Testing for Unobserved Heterogeneity in Exponential and Weibull Duration Models

We examine use of the likelihood ratio (LR) statistics 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 statistics 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 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 statistics to an information matrix (IM) text 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 aslo revisit the work of van den Berg and Ridder (1998) on unemployment durations and of Ghysels, Gourieroux, and Jasiak (2004)on interarrival times between stock trades, and, as it turns out, affirm their original informal inferences.