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An Information-Theoretic Approach to Partially Identified Problems

Author

Listed:
  • Amos Golan

    (American University and Santa Fe Institute)

  • Jeffrey Perloff

    (University of California, Berkeley)

Abstract

An information-theoretic maximum entropy (ME) model provides an alternative approach to finding solutions to partially identified models. In these models, we can identify only a solution set rather than point-identifying the parameters of interest, given our limited information. Manski (2021) proposed using statistical decision functions in general, and the minimax-regret (MMR) criterion in particular, to choose a unique solution. Using Manski's simulations for a missing data and a treatment problem, including an empirical example, we show that ME performs the same or better than MMR. In additional simulations, ME dominates various other statistical decision functions. ME has an axiomatic underpinning and is computationally efficient.

Suggested Citation

  • Amos Golan & Jeffrey Perloff, 2025. "An Information-Theoretic Approach to Partially Identified Problems," Working Papers 20205-009, Human Capital and Economic Opportunity Working Group.
    • Handle: RePEc:hka:wpaper:20205-009
    Note: MIP
    as

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    File URL: http://humcap.uchicago.edu/RePEc/hka/wpaper/Golan_Perloff_information-theor-approach-part-ID.pdf
    File Function: First version, September 2025
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    References listed on IDEAS

    as
    1. Tamer, Elie, 2010. "Partial Identification in Econometrics," Scholarly Articles 34728615, Harvard University Department of Economics.
    2. Valentyn Litvin & Charles F. Manski, 2021. "Evaluating the maximum regret of statistical treatment rules with sample data on treatment response," Stata Journal, StataCorp LLC, vol. 21(1), pages 97-122, March.
    3. Tetenov, Aleksey, 2012. "Statistical treatment choice based on asymmetric minimax regret criteria," Journal of Econometrics, Elsevier, vol. 166(1), pages 157-165.
    4. Charles F. Manski, 2004. "Statistical Treatment Rules for Heterogeneous Populations," Econometrica, Econometric Society, vol. 72(4), pages 1221-1246, July.
    5. Jun, Sung Jae & Pinkse, Joris, 2020. "Counterfactual prediction in complete information games: Point prediction under partial identification," Journal of Econometrics, Elsevier, vol. 216(2), pages 394-429.
    6. Leamer, Edward E, 1985. "Sensitivity Analyses Would Help," American Economic Review, American Economic Association, vol. 75(3), pages 308-313, June.
    7. Elie Tamer, 2010. "Partial Identification in Econometrics," Annual Review of Economics, Annual Reviews, vol. 2(1), pages 167-195, September.
    Full references (including those not matched with items on IDEAS)

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    Keywords

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    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory

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