Saturday, December 26, 2015

"Neutrality" in statistics: comparing the Palma inequality ratios of the United States with the social democracies

Image: Palma ratios--a measure of inequality--of selected countries (ordered by Palma v.3, source)

As the graph at the top of the page shows, the social democracies (marked with red squares) have lower inequality as measured by Palma ratios compared to the liberal countries, including the United States (marked with blue squares). My goal here is to argue that the social democracies really are better and limiting inequality, and since the Palma ratio is rarely used and the Gini coefficient has become the standard measure of inequality, the rest of this post is about why the Palma ratio is a better measure of inequality than the Gini.

I wrote previously about Gini coefficients and Palma ratios as measures of inequality. At that time, I noticed a nonsense conclusion someone had made: based on the fact that the pre-tax pre-transfer Gini coefficients of the United States and the social democracies are approximately equal, this writer had concluded that taxes and transfers were the only reason why the social democracies had less inequality than the United States.

Even at a glance, this simply cannot be correct. McDonald's workers in Denmark, for example, make three times the hourly wage of McDonald's workers in the United States. There's simply no way that pre-tax pre-transfer inequality can possibly be similar. Indeed--as I pointed out then--the richest 1% in the United States take home 18% of all pre-tax income, but the richest 1% in Denmark take home just 4%. Clearly, the Gini coefficients are wrong; pre-tax, pre-transfer inequality is not similar between the United States and Denmark.

This matters greatly from a social policy perspective. Taxes and transfers may indeed be effective policies for limiting inequality, but they're not the only effective policies. As I pointed out at the time, full employment is probably a more powerful tool against inequality than taxes and transfers, and I argued that inequality was too complex to capture with a single number, though the Palma ratio was probably the best option for a single measure of inequality.

Alex Cobham and Andy Sumner penned a review of the evidence against the Gini coefficient and in support of the Palma ratio. Before diving into their review, some background on inequality measures is necessary.

The Lorenz curve is simply a graph of the distribution of the wealth of a country. As you can see, perfect inequality would yeild a straight line, whereas any inequality bends the line downwards:

Greater inequality will result in a line that deviates further from the perfectly straight line running diagonally across the graph, but the Lorenz curve can also visually illustrate where inequality occurs. For example, take these hypothetical Lorenz curves:

We can see that inequality in the country represented by the green line is primarily due to the poor being very poor. The green line deviates most from the straight diagonal at the bottom of the income distribution; since the line rises so little for the first 30% of the population, it's clear that the bottom 30% are very poor relative to the standards of this country. And since the line is relatively straight after 30%, the richest 70% are fairly income equal to each other; inequality is thus caused by deprivation of the poorest 30%.

The red line, however, is nearly straight for the first 85% of the population. Since this line is so straight, it indicates that the bottom 85% are pretty equal in their share of national income. The abrupt turn upwards of the red line indicates that the richest 15% are far richer than the poorest 85%.

Finally, the country represented by the blue curve--because it does not bend as far away from the straight diagonal--has less inequality than the countries represented by the green and red lines.

As this hypothetical example shows, comparing Lorenz curves can be very valuable as Lorenz curves visually display both the magnitude of inequality and well as the points in the income distribution where inequality occurs.

Cobham and Sumner explain the limitations of the Gini coefficient:
Atkinson (1973) demonstrates just why this matters, and how it ensures that the Gini is far from a ‘neutral’ measure of inequality. He first highlights that, in comparing two countries where the Lorenz curves do not intersect, we can say--and the Gini will suffice to do so--that the country with the curve closer to the line of complete equality is more equal than the other. When Lorenz curves cross, however, things become less clear.

Atkinson presents the case of the United Kingdom and West Germany, for which the Lorenz curves then crossed at around 50% of the population. The income share of the lowest-income 50% is higher (closer to the 45-degree line) in West Germany, while that of the highest-income 50% is closer to the line in the UK--but the Gini coefficient shows the UK to be less unequal. Atkinson concludes:
Summary measures such as the Gini coefficient are often presented as purely 'scientific', but in fact they explicitly embody values about a desirable distribution of income (p.66).
Most people would agree this is a nonsense result; when more wealth is concentrated in the richest 50% in the UK, surely the UK has greater inequality. But Atkinson makes a more subtle point; inequality is a politically loaded term, and it doesn't mean the same thing to everyone.

In being somewhat difficult to explain and derive, the Gini coefficient has the aura of scientific neutrality. In reality, the Gini overrepresents inequality in the middle of the distribution and underrepresents inequality at the top and bottom. Thus, the Gini increases more for small differences in the middle of the income distribution than it increases for larger differences at the top and bottom of the income distribution. In other words, the Gini remains low for aristocratic levels of wealth at the top and destitution at the bottom, but rapidly increases due to small differences between the lower-middle and upper-middle classes.

If you agree that inequality in the United States is fundamentally a issue of an increasing concentration of wealth among the richest 1% or even 0.01%, the Gini is not a good measure since it will always underestimate inequality at the top of the income distribution. Thus, when we focus on the Gini, we applaud policies that redistribute from the upper-middle class to the lower-middle class--where there may be very little inequality to begin with--and ignore policies that transfer wealth away from the ultra-rich. However, if you believe that aristocratic concentrations of wealth among the super rich is good for society, then the Gini coefficient will be your preferred measure of inequality. Our choice of measure is necessarily a judgment of how we understand inequality and what we want to do about it; there is no neutrality in statistics.

The Palma Ratio
The Palma ratio was developed by Gabriel Palma, who noticed that the share of national income remains remarkably stable across time and around the world for the 50% of the population between the poorest 40% and 90%. Inequality is thus best measured by contrasting the poorest 40% with the richest 10%. For example, Cobham and Sumner created this graph (click for larger image):

The green lines represent the percent share of national income of the middle 50% between 40-90%; the consistency across so many countries is pretty amazing.

Much of the rest of their paper is devoted to marshalling evidence about the stability of the income share of the middle 50% between 40-90%. I will leave the interested reader to follow the link for more information. The Palma ratio is my preferred measure of inequality.

The graph at the top of the page compares Palma ratios (Palma v.1) for several countries, as well as two additional measures related to the Palma ratio: Palma v.2, which compares the poorest 40% to the richest 5%, and the Palma v.3, which compares the poorest 40% to the richest 1%. I've altered this image by highlighting the social democracies (red: Sweden, Austria, Iceland, Norway, Finland, Denmark) and the liberal countries (blue: United States, United Kingdom, Australia, Canada). Clearly, the social democracies have lower inequality as measured by the Palma ratio.

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