At Vox, Dylan Matthews claims that "government is the only reason the US has more inequality than Sweden." He bases this claim on the fact that the United States has a pretax Gini coefficient equal to that of Sweden, Norway, and Denmark; Finland's pretax Gini coefficient is actually

*higher*than that of the United States. But after government taxes and transfers are accounted for, the Gini coefficients of the social democracies drop precipitously, while the United States' decreases far less:

Matthews argues that these data prove that government taxes and transfers are the "only" reasons why Norway, Sweden, Denmark, and Finland have lower inequality than the United States. Nothing else explains why the pretax/pretransfer Gini coefficients would be equal and posttax/posttransfer Gini coefficients so different. Clearly, it's only government intervention that reduces inequality.

This is analysis wrong, however, and makes little sense even at first glance. McDonald's workers in Norway and Denmark make almost three times their American counterparts. With a paucity of the minimum wage McJobs that dominate the American underclass, how can Scandinavian pretax/pretransfer inequality possibly be equivalent to the United States?

Our interpretation of these data matters greatly. If Matthews is correct, then taxes and transfers are the only useful weapons against inequality, and policies that take aim at pretax/pretransfer inequality--like full employment and laws to make unionization easier--are not worth pursuing.

But Matthews is wrong here, and the fault lies with the Gini coefficient.

Death to the Gini coefficient

Matthews is off base here because the Gini coefficient is simply a terrible way to measure inequality. Comparisons using the Gini coefficient are frequently nonsense, and this is one of those times.

Wikipedia's page on the Gini coefficient has a surprisingly thorough critique of its use. For example, here are two hypothetical countries with identical Gini coefficients and total income, yet radically different income distributions:

Per Wikipedia,

Even when the total income of a population is the same, in certain situations two countries with different income distributions can have the same Gini index...[I]n a population where the lowest 50% of individuals have no income and the other 50% have equal income, the Gini coefficient is 0.5; whereas for another population where the lowest 75% of people have 25% of income and the top 25% have 75% of the income, the Gini index is also 0.5.I think it's also worth noting that the pretax Gini coefficients of the United States, Sweden, Denmark, and Norway are just over 0.5. In other words, the Gini coefficient is so unreliable that it is unable to tell the difference between the actual pretax income distribution of several real world countries and a hypothetical situation where 50% of people have no income whatsoever.

Clearly, countries with radically different income distributions can have similar (or exactly equal) Gini coefficients, and that's exactly what's happening here. Pretax/pretransfer income distribution in Sweden, Norway, and Finland is nothing like the United States; take this chart from a lecture by Emmanuel Saez (slide 26):

The y-axis is the pretax income share of the 1% highest incomes. In the United States, the top 1% took home nearly 18% of all

**pretax**

*income; in Norway, under 11%; Finland, 8%; Sweden under 7%; and Denmark just 4%. Obviously--despite the fact that the pretax/pretransfer Gini coefficients are nearly identical--pretax/pretransfer inequality in the social democracies is vastly different from that of the United States. Without doubt, the Gini coefficient is completely useless in this situation.*

Maddeningly, no one seems interested in keeping data on pretax/prestransfer income distributions. I spent hours looking for pretax data for other points in the income distribution of Norway, Sweden, Finland, and Denmark. Unfortunately, my usual sources for this type of data--World Bank, OECD, Eurostat--only report posttax/posttransfer data (sometimes referred to as disposable income). Nevertheless, the differences between the income share of the richest 1% are stark enough to conclude that Gini coefficients are useless for Matthews' comparison (again, just 1% of Americans capture nearly a fifth of all income; the richest 1% of Danes take home under 5%). Despite what the Gini coefficients say, pretax/pretransfer wages, poverty, and inequality in the social democracies are nothing like the United States.

Matthews is correct that government taxes and transfers limit inequality in the social democracies. But so do unions (the social democracies minus Norway have collective bargaining coverage of 80-100% of all workers) and full employment (Norway's unemployment rate is about 3% and barely approached 4% during the height of the Great Recession). Obviously, collective bargaining and full employment affect

*only*pretax/pretransfer incomes; they have no effect on posttax/posttransfer income. Thus, by using misleading Gini coefficients to measure inequality, Matthews erroneously dismisses policies that really are effective against inequality.

Why is the Gini coefficient such a terrible measure?

When we speak of inequality, we're really concerned with three things. The most obvious is the difference between the rich and poor, but the gaps between the middle class and rich and the poor and middle class are very important as well. There's simply no way to capture these three concepts in a single measure.*

The gap between rich and poor is often measured by the S80/S20** ratio, which compares the highest to lowest quintiles, and the P90/P10, which compares the highest and lowest deciles. To augment these measures, the P50/P10 compares the middle decile with the lowest decile, and the P90/P50 compares the middle decile to the highest decile.

Unfortunately, it's extraordinarily cumbersome to use three measures; for this reason, I admit to using the Gini for clarity. For example, imagine how confusing this graph would be if each country had three bars:

How could you possibly make sense of a graph with three bars for each country, each measuring a different aspect of inequality? Or imagine trying to make comparisons of countries over time; if the following graph had three indicators for every country, it would be nearly impossible to read:

Clearly, even the simplest comparisons would be nearly indecipherable.

And so the Gini was created to try to capture each type of inequality: rich vs poor; middle class vs rich; and poor vs middle class. To do so, the Gini simultaneously accounts for inequality between every member of a country.

But in trying to do everything, the Gini does everything poorly, and we wind up with an imperfect measure that can lead to downright misleading conclusions. The Gini has its uses--but--use with caution. There is no substitute for carefully analyzing data and understanding the strengths and weaknesses of each tool. In social science, there is no perfect measure for anything.

UPDATE: Pretax income shares of richest 1% and S20/S80 for many more European countries here.

*The Palma ratio is a worthwhile effort at measuring inequality in a single measure. The Palma ratio is named was named in honor Gabriel Palma, who first observed that the income share of the fifth through ninth deciles is remarkably constant across the entire world. In other words, the difference in inequality between two countries is simply the difference of how the remaining income is distributed between the richest 10% to the poorest 40%. Thus, the Palma ratio compares the income share of the richest 10% to the poorest 40%.

**In this notation, S indicates a quintile (or group of 20%) and P indicates a decile (or group of 10%).

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