Using the Kalman filter to test for convergence : a comparison to other methods using artificial data

Convergence is an important issue in economics. There is a convergence debate going on in growth theory. Convergence is also important in international trade theory (convergence of prices of goods and factors) and the word has found its way into the European Union economic and political jargon. The different implications of different growth models led to a surge in empirical methods to test for convergence. These different methods allow for different and conflicting results. This paper is an attempt to answer to two challenges that result from the recent empirical convergence literature. The first one is to understand how these different outcomes can arise using the same data set. The second is to progress in the search for a proper way of measuring convergence. We propose a Kalman filter method to test for convergence and construct a Monte Carlo study to assess the various methods of testing for convergence. Methods that use all the series at a time ("cross-section methods") are found to lose power or give misleading results when there is a situation of limited convergence. Methods that use two or more series at a time ("time series methods", Dickey-Fuller and Kalman filter ones) are robust to these situations. Our proposed Kalman filter method is found to be more powerful than the Dickey-Fuller test when there is a structural break in the convergence process.