The Influence of VAR Dimensions on Estimator Biases

18 Pages Posted: 15 Jan 2012

See all articles by Karim M. Abadir

Karim M. Abadir

Imperial College Business School

Kaddour Hadri

Queen's University Belfast

Elias Tzavalis

Athens University of Economics and Business - Department of Economics

Date Written: 1999


Vector AutoRegressions (VARs) have now become the most popular tool of Time Series analysis amongst econometricians. Unfortunately, little is known about the analytic finite-sample properties of parameter estimators for such systems. The asymptotic analysis of VARs published to date does not address questions regarding the influence of the number and nature of the system's variates on parameter estimates. Clearly, both questions will have repercussions on the way VARs are used, and we intend to address them here.

We consider the implications of varying the dimensions of VARs on the biases of Maximum Likelihood and Least Squares Estimators (MLE and LSE, respectively). In the purely nonstationary case (k-dimensional random walk), estimator biases are approximately equal to the dimension of the system (k) times the univariate bias, even when the variates are generated independently of each other. We show that the variance too increases with the dimension of the system, hence also raising the Mean Squared Error (MSE) of the estimator. When some stable linear combinations exist, the biases are generally smaller and are asymptotically proportional to the sum of the characteristic roots of the VAR. One source of such combinations is meaningful economic relations that are represented by the cointegration of some of the components of the VAR. Adding economically-irrelevant variables to a VAR is thus shown to have more serious negative consequences in integrated time series than in classical ergodic or cross section analyses. The findings strengthen the case for parsimonious modelling and for the reduction step of the general-to-specific marginalization method. They also support the use of seasonally unadjusted data whenever possible.

Suggested Citation

Abadir, Karim M. and Hadri, Kaddour and Tzavalis, Elias, The Influence of VAR Dimensions on Estimator Biases (1999). Econometrica, Vol. 67, No. 1, p. 163, January 1999, Available at SSRN:

Karim M. Abadir (Contact Author)

Imperial College Business School ( email )

South Kensington Campus
Exhibition Road
London SW7 2AZ, SW7 2AZ
United Kingdom

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Kaddour Hadri

Queen's University Belfast ( email )

25 University Square
Belfast, BT7 1NN

Elias Tzavalis

Athens University of Economics and Business - Department of Economics ( email )

76 Patission Street
GR-10434 Athens

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