On the Relation between Local Amenities and House Price Dynamics

Transcription

1 2016 V00 0: pp DOI: / REAL ESTATE ECONOMICS On the Relation between Local Amenities and House Price Dynamics Eli Beracha,* Ben T Gilbert,** Tyler Kjorstad*** and Kiplan Womack**** This study explores the extent to which local amenities are related to house price volatility, returns and risk-adjusted returns across 238 MSAs. We find strong evidence that high amenity areas experience greater price volatility. In regards to returns, high amenity areas experience greater (lower) real returns in appreciating (depreciating) markets. However, high amenity areas experience little to no abnormal risk-adjusted returns. Results from the study are robust to an endogenous treatment of amenities and land supply elasticity. Overall, we conclude that the desirability of a metropolitan area is a significant channel through which land values drive house price dynamics. Introduction It has been well documented that house prices have varied substantially across different metropolitan areas over the past few decades (see for example, Davis and Palumbo 2007, Nichols, Oliner and Mulhall 2013). However, recent studies have concluded that this variation does not appear to be adequately explained by many of the fundamental macroeconomic variables commonly suggested in the literature (Clark and Coggin 2011). Therefore, further research exploring microeconomic factors that can explain variations in house price dynamics is warranted. Although extensive bodies of literature examine local amenities and house price dynamics separately, we know very little about the intersection of these topics. While we do know that housing values are higher (lower) in high (low) amenity areas, we don t know if this translates into higher returns, volatility and risk-adjusted returns (collectively referred to hereafter as price *Hollo School of Real Estate, Florida International University, Miami, FL or eberacha@fiu.edu. **Department of Economics and Finance, University of Wyoming, Laramie, WY or bgilbe10@uwyo.edu. ***Department of Economics and Finance, University of Wyoming, Laramie, WY or tkjorsta@gmail.com. ****Department of Finance, Belk College of Business, University of North Carolina Charlotte, Charlotte, NC or kwomack4@uncc.edu. C 2016 American Real Estate and Urban Economics Association

2 2 Beracha et al. dynamics ). Moreover, we don t know if the responses are symmetrical in regards to market conditions (appreciating vs. depreciating time periods). Given that high volatility during a general downtrend in house prices is more concerning than during a general uptrend, the symmetry in the relation between house price dynamics and amenities should be explored. The purpose of this study is to empirically examine the extent to which local amenities as measured in Albouy (2015) are related to house price dynamics across 238 U.S. metropolitan areas from 1975 to The central hypothesis tested in this study is that the desirability of an area from the perspective of homeowners (measured by quality of life) and firms (measured by tradeproductivity) is a significant channel through which land values impact house price dynamics. If so, this would help explain why prior studies that utilize only macroeconomic variables do not adequately explain the variation in house price dynamics across different metropolitan areas. The foundation of our hypothesis is the well-established fact that urban land is valued primarily for its location and access to various amenities. Accordingly, because the amenity indices from Albouy (2015) provide an aggregate measure of the attributes important to consumer and firm location decisions, we can conduct a series of econometric analyses to formally test the relationship between local amenities and house price dynamics. In these models, we regress each measure of house price dynamics on an amenity index, as well as on the land supply elasticity measure of Saiz (2010), regional fixed effects, and a variety of other control variables that have been demonstrated to effect house price returns and or volatility. We also show that the results are robust to a GMM estimator that treats both the amenity indices and land supply elasticity as endogenous. A preview of the results from this study follows. Our findings reveal that amenities and land share (ratio of land value to total value) are highly positively correlated. Moreover, the two variables exhibit similar signs, statistical significance and adjusted R 2 in a regression model of land supply elasticity. These results allow us to reasonably expect that the price dynamics based on amenities will be similar to that from the land share literature, where returns and volatility increase as land comprises more of total property value. Furthermore, we hope these findings will encourage future studies to further analyze the relationship between amenities and land share, given that land values are notoriously difficult to measure directly with existing data sources (Albouy 2015). 1 1 For example, Albouy and Ehrlich (2012) use CoStar data to construct a land price index for 215 metropolitan areas. The summary statistics for the number of land sales

3 Relation between Local Amenities and House Price Dynamics 3 Additionally, this study provides unambiguous evidence of a strong positive relation between amenities and two different measures of house price volatility (standard deviation and beta). The positive relation holds across the full sample and is symmetrical across appreciating and depreciating markets. Also, when utilized by itself, the amenity variable explains approximately one third of the variation in volatility. Furthermore, a quintile analysis reveals a monotonic increase in both volatility measures as amenities increase. In regards to returns, we find that real rates of returns are greater in high amenity areas, but only when markets are appreciating. In markets where prices are decreasing, high amenity areas experience lower returns relative to low amenity areas. These results have important implications for the riskadjusted returns. This study also examines the relation between amenities and two different risk-adjusted return measures (Sharpe ratio and Jensen s alpha). In this study, the Sharpe ratio measures housing returns in each metropolitan area relative to the total risk (measured by standard deviation) of the returns. In contrast, the Jensen s alpha measures the excess returns in each metropolitan area relative to its exposure (measured by beta) to systematic risk from the broader U.S. real estate market. The results suggest that homeowners experience little to no excess real returns, on average, based on the level of amenities. In fact, both measures of risk-adjusted returns are unambiguously lower for high amenity areas in depreciating markets. These findings are consistent with the boom and bust patterns typically associated with many of the real estate high amenity areas (such as those in California and the other sand states ) and with the results from Han (2013) and Peng and Thibodeau (2016). Accordingly, we conclude that homeowners in high amenity areas are willing to accept additional risk in order to enjoy those amenities, which is consistent with the expectations of Saiz (2010). 2 Overall, the collective results from the study suggest that the desirability of a city from the perspective of both homeowners and firms is a significant channel through which land values drive house price dynamics. Accordingly, we believe this study not only provides a better understanding of the past (after applying various data screens) used in their sample are: mean (311), median (79), min (12) and max (5,946). 2 Saiz (2010) demonstrates that consumers in geographically constrained metropolitan areas should require either (1) higher wages or (2) higher amenities to compensate them for more expensive housing.

4 4 Beracha et al. variation of house price dynamics across different metropolitan areas, but also a deeper insight as to their future trajectory based on the local supply of and demand for amenities in those areas. The remainder of this study proceeds as follows. Section 2 provides a brief review of the related literatures. Section 3 presents our hypotheses. Section 4 discusses the data and presents various univariate analyses. In Sections 5 and 6, the methodology and results of our empirical tests are presented, respectively. Section 7 summarizes the key findings from the study and offers concluding remarks. Two appendices are provided. Appendix A presents a theoretical model used to derive predictions about the relationship between amenities and house price dynamics. Appendix B contains technical details from the GMM estimation. Literature Review To our knowledge, this study is the first attempt to explore the relationship between house price dynamics and local amenities. Therefore, because a developed literature does not yet exist for this combined topic, this brief literature review will focus on the separate lines of literature that form the foundation of our analysis and guides our selection of explanatory variables. Prior studies suggests that house price returns and volatility are driven primarily by land supply constraints (both natural and manmade) and land share (ratio of land value to total property value). Additionally, household and firm location preferences influence all of these factors. Accordingly, this literature review will briefly touch on each of these literatures. 3 Land Supply Constraint Literature The first set of studies that we consider involve land supply constraints. Glaeser and Gyourko (2003), Glaeser, Gyourko and Saks (2005), Saiz (2010), Paciorek (2013) and Kok, Monkkonen and Quigley (2014) collectively find that land supply constraints amplify house prices and volatility by creating scarcity, decreasing responsiveness of investment to demand shocks, increasing the time to develop (lags in the permit process, increasing the number of 3 A separate extensive literature explores the relation between a specific amenity (or disamenity) and house prices at the property-level, which is not the focus of this study. Examples include investigations of the effects of school quality (Black 1999; Bogart and Cromwell 2000), proximity to the ocean and ocean view (Landry and Hindsley 2011; Wyman, Hutchinson and Tiwari 2014) and susceptibility to flood hazards (Turnbull, Zahirovic-Herbert and Mothorpe 2013).

5 Relation between Local Amenities and House Price Dynamics 5 permit reviews, etc.) and adding costs of supplying new houses. 4 Accordingly, land supply elasticity is an important control variable in this study. Land Share Literature A second set of studies important to the analysis in this article is the land share literature. Bostic, Longhofer and Redfearn (2007), Davis and Heathcote (2007), Davis and Palumbo (2007) and Zou and Haurin (2010) show that house price appreciation and volatility are higher in areas where land comprises a larger share of total house value. 5 The underlying theory supporting land share as a key determinant of house price dynamics is straightforward. As discussed in the aforementioned studies, at any given location land and its associated amenities are limited in supply and are non-reproducible. In contrast, improvements can be reproduced in greater supply elsewhere and experience physical and functional obsolescence over time. These facts collectively imply two important points regarding price dynamics. First, structure appreciation is bound by the net effect of changes in construction costs and depreciation. Second, land appreciation is effectively unbound, as supply and demand shocks in the local economy are capitalized into land values, not structure values. Therefore, demand shocks for amenities specifically are correlated with demand for housing (more generally through local economic factors) and amenities are local public goods that are quasi-fixed from the household s perspective. Hence, the willingness to pay for amenities will be capitalized into house prices and will be a key component of the observed relationship between land share and house price dynamics. Accordingly, this literature provides the basis for our expectations of how amenities should impact house price dynamics. Household and Firm Location Preference Literature A third set of studies important to the analysis in this article examine household and firm location preferences. This literature helps provide an intuitive 4 This effect appears to be ubiquitous. A study by Grimes and Aitken (2010) of house supply elasticity and price dynamics in New Zealand find similar results. 5 In some studies such as Bostic, Longhofer and Redfearn (2007), land share is referred to as land leverage. Davis and Palumbo (2007) find substantial regional variation in 2004 land share (74% on the West Coast versus 36% in the Midwest). Albouy and Ehrlich (2012) find that land share varies from 11% to 48% with a national average of 37%.

6 6 Beracha et al. understanding of why amenities might be a significant determinant of house price dynamics. Of these studies, Tiebout (1956), Hoyt and Rosenthal (1997), Glaeser et al. (2004) and Chen and Rosenthal (2008) are particularly relevant. Hoyt and Rosenthal (1997) report empirical results consistent with the theory of Tiebout (1956), where households efficiently sort across locations based on household demand for locational amenities. Glaeser et al. (2004) find that educated cities have higher growth rates than comparable cities with less human capital, and that skilled cities are growing because they are more economically productive and more adaptable to economic shocks. Therefore, education is an important control variable when studying price dynamics. Chen and Rosenthal (2008) conclude that the locational preferences of consumers (warm, coastal and non-metropolitan locations) differ from preferences of firms (large growing cities), which helps explain why areas unattractive to both households and business have struggled (i.e., upstate New York) while areas attractive to both (i.e., the sun-belt) are thriving. 6 Therefore, our study controls for these natural amenities. Hypotheses In this section we present an intuitive explanation of our main hypotheses about the relationships between house price dynamics and amenities. In Appendix A, we provide a model to show explicitly that (A.1) price volatility is unambiguously greater in housing markets with more amenities and (2) amenities have a theoretically ambiguous effect on risk-adjusted returns because of the tradeoff between the capitalization of increasing amenity values in house prices as incomes rise, and the hypothesized increase in volatility due to amenities. The Effect of Amenities on House Price Volatility House prices can be thought of as a function of both property-level attributes and local attributes such as amenities. The way the market values each of these two components of house prices varies with macroeconomic conditions, such as expectations about permanent income. House price volatility is therefore also composed of these two sources of variation: fluctuations in the market s valuation of property-specific attributes, and fluctuations in the 6 The study also finds that highly educated households favor higher quality business environments, while retirees tend to move away from favorable business environments towards those with highly valued consumer amenities.

7 Relation between Local Amenities and House Price Dynamics 7 market s capitalized valuation of amenities into house prices, as well as the covariance between the two. 7 Both fluctuations are likely to be driven by macroeconomic shocks that affect homebuyers expectations of permanent income, and so they are likely to positively co-vary. For example, when the economy contracts, the willingness to pay for a fourth bedroom declines, but so does the willingness to pay for beach proximity; therefore, the total swing in prices in coastal locations will be greater than in inland locations for an equivalent house. As a result, ceteris paribus, the magnitude of house price fluctuations (volatility) in a particular location and the amenity value associated with that location are expected to be positively related. The Effect of Amenities on Risk-Adjusted Returns Next we consider whether we should expect homeowners to be compensated with greater risk-adjusted returns for the additional risks posed by the increased volatility, or should we expect homeowners to just accept additional risk for a given return in order to enjoy the amenities in a certain area. As discussed in Appendix A, we cannot make a definitive hypothesis about the direction of the relationship because there is a mean-variance tradeoff. The effect of amenities on risk-adjusted returns depends on the impact of amenities on mean price appreciation, relative to their effect on volatility. In a hedonic price framework, the contribution of amenities to price appreciation depends on the extent to which permanent income changes are capitalized into the amenity component versus the property-level attributes. We show in Section 6 that the empirical relationship between amenities and real (not risk-adjusted) returns is strong and positive. However, the extent to which this outweighs the relationship between amenities and volatility is an empirical question. In our empirical approach we utilize two measures of risk-adjusted returns: a housing market Sharpe ratio, calculated as the average house price growth rate in a market divided by the house price volatility (standard deviation) in that market, and Jensen s alpha calculated from a housing market CAPM described in detail in Appendix A. 8 While the Sharpe ratio is an absolute 7 Peng and Thibodeau (2016) make a similar argument in their analysis of idiosyncratic house price risk (the component of value not explainable by property or locational characteristics). 8 Recently, studies have proposed a multi-factor house price return model, which utilize various economic factors such as employment, change in foreclosures and affordability. See for example, Case et al. (2011).

8 8 Beracha et al. measure of risk-adjusted returns, Jensen s alpha is measured relative to the U.S. housing market as a whole. Therefore, Jensen s alpha for a particular market depends on the amenities in that market as well as the contribution of amenities to aggregate growth in the broader U.S. housing market. We show in Appendix A that if amenities are a large share of U.S. aggregate house price growth, then the volatility effect of amenities in a particular market has a negative effect on risk-adjusted returns in market i relative to the broader market. In other words, if amenities are a large driver of aggregate market growth, then volatility in amenity values drags down relative riskadjusted returns. Consistent with this framework, we show empirically that amenities are associated with higher Sharpe ratios, but there is no significant relationship between amenities and Jensen s alpha. Data This section discusses the various data collected to construct the sample and presents some preliminary analyses of the data. The primary dependent variables utilized in the regression models are imputed from house price returns calculated for 238 Metropolitan Statistical Areas (MSAs) across the United States using the House Price Index (HPI) published by the Federal Housing Finance Agency (FHFA). The FHFA publishes an HPI for just over 400 MSAs with quarterly frequency, beginning as early as the first quarter of 1975 for some MSAs. We utilize the full history of this series (as available at the beginning of this study), which spans from Q to Q We utilize real rather than nominal prices in the models in order to avoid the possibility that the earlier segment of the data (during which inflation was much higher compared to the later segment) would be overrepresented for non-housing related reasons. The primary independent variables of interest in this study are the quality of life, trade-productivity and total amenities indices estimated in Albouy (2015). The estimates are available for 276 MSAs across the United States. As detailed in Albouy (2015), the amenity estimates are derived as functions of housing costs and labor wages. The underlying intuition is straightforward, as both housing cost and labor wage differentials (relative to other areas) can be used to measure the willingness to pay to live or work in a certain area. In high amenity areas, people should be willing to pay more because they benefit from the amenities. In low amenity areas, the opposite is true. Therefore, these differentials in willingness to pay can be considered as estimates of the overall desirability of an

9 Relation between Local Amenities and House Price Dynamics 9 area to homeowners and firms. 9 More specifically, trade-productivity captures amenities valuable to firms, and may be thought of more as labor market opportunities or simply as jobs. In contrast, quality of life captures amenities valuable to households. The total amenity measure is a linear combination of the other two measures. Although this study utilizes all three measures of amenities, primary emphasis is placed on total amenities, because it is a comprehensive measure of an area s desirability. This emphasis is further supported by the results of Gabriel and Rosenthal (2004) and Chen and Rosenthal (2008), which collectively reveal that the objectives of households and firms (both consumers of cityspecific attributes) differ in their objectives (utility maximization versus profit maximization) and valuation of the same set of city attributes. Hence, they also may differ in their locational preferences. It is important to note that because the indices are calculated using data from the 2000 Integrated Public-Use Microdata Series (IPUMS), the indices are time invariant. This is not as troublesome of an issue as it first appears, as many amenities important to households are natural and are therefore also time invariant (or are approximately so). For example, Albouy (2012) finds that households pay substantially more to live in areas with coasts, slopes, sunshine, warm winters and mild summers and that these measures account for roughly 70% of the variation in the quality of life index. Accordingly, we rely on the same reasoning as in Glaeser, Gyourko and Saiz (2008), which notes that while many amenity variables don t change over time, demand for them might have so they provide a natural way of controlling for changes in housing demand. 10 To give the reader a general sense of the indices and the ranked order of the metropolitan areas, Table 1 reports the top and bottom five metropolitan areas (that are included in our final sample) in terms of total amenities, quality of life and trade-productivity. 11 The San Francisco-Oakland-San Jose, 9 Note that although amenities are derived in part from house prices, we are not regressing price on price. Rather, we are regressing second moments (volatility), first differences (returns) and a combination of these measures (risk-adjusted returns) on a nonlinear function of housing values, along with other explanatory variables, which is not the same as regressing y on a function of y. 10 While the explanatory variables in our study do not vary over time, they are observable for all MSAs and they do vary across the MSAs. Therefore, the model can be treated as an ordinary linear model and fit by OLS to provide consistent and efficient estimates (Greene 2012, pp ). 11 See Albouy (2015) for the full list of the 276 metropolitan areas and their respective amenity values, as well as for detailed information on how the indices are constructed.

10 10 Beracha et al. Table 1 Quality of life, trade-productivity, and total amenities rankings. Total Amenities Quality of Life Trade- Productivity Metropolitan Area Value Rank Value Rank Value Rank Total Amenities: Top 5 metro areas San Francisco-Oakland-San Jose, CA Santa Barbara-Santa Maria-Lompoc, CA Honolulu, HI Salinas (Monterey-Carmel), CA San Diego, CA Total Amenities : Bottom 5 metro areas Joplin, MO Fort Smith, AR-OK Johnstown, PA Brownsville-Harlingen-San Benito, TX McAllen-Edinburg-Mission, TX Quality of Life: Top 5 metro areas Honolulu, HI Santa Barbara-Santa Maria-Lompoc, CA San Francisco-Oakland-San Jose, CA Salinas (Monterey-Carmel), CA Santa Fe, NM Quality of Life: Bottom 5 metro areas Saginaw-Bay City-Midland, MI McAllen-Edinburg-Mission, TX Decatur, IL Beaumont-Port Arthur, TX Kokomo, IN

11 Relation between Local Amenities and House Price Dynamics 11 Table 1 Continued. Total Amenities Quality of Life Trade- Productivity Metropolitan Area Value Rank Value Rank Value Rank Trade-Productivity: Top 5 metro areas San Francisco-Oakland-San Jose, CA New York, New Jersey, Long Island Los Angeles-Riverside-Orange Co., CA Salinas (Monterey-Carmel), CA Chicago-Gary-Kenosha, IL-IN-WI Trade-Productivity: Bottom 5 metro areas Brownsville-Harlingen-San Benito, TX Abilene, TX Wichita Falls, TX McAllen-Edinburg-Mission, TX Joplin, MO Note: This table illustrates the variation in amenity values across MSAs, and is a subset of the data from table A1 of Albouy (2015).

12 12 Beracha et al. California MSA tops the list with a total amenity value of 0.323, while McAllen-Edinburg-Mission, Texas is at the bottom of the list with a total amenity value of Additionally, Table 1 reveals that MSAs with high total amenities are associated with both high trade-productivity and quality of life, rather than having a strong ranking in only one or the other. As explored in Albouy (2015) and as previously discussed in Section 2, there are several individual and directly observed variables commonly used in the literature to determine the attractiveness of different locations which are correlated with the amenity indices. Therefore, we make an effort to collect some of these characteristics to determine whether the estimated indices are an effective aggregate measure of local amenities apart from these attributes. In other words, we want to ensure that the amenity effect we observe is not just capturing population effects, income effects, etc. The characteristics we specifically control for include land supply elasticity, education, household income, census region fixed effects, weather and proximity to coasts and the Great Lakes. A brief discussion of these variables and the respective data sources follows. A widely used measure for land supply constraints is the land supply elasticity measure by Albert Saiz. Originally, Saiz (2010) published LSE estimates for 95 large U.S. cities, but because then it has been expanded to 269 U.S. cities. These values range between 0.60 for Miami, Florida where available land is scarce to for Pine Bluff, Arkansas where available land is plentiful. As Saiz s measures are available at the city rather than the MSA level, we use a weighted average based on 2010 population (obtained from the U.S. Census Bureau) to construct LSE values for the MSAs in our sample. Values for median household income and education level attained (percentage of population over the age of 25 with a bachelor s degree or higher) are obtained from the Census Bureau and are based on the American Community Survey. 12 Controlling for these factors is important, as Glaeser, Gyourko and Saks (2005) suggests a positive relationship between amenities and income. There is also usually a strong correlation between income and education. An increase in the supply of college graduates increases local wages directly as well as indirectly via a spillover effect that impacts the wages of local non-college graduates (Moretti 2004, Rosenthal and Strange 2008). 12 Accordingly, these variables represent the average characteristics during the five year period from

13 Relation between Local Amenities and House Price Dynamics 13 For general weather data, we use annual precipitation (in inches, scaled by 100), heating and cooling degree days (which reflect the variability in temperatures from a defined base temperature), and the annual mean percent of possible sunshine. 13 These values were obtained from Weather Base and Weather Data Depot, which compile these measures from the National Climatic Data Center. Finally, we create a dummy indicator (Coast/Lake) that equals 1 if a city is located within 70 miles from an ocean or within 40 miles of a Great Lake. Table 2 provides summary statistics of the MSA characteristics included in our data set. Also reported in the table are the land share (Land Share) values from Davis and Palumbo (2007), the supply elasticity (Elasticity) values from Saiz (2010) and the quality of life (Quality), trade-productivity (Productivity) and total amenities (Amenities) indices from Albouy (2015). 14 Note that in order to make the magnitudes of Quality and Productivity comparable (equivalent units in terms of household income), Productivity has been multiplied by The results of this adjustment are apparent in Table 3 Model 6, where the coefficients for both variables equal 1. In untabulated results, we begin our analysis of the relationship between local amenities and house price dynamics by examining the correlation coefficients between Amenities and Land Share. The results reveal that the correlations (.817 and.840 for the Spearman and Pearson coefficients, respectively) are positive, large in magnitude and statistically significant at the 1% level. These findings are notable, considering that Amenities is time invariant while Land Share is measured in this study as an average over time. 15 Moving beyond simple correlations, we report the results from a variety of auxiliary regression models in Table 3. In Models (A.1) and (2), Quality, 13 Heating and cooling degree days are calculated using year 2010 and 60 F asthe base. Any missing values in regards to weather proxies are replaced with the state average (or when the MSA is comprised of two states, the average from the two states is utilized). 14 Land Share as used in this study is calculated as the time series average of land share values from Q4:1984 to Q1:2014 for each city. The estimates are available for 46 cities, 40 of which match our sample. It should be noted that the land share values are measured at the city-level, while the amenity variables are measured at the MSA-level. However, this mismatch would likely result in this study understating the relationship between amenities (averaged across all the cities within the MSA, which presumably have fewer amenities than the central city) and land share (measured only in the amenity-rich central city where land is typically more expensive). 15 The correlations between Land Share and the two sub-components of Amenities (Quality and Productivity), while somewhat lower, are still positive and statistically significant.

14 14 Beracha et al. Table 2 Summary statistics. Variables Mean Std. Dev. Min Max Obs. House price returns Total return: over sample period 1 Total return: annual average Real return: annual average House price risk-adjusted returns Sharpe ratio (annual) Alpha (quarter) House price volatility Standard deviation (annual) Beta (quarter) Albouy (2015) measures Quality (quality of life) Productivity (trade-productivity) 2 Amenities (total amenities) Saiz (2010) measure Elasticity (land supply elasticity) Davis and Palumbo (2007) measure Land Share (land value/total value) Natural amenity control variables Heating Days (heating degree 3,160 1, , days) Cooling Days (cooling degree 2,690 1, , days) Sun (mean % possible sunshine) Precipitation (annual, inches) Coast/Lake (coastal/great Lakes, 1/0) Census control variables Population 928,577 2,080, ,541 21,000, Education (% bachelor s degree 25+) Income (median household income) 48,736 7,657 31,264 85, Notes: (1) The sample is an unbalanced panel data set. Sample time frame has an average of 125 quarters (72 min, 153 max) per MSA from 1975 to (2) To make the magnitudes of Quality and Productivity comparable (equivalent units in terms of household income), Productivity has been multiplied by The result of this adjustment is apparent in Table 3 Model 6, where the coefficients for both variables equal 1.(3) Although Saiz covers 269 cities, we infer elasticities for larger MSAs in our sample that comprise those cities based on a weighted average of population.

15 Relation between Local Amenities and House Price Dynamics 15 Table 3 Regression analysis: land share and amenities. (1) (2) (3) (4) (5) (6) Variables Land Share Land Share Elasticity Elasticity Elasticity Amenities Quality *** *** [6.76] [ ] Productivity *** *** [3.33] [ ] Amenities *** *** * [9.56] [ 4.24] [ 1.85] Land Share *** Amenities * Land Share [4.03] [ 0.98] [1.20] Constant *** *** *** *** *** [20.26] [20.13] [15.09] [10.02] [5.20] [.26] Obs Adj. R Notes: Observations decrease in the first five models due to Land Share, which is observed for 40 of the 238 metropolitan areas in our final sample. It should be noted that Land Share is measured at the city-level, while the amenity variables are MSAlevel estimates. T-values reported in brackets are calculated using White-corrected standard errors. The symbols ***, **, and * indicate statistical significance at the 1%, 5%, and 10% level, respectively. Productivity and Amenities are each found to be positive and statistically significant determinants of Land Share. Furthermore, the adjusted R 2 from these models indicate that amenity values explain between 70% and 73% of the variation in Land Share. In Models (A.3), (4) and (5) of Table 2 the relationship among the amenity variables and Elasticity is explored. In Models (A.3) and (4), both Amenities and Land Share are negatively related with Elasticity. The signs are negative because both variables are higher in areas with less elastic supply. In Model (5), an interaction term between Amenities and Land Share is utilized in order to test whether the impact of each variable depends on the level of the other. The results indicate a statistically insignificant relationship. However, Amenities remains significant while Land Share does not. Furthermore, the amenity models explain slightly more of the variation in Elasticity than does the land share model. The final model in the table (Model 6) is reported only to show that Amenities is a linear combination of Quality and Productivity.

16 16 Beracha et al. In summary, the findings from the various analyses in this section document a strong positive relationship between amenities and land share. These findings allow us to reasonably expect that the price dynamics based on amenities will be similar to that from the land share literature as previously discussed in Section 2, where returns and volatility are higher in areas with higher land share. Methodology House Price Volatility Two commonly used methodologies are employed in this article to measure house price volatility. The first measure is the standard deviation of the annual real returns calculated from the HPI series for each MSA using a four-quarter rolling window. The second measure is beta (β), which is often used in the finance literature as a measure for the systematic risk associated with individual stocks. As used in this article, beta captures the sensitivity of house price changes in each MSA to price changes in the broader U.S. real estate housing market. To calculate beta, we regress the quarterly returns of each MSA in our sample onto the corresponding returns for the U.S. market as a whole (see Appendix A for more specific details). 16 As an additional inquiry into house price dynamics, we calculate both volatility measures for the full time period of each HPI series as well as for seven subperiods. 17 The subperiods are defined by the peaks and troughs in the real prices of the overall U.S. housing market and accordingly capture appreciating (up markets) and depreciating (down markets) periods. This is similar to the approach used in Peng and Thibodeau (2016), except the extended sample of our study requires defining more subperiods. The subperiods of our sample are defined as the following: (1) Q Q st up market (2) Q Q st down market (3) Q Q nd up market 16 While the HPI is available for the United States as a whole as well as for some MSAs from the first quarter of 1975, the HPI series begins at some later date for other MSAs. 17 Given that the HPI series becomes available at a different time for each MSA, it is possible that the beta estimates for the first subperiod is extreme due to a short time period during which it is calculated. To attenuate the effect of this issue, we exclude the betas calculations for MSAs in the subperiod in which they enter our sample if it falls within the top or bottom 5% of our betas for that subperiod.

17 Relation between Local Amenities and House Price Dynamics 17 (4) Q Q nd down market (5) Q Q rd up market (6) Q Q rd down market (7) Q Q th up market Panel A of Figure 1 displays the real HPI series for the U.S. housing market from Q to Q along with the segmentations of the seven subperiods. Panel B of Figure 1 displays the inflation adjusted house price trends in two selected MSAs for which we observed relatively high (Stockton, CA) and relatively low (Louisville, KY) price volatility. The total amenities ranking for Stockton is 22, while the ranking for Louisville is 108. Accordingly, this panel visually illustrates the substantial variation in price volatility based on the level of local amenities in our sample of MSAs. To formally test the relation between house price volatility and amenities, we begin with a simple regression where the dependent variable is the measured house price volatility (standard deviation or beta) for each MSA and the independent variables are Quality, Productivity and Amenities. Because Quality and Productivity are used to construct Amenities, we make sure that we either include the former two measures or the later one in the regressions, but not all three simultaneously. We next include additional MSAs characteristics (previously discussed in the Section 4) in the regression in order examine the extent to which the amenity measures are able to explain house price volatility above and beyond other observed characteristics that prior studies have demonstrated to be determinants of volatility. Given the possibility that different regions within the United States include a cluster of higher or lower volatility MSAs, we introduce regional control dummies into the specifications. Specifically, we use the four major regions or nine sub-regions as classified by the U.S. Census of Bureau. 18 In our final set of models we repeat the above models after pooling observations in the appreciating markets (periods 1, 3, 5 and 7) and depreciating markets (periods 2, 4 and 6) in order to test for symmetry in the results during these periods. House Price Returns and Risk-Adjusted Returns To determine the extent to which amenity values are related to house price appreciation we investigate both real returns and risk-adjusted returns. 18 Using state-level dummy variables would consume too many degrees of freedom.

18 18 Beracha et al. Figure 1 House prices and volatility. Panel A: U.S. real house price index Q Q Inflation Adjusted Index Q1 1975= Note: dotted lines indicate divisions between appreciating and depreciating markets 175 Panel B: Real house price index - selected MSAs Infla on Adjusted Index Q1 2002= Louisville, KY Stockton, CA Note: dotted lines indicate divisions between appreciating and depreciating markets.

19 Relation between Local Amenities and House Price Dynamics 19 Examining the relation between MSA amenity values and real price appreciation is straightforward. We simply regress each MSA s real return (calculated from the percent change in the quarterly HPI, deflated by the consumer price index). To examine the relation between MSA amenity values and risk-adjusted price appreciation of housing, we regress two measures of risk-adjusted return on the amenity variables (alpha and Sharpe ratio). While the calculations for both measures are straightforward, we provide specific details in Appendix A. It is important to note that while Jensen s alpha and the Sharpe ratio are both widely used risk-adjusted return measures, they are fundamentally different from each other. Jensen s alpha captures the excess return of each MSA relative to the systematic risk associated from each MSA s exposure to the overall U.S. housing market. In contrast, the Sharpe ratio is an absolute measure of return per unit of total risk, and is calculated only with respect to the variation in each MSA s own return. Hence, it is possible that the regression coefficients from these two models will differ in sign, magnitude, as well as statistical significance. Results Volatility Table 4 reports results from the regression models of volatility. Standard deviation (total volatility) is the dependent variable in columns (A.1) through (4), while beta (systematic volatility) is the dependent variable in columns (5) through (A.8). 19 The positive and statistically significant coefficients for Quality and Productivity in column (A.1) indicate that house price volatility is higher in areas associated with higher quality of life and trade-productivity. Similarly, the positive statistically significant coefficient of the Amenities variable in column (2) indicates that areas with higher total amenities experience greater price volatility. Of particular importance, the single variable Amenities explains 37% of the variation in standard deviation. When including eight more explanatory variables, as discussed below, the adjusted R 2 increases to 64%. 19 In regards to the statistical significance of the beta estimates, we find that 90% are statistically significant at the 5% level. Furthermore, as robustness tests, we get very similar results to our existing findings when estimating any of the following models: (1) dropping observations with insignificant betas, (2) keeping all observations and replacing insignificant beta values with 0 and (3) keeping all observations and including a dummy variable =1 if beta is insignificant, 0 otherwise.

20 20 Beracha et al. Table 4 Regression analysis: volatility, amenities, and MSA characteristics. (1) (2) (3) (4) (5) (6) (7) (8) Variables Standard Deviation (total volatility) Beta (systematic volatility) Quality *** *** *** *** [9.18] [2.77] [7.28] [2.58] Productivity *** * *** *** [5.94] [1.66] [5.18] [2.73] Amenities *** *** *** *** [13.71] [2.89] [10.85] [3.51] Population ** ** *** *** [ 2.78] [ 3.86] [ 2.48] [ 3.01] Education *** *** *** *** [ 4.16] [ 4.09] [ 3.52] [ 4.02] Heating Days *** *** ** ** [ 3.77] [ 3.94] [ 2.18] [ 2.21] Cooling Days [0.16] [0.12] [0.84] [0.82] Precipitation *** *** *** *** [ 4.14] [ 4.37] [ 2.61] [ 2.64] Coast/Lake * * [1.82] [1.81] [1.19] [1.19] ln(income) *** *** [3.33] [3.21] [1.19] [1.35] Elasticity *** ***.096 *** *** [ 3.75] [ 3.97] [ 3.65] [ 3.80] Constant *** *** ** ** *** *** [35.05] [40.61] [ 2.16] [ 2.00] [27.95] [30.76] [ 0.29] [ 0.45] Obs Adj. R Notes: The number of observations in some models decreases to 208 due to the unavailability of Elasticity for some MSAs. T-values reported in brackets are calculated using White-corrected standard errors. The symbols ***, **, and * indicate statistical significance at the 1%, 5%, and 10% level, respectively.

21 Relation between Local Amenities and House Price Dynamics 21 Figure 2 House price volatility and total amenities. Columns (A.3) and (4) provide additional evidence that the positive relation between volatility all three amenity variables remain statistically significant even after controlling for characteristics that have been demonstrated by prior studies to be correlated with the desirability of each location, including a control for land supply elasticity. The latter is a particularly important finding, as studies such as Glaeser and Gyourko (2003), Glaeser, Gyourko and Saks (2005), Saiz (2010), Paciorek (2013) and Kok, Monkkonen and Quigley (2014) find that land supply constraints amplify house price volatility. The fact that the amenities and the supply constraint effects are both statistically significant provides new support for the theories in the aforementioned studies. The positive and significant results reported for beta and the adjusted R 2 in columns (5) through (A.8) are qualitatively similar to the results observed for standard deviation. This similarity in the results suggests that the specific method of measuring house price volatility does not play a major role when examining the relation between amenities and volatility. It should also be

22 22 Beracha et al. noted that the signs of the other control variables remain stable across the different specifications. Figure 2 visually illustrates the relationship between amenities and volatility as measured by standard deviation (Panel A) and beta (Panel B) for each MSA. Each graph includes a scatter plot of the volatility estimates and a fitted value line for the whole sample. These panels reveal that the estimates from Table 4 are indeed the general case across the majority of the observations in the sample and that the results are not driven by a small segment of the data or by a few outliers. Table 5 reports results from regression models of volatility with regional control variables added to the models. Regional controls are expected to be important determinants of volatility, as prior studies have shown that house prices varied substantially across different areas of the country (Davis and Palumbo 2007, Nichols, Oliner and Mulhall 2013). 20 Additionally, this serves as a test to determine whether the amenity variables maintain explanatory power after controlling for these fixed effects. Columns (A.1), (2), (5) and (6) use the U.S. Census classification of four major regions, while columns (A.3), (4), (A.7) and (A.8) use the classification of nine sub-regions. Variable names for the sub-regions used in the models are as follows: MA (Mid-Atlantic), ENC (East North Central), WNC (West North Central), SA (South-Atlantic), ESC (East South Central), WSC (West South Central), MTN (Mountain) and P (Pacific). Northeast and New England are the major region and sub-region omitted categories, respectively. In each model reported in Table 5, the coefficients for all three amenity variables are positive and significant. These results complement our findings from Table 4 by suggesting that the positive relation between amenities and house price volatility is not due to a specific regional area. That said, the negative coefficient for Midwest and the positive coefficient for West indicate that overall volatility is lower in the Midwest and higher in the West (relative to the omitted Northeast category) once amenities are accounted for. Similar results hold in the models utilizing the sub-regions. Figure 3 illustrates the relation between amenities and house price volatility (as measured by standard deviation) in each of the four major U.S. Census regions. Each graph includes a scatter plot of the volatility estimates and fitted value line for the region as well as for the United States as a whole. These graphs illustrate that the positive relation between house price volatility and 20 Also, Miao, Ramchander and Simpson (2011) find linkages of returns and volatility within geographic regions.

23 Relation between Local Amenities and House Price Dynamics 23 Table 5 Regression analysis: volatility and amenities (with census region controls). (1) (2) (3) (4) (5) (6) (7) (8) Variables Standard Deviation (total volatility) Beta (systematic volatility) Quality *** *** *** ** [3.65] [2.30] [3.08] [1.54] Productivity *** *** *** *** [6.25] [4.70] [5.58] [4.30] Amenities *** *** *** *** [7.69] [5.14] [6.89] [4.33] Four Census Major Regions Midwest *** *** ** ** [ 4.67] [ 4.66] [ 2.14] [ 2.12] South * [0.53] [0.46] [1.83] [01.62] West *** *** *** *** [3.79] [3.54] [2.92] [3.24] Nine Census Sub-Regions MA *** *** *** *** [ 5.24] [ 5.23] [ 4.01] [ 3.82] ENC *** *** *** *** [ 8.41] [ 8.53] [ 4.80] [ 4.60] WNC *** *** *** *** [ 7.78] [ 7.77] [ 4.10] [ 3.99] SA ** ** [ 2.28] [ 2.40] [0.65] [0.42] ESC *** *** *** ***