Specification tests for spatial panel data models

Specification of a model is one of the most fundamental problems in econometrics. In practice, specification tests are generally carried out in a piecemeal fashion, for example, testing the presence of one-effect at a time ignoring the potential presence of other forms of misspecification. Many of the suggested tests in the literature require estimation of complex models and even then those tests cannot account for multiple forms of departures from the model under the null hypothesis. Using Bera and Yoon (Econom Theory 9(04):649–658, 1993) general test principle and a spatial panel model framework, we first propose an overall test for “all” possible misspecification. Then, we derive adjusted Rao’s score tests for random effect, serial correlation, spatial lag and spatial error, which can identify the definite cause(s) of rejection of the basic model and thus aiding in the steps for model revision. For empirical researchers, our suggested procedures provide simple strategies for model specification search employing only the ordinary least squares residuals from a standard linear panel regression. Through an extensive simulation study, we evaluate the finite sample performance of our suggested tests and some of the existing procedures. We find that our proposed tests have good finite sample properties both in terms of size and power. Finally, to illustrate the usefulness of our procedures, we provide an empirical application of our test strategy in the context of the convergence theory of incomes of different economies, which is a widely studied empirical problem in macro-economic growth theory. Our empirical illustration reveals the problems in using and interpreting unadjusted tests, and demonstrates how these problems are rectified in using our proposed adjusted tests.