Can Persistent Homology Provide Earlier and Structurally Interpretable Detection of Poverty Trap Dynamics Compared to Econometric and Machine-Learning Models

This study was motivated by the need to understand how prolonged growth stagnation develops and persists over time. Rather than relying solely on fixed threshold rules, it examined whether topological patterns in macroeconomic data could provide insight into the emergence of poverty-trap dynamics. Three methods were compared: Topological Data Analysis (TDA) using persistent homology, threshold econometric regression, and Random Forest machine learning. For Zambia, the TDA approach signaled structural risk in 2000, seven years before the benchmark onset year of 2007. Traditional econometric models gave four-year and three-year leads for Malawi and Zambia respectively. Random Forest also detected both countries with three-year leads and the strongest fitted-sample predictive performance. The key finding is that persistent homology added value not captured by benchmark approaches: it provided earlier warning tied to observable geometric compression in development trajectories, rather than reproducing typical predictions. This study builds a bridge between nonlinear dynamic modeling and topological data analysis in development economics.