PurposeOur paper studies a central issue with a long history in economics: the relationship between population and economic growth. We analyze the joint dynamics of economic and demographic growth in 111 countries during the period 1960–2019.Design/methodology/approachUsing the concept of economic regime, the paper introduces the notion of distance between the dynamical paths of different countries. Then, a minimal spanning tree (MST) and a hierarchical tree (HT) are constructed to detect groups of countries sharing similar dynamic performance.FindingsThe methodology confirms the existence of three country clubs, each of which exhibits a different dynamic behavior pattern. The analysis also shows that the clusters clearly differ with respect to the evolution of other fundamental variables not previously considered [gross domestic product (GDP) per capita, human capital and life expectancy, among others].Practical implicationsOur results indirectly suggest the existence of dynamic interdependence in the trajectories of economic growth and population change between countries. It also provides evidence against single-model approaches to explain the interdependence between demographic change and economic growth.Originality/valueWe introduce a methodology that allows for a model-free topological and hierarchical description of the interplay between economic growth and population.