Finite sample comparison of alternative tests on the rank of a cointegration submatrix

This paper compares the finite sample performance of alternative tests for rank-dficiency of a submatrix of the cointegrating matrix. The paper focuses on the (implementation of the) likelihood ratio test proposed in Paruolo (2007, Oxford Bulletin of Economics and Statistics), and compares its finite sample performance with the ones of alternative tests proposed in Saikkonen (1999, Econometric Reviews) and Kurozumi (2005, Econometric Theory). All the tests have well-documented limit distributions; their finite sample performance is analyzed in this paper through a Monte Carlo simulation study. We use the Monte Carlo design used in Lukkonen, Ripatti and Saikkonen (1999, Journal of Business and Economic Statistics). It is found that the LR and the Kurozumi test perform remarkably better than the alternatives, with a marginal advantage of the LR test. The paper also investigates the properties and the numerical performance of the alternating maximization algorithm that is employed to maximize the likelihood under the null. Alternative ways to choose its starting values are also discussed. In the simulations it is found that the algorithm requires a few iterations when the null is correctly speci?ed and a rather limited number of iteration in 90% of the other cases. The choice of starting values is found to have a signi?cant e¤ect on the number of iteration required by the algorithm.