Econometrica: Nov 2003, Volume 71, Issue 6

Efficient Estimation of Models with Conditional Moment Restrictions Containing Unknown Functions
p. 1795-1843

Chunrong Ai, Xiaohong Chen

We propose an estimation method for models of conditional moment restrictions, which contain finite dimensional unknown parameters () and infinite dimensional unknown functions (). Our proposal is to approximate with a sieve and to estimate and the sieve parameters jointly by applying the method of minimum distance. We show that: (i) the sieve estimator of is consistent with a rate faster than under certain metric; (ii) the estimator of is √ consistent and asymptotically normally distributed; (iii) the estimator for the asymptotic covariance of the estimator is consistent and easy to compute; and (iv) the optimally weighted minimum distance estimator of attains 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.

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