Panel Data Hedonics: Rosen's First Stage and Difference-in-Differences as 'Sufficient Statistics'

Abstract

For decades, economists have used the hedonic model to estimate demands for the implicit characteristics of differentiated commodities. The traditional cross-sectional approach to hedonic estimation can recover marginal willingness to pay for characteristics, but has faltered over a difficult endogeneity problem when attempting non-marginal welfare measures. I show that when marginal prices can be reliably estimated, and when panel data on household demands is available, one can construct a second-order approximation to non-marginal welfare measures - using only the first-stage marginal prices. Under a single-crossing restriction, the approach re-mains valid for repeated cross sections of product prices.More recently, economists have questioned the assumptions under which one can identify these cross-sectional hedonic price functions, raising the possibility of unobservables that are correlated with the characteristic of interest. To overcome this problem, they have introduced difference-in-differences econometric models to identify capitalization effects. Unfortunately, the interpretation of these effects has not been clearly perceived in the literature. I additionally show these capitalization effects are the average direct unmediated on prices of a change in characteristics, which can be interpreted as a movement along the ex post hedonic price function. This effect is a lower bound on Hicksian equivalent surplus.