The Asymptotic Variance of Semi-parametric Estimators with Generated Regressors
نویسندگان
چکیده
We study the asymptotic distribution of three-step estimators of a nite dimensional parameter vector where the second step consists of one or more nonparametric regressions on a regressor that is estimated in the rst step. The rst step estimator is either parametric or non-parametric. Using Neweys (1994) path-derivative method we derive the contribution of the rst step estimator to the inuence function. In this derivation it is important to account for the dual role that the rst step estimator plays in the second step non-parametric regression, i.e., that of conditioning variable and that of argument. We consider three examples in more detail: the partial linear regression model estimator with a generated regressor, the Heckman, Ichimura and Todd (1998) estimator of the Average Treatment E¤ect and a semi-parametric control variable estimator. JEL Classi cation: C01, C14.
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