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Iterative GMM for partially linear single-index models with partly endogenous regressors

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  • Zhang, Hong-Fan

Abstract

In this paper, we consider the estimation method for the partially linear single-index model with endogenous regressors in the linear part. The Generalized Method of Moments (GMM) using instrumental variables is applied to cope with the problem that the parameter estimators may be inconsistent due to endogeneity. The GMM estimation is based on an iterative procedure, which has generalized the well known Minimum Average conditional Variance Estimation (MAVE) method, in the sense that in each iteration the estimates of the nonparametric components and the parameter vectors are obtained from the generalized moments equation instead of the least squares optimization. A specific algorithm to implement the estimation procedure concerning the choice of the instruments is provided. Asymptotic properties of the estimators are also established. Simulated experiments show that the proposed estimation method performs well in finite samples. Application to the National Longitudinal Survey of Young Men data illustrates the proposed model and method in analyzing the returns to schooling.

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  • Zhang, Hong-Fan, 2021. "Iterative GMM for partially linear single-index models with partly endogenous regressors," Computational Statistics & Data Analysis, Elsevier, vol. 156(C).
    • Handle: RePEc:eee:csdana:v:156:y:2021:i:c:s016794732030236x
    DOI: 10.1016/j.csda.2020.107145
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