‘The dark matter of inequality’: Max Greenberg on his 'fair' inequality paper with Wendy Carlin

Max Greenberg, a PhD student in economics at UMass Amherst, is visiting the Stone Centre at UCL for the academic year. Max is working on a paper that introduces a new way of measuring inequality without gender and parental advantage.

‍

The 'fair' ineqaulity paper, created with Sam Bowles, Wendy Carlin, and a team of collaborators, is planned for submission in January 2027. Following Max's presentation at the Stone Centre breakfast, we caught up with him to hear more about the paper.

‍

Hi Max, thanks for joining us. Could you tell us a bit about your academic background and how you first connected with Wendy and Sam?

‍

I am currently three years into a PhD in economics at UMass Amherst. Before that I did my bachelor’s at Cornell, where I double-majored in mathematics and economics, and I also received a master’s in systems engineering there.

‍

I connected with Wendy through Sam Bowles. I took Sam’s class in the fall of 2023, my first semester of the PhD, and we started working together shortly afterwards. The following summer I ended up in Santa Fe with Sam to do some research, and Wendy happened to be visiting. That summer, Sam and Wendy decided to write up a short two-page memo imagining a four-person population made up of two pairs of brothers, asking what you could say about a Gini coefficient computed on just the income differences between the brothers. They sent it to me, I had some thoughts, and that was the genesis of the current project. I am now visiting the Stone Centre at UCL for the year.

‍

Could you talk us through the central idea of the paper, and the ‘Fair Gini Coefficient’?

‍

The insight that motivated the paper is that, if the Gini coefficient is an average over all the absolute differences within a population, you could also average over a subset of those comparisons. Imagine a complete graph of pairwise comparisons in the population. What if you compute the Gini coefficient only on the edges that connect same-sex siblings? Every person is still being compared to at least one other person, so nobody is excluded, but you disregard all the comparisons between people who don’t share the same gender or the same parents. That’s what we do. We call the resulting quantity the Fair Gini Coefficient—which is a measure of ‘fair inequality’, i.e. the amount of inequality not attributable to gender or parental advantage—and the ratio of the Fair Gini Coefficient to the standard Gini coefficient we call the Fair Gini Ratio.

‍

Why is that a useful thing to compute?

‍

The Fair Gini Ratio essentially tells you what fraction of inequality would remain, as compared to the empirical baseline, in a world where gender and parental advantage were absent. This framing links back to Rawls, and the fair equality of opportunity principle. On that view, any income differences that are due to circumstances of birth outside a person’s control, such as being born a woman and facing a lower expected lifetime income, or being born into a low-income family and having to struggle for the same advantages as wealthier peers, are normatively objectionable and should be corrected by policy. To be clear, though, we are not advocating for this or any other definition of what is ‘fair’. The label simply describes the inequality that remains once gender and parental advantage have been stripped out.

‍

What our approach does that is different from most of the inequality of opportunity or intergenerational mobility literatures is that we are not attempting to observe or control for a specific set of circumstances that the researcher has to pre-select. When you look at differences between siblings, you are controlling for everything two siblings share. That is a very expansive view of parental advantage. It is not just parents’ income or broader socioeconomic status. It is also the neighbourhood, the values instilled in you, the school you were zoned to, and everything else. Siblings share it all. Adding a same-sex condition to the comparison also controls for gender.

‍

What did you expect to find, and what did you actually find?

‍

All three of us initially expected that the Gini coefficient computed just between same-sex siblings should be substantially lower than the overall Gini coefficient. The economics and sociology literatures have spent an enormous amount of time investigating the effects of race, gender, and parental SES on earnings, and in our minds those factors should have accounted for perhaps half of measured inequality.

‍

What we found is that a very large share of inequality persists even between same-sex siblings. Across the 16 countries in our data, the Fair Gini Ratio averages around 77%. Three-quarters of our observations fall between 0.72 and 0.80, which is a strikingly tight range given that the overall Gini coefficient in these countries ranges from about 0.3 in Sweden to 0.7 in Brazil. In other words, the fraction of inequality that survives even when you compare people who share the same parents and the same gender is remarkably consistent across a very varied set of countries.

‍

That result went against our priors. It also means that a lot of the inequality we observe is driven by things same-sex siblings do not share: some combination of preferences, choices, and luck.

‍

We cannot yet say all that much about what generates the wide distribution of income differences between siblings, other than that it is not parental and it is not gender. My preferred way to describe it is some combination of luck and preferences. I steer away from the word ‘effort’, which is common in the inequality of opportunity literature, because it implies that everything comes down to willingness to work hard, and it does not. Plenty of people accept a lower income than they could otherwise fetch because they find the work in a particular profession more rewarding or interesting.

‍

Does that mean parental advantage doesn’t matter?

‍

No, and this is important not to overstate. Parental advantage is still a very large component of actual inequality. If you imagine a version of the US in which gender and parental advantage were removed, the US would move from being somewhat more unequal than the UK to being in line with liberal democracies in continental Western Europe. That is a substantial change, and we do not want to downplay it as ‘only 20%’. But nor would the US become the most equal country in the world. A little more than 75% of the inequality would still be there.

‍

Does this have implications for wealth inequality, as well as income inequality?

‍

Yes. Even though our outcome variable is pre-tax labour market earnings, which is closer to a concept of income than of wealth, parental advantage can be thought of as a form of wealth. It is a latent variable in the process we imagine generating individual incomes: all of the assets a parent is endowed with, from their income and money holdings to their home, their neighbourhood, and the school their child was zoned to. In effect, we’re asking how important the distribution of wealth in the parents’ generation is for reproducing inequalities in income in the children’s generation.

‍

How does this fit with existing research on inequality?

‍

There is a substantial body of work pointing in a similar direction. The closest cousin is the sibling correlation literature, split between economics and sociology, which simply computes the correlation between siblings’ incomes. Björklund and Jäntti, two economists at the Swedish Institute for Social Research at Stockholm University, have found brothers’ correlations in countries represented in both their dataset and ours averaging around 0.25, which broadly implies that around 75% of the variance in log earnings is due to factors brothers do not share. Similarly, Miles Corak’s 2013 paper on the intergenerational elasticity of earnings, essentially the coefficient obtained from regressing children’s income on parents’ income, finds a cross-country average of around 0.27, which implies an even lower correlation between siblings’ incomes. There are a number of prominent papers from the past 10 to 15 years that point in the same direction: if you look inside families, where everyone has the same advantages, a great deal of inequality still remains.

‍

How did you assemble the data for your study?

‍

We have a team of around 40 people who have worked on the project. Our initial aspiration was to have as wide a global coverage as possible, using both survey and administrative data. Administrative data from government sources such as tax administrations or social security registries is generally much more comprehensive and more reliable, since survey respondents often over- or under-state their incomes. As the project developed, we ended up focusing on the countries for which we had administrative data.

‍

We currently cover 16 countries across five continents: the US, Canada, Brazil, Uruguay, Ecuador, Spain, Switzerland, the Netherlands, Denmark, Norway, Sweden, Finland, South Korea, Taiwan, Australia, and New Zealand.

‍

One of the contributions we hope to make with this paper is to harmonise the samples across countries. Papers in the sibling correlation and inequality of opportunity literatures often produce quite different estimates, and part of the reason is that they define who is in the sample, and how family linkages are established, differently. We look primarily at individuals born between 1966 and 1970 plus any siblings born within four years of that range, we use pre-tax labour market earnings including self-employment income, and we define siblings as individuals who share the same mother, either from a birth registry or, where that is not available, imputed from dependent claimants on tax returns.

‍

Where does this lead you to look next?

‍

One approach I would like to pursue is to separate the component of ‘fair inequality’ which derives from differences in preferences from that which derives from luck. One way to start to get a handle on this would be to look at Nordic conscription data. In some Nordic countries, all men at 18 have to sit a set of cognitive and personality tests as part of the conscription process. I would love to see what the distribution of income between brothers who are similar versus different on those measures looks like. If brothers with very similar personalities also have very similar incomes, that would push me towards thinking preferences do a lot of the work; if they don’t, it would nudge me more towards luck.

‍

The other direction is to look at the events that seem to matter, such as choice of major, choice of career, and the nature of the first job. Undergraduates going into computer science, finance, or consulting are always racing to get the most competitive internships, and the internship largely determines the first job, and the first job largely determines what follows. What determines who ends up with what is where a lot of the answer must lie.

‍

The 75 to 85% of inequality that remains between same-sex siblings having controlled for gender and parental advantage is, to borrow an analogy from astrophysics, almost like the dark matter of inequality. We do not really know what is in it. We just know it is not the things we have mostly studied so far. That does not mean we should stop studying gender, parental SES, race, and everything else. They matter, and they may well interact with luck and preferences in ways that cannot be cleanly separated.