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 perform 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.

中文翻译：

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具有部分内生回归量的部分线性单指数模型的迭代 GMM

摘要 在本文中，我们考虑了线性部分具有内生回归量的部分线性单指标模型的估计方法。使用工具变量的广义矩法（GMM）用于解决参数估计量可能因内生性而不一致的问题。GMM 估计基于迭代过程，该过程概括了众所周知的最小平均条件方差估计 (MAVE) 方法，即在每次迭代中，非参数分量和参数向量的估计都是从广义矩方程获得的而不是最小二乘优化。提供了一种用于实现与工具选择有关的估计程序的特定算法。估计量的渐近性质也被建立。仿真实验表明，所提出的估计方法在有限样本中表现良好。对全国青年男子纵向调查数据的应用说明了所提出的分析学校教育回报的模型和方法。