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# Dan Klein on Me on John Cassidy on Income Inequality and Mobility

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In response to my letter on John Cassidy’s take on rising income inequality [2], my great colleague Dan Klein e-mails to me the following defense of Cassidy.  (Note: Dan is not thereby defending policies to forcibly redistribute incomes.)

RE the “costs of getting stuck” part, there is some ambiguity about what the “cost” is based on:

Framework 1:
It is the old distribution of income and I am at bottom 10% vs. It is the new distribution and I am at the bottom 10%.
If this is the “cost” in question, then you are right, the move from the old to the new has not necessarily cost me anything.

Framework 2.
I don’t clamber and I stay at the 10% mark vs. I do clamber and I move up to the 30% mark.
Here the cost of not clambering (“getting stuck”) probably is higher in the new distribution.

Because Cassidy can say he means 2, he can say that he is not dismissing the possibility that individuals’ absolute incomes can rise. He can say that it is higher, and the cost of getting stuck there is higher.

Because I’m slow, I didn’t at first get what Dan is driving at, so I asked him to explain.  He did:

Say:
In the old situation, clambering from 10 %ile to 30 % gained you \$5k/yr.
In the new situation, clambering from 10% to 30% gains you \$7k/yr.

Thus, the cost of not clambering has gone up by \$2k. Before you forwent \$5k when you didn’t clamber, now you forgo \$7k.

I wrote back in response:

Ah, I see what you’re saying – but I find it damn near impossible to imagine that that’s what Cassidy had in mind, or that that’s what his readers take from his essay.

Moreover, because the chances of successfully clambering are the same today as in the past, it would be an odd complaint indeed to say that the person who chooses today not to clamber is incurring a higher cost because he or she is thereby passing up a chance at earning an even higher income.

So we’re left with the person today who chooses to clamber but fails in the attempt – who is, as Cassidy would say, “stuck” (although “stuck” is a poor term here, when you think about it).  This person’s failure today means that he or she misses an extra \$7K of income (rather than an extra \$5K).  I suppose that this \$2K difference is in some reckoning a higher cost, but looked at ex ante it’s odd to call the situation more costly for this person.

Let’s say (for simplicity) that the chance of clambering up from the bottom (tenth) decile to the seventh decile is 50 percent.  Before the rise in income inequality the person’s expected gain from exerting this quantum of clambering was \$2,500K annually (\$5K x .5).  Now, with the higher income inequality, the expected gain has risen to \$3,500 annually (\$7K x .5).  That’s a strange sort of cost.  And it’s an even stranger sort of cost when combined with the high probability that this person’s absolute income will rise even if he or she fails to clamber out of the bottom decile.

Don

Dan replied:

Don,

I think you are probably right about what he meant and how it will be understood.

He speaks of “getting stuck”, which sort of makes it sound like not a matter of choice at all.

Still, on a technicality, I think he could be cheezily defended as I indicate. Suppose someone “gets stuck” at 10% by spending three years in Thailand lolling around the beaches and giving scuba diving lessons, rather than learning a trade that will serve him long-term back in the United States. The cost of 3 years of lolling about in Thailand is now \$7k/yr, rather than \$5k/yr, so higher.

But I agree that it would be cheezy to describe such a choice as “getting stuck”, if that is what Cassidy is doing.

/Dan

I almost always agree with Dan – he’s far smarter, much better read, and a great deal wiser than I am – but on this matter I stick to my original conclusion about Cassidy’s argument.  And I do so not only on the (firm-enough) ground that Cassidy almost certainly didn’t have Dan’s point in mind, but also – indeed, more importantly – on the ground that having an unchanged probability of securing a higher income gain is not plausibly described as a higher cost simply because the absolute size of the prospective income gain has risen.

….

Bonus academic point: when Jim Buchanan’s understanding of cost [3] is applied to the matter, the issue, I think, goes away.  Cost as Buchanan explains is the satisfaction (“utility”) that the chooser subjectively believes he or she forgoes by making a choice.  This cost exists, and is relevant, only at the moment of choice.  Does an unchanged probability of securing a higher gain in income raise the cost to someone in the bottom ten percent of choosing whether or not to exert some quantum of effort to clamber up the income distribution?  The subjective cost to the person who clambers but fails seems to be no higher than before, although the subjective cost to that person of choosing not to exert the effort to clamber does rise as a result of rise in the expected gain in income.

UPDATE: Dan’s argument (following Cassidy’s argument) presumes that incomes are somehow ‘out there,’ and then people come along and grab them.  Some people grab large incomes; some grab middlin’ incomes; some, unfortunately, manage to grab only the smaller incomes.  But when it is recognized that incomes are produced, Cassidy’s argument (as posited as a possibility by Dan) is only weakened.

Suppose that income inequality grows because Smith’s unique genius leads her to produce (say) some new commodity that, when sold to the general public, causes Smith’s annual income to rise from \$75,000 to \$1 trillion.  Once a middle-class American, Smith is now the richest person in the world.  Smith’s innovation causes income inequality to rise.  But nothing about this rise in income inequality poses for bottom-decile-dweller Jones a higher opportunity cost of failing to succeed in clambering up the income distribution.  The reason is that Jones himself, while having a chance of clambering even into the highest income decile, never had a chance of doing what Smith did.