Friday 13 April 2018

Lorenz Curve: Hunting Wolves.

“Seek, and ye shall find.” Matthew 7:7, KJV.

Surfing the net is a peculiar pastime. Often you find absolute crap (just take my word for it). But every now and again, out of sheer serendipity, you do find genuine gems. Maybe it’s something educative or interesting; it may just make you smile.

I learned of Max Otto Lorenz (1876-1959) by chance. I don’t expect his name should ring a bell with most readers (Marxist readers least of all, but no-frills lefties aren’t exempt). That’s for several reasons; one of them is that (and I mean no disrespect to Lorenz) what little I found about him suggests he was a rather obscure American economist.

His claim to fame seems to be the invention of the Lorenz Curve (see above). Readers more attuned to what’s hot and what’s not in economics may find that name more familiar.

Lorenz’s invention proved to be important for the measurement of economic inequality (Hint: “economic inequality” is the modern equivalent of the old-fashioned “concentration of wealth”, as you’ll see next).

He introduced his invention to the world in June 1905 in a short paper entitled “Methods of Measuring the Concentration of Wealth” (Publications of the American Statistical Association, Vol. 9, No. 70, pp.209-219).

It teaches how to draw the chart above. Lorenz himself provided the data (Prussian incomes). There's nothing technical involved beyond arithmetic calculations; a garden-variety spreadsheet package comes in handy, but isn't strictly necessary. I only had to make Lorenz’s vertical axis, my horizontal axis, and his horizontal axis, my vertical axis (as is the current convention).


Okay, what does it all mean? In Lorenz’s words: “It is evident at a glance that the figures of 1901 show a greater concentration [of income] than those for 1892”. The modern and somewhat less precise way of saying that is "the rich got richer" at least in the case of Prussia. This provided evidence against what others were saying at the time (more on this below).

In my chart the yellow hashed line shows a hypothetical situation where equal percentages of the population earn equal percentages of the aggregate income: 10% of the population earns 10% of income, 51.41% of the population earns 51.41% of income, X% of the population … you get the idea. Everybody earns exactly as much as everybody else. That forms the 45° line in the chart: the description of perfect absolute equality. It's not meant to be a realistic description of anything, but only an ideal case.

The green hashed line shows another hypothetical situation: only one person earns all the income. One picks 10% of the population (making sure the one rich bastard isn’t there) and they all earn shit: 0%. Provided X% is less than 100%, the same applies to X%: they earn nothing. When one reaches 100% one must include Mr. Megabucks who earns all income: 100% earns 100% of all income. In the chart, the "inverted L" line represents the ideal case of absolute inequality.

Real-life situations (the red and blue lines) fall between those two extremes: their own shapes are "intermediate" between the 45° absolute equality line and the "inverted L" absolute inequality line. The closer they are to the yellow line, the lesser the concentration of income; vice versa, the closer they are to the green line, the greater the concentration. That’s why Lorenz concluded the way he did: the blue line (1892) is nowhere under the red line (1901). Makes sense?

The same technique can be applied if the data represented wealth levels, instead of income flows (indeed, it doesn't need to be economic data at all). 


Okay, readers might say, that shows the paper is instructive. Why is it interesting or makes one smile?

It’s interesting because the two decades from the 1890s to the 1910s saw a theoretical onslaught against Marxism. Marxism no longer was merely a theory advanced by some isolated characters: socialist parties at least partly inspired on Marx's ideas were not only appearing, but having some success. This was bound to cause concern among the literati beholden to the status quo (one can see similar examples in our own time). We’ve been discussing a particularly sensitive aspect of that: the internal dissent. However, we should not forget external critics.

For all the merits of people like Engels, Luxemburg, Lenin, Plekhanov, Marxist theoreticians of the time were unprepared to meet the external challenge. Yet, a careful examination of economics could have provided tools to counter it: the Lorenz Curve among them. That paper was as conceptually accessible to them then, as it is to us now: it’s short, written in plain language, no maths required. Even an old grunt like me could understand it.

The “oldsters” could argue something in their own defence: as it was, they had their plates full already. It's a good defence, too. We “youngsters” have no excuse. It would be unforgivable if modern Marxists repeated that failing. In the near future I’ll enjoy applying Lorenz Curve.


That paper made me smile because Lorenz discussed the flawed methods used at the time (he didn't mention it, but I suspect largely against Marxism); his curve was an improvement on them.

In particular, he mentioned one Dr. Julius Wolf, whose “method of interpretation is fallacious”. Plekhanov would have appreciated reading that as Wolf was attempting to show that wealth was, against all evidence and common sense, being diffused. The rich -- to put what Wolf was trying to show in modern speak -- were not getting richer (himself a Bernstein-Schmidt cheerleader, Wolf was arguing that -- you guessed it -- Marx was wrong).

There’s something perversely pleasurable in seeing the inept and arrogant humiliated in their own turf, probably by their own colleagues. You've gotta love serendipity.


Don’t wait for the intellectuals or we may wait forever. Commie workers also need to fight back in terms of theory. Seek and ye shall find, comrades.

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