The Roots of Inequality: Estimating Inequality of Opportunity from Regression Trees

Abstract

We propose a set of new methods to estimate inequality of opportunity based on conditional inference regression trees. In particular, we illustrate how these methods represent a substantial improvement over existing empirical approaches to measure inequality of opportunity. First, they minimize the risk of arbitrary and ad-hoc model selection. Second, they provide a standardized way of trading off upward and downward biases in inequality of opportunity estimations. Finally, regression trees can be graphically represented; their structure is immediate to read and easy to understand. This will make the measurement of inequality of opportunity more easily comprehensible to a large audience. These advantages are illustrated by an empirical application based on the 2011 wave of the European Union Statistics on Income and Living Conditions.

A latent class approach to inequity in health using biomarker data

“…It should be explicitly mentioned here that our paper builds on precedents for the use of latent class models in analysis of health equity (e.g., Bago d'Uva et al, 2009; Balia & Jones, 2011; Li Donni et al, 2015) to highlight the role that FMMs can play in modelling unobserved heterogeneity (treating Roemerian types as unobserved latent classes). However, we view our approach as a complement to recent data‐driven perspectives of statistical learning methods (Brunori, Hufe, & Gerszon Mahler, 2018; Hufe, Peichl, & Weishaar, 2019). Specifically, the latter focuses mainly on an ex ante IOp approach and the problem of making a parsimonious selection of variables from the observed set of circumstances in a nonarbitrary and data‐driven way.…”

The Evolution of Inequality of Opportunity in Germany: A Machine Learning Approach

“…In light of this Brunori et al (2018a) propose the use of a machine learning algorithm, known as conditional inference regression trees, to identify Romerian types. Regression trees are prediction algorithms introduced by Morgan and Sonquist (1963) and popularized by Breiman et al (1984) almost 20 years later.…”

“…Recent contributions have proposed approaches to improve the empirical specification of the underlying models, finding consistent econometric methods to identify the relevant circumstances, and eventually estimate inequality of opportunity. Within this literature, Li Donni et al (2015) and Brunori et al (2018a) propose data-driven approaches to identify Roemerian types (i.e. sets of individuals characterized by identical circumstances).…”

“…In this study, we propose a method that builds on a data-driven approach and exploits two machine learning algorithms (namely, regression trees and polynomial approximation) to estimate inequality of opportunity consistent with Roemer's original theory. In a first step, we follow Brunori et al (2018a) to identify types and estimate opportunity trees. Then, we develop a new approach to estimate the degree of effort by polynomial approximation of the conditional distribution of household income for each type.…”

Equality of Opportunity in Four Measures of Well‐Being

“…This regression obviously suffers from omitted variable bias, which makes the interpretation of the coefficients from the regression problematic. As long as the regression does not overfit the data, an implication of the omitted variables is that the regression provides a lower-bound estimate of the amount of inequality attributable to circumstances(Ferreira and Gignoux, 2011;Brunori et al, 2018).…”