A J test for dynamic panel model with fixed effects, and nonparametric spatial and time dependence

In this paper, we suggest a J test in a dynamic spatial panel framework of a null model against one or more alternatives. The null model we consider has fixed effects, along with nonparametrically specified spatial and time dependence. The alternatives can have either fixed or random effects with the same complications. We implement our procedure to test the specifications of a demand for cigarette model. We find that the most appropriate specification is one that contains the average price of cigarettes in neighboring states, as well as the spatial lag of the dependent variable. Along with formal large sample results, we also give small sample Monte Carlo results. Our large sample results are based on the assumption N→ ∞ and T is fixed. Our Monte Carlo results suggest that our proposed J test has good power and proper size even for small to moderately sized samples. © 2016, Springer-Verlag Berlin Heidelberg.