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Inferring Welfare Maximizing Treatment Assignment under Budget Constraints

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  • Debopam Bhattacharya
  • Pascaline Dupas

Abstract

This paper concerns the problem of allocating a binary treatment among a target population based on observed covariates. The goal is to (i) maximize the mean social welfare arising from an eventual outcome distribution, when a budget constraint limits what fraction of the population can be treated and (ii) to infer the dual value, i.e. the minimum resources needed to attain a specific level of mean welfare via efficient treatment assignment. We consider a treatment allocation procedure based on sample data from randomized treatment assignment and derive asymptotic frequentist confidence interval for the welfare generated from it. We propose choosing the conditioning covariates through cross-validation. The methodology is applied to the efficient provision of anti-malaria bed net subsidies, using data from a randomized experiment conducted in Western Kenya. We find that subsidy allocation based on wealth, presence of children and possession of bank account can lead to a rise in subsidy use by about 9 percentage points compared to allocation based on wealth only, and by 17 percentage points compared to a purely random allocation.

Suggested Citation

  • Debopam Bhattacharya & Pascaline Dupas, 2008. "Inferring Welfare Maximizing Treatment Assignment under Budget Constraints," NBER Working Papers 14447, National Bureau of Economic Research, Inc.
  • Handle: RePEc:nbr:nberwo:14447
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    1. Esther Duflo & Rema Hanna, 2005. "Monitoring Works: Getting Teachers to Come to School," Working Papers id:301, eSocialSciences.
    2. Jinyong Hahn & Keisuke Hirano & Dean Karlan, 2011. "Adaptive Experimental Design Using the Propensity Score," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 29(1), pages 96-108, January.
    3. Keisuke Hirano & Jack R. Porter, 2009. "Asymptotics for Statistical Treatment Rules," Econometrica, Econometric Society, vol. 77(5), pages 1683-1701, September.
    4. Pagan,Adrian & Ullah,Aman, 1999. "Nonparametric Econometrics," Cambridge Books, Cambridge University Press, number 9780521355643.
    5. Altonji, Joseph G & Segal, Lewis M, 1996. "Small-Sample Bias in GMM Estimation of Covariance Structures," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(3), pages 353-366, July.
    6. César Martinelli & Susan Wendy Parker, 2009. "Deception and Misreporting in a Social Program," Journal of the European Economic Association, MIT Press, vol. 7(4), pages 886-908, June.
    7. Xiaohong Chen & Oliver Linton & Ingrid Van Keilegom, 2003. "Estimation of Semiparametric Models when the Criterion Function Is Not Smooth," Econometrica, Econometric Society, vol. 71(5), pages 1591-1608, September.
    8. Keisuke Hirano & Guido W. Imbens & Geert Ridder, 2003. "Efficient Estimation of Average Treatment Effects Using the Estimated Propensity Score," Econometrica, Econometric Society, vol. 71(4), pages 1161-1189, July.
    9. Lechner, Michael & Smith, Jeffrey, 2007. "What is the value added by caseworkers?," Labour Economics, Elsevier, vol. 14(2), pages 135-151, April.
    10. Tetenov, Aleksey, 2012. "Statistical treatment choice based on asymmetric minimax regret criteria," Journal of Econometrics, Elsevier, vol. 166(1), pages 157-165.
    11. Pakes, Ariel & Pollard, David, 1989. "Simulation and the Asymptotics of Optimization Estimators," Econometrica, Econometric Society, vol. 57(5), pages 1027-1057, September.
    12. Delgado, Miguel A & Mora, Juan, 1995. "Nonparametric and Semiparametric Estimation with Discrete Regressors," Econometrica, Econometric Society, vol. 63(6), pages 1477-1484, November.
    13. Pascaline Dupas, 2014. "Short‐Run Subsidies and Long‐Run Adoption of New Health Products: Evidence From a Field Experiment," Econometrica, Econometric Society, vol. 82(1), pages 197-228, January.
    14. Newey, Whitney K., 1994. "Kernel Estimation of Partial Means and a General Variance Estimator," Econometric Theory, Cambridge University Press, vol. 10(2), pages 1-21, June.
    15. Duflo, Esther & Glennerster, Rachel & Kremer, Michael, 2008. "Using Randomization in Development Economics Research: A Toolkit," Handbook of Development Economics, in: T. Paul Schultz & John A. Strauss (ed.), Handbook of Development Economics, edition 1, volume 4, chapter 61, pages 3895-3962, Elsevier.
    16. Chunrong Ai & Xiaohong Chen, 2003. "Efficient Estimation of Models with Conditional Moment Restrictions Containing Unknown Functions," Econometrica, Econometric Society, vol. 71(6), pages 1795-1843, November.
    17. Bryan S. Graham & Guido W. Imbens & Geert Ridder, 2014. "Complementarity and aggregate implications of assortative matching: A nonparametric analysis," Quantitative Economics, Econometric Society, vol. 5, pages 29-66, March.
    18. Hansen, Bruce E., 2008. "Uniform Convergence Rates For Kernel Estimation With Dependent Data," Econometric Theory, Cambridge University Press, vol. 24(3), pages 726-748, June.
    19. Stoye, Jörg, 2009. "Minimax regret treatment choice with finite samples," Journal of Econometrics, Elsevier, vol. 151(1), pages 70-81, July.
    20. Hall, Peter & Wolff, Rodney C. L. & Yao, Qiwei, 1999. "Methods for estimating a conditional distribution function," LSE Research Online Documents on Economics 6631, London School of Economics and Political Science, LSE Library.
    21. Dehejia, Rajeev H., 2005. "Program evaluation as a decision problem," Journal of Econometrics, Elsevier, vol. 125(1-2), pages 141-173.
    22. Donald W. K. Andrews, 1999. "Estimation When a Parameter Is on a Boundary," Econometrica, Econometric Society, vol. 67(6), pages 1341-1384, November.
    23. Bhattacharya, Debopam, 2007. "Inference on inequality from household survey data," Journal of Econometrics, Elsevier, vol. 137(2), pages 674-707, April.
    24. Pascaline Dupas, 2009. "What Matters (and What Does Not) in Households' Decision to Invest in Malaria Prevention?," American Economic Review, American Economic Association, vol. 99(2), pages 224-230, May.
    25. Aprajit Mahajan & Alessandro Tarozzi & Joanne Yoong & Brian Blackburn, 2009. "Bednets, Information and Malaria in Orissa," Working Papers 10-78, Duke University, Department of Economics.
    26. Awash Teklehaimanot & Gordon C. McCord & Jeffrey D. Sachs, 2007. "Scaling Up Malaria Control in Africa: An Economic and Epidemiological Assessment," NBER Working Papers 13664, National Bureau of Economic Research, Inc.
    27. Charles F. Manski, 2004. "Statistical Treatment Rules for Heterogeneous Populations," Econometrica, Econometric Society, vol. 72(4), pages 1221-1246, July.
    28. Jessica Cohen & Pascaline Dupas, 2010. "Free Distribution or Cost-Sharing? Evidence from a Randomized Malaria Prevention Experiment," The Quarterly Journal of Economics, Oxford University Press, vol. 125(1), pages 1-45.
    29. Claeskens,Gerda & Hjort,Nils Lid, 2008. "Model Selection and Model Averaging," Cambridge Books, Cambridge University Press, number 9780521852258.
    30. Frolich, Markus, 2008. "Statistical Treatment Choice: An Application to Active Labor Market Programs," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 547-558, June.
    31. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, number 8355.
    32. Horowitz, Joel L, 1992. "A Smoothed Maximum Score Estimator for the Binary Response Model," Econometrica, Econometric Society, vol. 60(3), pages 505-531, May.
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    More about this item

    JEL classification:

    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • I38 - Health, Education, and Welfare - - Welfare, Well-Being, and Poverty - - - Government Programs; Provision and Effects of Welfare Programs

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