Tests for Cointegration Rank and the Initial Condition

We investigate the impact of the initial condition on tests for cointegration rank. The results will be exploited to study price convergence. (1) Ahlgren, N. and Juselius, M. (2011), Tests for Cointegration Rank and the Initial Condition, Empirical Economics, forthcoming. Abstract Many economic events involve initial observations that substantially deviate from long-run steady state. Such initial conditions are known to affect the power of univariate unit root tests diversely, whereas their impact on multivariate tests is largely unknown. This paper investigates the impact of the initial condition on the power of tests for cointegration rank, such as Johansen's widely used likelihood ratio test, tests with prior adjustment for deterministic terms, and a test based on the eigenvalues of the companion matrix. We find that the power of the likelihood ratio test is increasing in the magnitude of the initial condition, whereas the power of the other tests is generally decreasing. We exploit these findings in an application to price convergence.