Catching-up Convergence and its Speed : Representation and Testing

This paper provides a new, unified, and flexible framework to measure and characterize a convergence process. Specifically, we formally define a general notion of asymptotic price convergence, which encompasses convergence as steady-state and catching-up, and propose a model to represent a wide range of transition paths. Our framework enables the econometric measurement of such transitional behaviors and the development of testing procedures. In particular, we use unit root tests (with and without breaks) to determine whether asymptotic convergence exists and, if so, its starting point and its type: as steady-state or catching-up and in its weak or strong version. We apply this methodology to illustrate the convergence process in two very different cases: (1) the aggregated price level of the Eurozone’s largest economies (Germany, France and Italy) and, (2) the transatlantic 19th Century wheat prices