IDEAS home Printed from https://ideas.repec.org/p/nor/wpaper/2012035.html
   My bibliography  Save this paper

A Simple GMM Estimator for the Semiparametric Mixed Proportional Hazard Model

Author

Listed:
  • Govert Bijwaard

    () (Netherlands Interdisciplinary Demographic Institute (NIDI))

  • Geert Ridder

    () (University of Southern California)

  • Tiemen Woutersen

    (Johns Hopkins University)

Abstract

Ridder and Woutersen (2003) have shown that under a weak condition on the baseline hazard, there exist root-N consistent estimators of the parameters in a semiparametric Mixed Proportional Hazard model with a parametric baseline hazard and unspecified distribution of the unobserved heterogeneity. We extend the Linear Rank Estimator (LRE) of Tsiatis (1990) and Robins and Tsiatis (1991) to this class of models. The optimal LRE is a two-step estimator. We propose a simple one-step estimator that is close to optimal if there is no unobserved heterogeneity. The efficiency gain associated with the optimal LRE increases with the degree of unobserved heterogeneity.

Suggested Citation

  • Govert Bijwaard & Geert Ridder & Tiemen Woutersen, 2012. "A Simple GMM Estimator for the Semiparametric Mixed Proportional Hazard Model," Norface Discussion Paper Series 2012035, Norface Research Programme on Migration, Department of Economics, University College London.
  • Handle: RePEc:nor:wpaper:2012035
    as

    Download full text from publisher

    File URL: http://www.norface-migration.org/publ_uploads/NDP_35_12.pdf
    Download Restriction: no

    Other versions of this item:

    References listed on IDEAS

    as
    1. Heckman, James & Singer, Burton, 1984. "A Method for Minimizing the Impact of Distributional Assumptions in Econometric Models for Duration Data," Econometrica, Econometric Society, vol. 52(2), pages 271-320, March.
    2. Jinyong Hahn, 1994. "The Efficiency Bound of the Mixed Proportional Hazard Model," Review of Economic Studies, Oxford University Press, vol. 61(4), pages 607-629.
    3. Gorgens, Tue & Horowitz, Joel L., 1999. "Semiparametric estimation of a censored regression model with an unknown transformation of the dependent variable," Journal of Econometrics, Elsevier, vol. 90(2), pages 155-191, June.
    4. Kenneth Manton & Eric Stallard & James Vaupel, 1981. "Methods For Comparing The Mortality Experience of Heterogeneous Populations," Demography, Springer;Population Association of America (PAA), vol. 18(3), pages 389-410, August.
    5. Songnian Chen, 2002. "Rank Estimation of Transformation Models," Econometrica, Econometric Society, vol. 70(4), pages 1683-1697, July.
    6. Bijwaard, G.E., 2002. "Instrumental variable estimation for duration data," Econometric Institute Research Papers EI 2002-39, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    7. Woodbury, Stephen A & Spiegelman, Robert G, 1987. "Bonuses to Workers and Employers to Reduce Unemployment: Randomized Trials in Illinois," American Economic Review, American Economic Association, vol. 77(4), pages 513-530, September.
    8. Amemiya, Yasuo, 1985. "Instrumental variable estimator for the nonlinear errors-in-variables model," Journal of Econometrics, Elsevier, vol. 28(3), pages 273-289, June.
    9. Bijwaard, Govert E. & Ridder, Geert, 2005. "Correcting for selective compliance in a re-employment bonus experiment," Journal of Econometrics, Elsevier, vol. 125(1-2), pages 77-111.
    10. Borjas, George J & Bratsberg, Bernt, 1996. "Who Leaves? The Outmigration of the Foreign-Born," The Review of Economics and Statistics, MIT Press, vol. 78(1), pages 165-176, February.
    11. Amemiya, Takeshi, 1974. "The nonlinear two-stage least-squares estimator," Journal of Econometrics, Elsevier, vol. 2(2), pages 105-110, July.
    12. Baker, Michael & Melino, Angelo, 2000. "Duration dependence and nonparametric heterogeneity: A Monte Carlo study," Journal of Econometrics, Elsevier, vol. 96(2), pages 357-393, June.
    13. Pierre-Andre Chiappori & Bernard Salanie, 2000. "Testing for Asymmetric Information in Insurance Markets," Journal of Political Economy, University of Chicago Press, vol. 108(1), pages 56-78, February.
    14. Lancaster, T, 1976. "Redundancy, Unemployment and Manpower Policy: A Comment," Economic Journal, Royal Economic Society, vol. 86(342), pages 335-338, June.
    15. Geert Ridder & Tiemen Woutersen, 2001. "The Singularity of the Efficiency Bound of the Mixed Proportional Hazard Model," UWO Department of Economics Working Papers 20019, University of Western Ontario, Department of Economics.
    16. Horowitz, Joel L, 1996. "Semiparametric Estimation of a Regression Model with an Unknown Transformation of the Dependent Variable," Econometrica, Econometric Society, vol. 64(1), pages 103-137, January.
    17. Joel L. Horowitz, 1999. "Semiparametric Estimation of a Proportional Hazard Model with Unobserved Heterogeneity," Econometrica, Econometric Society, vol. 67(5), pages 1001-1028, September.
    18. Heckman, James J. & Singer, Burton, 1984. "Econometric duration analysis," Journal of Econometrics, Elsevier, vol. 24(1-2), pages 63-132.
    19. Khan, Shakeeb, 2001. "Two-stage rank estimation of quantile index models," Journal of Econometrics, Elsevier, vol. 100(2), pages 319-355, February.
    20. Han, Aaron K., 1987. "Non-parametric analysis of a generalized regression model : The maximum rank correlation estimator," Journal of Econometrics, Elsevier, vol. 35(2-3), pages 303-316, July.
    21. Honore, Bo E, 1990. "Simple Estimation of a Duration Model with Unobserved Heterogeneity," Econometrica, Econometric Society, vol. 58(2), pages 453-473, March.
    22. Khan, Shakeeb & Tamer, Elie, 2007. "Partial rank estimation of duration models with general forms of censoring," Journal of Econometrics, Elsevier, vol. 136(1), pages 251-280, January.
    23. Lancaster, Tony, 1979. "Econometric Methods for the Duration of Unemployment," Econometrica, Econometric Society, vol. 47(4), pages 939-956, July.
    24. Govert Bijwaard, 2010. "Immigrant migration dynamics model for The Netherlands," Journal of Population Economics, Springer;European Society for Population Economics, vol. 23(4), pages 1213-1247, September.
    25. Sherman, Robert P, 1993. "The Limiting Distribution of the Maximum Rank Correlation Estimator," Econometrica, Econometric Society, vol. 61(1), pages 123-137, January.
    26. Tiemen Woutersen, 2000. "Estimators for Panel Duration Data with Endogenous Censoring and Endogenous Regressors," Econometric Society World Congress 2000 Contributed Papers 1581, Econometric Society.
    27. Heckman, James J, 1991. "Identifying the Hand of the Past: Distinguishing State Dependence from Heterogeneity," American Economic Review, American Economic Association, vol. 81(2), pages 75-79, May.
    28. Chris Elbers & Geert Ridder, 1982. "True and Spurious Duration Dependence: The Identifiability of the Proportional Hazard Model," Review of Economic Studies, Oxford University Press, vol. 49(3), pages 403-409.
    29. Bearse, Peter & Canals-Cerd , Jos & Rilstone, Paul, 2007. "Efficient Semiparametric Estimation Of Duration Models With Unobserved Heterogeneity," Econometric Theory, Cambridge University Press, vol. 23(02), pages 281-308, April.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Janys, Lena, 2017. "A General Semiparametric Approach to Inference with Marker-Dependent Hazard Rate Models," Annual Conference 2017 (Vienna): Alternative Structures for Money and Banking 168077, Verein für Socialpolitik / German Economic Association.
    2. Wolter, James Lewis, 2016. "Kernel estimation of hazard functions when observations have dependent and common covariates," Journal of Econometrics, Elsevier, vol. 193(1), pages 1-16.
    3. Hausman, Jerry A. & Woutersen, Tiemen, 2014. "Estimating a semi-parametric duration model without specifying heterogeneity," Journal of Econometrics, Elsevier, vol. 178(P1), pages 114-131.
    4. James Wolter, 2015. "Kernel Estimation Of Hazard Functions When Observations Have Dependent and Common Covariates," Economics Series Working Papers 761, University of Oxford, Department of Economics.
    5. Govert Bijwaard & Christian Schluter, 2016. "Interdependent Hazards, Local Interactions, and the Return Decision of Recent Migrants," CReAM Discussion Paper Series 1620, Centre for Research and Analysis of Migration (CReAM), Department of Economics, University College London.

    More about this item

    Keywords

    mixed proportional hazard; linear rank estimation; counting process.;

    JEL classification:

    • C41 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Duration Analysis; Optimal Timing Strategies
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:nor:wpaper:2012035. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Norface Migration Administrator) or (Thomas Cornelissen). General contact details of provider: http://edirc.repec.org/data/cmucluk.html .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.