Testing spatial dynamic panel data models with heterogeneous spatial and regression coefficients

Spatio-temporal data are often analysed by means of spatial dynamic panel data (SDPD) models. In the last decade, several versions of these models have been proposed, generally based on specific assumptions and estimator properties. We focus on an SDPD model with heterogeneous coefficients both in the spatial and exogeneous regression components. We propose a strategy to identify the specific structure of the SDPD model through a multiple testing procedure that allows to choose between a general version of the model and a nested version derived from the general one by imposing restrictions on the parameters. Our proposal can be used to test the homogeneity of the model parameters as well as the absence of specific components, such as spatial effects, dynamic effects or exogenous regressors. It is also possible to use the proposed testing procedure for the identification of relevant locations. The theoretical results highlight the consistency of the testing procedure in the high-dimensional setup, when the number of spatial units goes to infinity and exceeds the number of time-observations per spatial unit. Further, we also conduct a Monte Carlo simulation study, which gives empirical evidence of the good performance of the testing procedure in finite samples.