Estimation and inference in nearly unbalanced nearly cointegrated systems

This paper considers the role of normalization in least-squares estimation of cointegrating vectors. It is shown, using an empirical example and Monte-Carlo simulations of bivariate models, that the least-squares estimates can have very poor finite sample properties when normalized in one direction but are well behaved when normalized in the other. This occurs when one of the I(1) variables is a weak random walk or is nearly stationary. The choice of the regressand also has implications for residual based unit root tests for cointegration. We provide theoretical explanations for why the least-squares estimates from one normalization can be outright inconsistent in well-defined local asymptotic frameworks. Ranking the spectral density at frequency zero of the first differenced series is suggested as a practical guide to determining which variable to use as the regressand.