Treatment effect heterogeneity is of major interest in economics, but its assessment is often hindered by the fundamental lack of identification of the individual treatment effects. For example, we may want to assess the effect of insurance on the health of otherwise unhealthy individuals, but it is infeasible to insure only the unhealthy, and thus the causal effects for those are not identified. Or, we may be interested in the shares of winners from a minimum wage increase, while without observing the counterfactual, the winners are not identified. Such heterogeneity is often assessed by quantile treatment effects, which do not come with clear interpretation and the takeaway can sometimes be equivocal. We show that, with the quantiles of the treated and control outcomes, the ranges of these quantities are identified and can be informative even when the average treatment effects are not significant. Two applications illustrate how these ranges can inform us about heterogeneity of the treatment effects.

翻译：处理效应的异质性是经济学研究的重要关注点，但个体处理效应的根本性不可识别性往往阻碍其评估。例如，我们可能希望评估保险对原本不健康个体健康的影响，但由于无法仅为不健康群体提供保险，因此无法识别针对该群体的因果效应。又如，我们可能关注最低工资上调中获益者的比例，然而在无法观测反事实的情况下，获益者无法被识别。此类异质性通常通过分位数处理效应进行评估，但其解释并不清晰，且结论有时模棱两可。研究表明，利用处理组和对照组结果的分位数，这些数量的取值范围可被识别，且即使在平均处理效应不显著时，这些范围仍能提供有效信息。两个应用案例展示了这些范围如何揭示处理效应的异质性。