The Asymptotic Influence of VAR Dimension on Estimator Biases.

We show that in a purely nonstationary Vector Autoregression (VAR), the biases of Maximum Likelihood and Least Squares Estimators are asymptotically proportional to the dimension of the system, even when the equations and regressors are generated independantly of each other. When some stable linear combinations exist, as when the variables are cointegrated, these biases are in general asymptotically proportional to the sum of the characteristic roots of the VAR. Adding 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.