TESTING FOR STATE DEPENDENCE IN HETEROGENEOUS POPULATIONS

This study examines tests for state dependence in heterogeneous populations with discrete panel data. In particular we consider testing a heterogeneous multinomial model against a heterogeneous Markov model. Two approaches are examined in detail, both utilize the fact that a heterogeneous multinomial model is characterized by exchangeability and a heterogeneous Markov model by partial exchangeability. The first approach, suggested by Lee (1987), is to use log linear probability models. These can be estimated and tested with standard maximum likelihood techniques and the testing procedure is non-parametric in the sense that it does not require assumptions regarding the form of the heterogeneity. These models easily becomes difficult to handle for longer panels and it is shown how the likelihood ratio test can be simplified for easier computational implementation. In the second approach, suggested by Quintana and Newton (1998), exact conditional tests are obtained. The conditional distribution of any test statistic can be computed given certain transition counts. A new test statistic based on the number of runs is suggested. Simulations are performed to study the size and the power of the tests, focusing on cases with short panels and small samples. It is shown that the exact conditional tests will perform well with the new test statistic, especially in situations with only moderate heterogeneity. It also appears that the degree of heterogeneity has a clear effect on the power to the tests.