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 larger than that of naive estimators ignoring endogeneity. This paper 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 the effect of price on demand in a fish market.

翻译：处理效应同质性假设是工具变量文献中的核心假设。该假设意味着所有个体的处理效应恒定不变，使得工具变量估计量可解释为整个研究群体的平均处理效应。当该假设不成立时，工具变量估计量的偏差可能大于忽略内生性的简单估计量。本文针对处理变量存在内生性且存在有效工具变量的情形，提出了两种处理效应同质性假设的检验方法。这两种检验利用了与误差项联合独立于工具变量某一分量的协变量（该协变量无需外生性）。第一种检验假设潜在结果关于回归变量呈线性关系，计算简便；第二种检验是非参数方法，基于吉洪诺夫正则化。处理变量可以是离散或连续形式。我们证明这两种检验具有渐近正确的显著性水平，且对多种备择假设的渐近功效为1。模拟研究表明，所提检验方法具有优异的小样本表现。该方法还被应用于教育收益率评估及鱼类市场价格对需求影响的实证分析。