Random Coefficients on Endogenous Variables in Simultaneous Equations Models
研究了经典线性联立方程模型中内生变量随机系数的识别问题，给出了两方程系统下系数边际分布点识别的充分条件，并提出了基于识别论证的非参数核估计方法，应用于教育中的同伴效应分析。
This article considers a classical linear simultaneous equations model with random coefficients on the endogenous variables. Simultaneous equations models are used to study social interactions, strategic interactions between firms, and market equilibrium. Random coefficient models allow for heterogeneous marginal effects. I show that random coefficient seemingly unrelated regression models with common regressors are not point identified, which implies random coefficient simultaneous equations models are not point identified. Important features of these models, however, can be identified. For two-equation systems, I give two sets of sufficient conditions for point identification of the coefficients’ marginal distributions conditional on exogenous covariates. The first allows for small support continuous instruments under tail restrictions on the distributions of unobservables which are necessary for point identification. The second requires full support instruments, but allows for nearly arbitrary distributions of unobservables. I discuss how to generalize these results to many equation systems, where I focus on linear-in-means models with heterogeneous endogenous social interaction effects. I give sufficient conditions for point identification of the distributions of these endogenous social effects. I propose a consistent nonparametric kernel estimator for these distributions based on the identification arguments. I apply my results to the Add Health data to analyse peer effects in education.