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Specification tests for spatial panel data models

  • Original Paper
  • Published:
Journal of Spatial Econometrics

Abstract

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.

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Notes

  1. Note that the variables in spatial models are allowed to depend on the number of cross-sectional units N to form triangular arrays (Kelejian and Prucha 2010). We suppress the subscript N in stating our model for notational simplicity.

  2. The regressors vector \(X_{it}\) can include the observations on (i) location and time varying variables, (ii) time invariant, but location varying variables and (iii) location invariant, but time varying variables.

  3. A sequence of \(n\times n\) matrix \(\{A_n\}\) is uniformly bounded in row sum in absolute value if \(\sup _{n\ge 1}\Vert A_n\Vert _\infty <\infty\), where \(\Vert \cdot \Vert _\infty\) is the row sum norm. Similarly, \(\{A_n\}\) is uniformly bounded in column sum in absolute value if \(\sup _{n\ge 1}\Vert A_n\Vert _1<\infty\), where \(\Vert \cdot \Vert _1\) is the column sum norm.

  4. In reporting the non-centrality parameters, we use \(\psi\) and \(\phi\) for \(\zeta\) and \(\delta\), respectively.

  5. A closed form expression for \(K(\theta _0)\) is given in Lee and Yu (2012) for a model that nests our specification.

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Authors and Affiliations

  1. Department of Economics, University of Illinois at Urbana-Champaign, Champaign, USA

    Anil K. Bera, Osman Doğan & Monalisa Sen

  2. Department of Economics, Queens College, The City University of New York, New York, USA

    Süleyman Taşpınar

Authors
  1. Anil K. Bera
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  2. Osman Doğan
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  3. Süleyman Taşpınar
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  4. Monalisa Sen
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Correspondence to Osman Doğan.

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Bera, A.K., Doğan, O., Taşpınar, S. et al. Specification tests for spatial panel data models. J Spat Econometrics 1, 3 (2020). https://doi.org/10.1007/s43071-020-00003-y

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