Early Childhood Development, Earnings Inequality, and Social Mobility in an Education Signaling Model

Abstract

Much of earnings inequality results from the inequality of skill formation: children of low socioeconomic status acquire less schooling than equally talented children of better-off parents. In modern technology-intensive economies, channeling high-quality education to talented individuals and matching them to highly productive jobs is crucial for economic growth, social mobility, and earnings inequality. This paper studies a signaling equilibrium in which education is a costly signal of unobserved cognitive ability and the cost of schooling falls with both ability and parental schooling. The equilibrium wage schedule solves a nonlinear first-order ODE written in terms of a general cost index. The ODE characterizes equilibrium exactly, including the concavity of the wage schedule, and its local well-posedness holds under a monotone-posterior condition (implied by log-concavity when the cost index is separable). For log-normal economies, equilibrium distributions, Gini coefficients, intergenerational dynamics, and the stationary distribution are derived in closed form by Gaussian conditioning. Relative to full information, signaling compresses the dispersion of log schooling and log wages by exactly the variance of ability that schooling fails to reveal, but raises the intergenerational elasticity of schooling. For economies with a finite number of ability and schooling types, schooling depends on agents only through a cost index; the pure-strategy equilibria of a two-type economy are fully characterized, mobility and talent utilization differ across Pareto-ranked equilibria, and Perron–Frobenius theory characterizes the long-run distribution.