Xiaohong Chen, Zhenxiao Chen, Wayne Yuan Gao
arXiv 29 Oct 2025 · Econometrics
arXiv:2510.25607 · PDF · Extracted main text
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.
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| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Kitagawa, T. and Tetenov, A (2018) Who should be treated? empirical welfare maximization methods for treatment choice | 1.000 | 13 | 3 | 100% |
| 2 | –- and Gao, W. Y (2025) Semiparametric learning of integral functionals on submanifolds | 0.969 | 11 | 4 | 91% |
| 3 | Chen, X., Christensen, T. and Kankanala, S (2025) Adaptive estimation and uniform confidence bands for nonparametric structural functions and elasticities self | 0.737 | 3 | 2 | 100% |
| 4 | –- and Liao, Z (2014) Sieve m inference on irregular parameters | 0.644 | 2 | 2 | 100% |
| 5 | –- and Christensen, T. M (2018) Optimal sup-norm rates and uniform inference on nonlinear functionals of nonparametric iv regression | 0.511 | 2 | 2 | 50% |
| 6 | Cattaneo, M. D., Titiunik, R. and Yu, R. R (2025) a) | 0.511 | 2 | 1 | 100% |
| 7 | –-, –- and –- (2025) b) | 0.511 | 2 | 1 | 100% |
| 8 | –- and Pouzo, D (2015) Sieve wald and qlr inferences on semi/nonparametric conditional moment models | 0.511 | 2 | 1 | 100% |
| 9 | Whitehouse, J., Austern, M. and Syrgkanis, V (2025) Inference on optimal policy values and other irregular functionals via smoothing | 0.511 | 2 | 1 | 100% |
| 10 | Bloom, 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 study | 0.405 | 1 | 1 | 100% |
Showing the top 10 of 19 scored citations.
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| Citing paper | Intensity | Mentions | Sections | |
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| 1 | Nonparametric Uniform Inference in Binary Classification and Policy Values | 0.405 | 1 | 1 |
| 2 | Semiparametric Efficiency in Policy Learning with General Treatments | 0.405 | 1 | 1 |