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Efficient semiparametric estimation for endogenously stratified regression via smoothed likelihood

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  • Cosslett, Stephen R.

Abstract

This paper presents efficient semiparametric estimators for endogenously stratified regression with two strata, in the case where the error distribution is unknown and the regressors are independent of the error term. The method is based on the use of a kernel-smoothed likelihood function which provides an explicit solution for the maximization problem for the unknown density function without losing information in the asymptotic limit. We consider both standard stratified sampling and variable probability sampling, and allow for the population shares of the strata to be either unknown or known a priori.

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  • Cosslett, Stephen R., 2013. "Efficient semiparametric estimation for endogenously stratified regression via smoothed likelihood," Journal of Econometrics, Elsevier, vol. 177(1), pages 116-129.
    • Handle: RePEc:eee:econom:v:177:y:2013:i:1:p:116-129
    DOI: 10.1016/j.jeconom.2013.07.003
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    References listed on IDEAS

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    1. Cosslett, Stephen R, 1981. "Maximum Likelihood Estimator for Choice-Based Samples," Econometrica, Econometric Society, vol. 49(5), pages 1289-1316, September.
    2. Stephen R. Cosslett, 2004. "Efficient Semiparametric Estimation of Censored and Truncated Regressions via a Smoothed Self-Consistency Equation," Econometrica, Econometric Society, vol. 72(4), pages 1277-1293, July.
    3. Newey, Whitney K, 1994. "The Asymptotic Variance of Semiparametric Estimators," Econometrica, Econometric Society, vol. 62(6), pages 1349-1382, November.
    4. Barnett,William A. & Powell,James & Tauchen,George E. (ed.), 1991. "Nonparametric and Semiparametric Methods in Econometrics and Statistics," Cambridge Books, Cambridge University Press, number 9780521370905, October.
    5. Stephen R. Cosslett, 2007. "Efficient Estimation Of Semiparametric Models By Smoothed Maximum Likelihood," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 48(4), pages 1245-1272, November.
    6. Powell, James L & Stock, James H & Stoker, Thomas M, 1989. "Semiparametric Estimation of Index Coefficients," Econometrica, Econometric Society, vol. 57(6), pages 1403-1430, November.
    7. Barnett,William A. & Powell,James & Tauchen,George E. (ed.), 1991. "Nonparametric and Semiparametric Methods in Econometrics and Statistics," Cambridge Books, Cambridge University Press, number 9780521424318, October.
    8. Sherman, Robert P., 1994. "U-Processes in the Analysis of a Generalized Semiparametric Regression Estimator," Econometric Theory, Cambridge University Press, vol. 10(2), pages 372-395, June.
    9. Chunrong Ai, 1997. "A Semiparametric Maximum Likelihood Estimator," Econometrica, Econometric Society, vol. 65(4), pages 933-964, July.
    10. Severini, Thomas A. & Tripathi, Gautam, 2001. "A simplified approach to computing efficiency bounds in semiparametric models," Journal of Econometrics, Elsevier, vol. 102(1), pages 23-66, May.
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    Cited by:

    1. Yi Qian & Hui Xie, 2022. "Simplifying Bias Correction for Selective Sampling: A Unified Distribution-Free Approach to Handling Endogenously Selected Samples," Marketing Science, INFORMS, vol. 41(2), pages 336-360, March.
    2. Ahmed, M.S. & Attouch, M.K. & Dabo-Niang, S., 2018. "Binary functional linear models under choice-based sampling," Econometrics and Statistics, Elsevier, vol. 7(C), pages 134-152.

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    More about this item

    Keywords

    Semiparametric estimation; Asymptotic efficiency; Endogenously stratified regression;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C24 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Truncated and Censored Models; Switching Regression Models; Threshold Regression Models
    • C25 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions; Probabilities

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