Testing for homogeneous treatment effects in linear and nonparametric instrumental variable models
针对内生处理变量和工具变量，提出两种检验同质处理效应假设的方法，一种基于线性模型计算简单，另一种非参数方法使用Tikhonov正则化，适用于离散或连续处理变量。
.The hypothesis of homogeneous treatment effects is central to the instrumental variables literature. This assumption signifies that treatment effects are constant across all subjects. It allows to interpret instrumental variable estimates as average treatment effects over the whole population of the study. When this assumption does not hold, the bias of instrumental variable estimators can be greater than that of naive estimators ignoring endogeneity. This article develops two tests for the assumption of homogeneous treatment effects when the treatment is endogenous and an instrumental variable is available. The tests leverage a covariable that is (jointly with the error terms) independent of a coordinate of the instrument. This covariate does not need to be exogenous. The first test assumes that the potential outcomes are linear in the regressors and is computationally simple. The second test is nonparametric and relies on Tikhonov regularization. The treatment can be either discrete or continuous. We show that the tests have asymptotically correct level and asymptotic power equal to one against a range of alternatives. Simulations demonstrate that the proposed tests attain excellent finite sample performances. The methodology is also applied to the evaluation of returns to schooling and demand estimation in a fish market.