Varying coefficient model with correlated error components and application to disparities between mental health service by councils in England

In this paper, we discuss estimation procedure and various inferential methods for varying coefficient panel data models that include spatially correlated error components. Our estimation procedure is an extension of the quasi-maximum likelihood method for spatial panel data regression to the conditional local kernel-weighted likelihood. We allow both relevant and irrelevant regressors in our model and propose a variable selection procedure that we show to perform well for models that involve spatial error dependence. We also extend our procedure so that it allows empirical modelling and testing of the so-called semi-varying coefficient specification. To ensure the statistical validity of our methods, we derive a set of asymptotic properties based on a collection of primitive assumptions that appear regularly in the nonparametric literature. Finally, we use the proposed model and methods to analyse the municipal disparities in mental health service spending by local authorities in England in order to illustrate practicability and empirical relevance.