This paper discusses the concept of convergence in economic growth and distribution dynamics. Convergence refers to whether poorer economies can catch up with richer ones. However, the traditional approach to convergence analysis focuses on cross-sectional regressions and production-function accounting, which may not fully capture the dynamics of income distribution across economies. The paper argues that the traditional approach fails to distinguish between two key dimensions of economic growth: the mechanism by which economies push back technological and capacity constraints (growth mechanism) and the mechanism that determines the relative performance of rich and poor economies (convergence mechanism). The new approach to convergence analysis models the dynamics of cross-sectional income distributions, revealing patterns such as persistence, stratification, and the formation of convergence clubs. These findings suggest that income distributions may polarize into twin peaks of rich and poor, with the middle-income group eventually vanishing. The new approach also highlights the importance of understanding the economic forces behind cross-country interactions and coalition formation. It suggests that the traditional approach, which focuses on cross-sectional regressions, may not adequately address the complexities of economic growth and convergence. Instead, it emphasizes the need for a more comprehensive understanding of distribution dynamics, including the role of capital market imperfections, heterogeneity, and country size. The paper concludes that the traditional approach to convergence analysis is insufficient and that new empirical research is needed to better understand the dynamics of economic growth and convergence. The new approach provides insights into the mechanisms that drive economic growth and convergence, and highlights the importance of considering the broader economic context in which these processes occur.This paper discusses the concept of convergence in economic growth and distribution dynamics. Convergence refers to whether poorer economies can catch up with richer ones. However, the traditional approach to convergence analysis focuses on cross-sectional regressions and production-function accounting, which may not fully capture the dynamics of income distribution across economies. The paper argues that the traditional approach fails to distinguish between two key dimensions of economic growth: the mechanism by which economies push back technological and capacity constraints (growth mechanism) and the mechanism that determines the relative performance of rich and poor economies (convergence mechanism). The new approach to convergence analysis models the dynamics of cross-sectional income distributions, revealing patterns such as persistence, stratification, and the formation of convergence clubs. These findings suggest that income distributions may polarize into twin peaks of rich and poor, with the middle-income group eventually vanishing. The new approach also highlights the importance of understanding the economic forces behind cross-country interactions and coalition formation. It suggests that the traditional approach, which focuses on cross-sectional regressions, may not adequately address the complexities of economic growth and convergence. Instead, it emphasizes the need for a more comprehensive understanding of distribution dynamics, including the role of capital market imperfections, heterogeneity, and country size. The paper concludes that the traditional approach to convergence analysis is insufficient and that new empirical research is needed to better understand the dynamics of economic growth and convergence. The new approach provides insights into the mechanisms that drive economic growth and convergence, and highlights the importance of considering the broader economic context in which these processes occur.