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Improving Some Instrumental Variables Test Procedures

Published online by Cambridge University Press:  18 October 2010

Michael A. Magdalinos
Affiliation:
Athens School of Economics and Business Science

Abstract

This paper is concerned with Cornish–Fisher corrections of some instrumental variables test statistics. The tests based on the corrected statistics have size with error of a smaller order of magnitude than the original tests. Symmetric Edgeworth-corrected confidence regions are also defined for the structural parameters. All these corrections are given as analytic formulas that require only limited information, so their implementation is a relatively easy task.

Type
Articles
Copyright
Copyright © Cambridge University Press 1985

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References

REFERENCES

1.Basmann, R. L.On finite sample distributions of generalized classical linear identifiability test statistics. Journal of the American Statistical Association 55 (1960): 650659.CrossRefGoogle Scholar
2.Cornish, E. A. and Fisher, R. A.. Moments and cumulants in the specification of distributions. Revue de l' Institute International de Statistic 4 (1937): 114.Google Scholar
3.Fisher, R. A. Expansion of Student's integral in powers of n–1. Metron 5 (1925): 109112.Google Scholar
4.Fisher, R. A. and Cornish, E. A.The percentile of distributions having known cumulants. Technometrics 2 (1960): 209225.CrossRefGoogle Scholar
5.Hill, G. W. and Davis, A. W.Generalized asymptotic expansions of the Cornish-Fisher type. Annals of Mathematical Statistics 39 (1968): 12681273.CrossRefGoogle Scholar
6.Kloek, T. and Mennes, L. B.Simultaneous equation estimation based on principal components of predetermined variables. Econometrica 28 (1960): 4561.CrossRefGoogle Scholar
7.Kunitomo, N. K., Morimune and Tsukuda, Y.Asymptotic expansions of the distribution of the test statistic for overidentifying restrictions in a system of simultaneous equations. International Economic Review 24 (1983): 199215.CrossRefGoogle Scholar
8.Maddala, G. S.Some small sample evidence on tests of significance in simultaneous equation models. Econometrica 42 (1974): 825851.CrossRefGoogle Scholar
9.Maekawa, K.Asymptotic distributions of the Chow test statistics for the simultaneous equation system when the disturbances are small. The Hiroshima Economic Review 6 (1982): 99107.Google Scholar
10.Magdalinos, M. A. Applications of the refined asymptotic theory in econometrics. Ph.D. Thesis, University of Southampton, 1983.Google Scholar
11.Morgan, A. and Vandaele, W.On testing hypotheses in simultaneous equation models. Journal of Econometrics 2 (1974): 5565.CrossRefGoogle Scholar
12.Morimune, K. and Tsukuda, Y.Testing a subset of coefficients in a structural equation. Econometrica 52 (1984): 427448.CrossRefGoogle Scholar
13.Pfanzagl, J. Asymptotic expansions in parametric statistical theory. In Krishnaiah, P. R. (ed.), Developments in Statistics, Chap. 1 and pp. 190. New York: Academic, 1980.Google Scholar
14.Sargan, J. D.The estimation of economic relationships using instrumental variables. Econometrica 26 (1958): 393415.CrossRefGoogle Scholar
15.Sargan, J. D.Gram–Charlier approximations applied to tratios of Ic-class estimators. Econometrica 43 (1975): 327346.CrossRefGoogle Scholar
16.Sargan, J. D.Some approximations to the distribution of econometric criteria which are asympotically distributed as chi squared. Econometrica 48 (1980): 11081148.CrossRefGoogle Scholar