Financial support for this research was generously provided through NSF Grants SES 0819612 and 0819638. We thank a co-editor and anonymous referees for helpful comments and suggestions. We also thank Guido Imbens and seminar participants at UC Riverside, UCLA, UCSD, the Tinbergen Institute, Yale, FGV–Rio de Janeiro, FGV–São Paulo, Harvard/MIT, Brown, Princeton, Mannheim, Sciences Po, and CEMFI for comments. Geert Ridder thanks the Department of Economics, PUC, Rio de Janeiro for their hospitality.
Asymptotic Variance of Semiparametric Estimators With Generated Regressors
Article first published online: 24 JAN 2013
© 2013 The Econometric Society
Volume 81, Issue 1, pages 315–340, January 2013
How to Cite
Hahn, J. and Ridder, G. (2013), Asymptotic Variance of Semiparametric Estimators With Generated Regressors. Econometrica, 81: 315–340. doi: 10.3982/ECTA9609
- Issue published online: 21 JAN 2013
- Article first published online: 24 JAN 2013
- Manuscript received October, 2010; final revision received May, 2012.
- Semiparametric estimation;
- generated regressors;
- asymptotic variance
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.