Considering the shape of income inequality
After a university committee meeting on a Tulane data science initiative, the executive director of the political economy-focused Murphy Institute had a “simple” question for me.
What is the “right” probability distribution to use for studying annual incomes?
A mere two years later, we think we have the start of a decent answer.
Modeling emergent income inequality via quantile-dependent growth
Say that raises were handed out at the end of the year according to each of the following schemes. Which of these raise mechanisms leads to systemic change in inequality, and which do not?
It is tempting to guess that the Absolute Change rule preserves inequality while the two proportional changes increase inequality, but using a few standards for assessing relative incomes you can readily show that the Absolute Change rule decreases inequality; the Proportional Change+ Rule increases inequality; and the Proportional Change Rule keeps inequality the same. (The last scenario is like telling everyone to add a zero to all the bills in their pocket. Because you need ten $\$10$s to make one $\$100$ before the change, after relabeling, you will still need ten $\$100$s to make one $\$1000$.)
In our forthcoming manuscript, we develop a partial differential equation model for the time-evolution of income distributions in which populations have some degree of randomness in their annual raises and importantly individuals that have higher-ranking incomes are likely to have raises proportionally larger than those with lower-ranking incomes. This quantile-dependent growth rate, which we term $R(q)$, is something we can observe in income data from all over the world (see below), but is not something commonly addressed in the mathematical economics literature.
-
Tulane University
Executive Director, Murphy Institute
Professor of Economics
and Affiliate Professor of Law
Assessing quantile-dependent growth around the world
Rising sophomore Kayla Rutner aced my Statistics for Scientists class and later asked about possible research opportunities. Through the Murphy Institute we were able to sponsor her as she investigated income distribution data from around the world. In particular, she collected data from over 80 countries using the World Bank’s Poverty and Inequality Platform to assess quantile-dependent income growth both long-term and through short-term downturns and upturns in mean income.
Based on her research we compiled an app that allows for a quick assessment of a country’s mean, median, upper 10%, and lower 10% income levels over time; a country’s Gini coefficient over time; and long- and short-term estimates of $R(q)$ for each decile. One of her primary findings was that, for countries labeled “High-Income” like the US and UK, $R(q)$ was increasing in $q$ meaning that the average annual raise for people at high quantile levels is higher than those at lower levels. On the other hand, those labeled Latin America and the Caribbean tended to have decreasing $R(q)$. This pattern matched with changes observed over time in the Gini coefficients of each country, meaning that $R(q)$ is a meaningful predictive statistic in terms of income inequality change.
-
Tulane University
Economics and Finance major
Expected class of 2026
Kayla Rutner’s summer project.
Use the drop-down menu to select a country. On mobile phones, you may want to remove the legend for the graphs to display correctly. Note that you can focus on short term events by changing the “subregression” beginning and end. We will present a more thorough explanation of the methodology down the road.