Kirill Ponomarev, Vira Semenova
arXiv 9 Oct 2024 · Econometrics
arXiv:2410.07443 · PDF · DOI · OpenAlex · Extracted main text
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.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Chernozhukov, V., S. Lee, and A. Rosen (2013) Intersection bounds: Estimation and inference | 1.000 | 8 | 3 | 100% |
| 2 | Kitagawa, T. and A. Tetenov (2018) Who should be treated? empirical welfare maximization methods for treatment choice | 1.000 | 7 | 4 | 100% |
| 3 | Andrews, D. W. and G. Soares (2010) Inference for parameters defined by moment inequalities using generalized moment selection | 0.941 | 6 | 4 | 83% |
| 4 | Luedtke, A. and M. van der Laan (2016) Statistical inference for the mean outcome under a possibly non-unique optimal treatment strategy | 0.928 | 5 | 3 | 80% |
| 5 | Tsybakov, A. B (2004) Optimal aggregation of classifiers in statistical learning | 0.874 | 6 | 4 | 67% |
| 6 | Athey, S. and S. Wager (2021, January) (2021) Policy learning with observational data | 0.843 | 3 | 3 | 100% |
| 7 | Mbakop, E. and M. Tabord-Meehan (2021, March) (2021) Model selection for treatment choice: Penalized welfare maximization | 0.843 | 3 | 3 | 100% |
| 8 | Canay, I. A. and A. M. Shaikh (2017) Practical and theoretical advances in inference for partially identified models | 0.811 | 4 | 2 | 100% |
| 9 | Hirano, K. and J. Porter (2012) Impossibility results for nondifferentiable functionals | 0.737 | 3 | 2 | 100% |
| 10 | Romano, J. P., A. M. Shaikh, and M. Wolf (2014) A practical two-step method for testing moment inequalities | 0.737 | 3 | 2 | 100% |
Showing the top 10 of 67 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | Nonparametric Uniform Inference in Binary Classification and Policy Values | 0.644 | 2 | 2 |
| 2 | Nonparametric Bayesian Policy Learning | 0.644 | 2 | 2 |