EconBase
← All papers

Inference on Welfare and Value Functionals under Optimal Treatment Assignment

Xiaohong Chen, Zhenxiao Chen, Wayne Yuan Gao

arXiv 29 Oct 2025 · Econometrics

arXiv:2510.25607 · PDF · Extracted main text

Abstract

We provide theoretical results for the estimation and inference of a class of welfare and value functionals of the nonparametric conditional average treatment effect (CATE) function under optimal treatment assignment, i.e., treatment is assigned to an observed type if and only if its CATE is nonnegative. For the optimal welfare functional defined as the average value of CATE on the subpopulation with nonnegative CATE, we establish the $\sqrt{n}$ asymptotic normality of the semiparametric plug-in estimators and provide an analytical asymptotic variance formula. For more general value functionals, we show that the plug-in estimators are typically asymptotically normal at the 1-dimensional nonparametric estimation rate, and we provide a consistent variance estimator based on the sieve Riesz representer, as well as a proposed computational procedure for numerical integration on submanifolds. The key reason underlying the different convergence rates for the welfare functional versus the general value functional lies in that, on the boundary subpopulation for whom CATE is zero, the integrand vanishes for the welfare functional but does not for general value functionals. We demonstrate in Monte Carlo simulations the good finite-sample performance of our estimation and inference procedures, and conduct an empirical application of our methods on the effectiveness of job training programs on earnings using the JTPA data set.

Citation extraction

19
references
49
in-text mentions
19
distinct cited
1
self-citations
12,490
main-text words

appendix boundary found by appendix_command · 69% of the source is main text. Read the extracted text to check this.

Most heavily cited references

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.

ReferenceIntensityMentionsSectionsMain text
1Kitagawa, T. and Tetenov, A (2018) Who should be treated? empirical welfare maximization methods for treatment choice1.000133100%
2–- and Gao, W. Y (2025) Semiparametric learning of integral functionals on submanifolds0.96911491%
3Chen, X., Christensen, T. and Kankanala, S (2025) Adaptive estimation and uniform confidence bands for nonparametric structural functions and elasticities self0.73732100%
4–- and Liao, Z (2014) Sieve m inference on irregular parameters0.64422100%
5–- and Christensen, T. M (2018) Optimal sup-norm rates and uniform inference on nonlinear functionals of nonparametric iv regression0.5112250%
6Cattaneo, M. D., Titiunik, R. and Yu, R. R (2025) a)0.51121100%
7–-, –- and –- (2025) b)0.51121100%
8–- and Pouzo, D (2015) Sieve wald and qlr inferences on semi/nonparametric conditional moment models0.51121100%
9Whitehouse, J., Austern, M. and Syrgkanis, V (2025) Inference on optimal policy values and other irregular functionals via smoothing0.51121100%
10Bloom, H. S., Orr, L. L., Bell, S. H., Cave, G., Doolittle, F., Lin,… (1997) The benefits and costs of jtpa title ii-a programs: Key findings from the national job training partnership act study0.40511100%

Showing the top 10 of 19 scored citations.

Cited by, within the corpus

arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.

Citing paperIntensityMentionsSections
1Nonparametric Uniform Inference in Binary Classification and Policy Values0.40511
2Semiparametric Efficiency in Policy Learning with General Treatments0.40511