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A Simple Matching Method for Estimating Sample Selection Models Using Experimental Data

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  • Songnian Chen

    (The Hong Kong University of Science and Technology)

  • Yahong Zhou

    (The Shanghai University of Economics and Finance)

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    Abstract

    In this paper estimation of sample selection models using experimental data is considered with some weak restriction imposed on the error distribution. Under a normality setting, the most popular approach is the two-step method proposed by Heckman (1979). But Heckman¡¯s approach relies on the nonlinearity of the probit function (i.e. the nonlinearity of the selection correction function) unless some exclusion restriction is imposed. Furthermore, Heckman¡¯s method is sensitive to the underlying distributional assumption. Following this two-step method, several semiparametric estimators have been proposed for sample selection models by explicitly imposing the exclusion restriction. Using experimental data, this paper proposes a simple semiparametric matching method. There are certain advantages of our estimator over Heckman¡¯s estimator and the existing semiparametric estimators under either the parametric setting and semiparametric setting. We do not rely on the nonlinearity of the selection correction function or the exclusion restriction. In addition, unlike other semiparametric methods, we can also estimate the intercept term in the equation of interest. The estimator is shown to be consistent and asymptotically normal under some regularity conditions. A small monte carlo study illustrates the usefulness of the new estimator.

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    Bibliographic Info

    Article provided by Society for AEF in its journal Annals of Economics and Finance.

    Volume (Year): 6 (2005)
    Issue (Month): 1 (May)
    Pages: 155-167

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    Handle: RePEc:cuf:journl:y:2005:v:6:i:1:p:155-167

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    Keywords: Matching method; Experimental data;

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    1. James J. Heckman, 1976. "The Common Structure of Statistical Models of Truncation, Sample Selection and Limited Dependent Variables and a Simple Estimator for Such Models," NBER Chapters, National Bureau of Economic Research, Inc, in: Annals of Economic and Social Measurement, Volume 5, number 4, pages 475-492 National Bureau of Economic Research, Inc.
    2. Klein, R.W. & Spady, R.H., 1991. "An Efficient Semiparametric Estimator for Binary Response Models," Papers, Bell Communications - Economic Research Group 70, Bell Communications - Economic Research Group.
    3. Nawata, Kazumitsu, 1993. "A note on the estimation of models with sample-selection biases," Economics Letters, Elsevier, Elsevier, vol. 42(1), pages 15-24.
    4. Han, Aaron K., 1987. "Non-parametric analysis of a generalized regression model : The maximum rank correlation estimator," Journal of Econometrics, Elsevier, Elsevier, vol. 35(2-3), pages 303-316, July.
    5. Sherman, Robert P., 1994. "U-Processes in the Analysis of a Generalized Semiparametric Regression Estimator," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 10(02), pages 372-395, June.
    6. James Heckman & Hidehiko Ichimura & Jeffrey Smith & Petra Todd, 1998. "Characterizing Selection Bias Using Experimental Data," Econometrica, Econometric Society, Econometric Society, vol. 66(5), pages 1017-1098, September.
    7. Donald, Stephen G., 1995. "Two-step estimation of heteroskedastic sample selection models," Journal of Econometrics, Elsevier, Elsevier, vol. 65(2), pages 347-380, February.
    8. Lee, Lung-Fei, 1994. "Semiparametric instrumental variable estimation of simultaneous equation sample selection models," Journal of Econometrics, Elsevier, Elsevier, vol. 63(2), pages 341-388, August.
    9. Andrews, Donald W K, 1991. "Asymptotic Normality of Series Estimators for Nonparametric and Semiparametric Regression Models," Econometrica, Econometric Society, Econometric Society, vol. 59(2), pages 307-45, March.
    10. Heckman, James J, 1974. "Shadow Prices, Market Wages, and Labor Supply," Econometrica, Econometric Society, Econometric Society, vol. 42(4), pages 679-94, July.
    11. Leung, Siu Fai & Yu, Shihti, 1996. "On the choice between sample selection and two-part models," Journal of Econometrics, Elsevier, Elsevier, vol. 72(1-2), pages 197-229.
    12. Horowitz, Joel L, 1992. "A Smoothed Maximum Score Estimator for the Binary Response Model," Econometrica, Econometric Society, Econometric Society, vol. 60(3), pages 505-31, May.
    13. Cosslett, Stephen R, 1983. "Distribution-Free Maximum Likelihood Estimator of the Binary Choice Model," Econometrica, Econometric Society, Econometric Society, vol. 51(3), pages 765-82, May.
    14. Manski, Charles F., 1985. "Semiparametric analysis of discrete response : Asymptotic properties of the maximum score estimator," Journal of Econometrics, Elsevier, Elsevier, vol. 27(3), pages 313-333, March.
    15. 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.
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