Interpreting Tests of the Convergence Hypothesis

This paper provides a framework for understanding the cross- section and time series approaches which have been used to test the convergence hypothesis. First, we present two definitions of convergence which capture the implications of the neoclassical growth model for the relationship between current and future cross-country output differences. Second, we identify how the cross-section and time series approaches relate to these definitions. Cross-section tests are shown to be associated with a weaker notion of convergence than time series tests. Third, we show how these alternative approaches make different assumptions on whether the data are well characterized by a limiting distribution. As a result, the choice of an appropriate testing framework is shown to depend on both the specific null and alternative hypotheses under consideration as well as on the initial conditions characterizing the data being studied.