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The price process of real assets, in particular real estate, is of interest to financial economists for a number of reasons. For example, since real estate is often used as collateral for loans that are used for other types of corporate investments, changes in real estate prices can affect the level of investment expenditures more generally. This relation between real estate prices and corporate investment choices is examined in Gan (2007), who reports that between 1994 and 1998, Japanese manufacturing firms experienced a 0.8% decline in their investment rates for every 10% decrease in land value. In a more recent study of firms in the United States over the 1993–2007 period, Chaney, Sraer, and Thesmar (2012) find that a 20% decline in real estate prices reduces the aggregate investment of public firms by 3%. More recent papers examine how housing prices influence entrepreneurs, who use their houses as collateral to start new businesses (e.g., Corradin and Popov, 2012; Adelino, Schoar, and Severino, 2013). Finally, as the recent financial crisis illustrates, since real estate represents a large fraction of the overall capital in the economy, financial institutions are particularly vulnerable to the changes in the value of real estate. In this paper, we empirically examine the price process of residential real estate. In contrast to financial securities, whose prices tend to approximate a random walk, we find that housing price changes are positively correlated over yearly intervals, with partial reversals of price changes over longer horizons (e.g., Case and Shiller, 1989; Campbell, Davis, Gallin, and Martin, 2009). As we show, these serial correlations are related to a variety of city characteristics that relate to the persistence in the housing demand growth and the elasticity of the supply of new housing. To motivate our empirical tests, we present a reduced form four-date model that illustrates the economic forces that influence the price process. The model includes 2 8 4 u T i t m a n , W a n g , a n d Y a n g a number of features, which we believe approximate reality. The first feature is that demand growth within a metropolitan area is positively serially correlated. The idea is that a city can build on its past success. For example, a positive shock to a large manufacturing industry within a city leads to an immediate increase in demand for housing from the workers hired directly in the manufacturing sector, and then a subsequent increase in demand from workers (e.g., teachers and restaurant workers) who provide services to individuals in the manufacturing sector. The second feature is that construction takes time, which means that the supply of housing responds to changes in price with a lag. In addition, because tearing down houses only makes sense in extreme situations, there is likely to be an asymmetry in the reaction to positive and negative shocks. Finally, we assume that there are frictions in the real asset markets that limit the ability of investors to arbitrage away the short-term predictability of prices. In the case of owner-occupied housing, there are transaction costs associated with buying and selling and the cost of renting out a home that one owns but does not occupy. To capture these costs, we assume that housing is constrained to be owneroccupied, and that buyers and sellers are myopic. Specifically, they do not buy more housing today in anticipation of a price increase in the future. A plausible rationale for this assumption, which has been explored in prior research, is that homeowners tend to be financially constrained. Although the extreme form of this last assumption is not needed to generate serially correlated prices, it considerably simplifies the model and results in simple closed form solutions for prices in all periods. Within this setting, a positive demand shock triggers an immediate price response, as well as a subsequent response on the next date that is generated because demand is expected to continue to grow. The adjustment on the second date depends on the supply response. Because it takes time to build, this price response results in additional supply in both the second and third periods. As we show, price changes in this simple setting tend to be positively correlated between the first and second periods, but negatively correlated between the first and third periods. The magnitudes of these serial correlations depend on the persistence of the demand shocks and the elasticity of the supply response on the second and third dates. Using quarterly U.S. metropolitan-level housing market data that covers 97 metropolitan statistical areas (MSAs) from 1980 to 2011, we empirically explore the implications of our model. Our sample is divided into pre(before 2007) and post(after 2007) crisis periods. The post-crisis period is of interest because it allows us to explore the implications of negative economic shocks (prior to the crisis there were very few negative yearly price changes). However, the volume of transactions significantly decreases in a number of housing markets in the post2007 period, so these observations may be less reliable. Consistent with the model’s implications, housing prices are positively serially correlated over yearly intervals. We also document evidence of a longer-term reversal, which is also consistent with the model. However, the magnitude of the T h e D y n a m i c s o f H o u s i n g P r i c e s u 2 8 5 J R E R u V o l . 3 6 u N o . 3 – 2 0 1 4 reversal is actually stronger in the post-2007 period. This last observation is inconsistent with our model, because we do not expect significant supply responses subsequent to falling housing prices, suggesting that there may have been some over-reaction during the crisis period. The observed serial correlations tend to differ across MSAs, which is the focus of most of our analysis. In particular, at least prior to the crisis, proxies for demand persistence and supply rigidities in different MSAs partially explain the observed differences in housing price dynamics across MSAs. Specifically, we find that larger cities, whose demand shocks tend to exhibit stronger positive short-run serial correlation, tend to exhibit stronger positive short-run serial correlations in property appreciation rates. In addition, cities that put constraints on the initiation and completion of development projects (i.e., those with stringent regulatory constraints and high population densities) tend to exhibit stronger positive shortrun serial correlations and more negative long-run serial correlations in property appreciation rates. In addition to the previously cited research on the interaction of real estate prices and real investment choices, our research is related to a number of papers in the housing literature. Topel and Rosen (1988) provide the seminal analysis of the effect of demand shocks on housing construction. In addition to their empirical work, that shows that construction reacts to prices with a lag, they provide a fully rational model with forward looking builders who respond to demand shocks with a lag because of adjustment costs. Although Topel and Rosen provide a much more detailed analysis of the implications of adjustment costs, they do not explore how these costs influence the time series of price appreciation rates, which is our central focus. Case and Shiller (1988, 1989), however, do consider the time series pattern of housing prices, and were the first to show that housing prices exhibit positive serial correlation over yearly intervals. They attribute the serial correlation to investors’ ‘‘irrational expectations’’ about price growth persistence. A more recent paper by Piazzesi and Schneider (2009) provides survey data taken during the housing boom in the 2000s. They suggest that homeowners tend to irrationally extrapolate from past price trends and provide a theoretical model that indicates that because of an absence of short-selling, a small number of optimistic individuals can have a large effect on prices. In contrast, the homeowners in our model are myopic but are not necessarily irrational, and in addition to the observed positive serial correlation at yearly intervals, our model generates price changes that are partially reversed in the future. Capozza, Hendershott, and Mack (2004) also examine how the characteristics of urban areas influence serial correlation. While they do not provide a model, they estimate a price process that assumes that in addition to serially correlated price changes, prices in each metropolitan area revert towards a long-run equilibrium level. Nneji, Brooks, and Ward (2013) examine whether deviations of real estate prices from their fundamentals can be caused by two types of bubbles: intrinsic bubbles and rational speculative bubbles. More recently, Glaeser, Gyourko, and Saiz (2008) and Saiz (2010) consider the geographical features of metropolitan 2 8 6 u T i t m a n , W a n g , a n d Y a n g areas that affect the elasticity of housing supply and examine how these features influence housing prices. We also consider geography and supply elasticity; however, in contrast to Glaeser, Gyourko, and Saiz (2008) and Saiz (2010), our focus is more on shorter term supply rigidities and its effect on shorter term price patterns, rather than on the longer term effects of geography on prices. More recently, in work that is contemporaneous with ours, Glaeser, Gyourko, Morales, and Nathanson (2011) develop and calibrate a model of price movements in the housing market. In contrast to our model, they model the production choice of builders, as well as the location choice of homeowners. However, the structure that they put on the choices of homeowners (they each buy one housing unit) makes the model and its implications very similar to our simple reduced-form model. Moreover, they do not focus on cross-city differences, which is the focus of our paper. Finally, this research is tangentially related to research that examines the return patterns of common stocks. In particular, Jegadeesh and Titman (1993) document a pattern of momentum over 3-12 month intervals and reversals over longer intervals. Hong, Lim, and Stein (1999) attribute these patterns to slow moving information. We would expect that slowly moving information is more relevant for real estate than for the stock market, and that it should be particularly relevant in smaller urban areas with less active real estate markets. However, we find that the shorter term momentum is actually stronger in larger cities, suggesting that the higher serial correlation in demand shocks, which is a feature of our model, may be more important for real estate price patterns than slow moving information, which is not a feature of our model. We present our model next and derive testable hypotheses. We then describe our empirical study methods, data-gathering procedure, and summary statistics of the data. We test our model implications next and close with concluding remarks. u M o d e l a n d H y p o t h e s e s In this section, we presents a four-date model that provides conditions under which property appreciation rates can exhibit positive and negative serial correlations. In this simple reduced-form model, the buyers and sellers, either because of their limited rationality or because of credit constraints, are myopic. In other words, their buying and selling choices are not influenced by the expectations of future price changes, but based only on their current consumption needs. Consequently, the price is determined by current supply and demand conditions. We specify the demand function for housing as: D 5 z 2 bp , (1) t t t T h e D y n a m i c s o f H o u s i n g P r i c e s u 2 8 7 J R E R u V o l . 3 6 u N o . 3 – 2 0 1 4 where at date t (t 5 0, 1, 2, or 3), demand Dt is positively affected by an exogenous shock, which is captured by changes in the intercept (zt) of the demand function, and is negatively affected by the current housing price, pt. The slope, b, measures the sensitivity of the demand change to the price change. We assume that demand shocks in two consecutive periods can be expressed as: z 2 z z 2 z t t21 t21 t22 5 x 1 s , (2) S D 1 t z z t21 t22 Where x1 captures the serial correlation of two consecutive demand shocks and st is a random error term. We assume that there is positive serial correlation in the demand shock between the first and the second periods, that is, x1 . 0, which is consistent with the time series properties of aggregate output reported in the literature. The supply of housing, St, is exogenously determined at t 5 0, but will endogenously grow in later periods depending on the realization of house prices. In our model, the change in the supply of housing St is determined as a function of the price changes on the previous dates, and is expressed as: s 2 s 1 p 2 p t t21 t2i t2i21 t21 5 d 1 o , (3) S D t i51 s k p t21 i t2i21 Where ki is a supply rigidity factor, which measures the magnitude of the supply change in response to the i-th period lagged appreciation rate, and dt captures the natural growth in supply (or, the replacement of depreciated properties). Correspondingly, 1/ki captures the sensitivity of supply change to changes in housing prices. For simplicity, we are assuming that the relation between supply changes and price changes is linear. However, in our empirical work we will consider the possibility that supply responds to price increases more than to price decreases. The above characterization of the supply function captures the idea that because construction takes time, supply reacts to price increases with a lag. Specifically, we assume that there is a partial response in one year and a further response in two years. As mentioned, these supply responses may be different in declining and growing markets and their magnitudes may also depend on various characteristics of cities that can influence the approval and development process. A large short-run supply rigidity factor k1 means that the supply adjusts slowly to price increases. This will be the case in cities where the regulatory approval process is slow or in cities with dense populations where the construction process is difficult to control. However, it should be noted that, depending on the 2 8 8 u T i t m a n , W a n g , a n d Y a n g magnitude of the delay, supply will eventually enter the market at a later date. Given this, a larger short-run supply rigidity factor k1 should lead to a smaller long-run supply rigidity factor k2 . To facilitate our later discussions, we define y2 5 1/k2 as the long-run supply sensitivity factor. Applying the market-clearing condition to each of the four periods, we derive the equilibrium prices at the four dates as follows: z m 0 p* 5 , (4) 0 b z (e 1 m) 0 1 p* 5 , (5) 1 b z0 2 2 p* 5 {k m 1 e k mx 1 e [m(1 1 k 1 k x ) 2 1]}, (6) 2 1 1 1 1 1 1 1 1 bk m 1 z0 2 p* 5 (1 1 e )(1 1 e x )(1 1 e x ) 2 (1 2 m) H 3 1 1 1 1 1 b e e e (m(1 1 (1 1 e )k x ) 2 1) 1 1 1 1 1 1 z 1 1 1 1 1 , S DF GJ 2 k m k m k m(m 1 e ) 1 2 1 1 (7) where m 5 1 2 s0 /z0, and e1 5 (z1 2 z0)/z0 . An examination of the price changes derived from Equations (4) to (7) leads to Proposition 1. Proposition 1: If housing demand and supply are characterized by Equations (1) to (3), price changes exhibit the following two patterns: [i.] The price changes from date 1 to date 2 are positively correlated with the price changes from date 0 to date 1 if the short-run supply rigidity factor (k1) and the short-run serial correlation in the demand shock (x1 . 0) satisfy the condition that k1x1 . (z0 2 bp0)z0 /bp0z1. Furthermore, the magnitude of the one-period serial correlation of price changes is increasing in the serial correlation of demand shocks x1 and the supply rigidity k1 . [ii.] The price changes from date 2 to date 3 will be negatively correlated with the price changes from date 0 to date 1 if (p 2 , (z1 2 * p*)/p* 3 2 2 where a1 measures the sensitivity of the current appreciation 2 z )a /bp , 0 1 0 rate to last period’s appreciation rate. Furthermore, the magnitude of the negative correlation between the appreciate rate in the current period and the appreciation rate two periods earlier is increasing in the long-run supply sensitivity factor, y2 5 1/k2 . T h e D y n a m i c s o f H o u s i n g P r i c e s u 2 8 9 J R E R u V o l . 3 6 u N o . 3 – 2 0 1 4 Proof. See Appendix A. Proposition 1 illustrates that under fairly reasonable conditions, real estate price changes are likely to exhibit positive serial correlation over relatively short intervals. However, price changes partially reverse in the long run. This pattern arises because of the assumed persistence in the demand shocks combined with supply responses that take time. For example, prices may initially increase with a positive shock to demand, continue to increase as the demand shock persists, and then subsequently decrease as new supply comes on line. As our simple model illustrates, the magnitude of these price patterns are determined by the speed and strength of the supply response, which is likely to differ across cities. In addition, the price patterns are likely to be related to the overall state of the market, given that supply is likely to be more sensitive to the magnitude of price increases than decreases. u E m p i r i c a l Te s t s a n d S a m p l e D e s c r i p t i o n In this section, we discuss our empirical tests and describe the characteristics of our sample. In the first subsection, we describe our empirical tests. We provide details of our data and the selection of proxy variables in the second subsection. In the last subsection, we describe the characteristics of the MSAs we use in our sample. E m p i r i c a l Te s t s We run regressions using panel data to estimate the persistence of property appreciation rates and the degree to which that persistence is affected by serial correlations in demand and/or supply rigidity factors. These regressions include the property appreciation rate of each MSA as the dependent variable, a proxy for a contemporaneous demand shock, lagged appreciation rates, proxies for the serial correlation of demand shocks and supply rigidities, and the interactions of these proxies with past appreciation rates. The regressions take the following form: r 5 f 1 v r 1 v r 1 v r 1 xG j,t G G1 j,t21 G2 j,t22 G3 j,t23 j,t 1 u [r G ] 1 u [r G ] 1 u [r G ] G1 j,t21 j,t G2 j,t22 j,t G3 j,t23 j,t 1 g b 1 s , (8) G j,t G where j is the MSA index, t is the year index, rt is the annual appreciation rate at year t (we use overlapping year-on-year price changes calculated at each quarter), rt2i is the i 2 year lagged annual appreciation rate, with i 5 1, 2 or 3. G [ {x1 , k1 or k2} represents characteristics that proxy for the serial correlation of demand shocks or supply rigidity, rt2iGt is the interaction between the proxy 2 9 0 u T i t m a n , W a n g , a n d Y a n g variable and the i-th lagged term of the appreciation rate, bt is the annual growth rate of a fundamental economic variable at year t, which represents a contemporaneous demand shock, and sG is the error term. fG is the constant. The coefficients of the three lagged appreciated rates, vGi (where i 5 1,2,3), tell us whether the property appreciation rate of the current period is related to past appreciation rates. The coefficients of the three interaction variables, uGi (where i 5 1,2,3), tell us whether proxies for demand and supply characteristics affect the magnitude of the serial correlations in the property appreciation rates. We use the Fama-MacBeth procedure (Fama and MacBeth, 1973) to estimate the coefficients of the panel regression and adjust the standard errors using the NeweyWest method (Newey and West, 1987) modified for the use in a panel data set. Petersen (2009) provides a detailed discussion on the trade-offs among different methods used for panel data regressions. D a t a a n d P r o x y Va r i a b l e s We start with the quarterly property appreciation rates for 381 MSAs (based on 2004 MSA definitions). However, because of data limitations, we delete MSAs with short data series, leaving 97 MSAs covering all 50 states in the U.S. over the 1980:Q1 to 2011:Q4 sample period. Data on the appreciation rates were provided by Federal Housing Finance Agency (FHFA), formerly known as the Office of Federal Housing Enterprise Oversight (OFHEO). The FHFA quarterly housing price index is calculated using price changes on individual properties from repeat sales or refinancing on the same single-family houses whose mortgages have been purchased or securitized by Fannie Mae or Freddie Mac. Although the sample of houses is limited, this is probably the most widely used housing price index because of its broad coverage of MSAs and long time periods. It should be noted that in contrast to financial market prices, there is a problem of stale housing prices. There are a couple of reasons why this may be the case. The most direct reason is that buyers and sellers tend to agree on a price prior to when the sale actually closes. In addition, after listing their houses, sellers may be slow to adjust the price of their houses to reflect new information. Each of these reasons is likely to generate some positive serial correlation in observed price indexes. However, given the typical time span between when offers are accepted and when the sale closes, and the very minor costs associated with adjusting prices to reflect new information, it is unlikely that these mechanical effects will induce serial correlation over intervals that go beyond one quarter. If this is indeed the case, the serial correlation that is generated from stale prices is eliminated in regressions that skip a quarter between the measurements of the appreciation rates used as dependent variables and the lagged appreciation rates included as independent variables. Specifically, we estimate regressions where the dependent variable is the appreciation rate measured from quarter t to t 1 4 and the appreciate rates used as the independent variables are measured from quarter T h e D y n a m i c s o f H o u s i n g P r i c e s u 2 9 1 J R E R u V o l . 3 6 u N o . 3 – 2 0 1 4 t-5 to quarter t-1, from quarter t-9 to quarter t-5, and from quarter t-13 to quarter t-9, respectively. In addition to the housing price series, we need proxies for the serial correlation of the demand shock and supply rigidity for each MSA, as well as other control variables that might be related to the property appreciation rate of MSAs. Specifically, we use the employment growth rate and the population growth rate, provided by Moody’s Economy.com, as proxies for the growth in housing demand. The growth rate of the housing supply for each MSA is measured as the ratio of the number of new single-family housing starts to the total number of households, which we obtain from the U.S. Census Bureau. We use two measures to represent the short-run supply rigidity of MSAs. The first is the Wharton Residential Land Use Regulatory Index (WRLURI, and hereafter ‘‘regulation index’’) used in Gyourko, Saiz, and Summers (2008) to capture the intensity of local growth control policies. A high index value means that the MSA has zoning regulations or project approval practices that constrain new residential developments. The second proxy for the short-run supply rigidity is population density, since it tends to be more difficult to develop a project in a denser area. This is true because finding suitable land, obtaining building permits, and preparing the site for development are more difficult and time consuming in a denser area. We measure an MSA’s density as its population divided by the square miles of land area, where the land area size is reported in the 2000 Census Survey (by the Census Bureau). As in Saiz (2010), we adjust the area for the amount of water in the MSA; however, we do not try to come up with a proxy for unbuildable land. As an indication of the validity of the above supply rigidity measures, we estimate the relation between supply rigidity and price levels. In theory, prices should be higher when the option to build additional housing units is more limited. Indeed, in unreported regressions we show that prices in cities that are denser or more restricted tend to be higher. It should also be noted that unreported regressions that use the median housing price level in a city as a proxy for supply rigidity generate similar results as the other two measures of supply rigidity. In particular, cities with higher housing prices exhibit greater serial correlation at yearly intervals. Finally, we use the growth rate of the gross metropolitan product (GMP, obtained from the Bureau of Economic Analysis) to control for contemporaneous demand shocks. S a m p l e D e s c r i p t i o n Before proceeding, it is interesting to get a broad picture of the characteristics of regions that realized the highest price appreciation and population growth over our sample period. To do so, we sort our data of the 97 MSAs and report the top10 MSAs in terms of housing appreciation and population growth for each of the 2 9 2 u T i t m a n , W a n g , a n d Y a n g following periods: 1980–1989, 1990–1999, 2000–2006, and 2007–2011. As reported in Exhibit 1, for the most part, the MSAs that experienced the highest price appreciation were in relatively dense urban areas with relatively good weather. The evidence in Exhibit 1 also reveals that most of the cities that experienced the fastest population growth were in areas with relatively good weather and relatively low densities. The evidence of an interaction between good weather and density as determinants of population growth and price increases is broadly consistent with the existence of a demand shock over this time period, associated with a change in preferences for good weather, as discussed in studies by Rappaport (2007) and others, and the effect of supply rigidities associated with higher density on both prices and population. In other words, speaking very broadly, the interaction between supply rigidities and demand shocks, which is central to our model, seems to have some bite. We next examine how the time series patterns in appreciation rates and housing supply growth are associated with our two measures of supply rigidities. We do this by looking at four different periods with different levels of demand growth. For each period, we stratify areas into three supply-rigidity-level groups (high, medium, and low) based on our two short-run supply-rigidity proxies: population density and the regulation index, and report each MSA’s housing appreciation rate (the FHFA HPI index change) and its growth in housing supply (new singlefamily housing starts divided by the number of households). Exhibit 2 reports each subsample’s mean for each variable. When interpreting these numbers, it should be noted that in the 1983–1989 period and the 2000– 2006 period there was substantial appreciation in housing prices, and in these periods, the more constrained MSAs (denser and more regulated) tended to appreciate more. In the 1990s, when appreciation rates were relatively low, and the post-2006 period, when prices fell, the cross-MSA relation between constraints and appreciation rates is pretty weak. It should also be noted that our density measure is a good predictor of both MSA population and price growth rates; denser areas experienced greater price increases and less population increase. However, the relation between the regulation index and the growth rates are pretty weak, suggesting that the regulations may slow down growth, but may not have a long run effect. u A s s u m p t i o n Va l i d a t i o n a n d E m p i r i c a l R e s u l t s As described earlier, in our model we assume that the housing demand shock, as shown in Equation (2), is serially correlated, and the growth in housing supply is a function of past property appreciation rates, as shown in Equation (3). These patterns are indeed consistent with our data. S e r i a l C o r r e l a t i o n o f D e m a n d S h o c k s We estimate the serial correlation of demand shocks in two ways. We first estimate a series of cross-sectional regressions of demand changes (i.e., employment and T h e D y n a m i c s o f H o u s i n g P r i c e s u 2 9 3 J R E R u V o l . 3 6 u N o . 3 – 2 0 1 4 Exhibi t 1 u MSA Ranking Based on Property Appreciation Rate and Population Growth Rate by Period MSA State Annualized Housing Appreciation Rate Average Population (000) Average GMP (mil. $) Year 2000 Population Density (per sq. mile) MSA State Annualized Housing Appreciation Rate Average Population (000) Average GMP (mil. $) Year 2000 Population Density (per sq. mile) Top 10 MSAs by Property Appreciation Rate Top 10 MSAs by Property Appreciation Rate [1980–1989] [1980–1989] Nassau-Suffolk NY 14.30% 2620.00 43.5