This article addresses the question of reporting a lower confidence band (LCB) for optimal welfare in policy learning problems. A straightforward procedure inverts a one-sided t-test based on an efficient estimator of the optimal welfare. We argue that in an empirically relevant class of data-generating processes, a LCB corresponding to suboptimal welfare may exceed the straightforward LCB, with the average difference of order N-{1/2}. We relate this result to a lack of uniformity in the so-called margin assumption, commonly imposed in policy learning and debiased inference. We advocate for using uniformly valid asymptotic approximations and show how existing methods for inference in moment inequality models can be used to construct valid and tight LCBs for the optimal welfare. We illustrate our findings in the context of the National JTPA study.

翻译：本文探讨了在政策学习问题中如何报告最优福利的下置信带（LCB）。一种直接方法基于最优福利的有效估计量，通过单侧t检验进行逆推构建。我们证明，在一类具有实证相关性的数据生成过程中，对应于次优福利的LCB可能超过直接构建的LCB，其平均差异量级为N^{-1/2}。我们将这一结果与政策学习和去偏推断中常被采用的所谓边界假设缺乏均匀性联系起来。我们主张使用具有均匀有效性的渐近近似方法，并展示了如何利用矩不等式模型中的现有推断方法来构建有效且紧致的最优福利下置信带。我们通过国家JTPA研究案例对研究结论进行了实证说明。