The secrets they never taught you: Threshold returns to human capital and intergenerational mobility

We develop a model of intergenerational mobility in which returns to parental human-capital investment rise discretely once investment crosses a tuition threshold associated with elite private schooling and the networks it provides. This non-convexity generates two investment regimes and, on the support where both branch-specific interior optima are feasible, a piecewise affine intergenerational earnings correlation: persistence is weak below the switching region and stronger above it. The mechanism is consistent with evidence from Chile showing that the intergenerational earnings correlation is approximately flat through most of the parental distribution but rises sharply in the upper tail. We also endogenize the threshold through a screening equilibrium in which private elite schools set tuition to preserve club composition. Finally, we show that progressive taxation and public investment in human capital reduce upper-tail persistence and, on the relevant support, can eliminate selection into private schools.