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

This work explores if persistent homology - a tool from topological data analysis - offers faster, clearer signals of poverty traps compared to threshold-based econometric approaches alongside Random Forest techniques. Drawing on standardized economic metrics across lower- and middle-income nations, such as output per person, investment levels, education indices, and efficiency trends, it defines a shared criterion for trap emergence rooted in prolonged sluggish expansion. While one approach emphasizes geometric patterns in data structure, others rely on statistical splits or rigid cutoffs. Detection speed together with ease of explanation becomes the basis for comparison. Although machine learning models capture nonlinearities well, their outputs often resist straightforward interpretation. Topological features, by contrast, reflect shape-driven transitions that align closely with theoretical mechanisms. Because the method tracks how holes or loops form within point clouds, shifts in these forms may precede conventional alerts. When applied to real-world aggregates, the technique identifies critical slowdowns slightly ahead of traditional benchmarks. Interpretation follows naturally from visual scaffolding embedded in the results. Where decision trees fragment variables into thresholds, topology preserves continuity in change. Thus, structural insight emerges not from variable importance scores but from evolving data shapes. Earlier warnings appear without sacrificing clarity.

Starting from raw economic figures, every nation's path gets mapped into a dynamic cloud of points shaped by topology. Instead of static models, shifting windows capture evolving patterns through persistent homology’s lens. Rather than relying solely on traditional cutoffs, comparisons emerge alongside a Random Forest model built on identical inputs and forecast timing. Because only a limited set of crisis beginnings qualify under tight criteria, findings hint at possibilities more than broad truths. Though statistical rigor holds, generalizations remain untested due to narrow case counts.

What stands out clearly is how early the TDA approach flagged a warning in the data. In Zambia, its signal passed the alert level back in 2000, years ahead of the reference point set for 2007. While the standard statistical model picked up Zambia three years prior to crisis start, and Malawi four, the machine learning tool spotted both countries three years in advance. Even so, the strong fit seen with the Random Forest comes with caveats due to sparse and uneven case numbers. So the real value of the TDA outcome lies less in claiming better forecasts, more in showing that shape-based analysis can uncover hidden strain in growth paths well before traditional markers shift.