Distribution Sensitive Modeling of Poverty Exit Dynamics under Uganda’s Parish Development Model: A Simulation Approach Using MGFs, PGFs, and Survival Analysis

Mathematics

Poverty remains persistently high in Uganda despite ongoing policy interventions, with many rural households still dependent on low productivity subsistence agriculture, limiting sustainable economic transition. The Parish Development Model (PDM) was introduced as a decentralized financial inclusion strategy aimed at accelerating household level poverty exit through structured credit delivery. This study simulates poverty exit dynamics under the PDM using a distribution sensitive framework that integrates Moment Generating Functions, Probability Generating Functions, and survival analysis within a policy simulation design. Poverty exit is modeled as a Bernoulli process across loan cycles, where each cycle represents a two-year repayment period under standardized loan conditions. The analysis uses regional administrative data and policy parameters rather than household survey data to estimate expected poverty exit time, variability, and risk adjusted outcomes across Uganda’s statistical regions. Results from the simulation indicate a baseline exit probability of 0.25 per loan cycle, corresponding to an average of four cycles or approximately eight years for poverty exit under normal conditions. However, substantial regional variation is observed, with higher exit times in regions exposed to greater agricultural and demographic pressure. Incorporating agricultural risks such as rainfall variability, pest outbreaks, and market shocks reduces effective exit probabilities and increases both mean exit time and variance, extending poverty duration beyond thirteen years in high-risk scenarios. Sensitivity analysis further shows that small improvements in exit probability significantly reduce poverty duration, while increases in risk intensity produce nonlinear deterioration in outcomes. The study concludes that poverty exit under the PDM is distribution dependent and highly sensitive to structural and environmental conditions. The proposed framework provides policymakers with a quantitative tool for evaluating loan design, regional targeting, and risk mitigation strategies under uncertainty.

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