This paper provides a framework for understanding the cross-section and time series approaches used to test the convergence hypothesis in economic growth. The authors define two types of convergence: "catching up" and "equality of long-term forecasts." They show that cross-section tests, which examine the correlation between initial per capita output levels and subsequent growth rates, are associated with a weaker notion of convergence compared to time series tests, which focus on the long-run behavior of output differences. The choice between these testing frameworks depends on the specific null and alternative hypotheses and the initial conditions of the data being studied. Cross-section tests can reject the no-convergence null for data generated by economies with different long-run steady states, while time series tests do not spuriously reject the no-convergence null for data with multiple long-run equilibria. However, time series tests assume that the data are well characterized by a limiting distribution, which may not hold for data driven by transition dynamics. The paper concludes that neither testing framework is likely to yield unambiguous conclusions and suggests integrating transition and steady-state information to create a more general empirical methodology.This paper provides a framework for understanding the cross-section and time series approaches used to test the convergence hypothesis in economic growth. The authors define two types of convergence: "catching up" and "equality of long-term forecasts." They show that cross-section tests, which examine the correlation between initial per capita output levels and subsequent growth rates, are associated with a weaker notion of convergence compared to time series tests, which focus on the long-run behavior of output differences. The choice between these testing frameworks depends on the specific null and alternative hypotheses and the initial conditions of the data being studied. Cross-section tests can reject the no-convergence null for data generated by economies with different long-run steady states, while time series tests do not spuriously reject the no-convergence null for data with multiple long-run equilibria. However, time series tests assume that the data are well characterized by a limiting distribution, which may not hold for data driven by transition dynamics. The paper concludes that neither testing framework is likely to yield unambiguous conclusions and suggests integrating transition and steady-state information to create a more general empirical methodology.