Abstract
This paper develops a concrete formula for the asymptotic distribution of two-step, possibly non-smooth semiparametric M-estimators under general misspecification. Our regularity conditions are relatively straightforward to verify and also weaker than those available in the literature. The first-stage nonparametric estimation may depend on finite dimensional parameters. We characterize: (1) conditions under which the first-stage estimation of nonparametric components do not affect the asymptotic distribution, (2) conditions under which the asymptotic distribution is affected by the derivatives of the first-stage nonparametric estimator with respect to the finite-dimensional parameters, and (3) conditions under which one can allow non-smooth objective functions. Our framework is illustrated by applying it to three examples: (1) profiled estimation of a single index quantile regression model, (2) semiparametric least squares estimation under model misspecification, and (3) a smoothed matching estimator.
Original language | English (US) |
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Pages (from-to) | 252-266 |
Number of pages | 15 |
Journal | Journal of Econometrics |
Volume | 159 |
Issue number | 2 |
DOIs | |
State | Published - Dec 2010 |
Externally published | Yes |
Keywords
- Semiparametric estimation
- Two-step estimators
ASJC Scopus subject areas
- Economics and Econometrics