The hypothesis of error invariance is central to the instrumental variable literature. It means that the error term of the model is the same across all potential outcomes. In other words, 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 error invariance when the treatment is endogenous, an instrumental variable is available and the model is separable. 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.

中文翻译：

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检验可分离工具变量模型中的误差不变性

误差不变性假设是工具变量文献的核心。这意味着模型的误差项在所有潜在结果中都是相同的。换句话说，这个假设意味着所有受试者的治疗效果都是恒定的。它允许将工具变量估计解释为整个研究人群的平均治疗效果。当这个假设不成立时，工具变量估计的偏差可能大于忽略内生性的朴素估计的偏差。当处理是内生的、工具变量可用且模型可分离时，本文针对误差不变性假设开发了两个检验。第一个测试假设潜在结果在回归变量中是线性的并且计算简单。第二个测试是非参数的，依赖于 Tikhonov 正则化。处理可以是离散的或连续的。我们证明了测试具有渐近正确的水平和渐近功率等于一个针对一系列替代方案。模拟表明，所提出的测试获得了出色的有限样本性能。该方法也适用于评估学校教育的回报和鱼市价格对需求的影响。