Adjustments of Rao’s Score Test for Distributional and Local Parametric Misspecifications

Bera Anil K., Bilias Yannis, Yoon Mann J., Taşpınar Süleyman () and Doğan Osman
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Bera Anil K.: Department of Economics, University of Illinois at Urbana-Champaign (UIUC), Champaign, IL, USA
Bilias Yannis: Department of International and European Economic Studies, Athens University of Economics and Business, Athens, Greece
Yoon Mann J.: Department of Economics, California State University at Los Angeles, Los Angeles, CA, USA
Taşpınar Süleyman: Economics Program, Queens College, The City University of New York, New York, NY, USA
Doğan Osman: Department of Economics, University of Illinois at Urbana-Champaign (UIUC), Champaign, IL, USA

Journal of Econometric Methods, 2020, vol. 9, issue 1, 29

Abstract: Rao’s (1948) seminal paper introduced a fundamental principle of testing based on the score function and the score test has local optimal properties. When the assumed model is misspecified, it is well known that Rao’s score (RS) test loses its optimality. A model could be misspecified in a variety of ways. In this paper, we consider two kinds: distributional and parametric. In the former case, the assumed probability density function differs from the data generating process. Kent (1982) and White (1982) analyzed this case and suggested a modified version of the RS test that involves adjustment of the variance. In the latter case, the dimension of the parameter space of the assumed model does not match with that of the true one. Using the distribution of the RS test under this situation, Bera and Yoon (1993) developed a modified RS test that is valid under the local parametric misspecification. This involves adjusting both the mean and variance of the standard RS test. This paper considers the joint presence of the distributional and parametric misspecifications and develops a modified RS test that is valid under both types of misspecification. Earlier modified tests under either type of misspecification can be obtained as the special cases of the proposed test. We provide three examples to illustrate the usefulness of the suggested test procedure. In a Monte Carlo study, we demonstrate that the modified test statistics have good finite sample properties.

Keywords: inference; Lagrange multiplier tests; locally misspecified models; QMLE; Rao’s score tests; robust LM tests; specification testing (search for similar items in EconPapers)
JEL-codes: C13 C21 C31 (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (1)

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DOI: 10.1515/jem-2017-0022

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