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Bias in Regressions With a Lagged Dependent Variable

Published online by Cambridge University Press:  11 February 2009

David Grubb  and
James Symons
David Grubb
Affiliation:
OECD, Paris and University College, London
James Symons
Affiliation:
OECD, Paris and University College, London
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Abstract

We give an expression to order O(T-1), where T is the sample size, for bias to the estimated coefficient on a lagged dependent variable when all other regressors are exogenous. The general expression is a nonlinear function of the coefficient on the lagged dependent variable, the autoregressive structure of the exogenous variables, and the coefficients on the exogenous variables. The maximum bias that can arise is a linear function of the number of exogenous regressors in the estimating equation.

Type
Research Article
Information
Econometric Theory , Volume 3 , Issue 3 , June 1987 , pp. 371 - 386
Copyright
Copyright © Cambridge University Press 1987

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References

1.Anderson, T.W.The statistical analysis of time series. New York: Wiley, 1971.Google Scholar
2.Evans, G.B.A. & Savin, N.E.. Testing for unit roots: 1. Econometrica 49 (1981): 753–779.CrossRefGoogle Scholar
3.Evans, G.B.A. & Savin, N.E.. Testing for unit roots: 2. Econometrica 52 (1984): 1241–1269.CrossRefGoogle Scholar
4.Fuller, W.A.Introduction to statistical time series. New York: Wiley, 1976.Google Scholar
5.Grubb, D.Lag invariance in auloregressive processes. Centre for Labour Economics Working Paper No. 736, 1985.Google Scholar
6.Maekawa, K.An approximation to the distribution of the least-squares estimator in an autoregressive model with exogenous variables. Econometrica 51 (1983): 229–238.CrossRefGoogle Scholar
7.Marriott, F.H.C. & Pope, J.A.. Bias in the estimation of autocorrelations. Biometrika 41 (1954): 390–402.CrossRefGoogle Scholar
8.Orcutt, G.H. & Winokur, H.S., Jr. First-order autoregression: Inference, estimation and prediction. Econometrica 37 (1969): 1–14.CrossRefGoogle Scholar
9.Sawa, T.The exact moments of the least-squares estimator for the autoregressive model. Journal of Econometrics 8 (1978): 159–172.CrossRefGoogle Scholar
10.Shenton, L.R. & Johnson, W.L.. Moments of a serial correlation coefficient. Journal of the Royal Statistical Society, Series B 27 (1965): 308–320.Google Scholar
11.Srivastava, V.K. & Tiwari, R.. Evaluations of expectations of products of stochasticmatrices. Scandinavian Journal of Statistics 3 (1976): 135–138.Google Scholar
12.Tanaka, K.Asymptotic expansions associated with the AR(1) model with unknown mean. Econometrica 51 (1983): 1221–1231.CrossRefGoogle Scholar
13.Tse, Y.K.Edgeworth approximations in first-order stochastic difference equations withexogenous variables. Journal of Econometrics 20 (1982): 175–195.CrossRefGoogle Scholar
14.White, J.S.Asymptotic expansions for the mean and variance of the serial correlation coefficient. Biometrika 48 (1961): 85–95.CrossRefGoogle Scholar