Eleven E.U. member states matched their interest rates in January 1999, marking the culmination of a lengthy convergence process. In this paper, we apply unit root tests with gradual change developed by Leybourne, Newbold and Vougas (1998) in order to analyse this convergence process among interest rates. We use Monte Carlo simulations to compare these tests with traditional unit root tests, which impose that breaks, when present, must occur instantaneously. We show that the advantage of the Leybourne, Newbold and Vougas tests is not only in terms of effectiveness when the deterministic component of the model changes gradually, but also of their they have power in a wider class of alternative processes. Besides, using Leybourne, Newbold and Vougas tests we obtain very precise estimations of the deterministic component. Therefore, these tests are a very helpful tool to analyse the convergence process. This study allows us to distinguish between catching-up and long-run convergence, and shows very important differences on the road towards the matching of interest rates among the countries belonging to the European Monetary Union.

Key words: long run convergence, catching up, interest rates, unit root tests, structural change, nonlinear smooth transition model.
JEL classification: C12, C15, C22, E43, F36.