We propose a method for conducting asymptotically valid inference for treatment effects in a multi-valued treatment framework where the number of units in the treatment arms can be small and do not grow with the sample size. We accomplish this by casting the model as a semi-/non-parametric conditional quantile model and using known finite sample results about the law of the indicator function that defines the conditional quantile. Our framework allows for structural functions that are non-additively separable, with flexible functional forms and heteroskedasticy in the residuals, and it also encompasses commonly used designs like difference in difference. We study the finite sample behavior of our test in a Monte Carlo study and we also apply our results to assessing the effect of weather events on GDP growth.

翻译：我们建议一种方法,在一个多值处理框架内对治疗效果进行无症状、有效的推断,在这个框架内,处理武器中的单位数量可能很小,而且不会随着抽样规模的扩大而增加。我们通过将模型作为半/非参数性有条件孔蒂模型并使用界定有条件孔蒂的指标功能法则已知的有限抽样结果,实现这一点。我们的框架允许结构功能不相容,具有灵活的功能形式,残余物具有不相容性,而且还包括常用的设计,如差异差异等。我们在蒙特卡洛研究中研究我们试验的有限抽样行为,我们还运用我们的结果评估天气事件对GDP增长的影响。