Student Flow Modeling for School Decongestion via Stochastic Gravity Estimation and Constrained Spatial Allocation

Abstract: School congestion, where student enrollment exceeds school capacity, is a major challenge in low- and middle-income countries. It highly impacts learning outcomes and deepens inequities in education. While subsidy programs that transfer students from public to private schools offer a mechanism to alleviate congestion without capital-intensive construction, they often underperform due to fragmented data systems that hinder effective implementation. The Philippine Educational Service Contracting program, one of the world's largest educational subsidy programs, exemplifies these challenges, falling short of its goal to decongest public schools. This prevents the science-based and data-driven analyses needed to understand what shapes student enrollment flows, particularly how families respond to economic incentives and spatial constraints. We introduce a computational framework for modeling student flow patterns and simulating policy scenarios. By synthesizing heterogeneous government data across nearly 3,000 institutions, we employ a stochastic gravity model estimated via negative binomial regression to derive behavioral elasticities for distance, net tuition cost, and socioeconomic determinants. These elasticities inform a doubly constrained spatial allocation mechanism that simulates student redistribution under varying subsidy amounts while respecting both origin candidate pools and destination slot capacities. We find that geographic proximity constrains school choice four times more strongly than tuition cost and that slot capacity, not subsidy amounts, is the binding constraint. Our work demonstrates that subsidy programs alone cannot resolve systemic overcrowding, and computational modeling can empower education policymakers to make equitable, data-driven decisions by revealing the structural constraints that shape effective resource allocation, even when resources are limited.