Growth and Development of Higher Education in Nepal: A Time-Series Analysis Using Differential-Equation Models and Machine Learning

Abstract

This paper presents a time-series analysis of the growth and development of higher education in Nepal over more than six decades (1959–2026), jointly modelling two documented national series: total higher-education enrolment (eight observations, 1975–2026) and the cumulative number of universities established (eleven observations, 1959–2026). Three competing differential-equation growth models—logistic, Gompertz, and Bass diffusion—are fitted and compared using Akaike and Bayesian Information Criteria. A Chow structural-break test examines whether the 1990 policy transition coincided with a statistically detectable change in the enrolment growth regime. A Hodrick–Prescott filter is used to separate trend and cyclical components, while Granger-causality tests examine lead–lag relationships between institutional and enrolment growth. Numerical convergence is assessed by comparing explicit-Euler integration with fourth-order Runge–Kutta integration, and parameter uncertainty is quantified using a 2,000-iteration residual-resampling bootstrap propagated through a Monte Carlo forecast envelope. A random-forest module provides exploratory feature-importance estimates for era-level covariates. The results indicate that the Gompertz model provides the lowest AIC (173.73), the Chow test identifies a statistically significant break at 1990 (F = 8.58, p = 0.036), and neither direction of Granger causality is statistically significant. The institutional growth model remains constrained by a boundary estimate for its carrying capacity, while the sparse underlying data limit the strength of time-series inference. Overall, Nepal’s higher-education development is characterised as a capacity-constrained process punctuated by policy-associated regime shifts. The study provides a reproducible Python/MATLAB-compatible framework for analysing long-run national higher-education development.