Varying coefficient panel data models and methods under correlated error components: Application to disparities in mental health services in England

Abstract

The contribution of this paper is twofold. Firstly, it introduces novel regression models that combine two important areas of the methodological development in panel data analysis, namely a varying coefficient specification and spatial error dependence. The former allows relatively flexible nonlinear interactions; the latter enables spatial correlations of the disturbance and thus differ significantly from the other random effect models in the literature. To estimate the model, a new estimation procedure is established that can be viewed as a generalization of the quasi-maximum likelihood method for a spatial panel data model to the well-known conditional local likelihood procedure. Novel inference methods, particularly variable selection and hypothesis testing of the parameter constancy, are introduced and are shown to be effective under the complex spatial error dependence. Equally importantly, this paper makes a substantial contribution to the understanding of financing and expenditure for health and social care. In particular, we empirically analyze and explain the effects of political ideologies on the local fiscal policy in England, especially the expenditure on mental health services.