Identification of average marginal effects under misspecification when covariates are normal
扩展了协变量联合正态分布时，误设为线性模型的非线性估计可解释为平均边际效应的识别结果，涵盖外生与内生情形，并通过模拟验证了该方法的有效性及对正态性假设的敏感性。
A previously known result in the econometrics literature is that when covariates of an underlying data generating process are jointly normally distributed, estimates from a nonlinear model that is misspecified as linear can be interpreted as average marginal effects. This has been shown for models with exogenous covariates and separability between covariates and errors. In this paper, we extend this identification result to a variety of more general cases, in particular for combinations of separable and nonseparable models under both exogeneity and endogeneity. So long as the underlying model belongs to one of these large classes of data generating processes, our results show that nothing else must be known about the true DGP—beyond normality of observable data, a testable assumption—in order for linear estimators to be interpretable as average marginal effects. We use simulation to explore the performance of these estimators using a misspecified linear model and show they perform well when the data are normal but can perform poorly when this is not the case.