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On Small Sample Properties of R2 in a Linear Regression Model with Multivariate t Errors and Proxy Variables

Published online by Cambridge University Press:  11 February 2009

Kazuhiro Ohtani  and
Hikaru Hasegawa
Kazuhiro Ohtani
Affiliation:
Kobe University
Hikaru Hasegawa
Affiliation:
Hokkaido University
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Abstract

In this paper we consider the small sample properties of the coefficient of determination in a linear regression model with multivariate t errors when proxy variables are used instead of unobservable regressors. The results show that if the unobservable variable is an important variable, the adjusted coefficient of determination can be more unreliable in small samples than the unadjusted coefficient of determination from both viewpoints of the bias and the MSE.

Type
Miscellanea
Information
Econometric Theory , Volume 9 , Issue 3 , June 1993 , pp. 504 - 515
Copyright
Copyright © Cambridge University Press 1993

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References

1.Aigner, D. J.MSE dominance of least squares with errors-in-observation. Journal of Econometrics 2 (1974): 365–372.CrossRefGoogle Scholar
2.Battese, G.E. & Griffiths, W.E.. On R 2-statistics for the general linear model with non-scalar covariance matrix. Australian Economic Papers 19 (1980): 343–348.CrossRefGoogle Scholar
3.Blattberg, R.C. & Gonedes, N.J.. A comparison of the stable and Student distributions as statistical models for stock prices. Journal of Business 47 (1974): 244–280.CrossRefGoogle Scholar
4.Cramer, J.S.Mean and variance of R 2 in small and moderate samples. Journal of Econometrics 35 (1987): 253–266.CrossRefGoogle Scholar
5.Fama, E.F.The behaviour of stock market prices. Journal of Business 38 (1965): 34–105.CrossRefGoogle Scholar
6.Frost, P.A.Proxy variables and specification bias. Review of Economics and Statistics 61 (1979): 323–325.CrossRefGoogle Scholar
7.Giles, J.A. Preliminary-test estimation of a mis-specified linear model with spherically symmetric disturbances. Ph.D. Thesis, University of Canterbury, 1990.Google Scholar
8.Giles, J.A.Pre-testing for linear restrictions in a regression model with spherically symmetric disturbances. Journal of Econometrics 50 (1991): 377–398.CrossRefGoogle Scholar
9.Johnson, N.L. & Kotz, S.. Distributions in statistics: continuous univariate distributions-2. New York: Wiley, 1970.Google Scholar
10.McCallum, B.T.Relative asymptotic bias from errors of omission and measurement. Econometrica 40 (1972): 757–758.CrossRefGoogle Scholar
11.Ohtani, K.On the use of a proxy variable in prediction: An MSE comparison. Review of Economics and Statistics 63 (1981): 627–628.CrossRefGoogle Scholar
12.Ohtani, K.Small sample properties of interval constrained least squares estimator when error terms have a multivariate t distribution. Journal of the Japan Statistical Society 21 (1991): 197–204.Google Scholar
13.Ohtani, K.Small sample properties of R 2 based on the Stein-Rule estimator in a misspecified linear regression model. The Economic Studies Quarterly (forthcoming).Google Scholar
14.Ohtani, K. & Giles, J.A.. Testing linear restrictions on coefficients in a linear regression model with proxy variables and spherically symmetric disturbances. Journal of Econometrics 57 (1993): 393–406.CrossRefGoogle Scholar
15.Press, S.J. & Zellner, A.. Posterior distribution for the multiple correlation coefficient with fixed regressors. Journal of Econometrics 8 (1978): 307–321.CrossRefGoogle Scholar
16.Singh, R.S.Estimation of error variance in linear regression models with errors having multivariate Student-t distribution with unknown degrees of freedom. Economics Letters 27 (1988): 47–53.CrossRefGoogle Scholar
17.Sutradhar, B.C.Testing linear hypothesis with t error variable. Sankhya B50 (1988): 175–180.Google Scholar
18.Sutradhar, B.C. & Ali, M.M.. Estimation of the parameters of a regression model with a multivariate t error variable. Communications in Statistics-Theory and Methods 15 (1986): 429–450.CrossRefGoogle Scholar
19.Ullah, A. & Zinde-Walsh, V.. On the robustness of LM, LR, and Wald tests in regression model. Econometrica 52 (1984): 1055–1066.CrossRefGoogle Scholar
20.Wickens, M.R.A note on the use of proxy variables. Econometrica 40 (1972): 759–761.CrossRefGoogle Scholar
21.Zellner, A.Bayesian and non-Bayesian analysis of the regression model with multivariate Student-t error terms. Journal of the American Statistical Association 71 (1976): 400–405.Google Scholar