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The Singularity of the Efficiency Bound of the Mixed Proportional Hazard Model

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Abstract

We reconsider the efficiency bound for the semi-parametric Mixed Proportional Hazard (MPH) model with parametric baseline hazard and regression function. This bound was first derived by Hahn (1994). One of his results is that if the baseline hazard is Weibull, the efficiency bound is singular, even if the model is semi-parametrically identified. This implies that neither the Weibull parameter nor the regression coefficients can be estimated at the root N rate. We show that Hahn's results are confined to a class of models that is closed under the power transformation. The Weibull model is the most prominent model of this class. We also present a new nonparametric identification result. This identification results allows for infinite mean of the mixing distribution and ensures that the efficiency bound is nonsingular. This implies that root N estimation is possible.

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  • Geert Ridder & Tiemen Woutersen, 2001. "The Singularity of the Efficiency Bound of the Mixed Proportional Hazard Model," University of Western Ontario, Departmental Research Report Series 20019, University of Western Ontario, Department of Economics.
    • Handle: RePEc:uwo:uwowop:20019
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    File URL: https://ir.lib.uwo.ca/cgi/viewcontent.cgi?article=1381&context=economicsresrpt
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    Cited by:

    1. Bijwaard Govert E. & Ridder Geert & Woutersen Tiemen, 2013. "A Simple GMM Estimator for the Semiparametric Mixed Proportional Hazard Model," Journal of Econometric Methods, De Gruyter, vol. 2(1), pages 1-23, July.
    2. 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.
    3. G.E. Bijwaard, 2002. "Instrumental Variable Estimation for Duration Data: A Reappraisal of the Illinois Reemployment Bonus Experiment," Econometrics 0204001, University Library of Munich, Germany.
    4. Bijwaard, Govert, 2011. "Unobserved Heterogeneity in Multiple-Spell Multiple-States Duration Models," IZA Discussion Papers 5748, Institute of Labor Economics (IZA).
    5. Govert Bijwaard, 2014. "Multistate event history analysis with frailty," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 30(58), pages 1591-1620.

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    Keywords

    Duration; Semi-parametric Efficiency Bound; Mixed Proportional Hazard;
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