On the Lower Confidence Band for the Optimal Welfare in Policy Learning

Kirill Ponomarev and Vira Semenova

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Abstract: We study inference on the optimal welfare in a policy learning problem and propose reporting a lower confidence band (LCB). A natural approach to constructing an LCB is to invert a one-sided t-test based on an efficient estimator for the optimal welfare. However, we show that for an empirically relevant class of DGPs, such an LCB can be first-order dominated by an LCB based on a welfare estimate for a suitable suboptimal treatment policy. We show that such first-order dominance is possible if and only if the optimal treatment policy is not ``well-separated'' from the rest, in the sense of the commonly imposed margin condition. When this condition fails, standard debiased inference methods are not applicable. We show that uniformly valid and easy-to-compute LCBs can be constructed analytically by inverting moment-inequality tests with the maximum and quasi-likelihood-ratio test statistics. As an empirical illustration, we revisit the National JTPA study and find that the proposed LCBs achieve reliable coverage and competitive length.

Date: 2024-10, Revised 2025-09
New Economics Papers: this item is included in nep-ecm
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