arXiv 18 Dec 2022 · Econometrics
arXiv:2212.09007 · PDF · DOI · OpenAlex · Extracted main text
This paper considers the estimation of treatment assignment rules when the policy maker faces a general budget or resource constraint. Utilizing the PAC-Bayesian framework, we propose new treatment assignment rules that allow for flexible notions of treatment outcome, treatment cost, and a budget constraint. For example, the constraint setting allows for cost-savings, when the costs of non-treatment exceed those of treatment for a subpopulation, to be factored into the budget. It also accommodates simpler settings, such as quantity constraints, and doesn't require outcome responses and costs to have the same unit of measurement. Importantly, the approach accounts for settings where budget or resource limitations may preclude treating all that can benefit, where costs may vary with individual characteristics, and where there may be uncertainty regarding the cost of treatment rules of interest. Despite the nomenclature, our theoretical analysis examines frequentist properties of the proposed rules. For stochastic rules that typically approach budget-penalized empirical welfare maximizing policies in larger samples, we derive non-asymptotic generalization bounds for the target population costs and sharp oracle-type inequalities that compare the rules' welfare regret to that of optimal policies in relevant budget categories. A closely related, non-stochastic, model aggregation treatment assignment rule is shown to inherit desirable attributes.
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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 | Kitagawa, T. and Tetenov, A (2018) Who should be treated? empirical welfare maximization methods for treatment choice | 1.000 | 13 | 5 | 100% |
| 2 | Sun, L (2021) Empirical welfare maximization with constraints | 1.000 | 6 | 3 | 100% |
| 3 | Catoni, O (2007) Pac-bayesian supervised classification: The thermodynamics of statistical learning | 1.000 | 5 | 3 | 100% |
| 4 | Sun, H., Du, S., and Wager, S (2021) Treatment allocation under uncertain costs | 0.971 | 12 | 5 | 92% |
| 5 | Mbakop, E. and Tabord-Meehan, M (2021) Model selection for treatment choice: Penalized welfare maximization | 0.928 | 4 | 3 | 100% |
| 6 | Alquier, P., Ridgway, J., and Chopin, N (2016) On the properties of variational approximations of gibbs posteriors | 0.920 | 9 | 6 | 78% |
| 7 | Lever, G., Laviolette, F., and Shawe-Taylor, J (2010) Distribution-dependent pac-bayes priors | 0.754 | 7 | 3 | 43% |
| 8 | Seeger, M (2002) Pac-bayesian generalisation error bounds for gaussian process classification | 0.737 | 5 | 3 | 40% |
| 9 | Bhattacharya, D. and Dupas, P (2012) Inferring welfare maximizing treatment assignment under budget constraints | 0.737 | 3 | 2 | 100% |
| 10 | Manski, C. F (2004) Statistical treatment rules for heterogeneous populations | 0.737 | 3 | 2 | 100% |
Showing the top 10 of 52 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | Stochastic treatment choice with empirical welfare updating | 0.405 | 1 | 1 |