Partial Mean Processes with Generated Regressors: Continuous Treatment Effects and Nonseparable Models

Partial mean processes with generated regressors arise in several important econometric problems, such as the distribution of potential outcomes with continuous treatments and the quantile structural function in a nonseparable triangular model. This paper proposes a fully nonparametric estimator for the partial mean process, where the second step consists of a kernel regression on regressors that are estimated in the first step. The main contribution is a uniform expansion that characterizes in detail how the estimation error associated with the generated regressor affects the limiting distribution of the marginal integration estimator. The general results are illustrated with three examples: control variables in triangular models (Newey, Powell, and Vella, 1999; Imbens and Newey, 2009), the generalized propensity score for a continuus treatment (Hirano and Imbens, 2004), and the propensity score for sample selection (Das, Newey, and Vella, 2003).