# Equal Opportunity and Luck: Empirical Exploration Using the Canadian Longitudinal Study on Aging

## TL;DR

This paper explores how luck affects equality of opportunity in aging populations using data from the Canadian Longitudinal Study on Aging.

## Contribution

It introduces the 'playing field framework' to assess whether unexplained variation (luck) reflects unfair inequality in equality of opportunity analyses.

## Key findings

- Distributions of residuals (luck) are not always fair across age-sex groups.
- Luck should be explicitly considered in equality of opportunity frameworks.
- Ignoring residuals can lead to underestimating unfair inequality.

## Abstract

Equality of opportunity (EOp) is a broad category of egalitarian theories that has attracted considerable attention in recent decades. Empirical implementations of EOp primarily focus on the explained component of inequality, classifying determinants of the outcome (e.g., health) into effort—legitimate causes of inequality—and circumstance—illegitimate causes of inequality. Largely overlooked is unexplained variation, which in statistical analysis manifests as residuals and is often ignored as a statistical annoyance. The true random component of residuals is now often referred to as luck. In this paper, we propose the playing field framework that serves as a pragmatic test as to whether residuals signal unfairness in empirical EOp analyses and that enables empirical explorations of roles of luck within the EOp framework. Using a large sample of Canadian older adults, our empirical application of the playing field framework shows that distributions of residuals are not always fair, though there is no consistent pattern of unfairness across age-sex groups. The paper’s three main conclusions are: luck matters; luck should be explicitly incorporated in the EOp framework through the brute luck-effort characterization; and residuals are not just an innocuous statistical annoyance but can represent unfair inequality, and ignoring them can underestimate unfair inequality.