Efficient Estimation of Models with Conditional Moment Restrictions Containing Unknown Functions
Econometrica · 2003 · Volume 71 · Issue 6
Abstract
We propose an estimation method for models of conditional moment restrictions, which contain finite dimensional unknown parameters (θ) and infinite dimensional unknown functions (h). Our proposal is to approximatehwith a sieve and to estimateθand the sieve parameters jointly by applying the method of minimum distance. We show that: (i) the sieve estimator ofhis consistent with a rate faster thann-1/4under certain metric; (ii) the estimator ofθis √nconsistent and asymptotically normally distributed; (iii) the estimator for the asymptotic covariance of theθestimator is consistent and easy to compute; and (iv) the optimally weighted minimum distance estimator ofθattains the semiparametric efficiency bound. We illustrate our results with two examples: a partially linear regression with an endogenous nonparametric part, and a partially additive IV regression with a link function.
Keywords
Semi-/nonparametric conditional moment restrictions, sieve minimum distance, continuous updating, endogeneity, semiparametric efficiency
Enable JavaScript for citation tools and additional paper interactions.