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Minimax regret treatment choice with covariates or with limited validity of experiments

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  • Stoye, Jörg

Abstract

This paper continues the investigation of minimax regret treatment choice initiated by Manski (2004). Consider a decision maker who must assign treatment to future subjects after observing outcomes experienced in a sample. A certain scoring rule is known to achieve minimax regret in simple versions of this decision problem. I investigate its sensitivity to perturbations of the decision environment in realistic directions. They are as follows. (i) Treatment outcomes may be influenced by a covariate whose effect on outcome distributions is bounded (in one of numerous probability metrics). This is interesting because introduction of a covariate with unrestricted effects leads to a pathological result. (ii) The experiment may have limited validity because of selective noncompliance or because the sampling universe is a potentially selective subset of the treatment population. Thus, even large samples may generate misleading signals. These problems are formalized via a “bounds” approach that turns the problem into one of partial identification.

Suggested Citation

  • Stoye, Jörg, 2012. "Minimax regret treatment choice with covariates or with limited validity of experiments," Journal of Econometrics, Elsevier, vol. 166(1), pages 138-156.
  • Handle: RePEc:eee:econom:v:166:y:2012:i:1:p:138-156
    DOI: 10.1016/j.jeconom.2011.06.012
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    References listed on IDEAS

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    1. Charles F. Manski, 1989. "Anatomy of the Selection Problem," Journal of Human Resources, University of Wisconsin Press, vol. 24(3), pages 343-360.
    2. Stoye, Jörg, 2009. "Minimax regret treatment choice with finite samples," Journal of Econometrics, Elsevier, vol. 151(1), pages 70-81, July.
    3. Chamberlain, Gary, 2000. "Econometrics and decision theory," Journal of Econometrics, Elsevier, vol. 95(2), pages 255-283, April.
    4. Keisuke Hirano & Jack R. Porter, 2009. "Asymptotics for Statistical Treatment Rules," Econometrica, Econometric Society, vol. 77(5), pages 1683-1701, September.
    5. Dehejia, Rajeev H., 2005. "Program evaluation as a decision problem," Journal of Econometrics, Elsevier, vol. 125(1-2), pages 141-173.
    6. Brent Kreider & Steven C. Hill, 2009. "Partially Identifying Treatment Effects with an Application to Covering the Uninsured," Journal of Human Resources, University of Wisconsin Press, vol. 44(2).
    7. Dirk Bergemann & Karl Schlag, 2012. "Robust Monopoly Pricing," World Scientific Book Chapters,in: Robust Mechanism Design The Role of Private Information and Higher Order Beliefs, chapter 13, pages 417-441 World Scientific Publishing Co. Pte. Ltd..
    8. Dirk Bergemann & Karl H. Schlag, 2012. "Pricing Without Priors," World Scientific Book Chapters,in: Robust Mechanism Design The Role of Private Information and Higher Order Beliefs, chapter 12, pages 405-415 World Scientific Publishing Co. Pte. Ltd..
    9. Charles F. Manski, 2004. "Statistical Treatment Rules for Heterogeneous Populations," Econometrica, Econometric Society, vol. 72(4), pages 1221-1246, July.
    10. Tetenov, Aleksey, 2012. "Statistical treatment choice based on asymmetric minimax regret criteria," Journal of Econometrics, Elsevier, vol. 166(1), pages 157-165.
    11. Aleksey Tetenov, 2008. "Measuring Precision of Statistical Inference on Partially Identified Parameters," Carlo Alberto Notebooks 98, Collegio Carlo Alberto, revised 2012.
    12. Manski, Charles F., 2000. "Identification problems and decisions under ambiguity: Empirical analysis of treatment response and normative analysis of treatment choice," Journal of Econometrics, Elsevier, vol. 95(2), pages 415-442, April.
    13. William A. Brock, 2006. "Profiling Problems With Partially Identified Structure," Economic Journal, Royal Economic Society, vol. 116(515), pages 427-440, November.
    14. Charles F. Manski, 2006. "Search Profiling With Partial Knowledge of Deterrence," Economic Journal, Royal Economic Society, vol. 116(515), pages 385-401, November.
    15. Manski, Charles F., 2007. "Minimax-regret treatment choice with missing outcome data," Journal of Econometrics, Elsevier, vol. 139(1), pages 105-115, July.
    16. Stoye, J rg, 2007. "Minimax Regret Treatment Choice With Incomplete Data And Many Treatments," Econometric Theory, Cambridge University Press, vol. 23(01), pages 190-199, February.
    17. Edward Vytlacil, 2002. "Independence, Monotonicity, and Latent Index Models: An Equivalence Result," Econometrica, Econometric Society, vol. 70(1), pages 331-341, January.
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    Cited by:

    1. Charles F. Manski, 2017. "Improving Clinical Guidelines and Decisions under Uncertainty," NBER Working Papers 23915, National Bureau of Economic Research, Inc.
    2. Alexei Parakhonyak & Anton Sobolev, 2015. "Non‐Reservation Price Equilibrium and Search without Priors," Economic Journal, Royal Economic Society, vol. 0(584), pages 887-909, May.
    3. Charles F. Manski & Aleksey Tetenov, 2014. "The Quantile Performance Of Statistical Treatment Rules Using Hypothesis Tests To Allocate A Population To Two Treatments," Carlo Alberto Notebooks 361, Collegio Carlo Alberto.
    4. repec:kap:theord:v:83:y:2017:i:2:d:10.1007_s11238-017-9592-1 is not listed on IDEAS
    5. Evan Sadler, 2015. "Minimax and the value of information," Theory and Decision, Springer, vol. 78(4), pages 575-586, April.
    6. Charles F. Manski & Aleksey Tetenov, 2015. "Clinical trial design enabling e-optimal treatment rules," CeMMAP working papers CWP60/15, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    7. Keisuke Hirano & Jack R. Porter, 2016. "Panel Asymptotics and Statistical Decision Theory," The Japanese Economic Review, Japanese Economic Association, vol. 67(1), pages 33-49, March.
    8. Charles F. Manski & Aleksey Tetenov, 2015. "Clinical trial design enabling epsilon-optimal treatment rules," Carlo Alberto Notebooks 430, Collegio Carlo Alberto.

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