Economic Dynamics with Differential Fertility

39 Pages Posted: 21 Sep 2021 Last revised: 3 Mar 2025

See all articles by Francis Dennig

Francis Dennig

National University of Singapore (NUS) - Yale-NUS College

Bassel Tarbush

University of Oxford - Merton College

Date Written: October 28, 2023

Abstract

We characterize the outcomes of a canonical deterministic model for the intergenerational transmission of capital that features differential fertility. A fertility function determines the relationship between parental capital and the number of children, and a transmission function determines the relationship between the capital of a parent and that of their children. Together these functions generate an evolving cross-sectional distribution of capital. We establish easy-to-verify conditions on the fertility and transmission functions that guarantee (a) that the dynamical system has a steady state distribution that is either atomless (exhibiting inequality) or degenerate (not exhibiting inequality), and (b) that the system converges to such states from essentially any initial distribution. Our characterization provides new insights into the link between differential fertility and long-run cross-sectional inequality, and it gives rise to novel comparative statics relating the two. We apply our results to several parametric examples and to a model of economic growth that features endogenous differential fertility.

Keywords: Differential fertility, intergenerational dynamics, inequality, growth

JEL Classification: D31, E24, J13, O40

Suggested Citation

Dennig, Francis and Tarbush, Bassel, Economic Dynamics with Differential Fertility (October 28, 2023). Available at SSRN: https://ssrn.com/abstract=3926772 or http://dx.doi.org/10.2139/ssrn.3926772

Francis Dennig

National University of Singapore (NUS) - Yale-NUS College ( email )

12 College Ave West, #01-201
Singapore, 138610
Singapore

Bassel Tarbush (Contact Author)

University of Oxford - Merton College ( email )

Merton College
Oxford, OX1 4JD
United Kingdom

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