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Efficient Estimation of Average Treatment Effects under Treatment-Based Sampling

  • Kyungchul Song

    ()

    (Department of Economics, University of Pennsylvania)

Registered author(s):

    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. Rajeev H. Dehejia & Sadek Wahba, 2002. "Propensity Score-Matching Methods For Nonexperimental Causal Studies," The Review of Economics and Statistics, MIT Press, vol. 84(1), pages 151-161, February.
    2. Gautam Tripathi, 2005. "Moment Based Inference with Stratified Data," Working papers 2005-38, University of Connecticut, Department of Economics, revised Jan 2007.
    3. Jeffrey M. Wooldridge, 1999. "Asymptotic Properties of Weighted M-Estimators for Variable Probability Samples," Econometrica, Econometric Society, vol. 67(6), pages 1385-1406, November.
    4. 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.
    5. A. Smith, Jeffrey & E. Todd, Petra, 2005. "Does matching overcome LaLonde's critique of nonexperimental estimators?," Journal of Econometrics, Elsevier, vol. 125(1-2), pages 305-353.
    6. Imbens, G.W., 1990. "An Efficient Method of Moments Estimator for Discrete Choice Models with Choice-Based Sampling," Discussion Paper 1990-9, Tilburg University, Center for Economic Research.
    7. Jinyong Hahn & Keisuke Hirano & Dean Karlan, 2009. "Adaptive Experimental Design Using the Propensity Score," Working Papers 969, Economic Growth Center, Yale University.
    8. Keisuke Hirano & Guido W. Imbens & Geert Ridder, 2000. "Efficient Estimation of Average Treatment Effects Using the Estimated Propensity Score," NBER Technical Working Papers 0251, National Bureau of Economic Research, Inc.
    9. Orley Ashenfelter & David Card, 1984. "Using the Longitudinal Structure of Earnings to Estimate the Effect of Training Programs," NBER Working Papers 1489, National Bureau of Economic Research, Inc.
    10. 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.
    11. Imbens, Guido W. & Lancaster, Tony, 1996. "Efficient estimation and stratified sampling," Journal of Econometrics, Elsevier, vol. 74(2), pages 289-318, October.
    12. Manski, Charles F., 1986. "Semiparametric analysis of binary response from response-based samples," Journal of Econometrics, Elsevier, vol. 31(1), pages 31-40, February.
    13. 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.
    14. 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.
    15. Cosslett, Stephen R, 1981. "Maximum Likelihood Estimator for Choice-Based Samples," Econometrica, Econometric Society, vol. 49(5), pages 1289-1316, September.
    16. 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.
    17. 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.
    18. Newey, Whitney K, 1990. "Semiparametric Efficiency Bounds," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 5(2), pages 99-135, April-Jun.
    19. Heckman, James J & Ichimura, Hidehiko & Todd, Petra, 1998. "Matching as an Econometric Evaluation Estimator," Review of Economic Studies, Wiley Blackwell, vol. 65(2), pages 261-94, April.
    20. 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.
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