Testing for unit roots in panels by using a mixture model

This paper introduces a dynamic panel data model where the regression coefficients are allowed to vary across cross-section units. The framework is a mixture model obtained by mixing two dynamic panel data models with different parameters according to some mixing weights. The parameters in the model are estimated by the method of maximum likelihood, and it is shown that the maximum likelihood estimator is consistent and asymptotically normal. Within the mixture model it is possible to distinguish between different unit root hypotheses that cannot be distinguished by existing test procedures. More specifically, it is possible to test the hypothesis that a group of cross-section units has time-series processes with a unit root. The method is applied to income data from the PSID. For this sample there is no evidence of unit roots in the income processes but the processes differ substantially between individuals.