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Efficient Estimation of Average Treatment Effects under Treatment-Based Sampling

  • Kyungchul Song

    ()

    (Department of Economics, University of Pennsylvania)

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    Nonrandom sampling schemes are often used in program evaluation settings to improve the quality of inference. This paper considers what we call treatment-based sampling, a type of standard stratified sampling where part of the strata are based on treatments. This paper first establishes semiparametric efficiency bounds for estimators of weighted average treatment effects and average treatment effects on the treated. In doing so, this paper illuminates the role of information about the aggregate shares from the original data set. This paper also develops an optimal design of treatment-based sampling that yields the best semiparametric efficiency bound. Lastly, this paper finds that adapting the efficient estimators of Hirano, Imbens, and Ridder (2003) to treatment-based sampling does not always lead to an efficient estimator. This paper proposes different estimators that are efficient in such a situation.

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    File URL: http://economics.sas.upenn.edu/system/files/working-papers/09-011.pdf
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    Paper provided by Penn Institute for Economic Research, Department of Economics, University of Pennsylvania in its series PIER Working Paper Archive with number 09-011.

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    Length: 42 pages
    Date of creation: 06 Mar 2009
    Date of revision:
    Handle: RePEc:pen:papers:09-011
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    1. Imbens, G.W., 1991. "An Efficient Method Of Moments Estimator For Discrete Choice Models With Choice-Based Sampling," Harvard Institute of Economic Research Working Papers 1546, Harvard - Institute of Economic Research.
    2. Guido Imbens, 2000. "Efficient Estimation of Average Treatment Effects Using the Estimated Propensity Score," Econometric Society World Congress 2000 Contributed Papers 1166, Econometric Society.
    3. Tripathi, Gautam, 2011. "Moment-Based Inference With Stratified Data," Econometric Theory, Cambridge University Press, vol. 27(01), pages 47-73, February.
    4. Imbens, G. & Lancaster, T., 1991. "Efficient Estimation and Stratified Sampling," Papers 9145, Tilburg - Center for Economic Research.
    5. Newey, Whitney K, 1990. "Semiparametric Efficiency Bounds," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 5(2), pages 99-135, April-Jun.
    6. Hansen, Bruce E., 2008. "Uniform Convergence Rates For Kernel Estimation With Dependent Data," Econometric Theory, Cambridge University Press, vol. 24(03), pages 726-748, June.
    7. Jinyong Hahn & Keisuke Hirano & Dean Karlan, 2009. "Adaptive Experimental Design Using the Propensity Score," Working Papers 969, Economic Growth Center, Yale University.
    8. Wooldridge, Jeffrey M., 2001. "Asymptotic Properties Of Weighted M-Estimators For Standard Stratified Samples," Econometric Theory, Cambridge University Press, vol. 17(02), pages 451-470, April.
    9. Cosslett, Stephen R, 1981. "Maximum Likelihood Estimator for Choice-Based Samples," Econometrica, Econometric Society, vol. 49(5), pages 1289-1316, September.
    10. Rajeev H. Dehejia & Sadek Wahba, 1998. "Propensity Score Matching Methods for Non-experimental Causal Studies," NBER Working Papers 6829, National Bureau of Economic Research, Inc.
    11. Jeffrey M. Wooldridge, 1999. "Asymptotic Properties of Weighted M-Estimators for Variable Probability Samples," Econometrica, Econometric Society, vol. 67(6), pages 1385-1406, November.
    12. Jeffrey Smith & Petra Todd, 2003. "Does Matching Overcome Lalonde's Critique of Nonexperimental Estimators?," University of Western Ontario, Centre for Human Capital and Productivity (CHCP) Working Papers 20035, University of Western Ontario, Centre for Human Capital and Productivity (CHCP).
    13. Jinyong Hahn, 1998. "On the Role of the Propensity Score in Efficient Semiparametric Estimation of Average Treatment Effects," Econometrica, Econometric Society, vol. 66(2), pages 315-332, March.
    14. James J. Heckman & Hidehiko Ichimura & Petra Todd, 1998. "Matching As An Econometric Evaluation Estimator," Review of Economic Studies, Oxford University Press, vol. 65(2), pages 261-294.
    15. LaLonde, Robert J, 1986. "Evaluating the Econometric Evaluations of Training Programs with Experimental Data," American Economic Review, American Economic Association, vol. 76(4), pages 604-20, September.
    16. Powell, James L & Stock, James H & Stoker, Thomas M, 1989. "Semiparametric Estimation of Index Coefficients," Econometrica, Econometric Society, vol. 57(6), pages 1403-30, November.
    17. Manski, Charles F., 1986. "Semiparametric analysis of binary response from response-based samples," Journal of Econometrics, Elsevier, vol. 31(1), pages 31-40, February.
    18. Ashenfelter, Orley & Card, David, 1985. "Using the Longitudinal Structure of Earnings to Estimate the Effect of Training Programs," The Review of Economics and Statistics, MIT Press, vol. 67(4), pages 648-60, November.
    19. Escanciano, Juan Carlos & Song, Kyungchul, 2010. "Testing single-index restrictions with a focus on average derivatives," Journal of Econometrics, Elsevier, vol. 156(2), pages 377-391, June.
    20. Kyungchul Song, 2009. "Two-Step Extremum Estimation with Estimated Single-Indices," PIER Working Paper Archive 09-012, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
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