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Article Excerpt
A median-based quantile estimator suffers less bias from positive outliers, such as unobserved renovations, than a standard mean-based estimator. Quantile repeat-sales estimates for single-family homes in the city of Chicago show nominal price appreciation of 68.9% between 1993 and 2002, substantially smaller than the standard approach's estimate of 77.8%. Omitting observations with building permits reduces the mean and median-based estimates by 4.4 and 1.6 percentage points. The results imply that quality improvements account for much of the rapid rise in house prices, and that a median-based quantile estimator produces a more accurate view of the price performance of a typical house.
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An ideal house-price index tracks the rate of price appreciation over time for a standard or representative house. (1) Using sample averages to construct the index is generally inappropriate because the house-price distribution is typically asymmetric: the average price is generally higher than the price of a typical house because of the effect of a small number of sales of high-priced homes. Nonacademic estimates of price indexes, such as those reported by the National Association of Realtors or by local newspapers, typically use the sample median sale price during each time period to construct an index. The median reflects the price of a typical house. But the characteristics of the median house in the sample of houses that have sold can change over time. If relatively large or new houses dominate sales during later periods, for example, both mean and median prices may rise faster than the price of a house with a standard set of characteristics.
Academic researchers use regression methods to control for the effects of these changes in housing characteristics. One of two common approaches is to estimate a hedonic house price function. The data consist of observations on the sales prices and characteristics of houses that have sold in arms-length transactions. The natural logarithm of sales price is regressed on the observed housing characteristics and variables indicating the time of sale. The estimated coefficients on housing characteristics control for differences over time in the observed characteristics (such as house size and age) of the houses that sold, and the coefficients on the time-of-sale variables produce the constant-quality house-price index. In practice, potentially relevant housing characteristics are difficult to observe. Like the sample average, the hedonic price index is prone to bias by the omission of unobserved housing characteristics that are correlated with the time variables.
The other common approach, a repeat-sales estimator, further treats this problem of omitted housing and neighborhood characteristics. A repeat-sales price index is estimated by regressing the natural logarithm of the ratio of sales prices for two transactions of the same property on a vector of discrete variables representing the time of sale. The advantage of the repeat-sales estimator is that, by focusing on the change over time in the sales price of the same house, it avoids bias from the unobserved housing and neighborhood characteristics that remain unchanged over time. The repeat-sales estimator is, however, still prone to bias. First, house and neighborhood characteristics can change between sales. Second, the houses in repeat-sales samples are less likely to be representative of the population of houses because all houses that sell less than twice over the time period are excluded.
Ironically, bias can be reduced by adopting the commonsense approach used by nonacademics, that is, by using a median-based rather than a mean-based estimator. Almost all regression analyses of house prices use a least-squares estimator. The least-squares estimator produces an estimate of the mean rate of house-price appreciation conditional on the housing characteristics observed. As a mean-based estimator it is sensitive to asymmetries in the distribution of residuals that can result from unobserved housing and neighborhood characteristics. Though the standard repeat-sales estimator controls well for many housing characteristics, it remains prone to the same kind of bias as the sample average.
In this article, we propose the use of quantile regression to treat the bias in repeat-sales price indexes from unobserved renovations or remodels between sales. The quantile estimator relaxes the assumption that all estimated coefficients--including those on the critical time-of-sale variables--do not depend on whether the house is drawn from the tails or from the middle of the house-price error distribution. Renovations generally increase a home's market value; sales prices on homes that have been renovated between sales tend to show higher appreciation rates than those on houses that have not been renovated. If renovations are unobserved, as is the case in most data sets, the residuals on renovated houses tend to be large and positive. Positive outliers predominate in repeat-sales samples, and the mean appreciation rate is higher than the appreciation rate on the typical unrenovated house. This is precisely the issue that the quantile estimator is designed to address: variation in coefficient estimates across the error distribution. Estimates for the 50% quantile, that is, the median, are analogous to the median price indexes published in newspapers, but the observations on repeat sales control for most changes over time in sample housing characteristics.
We begin by providing a theoretical rationale for the effects of omitted housing characteristics on estimates of house-price appreciation across error-distribution quantiles. We then conduct simple two-period Monte Carlo simulations in which sales price depends on two housing characteristics, one of which is observed by the researcher and another that is both correlated with the time dummy and is unobserved by the researcher. The results indicate the expected quantile effects: the hedonic estimates of the time trend at the 50% quantile (the median) are not affected by the unobserved variable, but the estimated time trend varies as expected at the 25% and 75% quantiles. The median-based quantile estimator is less prone to bias from unobserved housing characteristics that are correlated with time.
We then estimate repeat-sales price indexes from observations on 12,792 pairs of sales of the homes in the city of Chicago that sold more than once in the period 1993-2002. As expected, the median quantile estimator indicates substantially lower appreciation rates over the 40 quarters (68.9%) than that indicated by the standard repeat-sales estimator (77.8%). Unlike many data sets, ours includes a variable indicating whether a building permit was issued for the home during the time period between sales. Omitting the 10.7% of the observations with a building permit leads to lower estimated appreciation rates using both methods. A significant portion of house-price appreciation reflects improvements in the quality of houses over time. But the drop in the quantile estimate is small: a 1.6 percentage-point drop compared to a 4.4 percentage-point drop in the least-squares estimate. The median quantile estimator is much less sensitive to the observations for which building permits have been issued, and it therefore produces estimates that more accurately reflect the appreciation rate of houses with median characteristics.
These results have important implications in practice. For example, the Office of Federal Housing...
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