Heterogeneous panel data models with cross-sectional dependence

This paper considers a semiparametric panel data model with heterogeneous coefficients and individual-specific trending functions, where the random errors are assumed to be serially correlated and cross-sectionally dependent. We propose mean group estimators for the coefficients and trending functions involved in the model. It can be shown that the proposed estimators can achieve an asymptotic consistency with rates of root−NT and root−NTh, respectively as (N,T)→(∞,∞), where N is allowed to increase faster than T. Furthermore, a statistic for testing homogeneous coefficients is constructed based on the difference between the mean group estimator and a pooled estimator. Its asymptotic distributions are established under both the null and a sequence of local alternatives, even if the difference between these estimators vanishes considerably fast (can achieve root-NT² rate at most under the null) and no consistent estimator for the covariance matrix is required. The finite sample performance of the proposed estimators together with the size and local power properties of the test are demonstrated by simulated data examples, and an empirical application with the OECD health care expenditure dataset is also provided.