has exhibited that about 20% of the house price could be attributed to homeownership. However, as this value seems rather high, we favor a more conservative value of 9% corresponding to the lower bound of the confidence interval. This estimate should however be taken with care and confronted to further empirical evidence. Several data issues might indeed have altered the estimation precision. First, house prices heavily depend on location. We have chosen here a rather small area, namely the city of Brussels, and the price and rent data were normalized by square-meter. However, even in Brussels huge price differences are observed for similar goods in different locations. Second, the evaluation of real-estate risk is a well-known empirical problem. We have used here a rather rough proxy for the price volatility. Other proxies could be taken but they all lack precision due to the low frequency of price observations. This problem is unfortunately unavoidable as higher frequency data would suffer from other drawbacks like the limited number of reported transactions. Also, seasonality would probably affect the series. Although the empirics are hampered by data limitations, the results look satisfactory and robust with respect to the inclusion of additional meaningful variables. In particular, the link between liquidity constraints and house prices documented in the literature is confirmed. Further work should include such constraints explicitly in the model. Lastly, extension of our results to other cities and countries could be interesting in at least two directions. First, Belgians tend to describe themselves as very attached to homeownership (they are supposed to have “a brick in the stomach”). Therefore, the case studied in this paper may be viewed as a rather special one. The application of our methodology to other places 14 could bring insights to whether this self-reputation is justified, that is whether Belgians do indeed value homeownership more than others. Second, a surprising side output concerns the insignificant impact of stock-market related variables on the price-rent differential. In our setting, house tenure is the only source of risk. However, households tend to possess other risky assets, whether correlated or not to the market value of their home. However, the results found here could be a consequence of the Belgians’ low risk aversion (remember the “Belgian dentist”), contrasting especially with American households, inducing them not to invest a large share of wealth, if any, in the stock market. 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