Specification tests for spatial panel data models
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ORIGINAL PAPER
Specification tests for spatial panel data models Anil K. Bera1 • Osman Dog˘an1
•
Su¨leyman Tas¸pınar2 • Monalisa Sen1
Received: 10 April 2020 / Accepted: 13 July 2020 Ó Springer Nature Switzerland AG 2020
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. Keywords Rao’s score (RS) test Robust RS test Specification test Spatial models Spatial panel data models
JEL Classification C13 C21 C31
Electronic supplementary material The online version of this article (https://doi.org/10.1007/s43071020-00003-y) contains supplementary material, which is available to authorized users. Extended author information available on the last page of the article
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1 Introduction Econometricians’ interest in problems that arise when the assumed model that is used in constructing a test deviates from the data generating process (DGP) goes a long way back. As emphasized by Haavelmo (1944), in testing any economic relations, specification of a set of possible alternatives, called the priori admissible hypothesis, X0 , is of fundamental importance. Misspecification of the priori admissible hypotheses was referred to as Type-III error by Bera and Yoon (1993), and Welsh (2011, p. 119) also pointed ou
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