Joint and separate score tests for state dependence and unobserved heterogeneity

The paper compares separate, conditional, and joint score tests of duration dependence and unobserved heterogeneity when the null is the exponential model and the alternative is the heterogeneous Weibull model. The score tests based on the conditional score function include the Neyman C(α) test as a special case. An examination of the non-null distribution of the joint test explains when all score tests have low power in the presence of multiple misspecifications. Monte Carlo experiments show that the conditional score tests are superior to the standard separate tests which confound unobserved heterogeneity and duration dependence.