Econometrica: Jan, 2013, Volume 81, Issue 1
Asymptotic Variance of Semiparametric Estimators With Generated Regressors
Jinyong Hahn, Geert Ridder
We study the asymptotic distribution of three‐step estimators of a finite‐dimensional parameter vector where the second step consists of one or more nonparametric regressions on a regressor that is estimated in the first step. The first‐step estimator is either parametric or nonparametric. Using Newey's (1994) path‐derivative method, we derive the contribution of the first‐step estimator to the influence function. In this derivation, it is important to account for the dual role that the first‐step estimator plays in the second‐step nonparametric regression, that is, that of conditioning variable and that of argument.
Supplement to "Asymptotic Variance of Semi-parametric Estimators with Generated Regressors"
This supplement addresses the derivative of Lemma 1.