Characteristics of a Sufficient Statistic to Measure City Housing Prices

For a variety of empirical purposes, it is important to be able to characterize the levels of and changes in housing price in cities, whether measured by rent or asset value. This task is complicated by the heterogeneity of the housing stock, the fact that neighborhood is consumed jointly with housing, and differences in accessibility. This paper concentrates on the issue of intra-city location which, based on economic theory, is systematically related to housing price. The final conclusion is that a sufficient statistic to describe both the level of and change in the average housing price requires that prices be measured as a function of distance from the city center and weighted by the fraction of the housing stock at each distance. Commonly used repeat sales and hedonic measures of price change are generally not weighted in this fashion, but could be modified to do so.