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Specification Testing with Locally Misspecified Alternatives

Published online by Cambridge University Press:  11 February 2009

Anil K. Bera  and
Mann J. Yoon
Anil K. Bera
Affiliation:
University of Illinois
Mann J. Yoon
Affiliation:
California State University
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Abstract

It is well known that most of the standard specification tests are not robust when the alternative is misspecified. Using the asymptotic distributions of standard Lagrange multiplier (LM) test under local misspecification, we suggest a robust specification test. This test essentially adjusts the mean and covariance matrix of the usual LM statistic. We show that for local misspecification the adjusted test is asymptotically equivalent to Neyman's C(α) test, and therefore, shares the optimality properties of the C(α) test. The main advantage of the new test is that, compared to the C(α) test, it is much simpler to compute. Our procedure does require full specification of the model and there might be some loss of asymptotic power relative to the unadjusted test if the model is indeed correctly specified.

Type
Articles
Information
Econometric Theory , Volume 9 , Issue 4 , August 1993 , pp. 649 - 658
Copyright
Copyright © Cambridge University Press 1993

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References

1.Basawa, I.V. Neyman-Le Cam tests based on estimating functions. In Le Cam, L.M. and Olshen, R.O. (eds.), Proceedings of the Berkeley Conference in Honor of Jerzy Neyman and Jack Kiefer. New York: Wadsworth, Inc., 1985.Google Scholar
2.Bera, A.K. & Byron, R.. A note on the effects of linear approximation on hypothesis testing. Economics Letters 12 (1983): 251–254.CrossRefGoogle Scholar
3.Bera, A.K. & Jarque, C.M.. Model specification tests: A simultaneous approach. Journal of Econometrics 20 (1982): 59–82.CrossRefGoogle Scholar
4.Bera, A.K. & McKenzie, C.R.. Additivity and separability of the Lagrange multiplier, likelihood ratio and Wald tests. Journal of Quantitative Economics 3 (1987): 53–63.Google Scholar
5.Bera, A.K. & Yoon, M.J.. Specification testing with misspecified alternatives. Bureau of Economic and Business Research Faculty Working Paper 91–0123, University of Illinois, 1991.Google Scholar
6.Breslow, N.Tests of hypotheses in overdispersed Poisson regression and other quasilikelihood models. Journal of the American Statistical Association 85 (1990): 565–571.CrossRefGoogle Scholar
7.Byron, R. & Bera, A.K.. Least squares approximation to unknown regression functions: A comment. International Economic Review 24 (1983): 255–260.Google Scholar
8.Chesher, A., Lancaster, T. & Irish, M.. On detecting the failure of distributional assumptions. Annales de L'INSEE 59/60 (1985): 7–44.CrossRefGoogle Scholar
9.Davidson, R. & MacKinnon, J.G.. The interpretation of test statistics. Canadian Journal of Economics 18 (1985): 38–57.CrossRefGoogle Scholar
10.Davidson, R. & MacKinnon, J.G.. Implicit alternatives and the local power of test statistics. Econometrica 55 (1987): 1305–1329.CrossRefGoogle Scholar
11.Godfrey, L.G.Misspecification Tests in Econometrics, the Lagrange Multiplier Principle and Other Approaches. Cambridge: Cambridge University Press, 1988.Google Scholar
12.Haavelmo, T.The probability approach in econometrics. Supplement to Econometrica 12 (1944).Google Scholar
13.Hall, W.J. & Mathiason, D.J.. On large-sample estimation and testing in parametric models. International Statistical Review 58 (1990): 77–97.CrossRefGoogle Scholar
14.Jaggia, S. & Trivedi, P.K.. Joint and separate score tests of state dependence and unobserved heterogeneity. Journal of Econometrics (1993) (forthcoming).Google Scholar
15.Neyman, J. Optimal asymptotic tests of composite statistical hypothesis. In Grenander, U. (ed.), Probability and Statistics, pp. 213–234. New York: Wiley, 1959.Google Scholar
16.Pagan, A.R.Evaluating models: A review of L.G. Godfrey, misspecification tests in econometrics. Econometric Theory 6 (1990): 273–281.CrossRefGoogle Scholar
17.Pagan, A.R. & Wickens, M.R.. A survey of some recent econometric methods. The Economic Journal 99 (1989): 962–1025.CrossRefGoogle Scholar
18.Saikkonen, P.Asymptotic relative efficiency of the classical test statistics under misspecification. Journal of Econometrics 42 (1989): 351–369.CrossRefGoogle Scholar
19.Smith, R.J.Alternative asymptotically optimal tests and their application to dynamic specification. Review of Economic Studies 54 (1987): 665–680.CrossRefGoogle Scholar
20.Stein, C. Efficient nonparametric testing and estimation. In Neyman, J. (ed.), Proceedings of the 3rd Berkeley Symposium on Mathematical Statistics and Probability, pp. 187–195. Berkeley: University of California Press, 1956.Google Scholar
21.White, H.Using least squares to approximate unknown regression functions. International Economic Review 21 (1980): 149–170.CrossRefGoogle Scholar
22.Wooldridge, J.M.A unified approach to robust, regression-based specification tests. Econometric Theory 6 (1990): 17–43.CrossRefGoogle Scholar