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Efficient Estimation of Average Treatment Effects under Treatment-Based Sampling

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  • Kyungchul Song

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    (Department of Economics, University of Pennsylvania)

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    Abstract

    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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    Bibliographic Info

    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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    Keywords: treatment-based sampling; semiparametric efficiency; treatment effects.;

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    1. Orley Ashenfelter & David Card, 1984. "Using the Longitudinal Structure of Earnings to Estimate the Effect of Training Programs," Working Papers, Princeton University, Department of Economics, Industrial Relations Section. 554, Princeton University, Department of Economics, Industrial Relations Section..
    2. Jinyong Hahn, 1998. "On the Role of the Propensity Score in Efficient Semiparametric Estimation of Average Treatment Effects," Econometrica, Econometric Society, Econometric Society, vol. 66(2), pages 315-332, March.
    3. Powell, James L & Stock, James H & Stoker, Thomas M, 1989. "Semiparametric Estimation of Index Coefficients," Econometrica, Econometric Society, Econometric Society, vol. 57(6), pages 1403-30, November.
    4. 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, Harvard - Institute of Economic Research 1546, Harvard - Institute of Economic Research.
    5. Rajeev H. Dehejia & Sadek Wahba, 2002. "Propensity score matching methods for non-experimental causal studies," Discussion Papers, Columbia University, Department of Economics 0102-14, Columbia University, Department of Economics.
    6. Tripathi, Gautam, 2011. "Moment-Based Inference With Stratified Data," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 27(01), pages 47-73, February.
    7. Manski, Charles F., 1986. "Semiparametric analysis of binary response from response-based samples," Journal of Econometrics, Elsevier, Elsevier, vol. 31(1), pages 31-40, February.
    8. Hahn, Jinyong & Hirano, Keisuke & Karlan, Dean, 2008. "Adaptive Experimental Design Using the Propensity Score," MPRA Paper 8315, University Library of Munich, Germany.
    9. Imbens, G. & Lancaster, T., 1991. "Efficient Estimation and Stratified Sampling," Papers, Tilburg - Center for Economic Research 9145, Tilburg - Center for Economic Research.
    10. A. Smith, Jeffrey & E. Todd, Petra, 2005. "Does matching overcome LaLonde's critique of nonexperimental estimators?," Journal of Econometrics, Elsevier, Elsevier, vol. 125(1-2), pages 305-353.
    11. Hansen, Bruce E., 2008. "Uniform Convergence Rates For Kernel Estimation With Dependent Data," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 24(03), pages 726-748, June.
    12. Newey, Whitney K, 1990. "Semiparametric Efficiency Bounds," Journal of Applied Econometrics, John Wiley & Sons, Ltd., John Wiley & Sons, Ltd., vol. 5(2), pages 99-135, April-Jun.
    13. Jeffrey M. Wooldridge, 1999. "Asymptotic Properties of Weighted M-Estimators for Variable Probability Samples," Econometrica, Econometric Society, Econometric Society, vol. 67(6), pages 1385-1406, November.
    14. LaLonde, Robert J, 1986. "Evaluating the Econometric Evaluations of Training Programs with Experimental Data," American Economic Review, American Economic Association, American Economic Association, vol. 76(4), pages 604-20, September.
    15. Heckman, James J & Ichimura, Hidehiko & Todd, Petra, 1998. "Matching as an Econometric Evaluation Estimator," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 65(2), pages 261-94, April.
    16. Wooldridge, Jeffrey M., 2001. "Asymptotic Properties Of Weighted M-Estimators For Standard Stratified Samples," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 17(02), pages 451-470, April.
    17. Cosslett, Stephen R, 1981. "Maximum Likelihood Estimator for Choice-Based Samples," Econometrica, Econometric Society, Econometric Society, vol. 49(5), pages 1289-1316, September.
    18. Keisuke Hirano & Guido W. Imbens & Geert Ridder, 2003. "Efficient Estimation of Average Treatment Effects Using the Estimated Propensity Score," Econometrica, Econometric Society, Econometric Society, vol. 71(4), pages 1161-1189, 07.
    19. Escanciano, Juan Carlos & Song, Kyungchul, 2010. "Testing single-index restrictions with a focus on average derivatives," Journal of Econometrics, Elsevier, Elsevier, vol. 156(2), pages 377-391, June.
    20. Kyungchul Song, 2009. "Two-Step Extremum Estimation with Estimated Single-Indices," PIER Working Paper Archive, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania 09-012, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
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