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Unformatted text preview: Testing for Unobserved Heterogeneity in Exponential and Weibull Duration Models JIN SEO CHO School of Economics and Finance Victoria University of Wellington P.O. Box 600, Wellington, 6001, New Zealand Email: [email protected] HALBERT WHITE Department of Economics University of California, San Diego 9500 Gilman Dr., La Jolla, CA, 92093-0508, U.S.A. Email: [email protected] First version: August 4, 2005. This version: November 30, 2006 Abstract We examine likelihood ratio (LR) statistic testing for unobserved heterogeneity by forming a mixture of exponential or Weibull duration models. The null hypothesis of interest is that given data conditional on other explanatory variables follow an exponential or Weibull distribution. The asymptotic null distribution of the LR test statistic is not a standard chi-square distribution because it violates regularity conditions. That is, there is a nuisance parameter identified only under the alternative, and its null parameter value is on the boundary of parameter space. We accommodate these and provide a methodology delivering asymptotic critical values consistently. Further, we implement various Monte Carlo simulations and compare the size and power of the LR test statistic with the information matrix equality test statistic. Our simulations show that the LR test statistic outperforms under numerous situations. Key Words : Unobserved Heterogeneity, Mixture of Duration Models, Log-likelihood Ratio Statistic, Search Theory of Labor Supply. Subject Class : C12, C41, C80, J22, J64. Acknowledgements : The authors are grateful to Robert Davies, Peter Thomson, Estate Khmaladze, and the workshop participants at NZESG05 (Auckland), NZSA (Dunedin), statistics seminar of VUW, and FEMES2006 (Beijing) for their helpful discussions. Preliminary Version : PLEASE, DON’T CITE OR CIRCULATE WITHOUT AUTHORS’ PERMISSION. 1 Introduction Econometric specifications using exponential and Weibull distributions are very popular for duration data. In labor economics, Lancaster (1979) exploits exponential and Weibull distributions for unemployment spells. In financial econometrics, Engle and Russell (1998) also use exponential and Weibull distributions to model interarrival times of stock transactions. Their popularity is not constrained only to economics. In medical statistics, they are also widely applied for lifespan measurements. Designed duration models can be flawed by unobserved heterogeneity. As pointed out by Heckman and Singer (1984) among others, estimated structural parameters are sensitive to the distributional assumption of heterogeneity. Thus, testing for unobserved heterogeneity often precedes estimating structural parameters. For this, Lancaster (1979) assumes a conventional gamma distribution for heterogeneity and test for unobserved heterogeneity by measuring the variance of the gamma distribution. Chesher (1984) also considers the same problem and exploits the information matrix equality test statistic as the information matrix equality has to...
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