Unobserved Heterogeneity and Estimation of Average Partial Effects

Abstract

I study the problem of identifying average partial effects (APEs), which are partial effects averaged across the population distribution of unobserved heterogeneity, under different assumptions. One possibility is that the unobserved heterogeneity is conditionally independent of the observed covariates. When the unobserved heterogeneity is independent of the original covariates, or conditional mean independent but heteroskedastic, the derivations of APEs provide a new view of traditional specification problems in widely used models such as probit and Tobit. In addition, the focus on average partial effects resolves scaling issues that arise in estimating the parameters of probit and Tobit models with endogenous explanatory variables.