The asymptotic variance of semi-parametric estimators with generated regressors

Jinyong Hahn and Geert Ridder ()
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Geert Ridder: Institute for Fiscal Studies and University of Southern California

No CWP23/10, CeMMAP working papers from Centre for Microdata Methods and Practice, Institute for Fiscal Studies

Abstract:

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 non-parametric. 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 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 Effect and a semi-parametric control variable estimator.

Date: 2010-08-06
New Economics Papers: this item is included in nep-ecm
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Related works:
Journal Article: Asymptotic Variance of Semiparametric Estimators With Generated Regressors (2013)
Working Paper: The Asymptotic Variance of Semi-parametric Estimators with Generated Regressors (2010)
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