GMM gradient tests for spatial dynamic panel data models

In this study, we formulate adjusted gradient tests when the alternative model used to construct tests deviates from the true data generating process for a spatial dynamic panel data (SDPD) model. Following Bera et al. (2010), we introduce these adjusted gradient tests along with their standard counterparts within a generalized method of moments framework. These tests can be used to detect the presence of (i) the contemporaneous spatial lag terms, (ii) the time lag term, and (iii) the spatial time lag terms in a high order SDPD model. These adjusted tests have two advantages: (i) their null asymptotic distribution is a central chi-squared distribution irrespective of the mis-specified alternative model, and (ii) their test statistics are computationally simple and require only the ordinary least-squares estimates from a non-spatial two-way panel data model. We investigate the finite sample size and power properties of these tests through a Monte Carlo study. Our results indicates that the adjusted gradient tests have good finite sample properties. Finally, using an application from the empirical growth literature we complement our findings.