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Two-step Empirical Likelihood Estimation under Stratified Sampling when Aggregate Information is Available

Author

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  • Joaquim J.S. Ramalho

    (Department of Economics, University of Évora)

  • Esmeralda A. Ramalho

    (Department of Economics, University of Évora)

Abstract

Empirical likelihood (EL) is appropriate to estimate moment condition models when a random sample from the target population is available. However, many economic surveys are subject to some form of stratification, in which case direct application of EL will produce inconsistent estimators. In this paper we propose a two-step EL (TSEL) estimator to deal with stratified samples in models defined by unconditional moment restrictions in presence of some aggregate information, which may consist, for example, of the mean and the variance of the variable of interest and/or the explanatory variables. A Monte Carlo simulation study reveals promising results for many versions of the TSEL estimator.

Suggested Citation

  • Joaquim J.S. Ramalho & Esmeralda A. Ramalho, 2005. "Two-step Empirical Likelihood Estimation under Stratified Sampling when Aggregate Information is Available," Economics Working Papers 6_2005, University of Évora, Department of Economics (Portugal).
  • Handle: RePEc:evo:wpecon:6_2005
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    File URL: http://hdl.handle.net/10174/8420
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    References listed on IDEAS

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    1. Imbens, Guido W, 1992. "An Efficient Method of Moments Estimator for Discrete Choice Models with Choice-Based Sampling," Econometrica, Econometric Society, vol. 60(5), pages 1187-1214, September.
    2. Whitney K. Newey & Richard J. Smith, 2004. "Higher Order Properties of Gmm and Generalized Empirical Likelihood Estimators," Econometrica, Econometric Society, vol. 72(1), pages 219-255, January.
    3. Imbens, Guido W, 2002. "Generalized Method of Moments and Empirical Likelihood," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(4), pages 493-506, October.
    4. Tripathi, Gautam, 2011. "Moment-Based Inference With Stratified Data," Econometric Theory, Cambridge University Press, vol. 27(1), pages 47-73, February.
    5. Judith K. Hellerstein & Guido W. Imbens, 1999. "Imposing Moment Restrictions From Auxiliary Data By Weighting," The Review of Economics and Statistics, MIT Press, vol. 81(1), pages 1-14, February.
    6. Cosslett, Stephen R, 1981. "Maximum Likelihood Estimator for Choice-Based Samples," Econometrica, Econometric Society, vol. 49(5), pages 1289-1316, September.
    7. Early, Dirk W., 1999. "A Microeconomic Analysis of Homelessness: An Empirical Investigation Using Choice-Based Sampling," Journal of Housing Economics, Elsevier, vol. 8(4), pages 312-327, December.
    8. Guido W. Imbens, 1997. "One-Step Estimators for Over-Identified Generalized Method of Moments Models," Review of Economic Studies, Oxford University Press, vol. 64(3), pages 359-383.
    9. Guido W. Imbens & Tony Lancaster, 1994. "Combining Micro and Macro Data in Microeconometric Models," Review of Economic Studies, Oxford University Press, vol. 61(4), pages 655-680.
    10. Wooldridge, Jeffrey M., 2001. "Asymptotic Properties Of Weighted M-Estimators For Standard Stratified Samples," Econometric Theory, Cambridge University Press, vol. 17(2), pages 451-470, April.
    11. Kitamura, Ryuichi & Yamamoto, Toshiyuki & Sakai, Hiromu, 2003. "A methodology for weighting observations from complex endogenous sampling," Transportation Research Part B: Methodological, Elsevier, vol. 37(4), pages 387-401, May.
    12. Jeffrey M. Wooldridge, 1999. "Asymptotic Properties of Weighted M-Estimators for Variable Probability Samples," Econometrica, Econometric Society, vol. 67(6), pages 1385-1406, November.
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    Cited by:

    1. Bayram, Deniz & Dayé, Modeste, 2014. "Asymptotic Properties of the Weighted Least Squares Estimator Under Moments Restriction," MPRA Paper 60465, University Library of Munich, Germany.
    2. Esmeralda A. Ramalho & Joaquim J. S. Ramalho & Rui Evangelista, 2017. "Combining micro and macro data in hedonic price indexes," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 26(2), pages 317-332, June.

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    More about this item

    Keywords

    Stratified Sampling; Empirical Likelihood; Weighted Estimation; Auxiliary Information;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation

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