Regime Shifts and Agricultural Divergence in Machinga District, Malawi: A Topological Analysis of Maize Yield Trajectories

Agricultural input subsidy programmes (AISPs) are widely implemented across sub-Saharan Africa to enhance smallholder productivity and food security, yet their long-term spatial and distributional impacts remain poorly characterized. We analyze nearly four decades (1986 to 2024) of maize yield data from 11 neighbouring administrative areas in Machinga District, Malawi, using a topological data analysis (TDA) framework to detect structural similarity, regime shifts, and performance divergence without relying on predefined administrative boundaries. Yield trajectories are examined across four historical policy waves namely, Structural Adjustment Programmes (SAPs) and Devaluation, Liberalization and Hunger Crises, Farm Input Subsidy Programme (FISP) Green Revolution, and Climate, Agricultural Finance Constraints, and Fragility (Climate, AFC, and Fragility), while quantile regression captures changes across the lower and upper tails of the yield distribution. Results show that formal administrative categories explain little of the observed similarity in long-term trajectories. Areas from different administrative types often follow closely aligned paths, whereas neighbouring areas of the same type frequently diverge. Simultaneously, the analysis reveals persistent and widening separation between high- and low-performing zones, with initially lagging areas reversing rank during the subsidy era and the productivity gap expanding in successive waves. Divergence elasticity between top and bottom quantiles increases monotonically across policy phases, corroborating the topologically derived regime separation. These findings indicate that maize productivity structure is path dependent, locally heterogeneous, and not well captured by inherited administrative labels, suggesting that future targeting and policy interventions should be guided by empirically derived performance groupings rather than administrative boundaries.