Job families and income inequality

Paul Krugman has an interesting blog post today about income distributions, and why the rich tend to feel poorer than they used to. He noted in passing that he had always been taught that income distributions were log-normal for most incomes, switching over to Pareto for large incomes.

I dug in to this dataset and found an interesting follow-up tidbit. His statement about distributions seems to be correct. What’s interesting is that the cross-over point between the two seems to be happening at roughly the 75th percentile, at an income of $87.5k. Apparently incomes above this threshold behave like “large incomes,” with a power-law scaling that suggests a self-similarity of the economies of the rich to the very rich to the really very rich; whereas incomes below this threshold are following a completely different model, bunching up more towards middle values.

Here’s a graph of this income data on log-log axes, to make it clear. The Y-axis is the (decimal) log of household income, in dollars; the X-axis is the (decimal) log of the percent of society, so +2 corresponds to the poorest members of society, 1 to the top 10%, 0 to the top 1%, etc. Note that the curve is linear on its left-hand side (i.e., a power-law curve, a Pareto distribution with α = 0.56) and curves down sharply at a log-percentile of 1.39, i.e. at the 75th percentile of the distribution. The original data is available here.

Income distribution on log-log axes

This suggests that incomes in these two ranges are driven by fundamentally different dynamics, which shouldn’t be surprising. What I think is surprising is that, once upon a time, the “two dynamics” were those of earned income versus investment income, but this cutoff point seems far too low for that to be the case. Instead I suspect that we’re seeing a switch between a “professional class” — which includes much of our modern super-rich [cf. Christina Freeland’s recent article in The Atlantic, and particularly her note that today’s rich tend to be rich from earned rather than inherited or purely passive income] — and a “working class.”

The boundary isn’t the old blue/white-collar boundary; many white-collar jobs are clearly on the bottom side of the hook. (And NB that jobs can pay more than $87.5k and still be logically on the bottom end of the hook; first, actual salaries include things like regional variation, which this chart averages over nationally; and second, a job could represent e.g. the upper end of a job ladder which has a log-normal distribution, and thus be a bit above the threshold. The distribution we’re seeing here is a sum of two distributions, Pareto for jobs which pay higher on the average and log-normal for ones which pay lower)

It may be very interesting to characterize the growing income gap in our society by trying to characterize individual job ladders (i.e., sets of positions which are roughly equivalent, which individuals are expected to move across over the course of their career — although not necessarily at a single company) by their geographically-normalized income distribution. I would bet that if we compared the income distributions for a few hundred job ladders, we would find that they tended to fall into two pretty clear buckets, and that looking at the qualitative characteristics of those two buckets would tell us a lot about who is actually winning and losing in this new world. I’d bet that some of the results would be surprising, especially for jobs close to the edge — e.g., traditionally white-collar jobs now in the low bucket, or blue-collar ones in the high bucket.

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Published in: on January 14, 2011 at 11:28  Comments Off on Job families and income inequality  
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Economics thoughts

Technical rambly post.

So last night I started reading MWG on microeconomics. One of the things which struck me was their use of a rather artificial-feeling mathematical framework, with consumption being a function of prices (a vector in an L-dimensional space) and of wealth (a single real number). Various bits of math follow from the statement that consumption is homogenous of degree zero as a function of these two sets of variables, which is just the statement that prices are only meaningful relative to overall wealth.

What’s a bit unnatural is the division of price and wealth into two separate variables, and the equations all reflect this. It seems a great deal more natural to merge these into an L+1-dimensional vector, with “commodity zero” being money. This is nice both mathematically (the equations are suddenly a lot more compact) and conceptually (it makes it a lot easier to think about, say, multiple kinds of money flowing around in a system) The Walras axiom then takes the form that the aggregate consumption of money over time is equal to total wealth, i.e. ultimately people spend all of their money.

But this led me to two questions which I think still need some pondering.

  1. In this context, the Walras axiom no longer seems so obvious, especially when you consider that there could be multiple “money-like” commodities in the system. What is special about money that causes people to ultimately spend all of it? In a utility model, I could see that money would be a utility-zero commodity, so if there’s anything with positive value to spend it on you would probably do so. (At least, so long as all interactions are linear — but I think that you can prove that they always are) But this non-obviousness suggests that there may be a more interesting way to phrase the axiom which ties more directly to the way that people relate to money.
  2. Once you start to treat money as Yet Another Commodity, the arbitrariness of using it as the scale for all the other variables seems significantly more obvious. Not in the moral sense, where it was pretty obvious to begin with, but simply mathematically; the choice of a preferred axis in commodity space seems almost perverse. One interesting alternative way to model things (which fits more naturally with choice models) would be to think about pairwise exchange costs rather than overall numerical costs — i.e., to think of everything as barter, with money simply a highly fungible good. What’s interesting is that this is significantly more general than numerical costs, in the same way that choice models are more general than preference models; it lets you model things such as nonfungible goods. (Money can buy time, but can’t necessarily buy loyalty; on the other hand, loyalty can buy loyalty) I suspect that there are some interesting techniques possible here — has this area been explored?
Published in: on June 17, 2010 at 08:25  Comments (4)  
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A stupid quote

From the Washington Post today:

Authorities and people familiar with the drug trade say violence in Mexico and increased enforcement — symbolized by the Flores case — are having a dramatic effect on Chicago street sales, at least for now. The wholesale price for a kilo of cocaine — about 2.2 pounds — has spiked over the past 18 months, from $18,000 to $29,000 and often more, according to authorities.

I wonder if the unnamed “authorities” in question are being deliberately misleading, or if they simply lack the sense to notice what they just said. The increase in the wholesale price of cocaine ends up, as such increases normally do, in the pockets of the people selling it.

What they have just said is that increased enforcement has increased profits for drug lords dramatically.

Published in: on December 30, 2009 at 17:46  Comments (7)  
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More fun with explosives…

Nice column by Paul Krugman on the issue of cover-ups and Porter Goss’ performance in his first few months at the CIA.

Meanwhile, our president is informing everyone that the missing explosives disappeared a while ago (which is somehow supposed to be better?) and reminding everyone that we’ve already destroyed over 243,000 munitions.

If someone is coming at you with an axe, the fact that there are hundreds of thousands of axes in the world that they’re not carrying is not really germane to the problem.

But the President’s unofficial flaks are trying to move attention elsewhere. (NB this article’s focus is on Bush’s campaigning, not the charges against him) I suggest that we don’t let him change the subject quite so quickly. Just what has this led to as far as force protection? How many of the roadside bombs that have been killing American soldiers in the past few months have come directly out of this stockpile? How many more are to come? As pointed out recently, that’s a whole lot of explosives.

Published in: on October 26, 2004 at 11:55  Comments Off on More fun with explosives…  
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