Abstract
All real estate markets are local, or so the conventional wisdom goes. But just how local is local? I address this question empirically using over 75,000 repeat-sales transactions from a large suburban county of Washington D.C.. I construct and evaluate a variety of local home price indices defined by geography, price, and home type. I also calculate “house-specific” indices using locally weighted regressions with maximized kernel bandwidths. On the whole, local indices add a moderate amount of explanatory power relative to metropolitan indices. In my sample, the metropolitan index explains 50–75% of the variation in home price shocks, and local indices add 3–7% more. In an index hedging framework, homeowners should be willing to pay 5–10% to hedge with a local index versus a metropolitan index alone.
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Notes
Applying locally weighted regression techniques to home transaction data is not, by itself, a novel approach. See McMillen (2004) for an example and relevant references. To my knowledge, however, it has never been used to construct “house-specific” price indices, where the weighting scheme is unique to each home.
See Bourassa et al. (2006) for overview and references.
The tax assessment database contains the price and date of the three previous transactions for each home. First, I link together consecutive sales at the same residence. This produces 121,210 repeat-sales pairs with complete price and date information. I consider only those transactions after 1985. I drop all sales that are not “arms-length,” indicating a non-competitive sale. For example, a sale from one family member to another would not be recorded as arms-length. I drop all repeat-sales that occur over less than 12 months since these are likely to be distressed sales. Next, I calculate an annualized return for each repeat-sales pair and drop observations beyond one-and-a-half standard deviations of the annual return distribution mean (2.6% of the sample) to eliminate homes which are most likely to have changed in quality. Finally, I drop all observations that cannot be located by address. The final sample contains 75,947 observations.
Because the data contain a maximum of three transaction per home, there is some concern of missing sales if a home has sold four or more times. A frequency plot suggests that this is unlikely to cause problems. Possible “missing” sales only affect 10% of homes built after 1995 and 20% of homes built after 1985. I calculate all indices from 1985–2006. Since the S&P/Case-Shiller indices are published only as early as 1987, I input the index values for these years using home appreciation in Montgomery County.
I attempted to assign high school districts to the sample based on official maps from the Montgomery County Public Schools web site, calibrating longitude/latitude coordinates into computer pixel coordinates with Google Maps. The result was a noisy high school district variable with less predictive power than the ‘District’ variable provided in the data. Still, the two measures had substantial overlap. In the end, I use the coded district variable.
I create eleven submarkets for both the Home Type and Price Band partitions to make them comparable to the District partition coded in the data. Experimenting with other sizes suggests that anywhere from 5 to 15 submarkets yields similar results.
The hedonic model regresses price at the time of sale on all available home characteristics for the 24,352 homes sold in 2005 and 2006. The right-hand side variables include: ln(square footage), ln(land area), (year built), (year built)2, and dummy variables for quarter of sale, construction grade, type of structure, number of stories, type of exterior, and maintenance condition. Districts and zip codes are intentionally omitted in order to make the price prediction over home characteristics without using geography. I use the estimated model to predict the value of every home in the sample for Q4-2006. The regression has an R 2 equal to 0.515 (0.558 for a regression that includes geographical dummies), which is less explanatory power than even the City Index in Table 4. As a validation check, the correlation between the predicted home prices and the official tax assessment value used by the State of Maryland is 0.826 for the homes included in the regression and 0.868 for the full sample. As before, the final partition also contains eleven submarkets.
Case and Shiller (1987) point out that sales pairs with longer times between them will have larger errors, on average, if the error term (ε ijt ) has a random walk component. They correct for this heteroskedasticity by estimating a second-stage regression of the squared error terms on the time between sales and rerun the first-stage regression using the square roots of the fitted values from the second-stage as weights. I adopt the convention throughout the paper in order to effectively down-weight repeat sales over longer periods of time. Still, the results are not sensitive to this adjustment.
There is some discussion in the literature regarding index revision and contract settlement using repeat-sales indices in financial markets. Index revisions occur when previously published index estimates are revised based on new data. See Clapham et al. (2005), Baroni et al. (2008), and Deng and Quigley (2007) for details and references. Although revision biases may be substantial in some contexts, I choose not to address them directly as they distract from the ultimate aim of examining within-market home price distributions. Still, the implication is that this paper estimates slightly more precise local market indices than might be possible in real time.
I also experimented with regressing the local index on the county and city indices and using the residual as an orthogonal market movement measure. The results were similar yet more difficult to interpret. The advantage of subtracting the county and city indices is that the regression results can be easily interpreted as if the full county and city indices were included.
The regression coefficient will mechanically equal 1 when the regression contains a single index and the same homes are used to construct the evaluate it. For this reason, leave-one-out cross-validation is a necessary choice. I have experimented with leaving all homes in the index construction, but this issue is especially problematic for kernel bandwidth maximization since problems are magnified in small samples. The “optimal” local indices occur at several hundred homes rather than several thousand since using the same home in construction and evaluation leads to substantial predictive power in small samples.
Still, I have experimented with constructing and testing the indices without leave-one-out cross-validation. That is, I include the home in the question to both create and evaluate the house-specific index. Results yield substantially “smaller” local markets since econometric power vastly improves when including the home in small samples. However, it would be incorrect to do so since it overestimates the predictive power of the local market.
I have also experimented with a 90% sample and 10% testing sample structure as an alternative to leave-one-out cross-validation. The results are similar in magnitude, but the econometric precision is greatly reduced. Thus, I present results for the leave-one-out methodology only.
Varying the bandwidth based on the number of homes is one of two ways to proceed. The choice is whether to have bandwidths defined by fixed values, such as distance in miles, or to allow the bandwidth to vary with home density. In the end, I choose the latter to achieve econometric consistency in index evaluation.
All locally weighted regressions in this paper use epanechnikov kernels which decrease observation weights smoothly over distance. Indicator kernels were also considered and tested but ultimately omitted due to lower overall performance.
I focus on futures contracts exclusively rather than consider alternative financial instruments,—most notably put options discussed in Shiller and Weiss (1999)—for two reasons. First, futures contracts are the most natural hedge for a homeowner wishing to reduce price risk; homeowners still take on home price exposure when hedging with put options. Second, the main qualitative results should carry over to other derivative contracts.
The same regression setup and solution applies to the general case where a homeowner hedges multiple homes at the same time. That is, a homeowner is naturally long his own home and short all the homes to which he might move. A previous version of this paper considered the case where \( \log w = \log {w_0} + \sum\nolimits_{i = 0}^N {{a_i}{\varepsilon_i}} + \sum\nolimits_{i = 0}^N {{k_i}{\nu_i}} \), where the coefficients a i represent the agent’s exposure to house i (positive for currently owned homes and negative for possible future homes). The optimal hedging strategy is still given by the coefficients of a regression of \( \sum\nolimits_{i = 0}^N {{a_i}{\varepsilon_i}} \) on ν 0, ν 1, … ν N, and the fraction of overall wealth reduction remains one minus the R 2. Due to space considerations, I remove the analysis from the current version of the paper.
One disadvantage of using a kernel bandwidth that adjusts with home density is that I report the local market size as a median or mean rather than as a fixed value for all homes. Still, the drawbacks are outweighed by the econometric consistency gained by using the same number of observations in each index calculation, as reviewed in “House-specific Indices”.
A $10,000 valuation of removing home price risk seems reasonable given that the standard deviation of home price shocks over a 5-year period is around 18% of home values, corresponding to roughly $95,000 for a home worth $500,000. Still, the risk aversion parameter is not meant to be a dogmatic assumption. The reader can easily adjust this value to his or her own liking. However, I choose it to provide some intuition for the magnitude of the value of hedging.
Since home price shocks vary over a typical real estate cycle, I tested whether these results were driven by any non-random sampling over time. I repeated the calculations while weighting observations by the inverse of their frequency by year. The results were not sensitive to this robustness check.
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Acknowledgments
I thank Markus Brunnermeier, Fernando Ferreira, David Lee, Burton Malkiel, Chris Mayer, John Quigley, Ricardo Reis, Jesse Rothstein, Hyun Shin, Albert Saiz, Todd Sinai, an anonymous referee, and seminar participants at the Industrial Relations Section, Bendheim Center for Finance, and the NBER Summer Institute for Real Estate & Local Public Finance for helpful conversations and suggestions. I would additionally like to thank the National Science Foundation and Princeton University for generous financial support throughout this project.
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McDuff, D. Home Price Risk, Local Market Shocks, and Index Hedging. J Real Estate Finan Econ 45, 212–237 (2012). https://doi.org/10.1007/s11146-010-9255-2
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DOI: https://doi.org/10.1007/s11146-010-9255-2