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Semiparametric Estimation of a Single-Index Model with Nonparametrically Generated Regressors

Published online by Cambridge University Press:  11 February 2009

Hyungtaik Ahn
Hyungtaik Ahn
Affiliation:
Virginia Polytechnic Institute & State University
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Abstract

This paper develops a theory of estimating parameters of a generated regressor model in which some explanatory variables in the equation of interest are the unknown conditional means of certain observable variables given other observable regressors. The paper imposes a weak nonparametric restriction on the form of the conditional means and maintains a single-index assumption on the distribution of the dependent variable in the equation of interest. The estimation method follows a two-step approach: The first step estimates the conditional means in the index nonparametrically, and the second step estimates the parameters by an analytically convenient weighted average derivative method. It is established that the two-step estimator is root-n-consistent and asymptotically normal. The asymptotic variance exceeds that of the one-step hypothetical estimator, which would be obtainable if the first-step regression were known.

Type
Articles
Information
Econometric Theory , Volume 13 , Issue 1 , February 1997 , pp. 3 - 31
Copyright
Copyright © Cambridge University Press 1997

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