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Statistical Treatment Rules for Heterogeneous Populations: With Application to Randomized Experiments

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  • Charles F. Manski

Abstract

This paper uses Wald's concept of the risk of a statistical decision function to address the question: How should sample data on treatment response be used to guide treatment choices in a heterogeneous population? Statistical treatment rules (STRs) are statistical decision functions that map observed covariates of population members and sample data on treatment response into treatment choices. I propose evaluation of STRs by their expected welfare (negative risk in Wald's terms), and I apply this criterion to compare two STRs when the sample data are generated by a classical randomized experiment. The rules compared both embody the reasonable idea that persons should be assigned the treatment with the best empirical success rate, but they differ in their use of covariate information. The conditional success (CS) rule selects treatments with the best empirical success rates conditional on specified covariates and the unconditional success (US) rule selects a treatment with the best unconditional empirical success rate. The main finding is a proposition giving finite-sample bounds on expected welfare under the two rules. The bounds, which rest on a large-deviations theorem of Hoeffding, yield explicit sample-size and distributional conditions under which the CS Rule is superior to the US rule.

Suggested Citation

  • Charles F. Manski, 1999. "Statistical Treatment Rules for Heterogeneous Populations: With Application to Randomized Experiments," NBER Technical Working Papers 0242, National Bureau of Economic Research, Inc.
  • Handle: RePEc:nbr:nberte:0242
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    References listed on IDEAS

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    1. Manski, Charles F, 1990. "Nonparametric Bounds on Treatment Effects," American Economic Review, American Economic Association, vol. 80(2), pages 319-323, May.
    2. Charles F. Manski, 1997. "Monotone Treatment Response," Econometrica, Econometric Society, vol. 65(6), pages 1311-1334, November.
    3. Manski, C.F., 1992. "Identification Problems in the Social Sciences," Working papers 9217, Wisconsin Madison - Social Systems.
    4. James J. Heckman & Jeffrey Smith & Nancy Clements, 1997. "Making The Most Out Of Programme Evaluations and Social Experiments: Accounting For Heterogeneity in Programme Impacts," Review of Economic Studies, Oxford University Press, vol. 64(4), pages 487-535.
    5. 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.
    6. Imbens, Guido W & Angrist, Joshua D, 1994. "Identification and Estimation of Local Average Treatment Effects," Econometrica, Econometric Society, vol. 62(2), pages 467-475, March.
    7. Frank Stafford, 1985. "Income-Maintenance Policy and Work Effort: Learning from Experiments and Labor-Market Studies," NBER Chapters,in: Social Experimentation, pages 95-144 National Bureau of Economic Research, Inc.
    8. Manski, C.F. & Nagin, D.S., 1995. "Bounding Disagreements About Treatment Effects: A Case Study of Sentencing and Recidivism," Working papers 9526, Wisconsin Madison - Social Systems.
    9. Dehejia, Rajeev H., 2005. "Program evaluation as a decision problem," Journal of Econometrics, Elsevier, vol. 125(1-2), pages 141-173.
    10. V. Joseph Hotz & Charles H. Mullin & Seth G. Sanders, 1997. "Bounding Causal Effects Using Data from a Contaminated Natural Experiment: Analysing the Effects of Teenage Childbearing," Review of Economic Studies, Oxford University Press, vol. 64(4), pages 575-603.
    11. Manski, C.F. & Sandefur, G.D. & Mclanahan, S. & Powers, D., 1990. "Alternative Estimates Of The Effect Of Family Stucture During Adolescence On Hight School Graduation," Working papers 90-31, Wisconsin Madison - Social Systems.
    12. Heckman, James J. & Robb, Richard Jr., 1985. "Alternative methods for evaluating the impact of interventions : An overview," Journal of Econometrics, Elsevier, vol. 30(1-2), pages 239-267.
    13. Charles F. Manski, 1997. "The Mixing Problem in Programme Evaluation," Review of Economic Studies, Oxford University Press, vol. 64(4), pages 537-553.
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    Cited by:

    1. Dehejia, Rajeev H., 2005. "Program evaluation as a decision problem," Journal of Econometrics, Elsevier, vol. 125(1-2), pages 141-173.
    2. Mark C. Berger & Dan Black & Jeffrey Smith, 2000. "Evaluating Profiling as a Means of Allocating Government Services," UWO Department of Economics Working Papers 200018, University of Western Ontario, Department of Economics.

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