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

This paper asks whether persistent homology, a technique from topological data analysis (TDA), can provide earlier and more structurally interpretable detection of poverty-trap dynamics than conventional econometric and machine-learning models. Poverty traps, self-reinforcing conditions that keep individuals or economies below a critical threshold, are notoriously hard to detect before they entrench, and the paper proposes that the 'shape' of economic data, captured topologically, may carry early-warning signals that standard methods miss. The study positions persistent homology against two comparison classes: threshold econometric models, which are interpretable but may detect regime shifts late, and machine-learning models such as Random Forest, which can be accurate but operate as black boxes. The central claim under investigation is that TDA can offer both earlier detection and structural interpretability, identifying the topological features that signal a system approaching or sitting within a trap, rather than only predicting an outcome. Grounded in applied mathematics, mathematical economics and computational economics, the paper's focus is methodological: it evaluates whether a topological lens adds genuine value for understanding macroeconomic dynamics and development economics, particularly the early-warning problem where timing and explanation both matter for policy. By framing poverty traps as a question of detecting changes in the geometric and topological structure of data over time, it explores whether persistent homology can serve as a complementary or superior diagnostic to established threshold and machine-learning approaches, contributing to the emerging use of topological methods in economics and to the practical goal of intervening in poverty dynamics before they become self-sustaining.