Additive Nonparametric Regression in the Presence of Endogenous Regressors
提出了一种在完全加性约束下估计结构方程模型的方法，估计量具有一致性、渐近正态性和无维数诅咒等优良性质，并应用于研究儿童保育与认知能力的关系，发现了一些与文献不同的结果。
In this article we consider nonparametric estimation of a structural equation model under full additivity constraint. We propose estimators for both the conditional mean and gradient which are consistent, asymptotically normal, oracle efficient, and free from the curse of dimensionality. Monte Carlo simulations support the asymptotic developments. We employ a partially linear extension of our model to study the relationship between child care and cognitive outcomes. Some of our (average) results are consistent with the literature (e.g., negative returns to child care when mothers have higher levels of education). However, as our estimators allow for heterogeneity both across and within groups, we are able to contradict many findings in the literature (e.g., we do not find any significant differences in returns between boys and girls or for formal versus informal child care). Supplementary materials for this article are available online.