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Testing for unobserved heterogeneity in exponential and Weibull duration models

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  • Cho, Jin Seo
  • White, Halbert

Abstract

We examine the use of the likelihood ratio (LR) statistic to test for unobserved heterogeneity in duration models, based on mixtures of exponential or Weibull distributions. We consider both the uncensored and censored duration cases. The asymptotic null distribution of the LR test statistic is not the standard chi-square, as the standard regularity conditions do not hold. Instead, there is a nuisance parameter identified only under the alternative, and a null parameter value on the boundary of the parameter space, as in Cho and White (2007a). We accommodate these and provide methods delivering consistent asymptotic critical values. We conduct a number of Monte Carlo simulations, comparing the level and power of the LR test statistic to an information matrix (IM) test due to Chesher (1984) and Lagrange multiplier (LM) tests of Kiefer (1985) and Sharma (1987). Our simulations show that the LR test statistic generally outperforms the IM and LM tests. We also revisit the work of van den Berg and Ridder (1998) on unemployment durations and of Ghysels et al. (2004) on interarrival times between stock trades, and, as it turns out, affirm their original informal inferences.

Suggested Citation

  • Cho, Jin Seo & White, Halbert, 2010. "Testing for unobserved heterogeneity in exponential and Weibull duration models," Journal of Econometrics, Elsevier, vol. 157(2), pages 458-480, August.
  • Handle: RePEc:eee:econom:v:157:y:2010:i:2:p:458-480
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Yae Ji Jun & Jin Seo Cho, 2015. "Analyzing the Interrelationship of the Statistics for Testing Neglected Nonlinearity under the Null of Linearity," Working papers 2015rwp-78, Yonsei University, Yonsei Economics Research Institute.
    2. Baek, Yae In & Cho, Jin Seo & Phillips, Peter C.B., 2015. "Testing linearity using power transforms of regressors," Journal of Econometrics, Elsevier, vol. 187(1), pages 376-384.
    3. Jin Seo Cho & Peter C.B. Phillips, 2016. "Sequentially Testing Polynomial Model Hypotheses using Power Transforms of Regressors," Working papers 2016rwp-90, Yonsei University, Yonsei Economics Research Institute.
    4. Kyu Lee Shin & Jin Seo Cho, 2013. "Testing for Neglected Nonlinearity Using Extreme Learning Machines (published in: International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 21, Suppl. 2 (2013), 117--129.)," Working papers 2013rwp-57, Yonsei University, Yonsei Economics Research Institute.
    5. Jin Seo Cho & Halbert White, 2014. "Testing the Equality of Two Positive-Definite Matrices with Application to Information Matrix Testing," Working papers 2014rwp-67, Yonsei University, Yonsei Economics Research Institute.

    More about this item

    Keywords

    Unobserved heterogeneity Mixture models Likelihood ratio test Search theory Interarrival times;

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C24 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Truncated and Censored Models; Switching Regression Models; Threshold Regression Models
    • C41 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Duration Analysis; Optimal Timing Strategies
    • C80 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - General
    • J22 - Labor and Demographic Economics - - Demand and Supply of Labor - - - Time Allocation and Labor Supply
    • J64 - Labor and Demographic Economics - - Mobility, Unemployment, Vacancies, and Immigrant Workers - - - Unemployment: Models, Duration, Incidence, and Job Search

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