Inherited inequality: a general framework and an application to South Africa

Working Paper 2023-658

Abstract

Scholars have sought to quantify the extent of inequality which is inherited from past generations in many different ways, including a large body of work on intergenerational mobility and inequality of opportunity. This paper makes three contributions to that broad literature. First, we show that many of the most prominent approaches to measuring mobility or inequality of opportunity fit within a general framework which involves, as a first step, a calculation of the extent to which inherited circumstances can predict current incomes. The importance of prediction has led to recent applications of machine learning tools to solve the model selection challenge in the presence of competing upward and downward biases. Our second contribution is to apply transformation trees to the computation of inequality of opportunity. Because the algorithm is built on a likelihood maximization that involves splitting the sample into groups with the most salient differences between their conditional cumulative distributions, it is particularly well-suited to measuring ex-post inequality of opportunity, following Roemer (1998). Our third contribution is to apply the method to data from South Africa, arguably the world’s most unequal country, and find that almost threequarters of its current inequality is inherited from predetermined circumstances, with race playing the largest role, but parental background also making an important contribution.

Authors: Paolo Brunori, Francisco H.G. Ferreira, Pedro Salas-Rojo.