Two-step series estimation and specification testing of (partially) linear models with generated regressors
研究了含生成回归元的线性与部分线性模型，提出两步级数估计量并证明其一致性与渐近正态性，同时开发了非参数设定检验，通过模拟和实证展示了方法的实用性。
This paper studies three semiparametric models that are useful and frequently encountered in applied econometric work—a linear and two partially linear specifications with generated regressors, i.e., the regressors that are unobserved, but can be nonparametrically estimated from the data. Our framework allows for generated regressors to appear in linear or nonlinear components of partially linear models. We propose two-step series estimators for the finite-dimensional parameters, establish their n-consistency (with sample size n) and asymptotic normality, and provide the asymptotic variance formulae that take into account the estimation error of generated regressors. Moreover, we develop a nonparametric specification test for the models considered. Numerical performances of the proposed estimators and test via simulation experiments and an empirical application illustrate the utility of our approach.