Homogeneity pursuit in single index models based panel data analysis

Panel data analysis is an important topic in statistics and econometrics. Traditionally, in panel data analysis, all individuals are assumed to share the same unknown parameters, e.g. the same coefficients of covariates when the linear models are used, and the differences between the individuals are accounted for by cluster effects. This kind of modelling only makes sense if our main interest is on the global trend, this is because it would not be able to tell us anything about the individual attributes which are sometimes very important. In this paper, we propose a modelling based on the single index models embedded with homogeneity for panel data analysis, which builds the individual attributes in the model and is parsimonious at the same time. We develop a data driven approach to identify the structure of homogeneity, and estimate the unknown parameters and functions based on the identified structure. Asymptotic properties of the resulting estimators are established. Intensive simulation studies conducted in this paper also show the resulting estimators work very well when sample size is finite. Finally, the proposed modelling is applied to a public financial dataset and a UK climate dataset, the results reveal some interesting findings.