Intergenerational Aspirations, Capital Dilution, and the Dynamics of Inequality

Abstract

We propose a dynamic stochastic model of the intergenerational transmission of capital that accounts for fertility differentials. The evolution of the distribution of capital depends on a parent-to-child capital transmission technology, which captures how capital is diluted across siblings, and on a fertility-capital relationship, which can be rationalised as the outcome of a decision problem in which parents have aspirational preferences over the outcomes of their children. We derive a simple and explicit mapping from fertility and technology to the long run distribution of capital and use our result to characterise the effects of policy interventions on long run inequality.

Keywords: Markov branching process, inequality, steady state distribution, Pareto, log-normal, aspirational preferences, intergenerational transmission

JEL Classification: D31, E24, J10