Abstract
Repeat sales indices are commonly used to estimate the trend in house prices. Two assumptions are made when estimating these indices: 1) that the house characteristics are unchanged between observed sales and 2) that the underlying shadow prices for those attributes are constant or change proportionally. The second assumption is the focus of this paper. First, using data from the American Housing Survey, we show that certain attribute prices in Chicago changed idiosyncratically between 1985 and 2011. These results confirm earlier reports of changing tastes and attribute prices. We show that such changes can be approximated in a hedonic model with a low order polynomial functional form. We find that a simple extension of the standard repeat sales methodology can be used to test for and estimate changes in characteristic prices attributable to changing tastes. Our results are of interest to all users of repeat sales indices, but especially those portfolio investors interested in estimating current values of homes securing loans in their portfolio to help manage delinquencies and defaults.
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Notes
Case Shiller Weiss was formed in 1991 to sell house price indices to market participants. The firm was acquired by FISERV in 2002 and together with Standard and Poor’s introduced tradable futures market contracts based on the indices. CoreLogic acquired the index generating business from FISERV in 2013.
Case et al. (1991) used a large transaction data base to study issues of bias and efficiency in various hedonic, hybrid (including the Case Quigley model) and repeat sales specifications. They find that hedonic models can suffer from bias if the regression relationship is misspecified either due to poor choice of functional form or regressors. They also conclude that the hedonic method is inefficient because it fails to take advantage of the controls inherent in the repeat sales approach. However, they also find the repeat sales model to be inefficient because most transactions are excluded from the analysis. Bias in repeat sales models arises if the subsample used for the estimation is not representative of all transactions and failure to allow for changing attributes (including age) and attribute prices. The authors conclude, however, that the hybrid approach does not provide clear efficiency gains in their data.
Several recent studies have shown variations in house price appreciation rates for different market segments within a single geographic market. Harding et al. (2012) provide evidence of segmentation of the market for foreclosed properties relative to the market for non-distressed properties. Liu et al. (2014) show different appreciation rates for small and large home in Phoenix, AZ. McMillen (2014) and McManus (2013) find different appreciation rates for different price tiers of homes. While evidence of different rates of appreciation for different market segments is consistent with changing tastes and changing demand as studied in the current paper, it does not prove changing attribute prices over time.
Fesselmeyer et al. use national data from the AHS for the 2 separate years: 1997 and 2005.
The authors do not report specific tests for changes in coefficients, but rather focus on the overall performance of the predictive model.
The real price for the second group of homes declined by 1.85 % per year.
As discussed more fully later in the paper, quality problems with the home also play a role in the relative price changes. In the above example, we assumed the larger home had no quality problems while the smaller home did. This factor also contributed to the different price performance of the large and small home.
Our model specification includes the natural log of house price as the dependent variable. The independent variables include the natural log of house size and natural log of lot size along with discrete variables measuring bedrooms, bathrooms and various other attributes. Thus technically, the coefficients on variables expressed as natural logarithms represent elasticities while the other coefficients represent an approximate percent change associated with an increment in the value of the independent variable.
The marginal costs were evaluated at the median values for all house characteristics, changing only the house size.
For example, some lenders apply a local repeat sales price index to the homes securing loans in their portfolios to estimate current loan-to-value ratios from which they assess the risk of future default. Academics have similarly used local house price indices to estimate current values. For a recent example, see Ferreira et al. (2010).
The modification we use is based on the original work of Case and Quigley (1991). However, those authors restricted their attention to linear changes in attribute prices and we consider higher order polynomial functional forms. Significantly, we find that a quadratic functional form provides the best fit for the coefficient on ln(House Size).
There is limited information on how the additional square feet were allocated. It is reasonable to assume that both the number of rooms and the average room size increased between the 1970s and 2012. Census reports that the percentage of homes with four or more bedrooms increased from 16.8 % in the 1960s to 34 % in the period from 2005 to 2009. Over the same period, the median total rooms increased from five to six. Based on American Housing Survey data, the number of rooms and total size are highly correlated with a correlation coefficient of .37.
Although this statement is true for some homes in the survey not every home in the survey is present for all 27 different survey years. The AHS adjusts its sample of homes each survey year in an effort to keep the sample representative of the total housing stock. Consequently, new homes are added in each survey and some homes are dropped (or destroyed). Once a home is added, it generally remains in the survey panel. Each home in the survey has a unique identifier which enables us to track individual homes over time.
Because some housing units exit the survey and new units are added to maintain the representativeness of the sample, over the 27 years covered by the sample, there are approximately 63,000 different housing units in the cumulative sample with at least one survey year reported as owner-occupied.
Kiel and Zabel (1999) found that the upward bias was larger for recent purchases and diminished with time in the home.
It is important to restrict the analysis to a single MSA to control for different tastes and prices in different markets. For example, climate, household income and other regional factors likely influence willingness to pay for certain attributes, including interior space versus exterior space. However, limiting the sample to a single MSA significantly reduces the sample size.
In the AHS, the New York metropolitan area is divided into two different MSAs with fewer observations in each MSA than either Los Angeles or Chicago.
These include both attached and detached structures.
If the unit’s size was reported as varying between 1700 and 1800 square feet over the sample period, we kept the home in the sample and used the average reported size for all survey years.
If values were reported for every survey for each house, the total number of observations would be 4872. The lower number of house/year observations is due to additions and deletions to the survey panel as well as temporary transitions to rental status. Our requirement that homes be observed in at least seven of the fourteen surveys assures a fairly constant set of homes. We have no choice but to accept the survey deletions and transitions to rental status, but we considered restricting the data sample by excluding new additions to the survey. Of the 348 homes in our sample, 316 were present in the 1985 survey and 32 were new additions in the years between 1987 and 1999. While we ultimately decided that the sample size benefits of including new additions outweighed any concerns about their representativeness, we reran all the models with the exception of the repeat sales analysis excluding new additions. We concluded that our findings were qualitatively similar—including the identification of characteristics with changing attribute prices and the best functional representation of those changes.
We use the Consumer Price Index for All Urban Consumers to adjust nominal dollars to real dollars.
Nominal and real values peaked in 2007 at $341,300 and $353,100, respectively. The 2011 values reflect declines of 28 % in nominal terms and 33 % in real terms from their peaks in 2007.
We provide these demographic variables for descriptive purposes only and do not use them as determinants of the home’s value.
As noted earlier, our results are robust to excluding these “new additions” to the sample. The primary change is reduced precision associated with smaller sample sizes.
Following common usage, two independent variables (interior living area and lot size) are measured in log form, but the majority of independent variables (e.g., number of rooms and indicator variables) are measured in nominal units or are inherently zero/one variables. We allow for a nonlinear effect of age by including age and age squared as independent variables.
Nationwide, roughly ten percent of homes have a pool. As might be expected, pools are most popular in California, the Southwest and other Sunbelt states. The percentage of homes in the Chicago market with a pool is significantly below the national average and we do not believe the exclusion of this indicator is significant for this analysis.
Discussion of the regression results for the two sub-periods is deferred to the discussion of Table 3.
The indicator for attached properties may be a proxy for other unmeasured location effects. For example, attached structures may be more commonly located in more densely developed locations.
These four variables were selected for Figure 2 based on the results of the next section which indicate that the coefficients of these characteristics have changed over the sample period.
A Chow test is generally viewed as a test of whether coefficients estimated using one group of observations are the same as those estimated using a different group of observations. It is essentially a Wald test of equality of coefficients in a fully interacted model. We take the direct approach of estimating the fully interacted model and testing the estimated coefficients on the interacted characteristics.
The coefficients on the fixed effects are suppressed in the tables but are available from the authors.
The fully interacted model also includes time fixed effects.
Equation (2) is written using group 2 (G2) as the base. The decomposition could be written using group 1 (G1) as the base subsample by reversing the differences and using XG1 and βG1. The conclusions about the decomposition are not materially altered by the ordering of the differencing.
A coefficient on the indicator for attached structures is again marginally significant for this grouping of years.
The indicator for a working fireplace enters this specification with a significant negative coefficient.
Rambaldi and Rao (2011) assume discrete jumps in characteristic prices:
$$ {\beta}^k(t) = {\beta}^k\left(t-1\right)+{\varepsilon}_t,\kern0.5em {\varepsilon}_t\sim NID\left(0,{\sigma}^2{I}_t\right) $$While we reported marginal evidence of price changes for both lot size and the indicator of attached structures, in this section we only include lot size because it plays a central role in the theory of property valuation and most hedonic studies. There are only 16 homes in the sample that are attached making it very difficult to estimate year to year trends in the coefficient for that characteristic.
The matrix D has one row for each house and columns that represent time. When house i sells at times t and t + τ, matrix D will have −1 in row i at time t and +1 in row i at time t + τ.
Note that other characteristics for which βk(t)Ci k(t) was constant over time would difference out and the resulting price Eq. (7) would be the same as with a single characteristic.
While the time between sales cannot be included directly in a repeat sales regression because it is collinear with the D matrix, as long as there is sufficient cross-sectional variation in the sample of the characteristic C1, the interaction term can be included.
This expression was first derived in Case and Quigley (1991).
Panel B of Table 6 reports the distribution of sales for one of the random draws used in the Monte Carlo simulations.
A home observation in 1985 can only enter the repeat sales sample as a first sale in a pair. A home in 1997 can enter the repeat sales sample as either (or both) a first or second sale. A similar sampling problem occurs in 2011 where homes can only enter the repeat sales sample as the second sale of a pair.
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Acknowledgments
The authors thank Stephen L. Ross for helpful comments and suggestions on an earlier version of this work. The authors also thank the anonymous referee for many helpful comments and suggestions. Harding gratefully acknowledges financial support for work related to this paper provided by the Center for Real Estate and Urban Economic Studies at the University of Connecticut. Any errors and omissions are the sole responsibility of the authors
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Chen, T., Harding, J.P. Changing Tastes: Estimating Changing Attribute Prices in Hedonic and Repeat Sales Models. J Real Estate Finan Econ 52, 141–175 (2016). https://doi.org/10.1007/s11146-015-9497-0
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DOI: https://doi.org/10.1007/s11146-015-9497-0