Nonparametric Two-Step Sieve M Estimation and Inference
Posted: 23 Mar 2016
Date Written: March 1, 2016
Abstract
This paper studies the two-step sieve M estimation of general semi/nonparametric models, where the second step involves sieve estimation of unknown functions that may use the nonparametric estimates from the first step as inputs, and the parameters of interest are functionals of unknown functions estimated in both steps. We establish the asymptotic normality of the plug-in two-step sieve M estimate of a functional that could be root-n estimable. They asymptotic variance may not have a closed form expression, but can be approximated by a sieve variance that characterizes the effect of the first-step estimation on the second-step estimates. We provide a simple consistent estimate of the sieve variance and hence a Wald type inference based on the Gaussian approximation. The finite sample performance of the two-step estimator and the proposed inference procedure are investigated in a simulation study.
Keywords: Two-Step Sieve Estimation; Nonparametric Generated Regressors; Asymptotic Normality; Sieve Variance Estimation
JEL Classification: C14, C31, C32
Suggested Citation: Suggested Citation