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Optimal Decision Rules when Payoffs are Partially Identified

Timothy Christensen, Hyungsik Roger Moon, Frank Schorfheide

arXiv 25 Apr 2022 · Econometrics · 3 citations (OpenAlex)

arXiv:2204.11748 · PDF · DOI · OpenAlex · Extracted main text

Abstract

We derive asymptotically optimal statistical decision rules for discrete choice problems when payoffs depend on a partially-identified parameter $\theta$ and the decision maker can use a point-identified parameter $\mu$ to deduce restrictions on $\theta$. Examples include treatment choice under partial identification and pricing with rich unobserved heterogeneity. Our notion of optimality combines a minimax approach to handle the ambiguity from partial identification of $\theta$ given $\mu$ with an average risk minimization approach for $\mu$. We show how to implement optimal decision rules using the bootstrap and (quasi-)Bayesian methods in both parametric and semiparametric settings. We provide detailed applications to treatment choice and optimal pricing. Our asymptotic approach is well suited for realistic empirical settings in which the derivation of finite-sample optimal rules is intractable.

Citation extraction

62
references
141
in-text mentions
62
distinct cited
1
self-citations
18,141
main-text words

appendix boundary found by appendix_titled_section at “Online Appendix” · 60% 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
1Hirano and Porter (2009) Asymptotics for Statistical Treatment Rules1.00074100%
2Manski (2023) Probabilistic Prediction for Binary Treatment Choice: with focus on personalized medicine1.00053100%
3Manski (2021) Econometrics for Decision Making: Building Foundations Sketched by Haavelmo and Wald0.87452100%
4Giacomini, Kitagawa, and Read (2021) Robust Bayesian Analysis for Econometrics0.81142100%
5Ishihara and Kitagawa (2021) Evidence Aggregation for Treatment Choice0.81142100%
6Manski (2000) Identification problems and decisions under ambiguity: Empirical analysis of treatment response and normative analysis of treatm…0.81142100%
7Hurwicz (1951) Some Specification Problems and Applications to Econometric Models0.73732100%
8Kitamura and Stoye (2019) Nonparametric counterfactuals in random utility models0.73732100%
9Clarke and Barron (1990) Information-theoretic asymptotics of Bayes methods0.7218338%
10Schwartz (1965) On Bayes procedures0.6443267%

Showing the top 10 of 62 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
1Inference for Interval-Identified Parameters Selected from an Estimated Set1.00063
2Optimal treatment assignment rules under capacity constraints0.894217
3Nonparametric Bayesian Policy Learning0.73732
4Statistical Decisions and Partial Identification: With Application to Boundary Discontinuity Design0.51121
5Policy Learning under Endogeneity Using Instrumental Variables0.40511
6Policy Learning with New Treatments0.40511
7Debiased Machine Learning of Aggregated Intersection Bounds and Other Causal Parameters0.40511
8Improving Robust Decisions with Data0.40511
9Debiased Machine Learning when Nuisance Parameters Appear in Indicator Functions0.40511
10Externally Valid Selection of Experimental Sites via the k-Median Problem0.40511