The Asymptotic Variance of Semi-parametric Estimators with Generated Regressors
AbstractWe 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.
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Date of creation: Sep 2010
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Semi-parametric estimation; generated regressors; asymptotic variance. JEL Code: C01; C14;
Find related papers by JEL classification:
- asy - - - - - -
- var - - - - - -
- JEL - Labor and Demographic Economics - - - - -
- Cod - Mathematical and Quantitative Methods - - - - -
- C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
- C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
This paper has been announced in the following NEP Reports:
- NEP-ALL-2010-10-30 (All new papers)
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