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Approximating the Approximate Slopes of LR, W, and LM Test Statistics

Published online by Cambridge University Press:  11 February 2009

Lonnie Magee
Lonnie Magee
Affiliation:
McMaster University
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Abstract

A Taylor series approach is used to derive approximations to the approximate slope of LR, W, and LM test statistics. These can be useful when the approximate slopes themselves are complicated. The results are applied to the test of linear coefficient restrictions in the linear model with a nonscalar covariance matrix. They can be used to find cases where the Wald test may badly over-reject in this model. The results shed some new light on the over-rejection that has been noted in the special cases of AR(1) disturbances and the SURE model.

Type
Articles
Information
Econometric Theory , Volume 3 , Issue 2 , April 1987 , pp. 247 - 271
Copyright
Copyright © Cambridge University Press 1987

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References

1.Bahadur, R. R.Stochastic comparison of tests. Annals of Mathematical Statistics 29(1960): 276–295.CrossRefGoogle Scholar
2.Beach, C. M. & MacKinnon, J. G.. A maximum likelihood procedure for regression with autocorrelated errors. Econometrica 46 (1978): 51–58.Google Scholar
3.Berndt, E. R. & Savin, N. E.. Conflict among criteria for testing hypotheses in the multivar-iate linear regression model. Econometrica 45 (1977): 1263–1278.CrossRefGoogle Scholar
4.Breusch, T. S.Conflict among criteria for testing hypotheses: Extension and comment. Econometrica 47 (1979): 203–208.CrossRefGoogle Scholar
5.Davidson, R. & MacKinnon, J. G.. Efficient estimation of tail-area probabilities in sampling experiments. Economics Letters 8 (1981): 73–77.CrossRefGoogle Scholar
6.Engle, R. F. Wald, likelihood ratio, and Lagrange multiplier tests in econometrics. In Griliches, Z. & Intriligator, M. (eds.), Handbook of Econometrics. Amsterdam: North-Holland, 1984.Google Scholar
7.Evans, G. B. A. & Savin, N. E.. Conflict among the criteria revisited: The W, LR, and LM tests. Econometrica 50 (1982): 737–748.Google Scholar
8.Gallant, A. R. & Holly, A.. Statistical inference in an implicit, nonlinear, simultaneous equation model in the context of maximum likelihood estimation. Econometrica 48 (1980): 697–720.CrossRefGoogle Scholar
9.Geweke, J.The approximate slopes of econometric tests. Econometrica 49 (1981): 1427–1442.CrossRefGoogle Scholar
10.Geweke, J.A comparison of tests of the independence of two covariance-stationary timeseries. Journal of the American Statistical Association 76 (1981): 363–373.Google Scholar
11.Geweke, J., Meese, R., & Dent, W.. Comparing alternative tests of causality in temporal systems: Analytic results and experimental evidence. Journal of Econometrics 21 (1983): 161–194.CrossRefGoogle Scholar
12.Griffiths, W. E. & Beesley, P. A. A.. The small sample properties of some preliminary testestimators in a linear model with autocorrelated errors. Journal of Econometrics 25 (1984): 49–61.Google Scholar
13.King, M. L. & Giles, D. E. A.. Autocorrelation pretesting in the linear model: Estimation, testing, and prediction. Journal of Econometrics 25 (1984): 35–48.CrossRefGoogle Scholar
14.Kwok, B. & Veall, M. R.. The jackknife and regression with AR(1) errors. University of Western Ontario: 1986.Google Scholar
15.Lee, Y.Asymptotic formulae for the distribution of a multivariate test statistic: Power comparisons of certain multivariate tests. Biometrika 58 (1971): 647–651.Google Scholar
16.Laitinen, E. K.Why is homogeneity so often rejected? Economics Letters 1 (1978): 187–191.CrossRefGoogle Scholar
17.Miyazaki, S. & Griffiths, W. E.. The properties of some covariance estimators in linear models with AR(1) errors. Economics Letters 14 (1984): 351–356.CrossRefGoogle Scholar
18.Nakamura, A. & Nakamura, M.. On the impact of the tests for serial correlation upon the test of significance of the regression coefficient. Journal of Econometrics 7 (1978): 199–210.CrossRefGoogle Scholar
19.Park, R. E. & Mitchell, B. M.. Estimating the autocorrelated model with trended data. Journal of Econometrics 13 (1980): 185–201.CrossRefGoogle Scholar
20.Pesaran, M. H.Asymptotic power comparisons of separate parametric families by Bahadur's approach. Biometrika 71 (1984): 245–252.CrossRefGoogle Scholar
21.Rothenberg, T. J.Hypothesis testing in linear models when the error covariance matrix is nonscalar. Econometrica 52 (1984): 827–842.CrossRefGoogle Scholar
22.Zellner, A.An efficient method of estimating seemingly unrelated regressions and tests for aggregation bias. Journal of the American Statistical Association 57 (1962): 348–368.Google Scholar