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GENERAL SPECIFICATION TESTING WITH LOCALLY MISSPECIFIED MODELS

Published online by Cambridge University Press:  22 March 2010

Anil K. Bera ,
Gabriel Montes-Rojas  and
Walter Sosa-Escudero
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Abstract

A well known result is that many of the tests used in econometrics, such as the Rao score (RS) test, may not be robust to misspecified alternatives, that is, when the alternative model does not correspond to the underlying data generating process. Under this scenario, these tests spuriously reject the null hypothesis too often. We generalize this result to generalized method of moments–based (GMM-based) tests. We also extend the method proposed in Bera and Yoon (1993, Econometric Theory 9, 649–658) for constructing RS tests that are robust to local misspecification to GMM-based tests. Finally, a further generalization for general estimating and testing functions is developed. This framework encompasses both likelihood and GMM-based results.

Type
Brief Report
Information
Econometric Theory , Volume 26 , Issue 6 , December 2010 , pp. 1838 - 1845
Copyright
Copyright © Cambridge University Press 2010

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Footnotes

We are grateful to the coeditor Jinyong Hahn and two anonymous referees for many pertinent comments and suggestions. However, we retain the responsibility for any remaining shortcomings.

References

REFERENCES

Anselin, L., Bera, A., Florax, R., & Yoon, M. (1996) Simple diagnostic tests for spatial dependence. Regional Science and Urban Economics 26, 77–104.CrossRefGoogle Scholar
Arellano, M. & Bond, S. (1991) Some tests of specification for panel data: Monte Carlo evidence and an application to employment equations. Review of Economic Studies 58, 277–297.CrossRefGoogle Scholar
Baltagi, B. & Li, D. (2001) LM tests for functional form and spatial error correlation. International Regional Science Review 24, 194–225.CrossRefGoogle Scholar
Bera, A. & Bilias, Y. (2001) On some optimality properties of Fisher-Rao score function in testing and estimation. Communications in Statistics—Theory and Methods 30, 1533–1559.CrossRefGoogle Scholar
Bera, A., Bilias, Y., & Yoon, M. (2007) Adjustments of Rao’s Score Test for Distributional and Local Parametric Misspecifications. Working paper, University of Illinois at Urbana-Champaign.Google Scholar
Bera, A., Sosa-Escudero, W., & Yoon, M. (2001) Tests for the error component model in the presence of local misspecification. Journal of Econometrics 101, 1–23.CrossRefGoogle Scholar
Bera, A. & Yoon, M. (1993) Specification testing with locally misspecified alternatives. Econometric Theory 9, 649–658.10.1017/S0266466600008021CrossRefGoogle Scholar
Davidson, J. & MacKinnon, J. (1987) Implicit alternatives and the local power of test statistics. Econometrica 55, 1305–1329.CrossRefGoogle Scholar
Godfrey, L. & Veall, M.R. (2000) Alternative approaches to testing by variable addition. Econometric Reviews 19, 241–261.CrossRefGoogle Scholar
González-Rivera, G. & Ullah, A. (2001) Rao’s score test with nonparametric density estimators. Journal of Statistical Planning and Inference 97, 85–100.CrossRefGoogle Scholar
Hall, A. (2005) Generalized Method of Moments. Oxford University Press.Google Scholar
Hansen, L.P. (1982) Large sample properties of generalized method of moments estimators. Econometrica 50, 1029–1054.CrossRefGoogle Scholar
Hansen, L.P., Heaton, J., & Yaron, A. (1996) Finite-sample properties of some alternative GMM estimators. Journal of Business & Economic Statistics 14, 262–280.CrossRefGoogle Scholar
Heckman, J.J. (1976) The common structure of statistical models of truncation, sample selection and limited dependent variables and simple estimator for such models. Annals of Economic and Social Measurement 5, 475–492.Google Scholar
Newey, W. (1985) Maximum likelihood specification testing and conditional moment tests. Econometrica 53, 1047–1070.CrossRefGoogle Scholar
Newey, W. & McFadden, D. (1994) Large sample estimation and hypothesis testing. In Engle, R. & McFadden, D. (eds.), Handbook of Econometrics, vol. 4, pp. 2111–2245. North-Holland.Google Scholar
Newey, W. & West, K. (1987) Hypothesis testing with efficient method of moments estimation. International Economic Review 28, 777–787.CrossRefGoogle Scholar
Neyman, J. (1959) Optimal asymptotic tests of composite statistical hypothesis. In Grenander, U. (ed.), Probability and Statistics, pp. 213–234. Wiley.Google Scholar
Saavedra, L. (2003) Tests for spatial lag dependence based on method of moments estimation. Regional Science and Urban Economics 33, 27–58.CrossRefGoogle Scholar
Saikkonen, P. (1989) Asymptotic relative efficiency of the classical tests under misspecification. Journal of Econometrics 42, 351–369.CrossRefGoogle Scholar
White, H. (1982) Maximum likelihood estimation of misspecified models. Econometrica 50, 1–25.10.2307/1912526CrossRefGoogle Scholar