Using the sample of the McCall data set from the empirical exercise in the previous chapter, reestimate the Weibull model for those transiting to full-time employment \((C E N S O R 1=1)\) under the assumption that unobserved heterogeneity (also called frailty in some computer packages, which may also have a subcommand for specifying it) has gamma distribution.

(a) Using generalized residuals as in Section 18.7.2 test the hypothesis of model misspecification.

(b) Does the new model display a duration dependence property? Does it provide a better fit to the data? Explain the results by reference to the interaction between unobserved heterogeneity and duration dependence.

(c) Repeat the exercise of part

(a) under the assumption of log-normal heterogeneity. Are the results about duration dependence significantly different from those for the gamma heterogeneity?