This paper provides asymptotically valid tests for the null hypothesis of no treatment effect heterogeneity. Importantly, I consider the presence of heterogeneity that is not explained by observed characteristics, or so-called idiosyncratic heterogeneity. When examining this heterogeneity, common statistical tests encounter a nuisance parameter problem in the average treatment effect which renders the asymptotic distribution of the test statistic dependent on that parameter. I propose an asymptotically valid test that circumvents the estimation of that parameter using the empirical characteristic function. A simulation study illustrates not only the test's validity but its higher power in rejecting a false null as compared to current tests. Furthermore, I show the method's usefulness through its application to a microfinance experiment in Bosnia and Herzegovina. In this experiment and for outcomes related to loan take-up and self-employment, the tests suggest that treatment effect heterogeneity does not seem to be completely accounted for by baseline characteristics. For those outcomes, researchers could potentially try to collect more baseline characteristics to inspect the remaining treatment effect heterogeneity, and potentially, improve treatment targeting.

翻译：本文提出了渐近有效的检验方法，用于检验“不存在治疗效应异质性”的原假设。本文特别关注了未被观测特征解释的异质性，即所谓的个体异质性。在检验此类异质性时，常见的统计检验会因平均处理效应中的冗余参数问题，导致检验统计量的渐近分布依赖于该参数。本文提出了一种基于经验特征函数的渐近有效检验方法，从而避免了对该参数的估计。模拟研究不仅验证了该检验的有效性，还表明其与现有检验相比，在拒绝错误原假设时具有更高的统计功效。此外，本文将该方法应用于波斯尼亚和黑塞哥维那的一项小额贷款实验，展示了其实用价值。在此实验中，与贷款获取和自雇就业相关的结果变量检验表明：处理效应异质性似乎并未完全被基线特征所解释。对于这些结果变量，研究者可能需进一步收集更多基线特征，以探查剩余的处理效应异质性，并有望优化干预措施的定向策略。