Specification Testing for Panel Spatial Models

Specification of a model is one of the most fundamental problems in econometrics. In most cases, specification tests are 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. It is also much to expect from a practioners to estimate a complex general model and then to carry out specification tests. Specification problems are paramount in the spatial panel models which are now increasingly being used in practice given the wide availability of longitudinal data. Using Bera and Yoon (1993) general test procedure under misspecification, in the context of simple spatial model, Anselin, Bera, Florax and Yoon (1996) developed ordinary least squares (OLS) based “robust” Rao’s score (RS) test for lag (error) dependence in the possible presence of error (lag) dependence. In a similar fashion, for standard panel data model, Bera, SosaEscudero and Yoon (2001) developed adjusted RS tests (for random effect and serial correlation) that can identify the correct source(s) of misspecification. In the context of specification tests for spatial panel models, there had been some important contributions, for example, see Baltagi, Song and Koh (2003). Baltagi, Song, Jung and Koh (2007), Baltagi and Liu (2008) and MontesRojas (2010). Many of the suggested tests require estimation of complex models and even then these tests cannot take account of multiple forms of departures, such as: the spatial lag, spatial error, random effect and time-series serial correlation. Using a general model we first propose an overall test for “all” possible misspecifications. Then we derive a number of adjusted RS tests that can identify the definite cause(s) of rejection of the basic model and thus adding in the steps for model revision. For empirical researchers, our suggested procedures provide simple strategies for model specification search using OLS residuals from standard linear model for spatial panel data. Through an extensive simulation study, we evaluate the finite sample performance of our suggested tests and available procedures. We find that the proposed tests have good finite sample properties both in terms of size and power. We also formulate a simple sequential strategy for use in empirical practice. 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. 1. Anil K. Bera: Professor, Department of Economics, University of Illinois at Urbana Champaign. Email: [email protected]. Monalisa Sen: PhD candidate, Department of Economics, University of Illinois at Urbana Champaign. Email: [email protected]. An earlier version of this paper was presented at Conference in Honor of Prof. Pesaran (July 1 2011, Cambridge UK), North America Econometric Society Summer Meeting (June 11, 2011, St Louis) and Vth World Conference of Spatial Econometrics Association (July 7, 2011, Toulouse, France). We are grateful to the participants at these conferences for comments and suggestions; though the remaining shortcomings are solely ours.