A1422
Title: Shape-constrained estimation of diminishing returns in the global literacy-income relationship.
Authors: Ioannis Demetriou - University of Athens (Greece) [presenting]
Abstract: The relationship between literacy rates and GDP per capita is investigated using a shape-constrained estimation approach designed to capture diminishing returns. Annual cross-country data from the World Bank for 20072021 are analyzed by least-squares fitting subject to concavity constraints, formulated as a quadratic programming problem. The approach estimates the literacyincome relationship without imposing a predetermined parametric functional form, while the resulting piecewise linear spline provides a transparent representation of changes in marginal literacy gains. The associated Lagrange multipliers provide sensitivity measures for assessing the influence of individual concavity constraints on the optimal fit. The results reveal a consistent pattern across the annual datasets: literacy rates increase rapidly at lower income levels, the gains diminish progressively as GDP per capita rises, and the fitted relationship approaches saturation at higher income levels, where marginal rates may become negative. Residuals, marginal rates, and Lagrange multipliers provide complementary diagnostics for identifying influential observations and regions of the income distribution that merit further investigation. The analysis illustrates how shape-constrained computational methods can combine interpretable estimation with a socially relevant application, providing quantitative information that may support more targeted educational strategies.
