Optimal Decision Rules Under Partial Identification
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2021
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| _version_ | 1866916636686024704 |
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| author | Yata, Kohei |
| author_facet | Yata, Kohei |
| contents | I consider a class of statistical decision problems in which the policymaker must decide between two policies to maximize social welfare (e.g., the population mean of an outcome) based on a finite sample. The framework introduced in this paper allows for various types of restrictions on the structural parameter (e.g., the smoothness of a conditional mean potential outcome function) and accommodates settings with partial identification of social welfare. As the main theoretical result, I derive a finite-sample optimal decision rule under the minimax regret criterion. This rule has a simple form, yet achieves optimality among all decision rules; no ad hoc restrictions are imposed on the class of decision rules. I apply my results to the problem of whether to change an eligibility cutoff in a regression discontinuity setup, and illustrate them in an empirical application to a school construction program in Burkina Faso. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2111_04926 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Optimal Decision Rules Under Partial Identification Yata, Kohei Econometrics Statistics Theory Methodology I consider a class of statistical decision problems in which the policymaker must decide between two policies to maximize social welfare (e.g., the population mean of an outcome) based on a finite sample. The framework introduced in this paper allows for various types of restrictions on the structural parameter (e.g., the smoothness of a conditional mean potential outcome function) and accommodates settings with partial identification of social welfare. As the main theoretical result, I derive a finite-sample optimal decision rule under the minimax regret criterion. This rule has a simple form, yet achieves optimality among all decision rules; no ad hoc restrictions are imposed on the class of decision rules. I apply my results to the problem of whether to change an eligibility cutoff in a regression discontinuity setup, and illustrate them in an empirical application to a school construction program in Burkina Faso. |
| title | Optimal Decision Rules Under Partial Identification |
| topic | Econometrics Statistics Theory Methodology |
| url | https://arxiv.org/abs/2111.04926 |