Panel Data Hedonics: Rosen's First Stage as a "Sufficient Statistic"

Traditional cross-sectional estimates of hedonic price functions can recover marginal willingness to pay for characteristics, but face endogeneity problems for estimating non-marginal welfare measures. I show that when panel data on household demands are available, one can construct a second-order approximation to non-marginal welfare measures using only the first-stage marginal prices. With repeated cross sections of product prices, the measure can be set identified or, under a single-crossing restriction, point identified. Bounds also can be constructed when there are mobility costs. Finally, a variant remains valid when individual preferences shift over time.