The Structure of the U.S. Income Distribution

TL;DR

This paper identifies that U.S. income distribution over fifty years can be modeled by a one-parameter family, with the inverse-gamma distribution fitting well but still overfitting, leading to a simplified one-dimensional model.

Contribution

It introduces the inverse-gamma distribution as a parsimonious model for income data and derives a one-dimensional model based on parameter relationships.

Findings

Inverse-gamma distribution fits income data well

A linear relationship exists between distribution parameters

A simplified one-dimensional model is proposed

Abstract

I show that U.S. incomes follow a one-parameter family of probability distributions over more than fifty years of data. I compare statistical models of income, and I highlight the inverse-gamma distribution as a parsimonious model that matches data particularly well and has straightforward theoretical interpretations. However, despite having relatively few parameters, the inverse-gamma distribution still overfits income data. I establish a linear relationship between parameter estimates, and a one-dimensional model emerges naturally when I exploit this relationship. I conclude with theoretical remarks about the model.