Stasis, Churn, and Growth

Paul Krugman and Brad DeLong have criticized Tyler (original and reply) on income mobility. In an effort to clarify, let us consider some simple societies. In each society there are three families, A,B,and C, each with two generations.

In society one there is no generational mobility, each generation has the same income as the previous generation. Let’s call this society Stasis.

Society Stasis
Family Generation 1 Generation 2
A 100 100
B 50 50
C 25 25
Total 175 175


In the second society, some generations rise and some generations fall but there is no growth, let’s call this society Churn.

Society Churn
Family Generation 1 Generation 2
A 100 25
B 50 50
C 25 100
Total 175 175


Brad DeLong thinks that Churn is “unambiguously” better than Stasis but he doesn’t tell us how he arrived at this conclusion. Paul Krugman also seems (it is a bit unclear) to think that Churn is better than Stasis and he adds that anyone who thinks otherwise is anti-American.

If someone likes the idea of riches going to rags almost as much as they like the idea of rags going to riches then I can see why they would think that Churn is unambiguously better than Stasis. In economics, however, we try to evaluate outcomes with more than our aesthetic preferences or moods and when we look more carefully at the preferences of the people in these societies I see ambiguity or, to be more precise, not much to choose between Stasis and Churn.

The most obvious metric is total aggregate utility and in a static sense total aggregate utility is identical in each society and in each generation. So not much to choose between Stasis and Churn on aggregate utility grounds. What about an individual choosing which society to join from behind a veil of ignorance? Again, no go, there is no difference in expected utility between Stasis and Churn from behind the veil of ignorance.

Tyler moves beyond static utility to consider some dynamic issues which could make Churn worse than Stasis, namely “habit formation and frame of reference effects.” I can see those possibilities but in my view they don’t resolve the tie.

We might resolve the tie by adding more considerations to the model; for example, perhaps society Churn has more liberty (desert/justice etc.) and that is why it churns. In this case, I personally would break the tie in favor of Churn but then the deciding factor would have been liberty not mobility. Thus, let’s keep the focus on mobility and look at one more society.

Let us consider a third society, Growth.

Society Growth
Family Generation 1 Generation 2
A 100 200
B 50 100
C 25 50
Total 175 350


Here at last we have some non-ambiguity. Growth is better than Stasis or Churn; aggregate utility is increasing over time and indeed every family is better off in Growth than in Stasis or Churn. Notice, however, that Growth has relative stasis, that is, there is no relative generational mobility. So now we come to the crux of the issue. Suppose that you agree with me that there isn’t much to choose between Stasis and Churn and that Growth is better than either Stasis or Churn. Do you want to add some Churn to Growth? Why? If there isn’t much difference between Stasis and Churn then how can adding Churn to Growth make it better? It doesn’t and that is why economic mobility measures are overrated. What we should care about is growth.


One possibility:
1) In zero sum games, there can be no growth.

2) Status and politics are zero sum games.

3) What the academic left cares about is status and politics.

Thus they care about relative position rather than absolute position.

Is Brad DeLong to be counted among the "academic left" and if so, can you cite ways in which he displays more concern for politics or status than for growth?

I don't know Brad well enough to comment about him personally. I only know my small sample of the professoriat that I have come in contact with.

The implicit assumption that TC and AT are unwilling to explicitly assert, and PK and BDL will cheerfully smack them on the head for, is whether Stasis is plausibly due to desert vs. inherited privilege/genetics/etc. as compared to Churn. We do regard desert as an unambiguous good, yes?

The comparison isn't unambiguous - Churn could have exactly the same degree of desert and simply much more luck. But in the context of state-enforced redistribution, it is not very plausible that this is the case. Welfare states reduce the role of luck for the same reason they reduce the reward for unobservable work.

TC went closest with this point, in the post that initially provoked the hullabaloo:

"5. How much of immobility is due to “inherited talent plus diminishing role for random circumstance”? Is not this cause of immobility very different — both practically and morally — from such factors as discrimination, bad schools, occupational licensing, etc.? What are you supposed to get when you combine genetics with meritocracy? I do not know how much of current American (or other) immobility is due to this factor, but I find it discomforting that complaints about mobility are so infrequently accompanied by an analysis of this topic."

Burnishing your enlightenment-liberal cred requires rejecting inherited privilege. I don't know why TC wants to provoke left-economist advocates of higher mobility into asserting that genetics has no ethically compelling role in desert, of course they're just going to say as much if you press them, is that at all surprising? This is the crowd that finds the height tax an entertaining topic of discussion. And then they publicly wonder what, exactly, TC was trying to suggest.

TC won't say "I think the rise in immobility is due to inherited talent plus a diminishing role for luck". He'll only say "I wonder whether the rise in immobility is due to inherited talent plus a diminishing role for luck." Which is fine, I don't think TC really knows. I think we can all observe that "so what is maintaining the immobile ranking in 'Stasis', hmm?" is immediately pertinent, though.

Isn't that what AT suggests in this passage?

"We might resolve the tie by adding more considerations to the model; for example, perhaps society Churn has more liberty (desert/justice etc.) and that is why it churns. In this case, I personally would break the tie in favor of Churn but then the deciding factor would have been liberty not mobility."

It's interesting that he uses liberty as the "core" reason. If society had more churn because of its social safety net, or because it offered free education through college, would he feel the same way?

Churn and growth are both important.

A low-churn society (Stasis) either:
a) does not reward individual achievement
b) does not provide opportunities for individual achievement in equal amounts to different income levels, or
c) is stratified genetically such that individuals with a higher chance for achievement are more likely to be born into higher-income families

I don't think a) or b) can be defended as a social benefit; they warp incentives for production. c) appears to be empirically untrue ... the correlation between intelligence and wealth is not very strong. This is why churn is important: it is a symptom that markets reward achievement.

+1 If you want to think of low churn, think of the Middle Ages or of the caste system of India, or slavery in the US. Using Jon's words, no reward for individual achievement, no opportunities for individual achievement in equal amounts to different income levels.

Were those dynamic, output expanding societies. No.

Churn matters. When you don't see it, it tells you something.

And here I'd point out that there is a world of difference between low- and no-churn. No nation on earth has zero churn. It's a strawman to claim this. What the actual argument is over is whether 23% churn is better or worse than 27% churn (or insert more accurate numbers), not over whether 100% churn is better than 0%. Both would skew incentives.

Bill, you totally miss the point. Tyler's point is precisely that the *reason for the churn* is what matters, not the churn itself. Tyler would obviously agree that stasis due to the reasons you listed is unambiguously bad. You may note, however, that all of these reasons are quite far from current states of affairs in first world countries today. Which is what Tyler is trying to say.

I agree that the reason for the churn is what is important; but I don't think that distinguishes churn from growth. Both are symptoms of a well-functioning economy; neither are the goals in and of themselves. It's pretty easy to imagine a situation in which growth is positive and yet social welfare decreases. I think you could argue that much of the last decade in the US meets those criteria. So if TC's point is to focus on growth rather than churn ... I don't think it's clear that he's right. If he's just observing that churn itself is not the goal ... I think that's not very relevant to proposing pragmatic solutions to our economic problems.

Tyler specifically discusses the importance of BROAD-BASED growth

John, Re: Your statement: "all of these reasons [for churn] are quite far from current states of affairs...."

So, John, you think that Tyler supports estate taxes. Do you think he favors equal treatment of taxation from earnings from wealth versus other earned income.

We have churned through are tax system to benefit the wealthy: As for reason for churn for the wealthy, one could also be a tax system that changes to favor the wealthy over time...cap gains treatment at 15%, dividend interest taxed at 15%, sales versus income taxes, reduction of programs that benefit the poor in climbing the ladder, etc.

Also, I am sick and tired, by the way, of people saying "What Tyler is trying to say" when Tyler either doesn't say it, or doesn't say it clearly. Either he says it or he doesn't. You are not appointed as the medium to say "What is Tyler thinking when he says..." which is an abreviation for "What Tyler is trying to say." I'm impressed by neither if it has to be cloaked in ambiguity.

At least, that, I think, is what Bill is trying to say.

Isn't lower taxation of capital gains widely accepted as beneficial by economists over a broad political spectrum? Maybe not in an election year?

Oh, and by the way, John, notice that this is Alex's post. So, what you mean is Alex is trying to say what Tyler is trying to say.

It gets confusing when people try to speak through mediums.

Like: John is saying what Tyler is trying to say but which is being said by Alex who is saying what Tyler is trying to say.

1% blah blah blah.

the middle class is undertaxed. awkward fact, so far unremarked on by politicians.

Cliff, all things being equal, the average economist probably favors lower taxation of capital gains. But all things are not equal.

Cliff, "Isn’t lower taxation of capital gains widely accepted as beneficial by economists over a broad political spectrum?" No.

Think of this: one of the arguments is double taxation, ie, you tax corporate earnings at the corporate level, and dividends at the recipient level, and since the rates at the corporate level are higher, therefore you tax at a total higher marginal rate at the individual level (putting aside for the moment the fact that corporations are people (ha ha) but not putting aside that that corporations consume governmental services, and when they do not pay taxes for what they receive in roads, and some other infrastructure, some other lucky ducky does pay--but put that aside for the moment).

Is it true that there dividend rates, for example, have to be at 15% to avoid double taxation, for example.

If I invest outside of the US, the foreign coroporation may pay no US taxes at all; and when they distribute the dividend to me, I only pay a marginal rate of 15%. Or, I invest in a US company that only pays an effective rate of 5%--as many do. Where is the double taxation?

If one were in favor of avoiding double taxation, you would come up with a rule to tax the individual at the marginal rate and give a deduction for taxes paid by the corporation. If the corp pays no taxes, you pay at your marginal rate without the deduction. This, in fact, was one of the early Bush proposals, but was withdrawn at the objection of the business community.

The other argument is tax incidence, which is funny, given the above, but even funnier when you consider if I were to tax the US corp, and you maintained that the incidence of the tax fell on the shareholder, then a US corp with Foreign Shareholders would be having their foreign shareholders paying US taxes. Not so bad in my mind.

Implied in the narrative of Churn is that whether fortunes rise or fall is not entirely arbitrary. It is on some level a product of behavior we find good. Hard work, deferred gratification, cleverness, daring. Stasis seems to reward stewardship or intergenerational responsibility but if one's fortune is more or less determined by initial conditions that's less attractive to a lot of people on it's own. People like seeing the good guys win. People like feeling that fortunes are deserved. People like thinking that they have a chance of winning. People generally don't want volatility for volatility's sake, rather they use volatility as an imperfect proxy for fairness. Fairness itself is difficult to define let alone measure, but it makes sense to people that in a more fair society the interests of the less powerful will do relatively better compared to the interests of the more powerful incumbents. Thus we should expect a fair society to have more churn than an unfair society.

I agree that growth is more important but this seems like a false dilemma. I see no reason to expect that stasis or churn oriented policies are systemically pro or anti growth. Indeed there exist edge cases where growth might be a subordinate priority to either stasis or churn.

Yes, thank you. This has been simplified to the point where it becomes a strawman argument. I doubt anyone is out there arguing that Churn vs Growth is our dichotomy, and that Churn is the better of those options. Furthermore, we are apparently supposed to take for granted that Stasis is the natural order of things, and that we have to expend work to get to either Churn or Growth. I think a lot of people would argue that the default scenario is Churn, and we have work to expend on either Stasis or Growth. More sane people would just argue that this has been simplified to the point of ridiculousness, though.


Even in a scenario where fortunes rise and fall arbitrarily I think Churn is preferable to Stasis.

e.g. Would you rather participate (a) in a onetime lottery that gave you even chances of winning an annual annuity of either $1 or $1M or (b) would you choose a scheme where there was a coin flip every year for annual winnings of $1 versus $1M?

I think most people will choose the later and to me that's speaking in favor of a Churn Society even in a totally arbitrary allocation world.

You've created a case where I agree with you but I don't think it necessarily reflects the terms of the argument. With extremely high and low values I think much of my preference is based on the diminishing marginal utility of the dollar. In the static case I am choosing between almost nothing and tens of millions of dollars. In the second case by the time the chances that a 10 year old would not have at least a million dollars are (I think; back of the envelope) less than 1%. So yes like most people I would favor the random year on year allocation but only because it is more egalitarian. While there aren't a whole lot of societies that have static but small class differences this is a possible outcome space and I think it is useful to separate churn (which I think in this version we are considering over a generation length time horizon) from equality.

Would you choose any differently had the payoffs been $1000 and $100, more reasonable values?

Your scenario does not seem at all related to the discussion at hand. Yours is pure risk-avoidance.

On what other basis do you choose between two social models (Churn versus Stasis) which have equal expected-value payoffs? Given that freedom, merit, etc. are extraneous factors that do not explicitly enter Alex's model, risk-avoidance seems the only way to discriminate.

Yes, churn >> status. T this is exactly what has been said about the law too: 'give a litigant their day in court' even if the case law is against them, because once in a while you get a reversal of fortune--the 'safety valve' theory of social conflict avoidance. Better (it is said) than a "status" rule where parties know they will never win in court. Keeps the masses from rioting (or so it's claimed). The flip side of this type of economy is constant uncertainty--you never know if you'll lose your status, no pun intended.

What about an individual choosing which society to join from behind a veil of ignorance? Again, no go, there is no difference in expected utility between Stasis and Churn from behind the veil of ignorance.

That seems totally wrong. From behind a veil of ignorance I think most individuals ought to choose "Society Churn". The expected value of utility is the same but the risk of being stuck in a low utility family of a churn society is lower.

Assuming individuals are risk averse I bet they would choose Churn.

I thought that initially, but read the tables again. Churn just plays Veil of Ignorance again at the end of the first generation.

But if you are a risk-averse person and you are interested in not only your utility but your descendants', churn gives you a pretty good chance of getting near the average while stasis does not.

That said, I doubt this is the reason why people support mobility. I bet it is because they see mobility as a proxy for equality of opportunity.

But Stasis doesn't. Once stuck in a low state you are forever low.

Say, if three ancestors had played Game-Stasis at the end of "n" generations they have guaranteed utilities of 100*n, 50*n and 25*n respectively.

OTOH, Game Stasis (played long enough) would lead to every one getting 58.3 * n

Overall payoff is the same however the variance of Game-Stasis is much higher than the variance of Game Churn (tends to zero at large n)

Maybe I am not seeing the obvious......

If you factor in inheritance, churn also seems more valuable.

In static, the poor always have poor relatives.
In churn, the poor may have rich relatives.

A rich person should be pretty much indifferent to whether or not their older relatives are rich, while a poor person prefers to have the possibility of having rich older relatives.

Indeed, dispersing rich people among families would seem to better enable the churn of the meritricious as social networks will be more economically diverse. Rich kids will have poor uncles to model their future poverty upon, poor kids will have rich aunts to model their future success upon.

Re: "dispersing rich people among families would seem to better enable the churn of the meritricious as social networks will be more economically diverse."

Do you have any rich families you care to disperse to me?

This is the "most interesting" argument I have heard today.

Now, if you are in favor of randomly dispersing "rich people" to poor people as their relatives, may I suggest that we in fact do that through Uncle Sam, so you need not bother assigning your rich grandparents to me. I'll take it through inheritance taxes used to educate the poor.

I didn't mean to recommend it as a policy, merely describe it as a potential effect of a high churn society. The more diverse outcomes are within families, the greater the wealth of experience one has relatively immediate access to.

Why would dispersing rich people among families better enable the churn of prostitutes?

(look up "meretricious"


Thanks for the heads up! I was unaware of that. As the Spanish would say, I'm muy embarazada.

I can't tell if you are being clever or not.

Embarazada means "pregnant," not "embarrassed." The context would suggest that you mean embarrassed.

Given the discussion of class/caste spreading of wealth by placing rich people in various families to raise rich children - a possibly meretricious act if it were done for pay - this could also be an incredibly clever bilingual pun.

That's the joke

Well, people have defected to North Korea........

I don't think anybody misunderstood Tyler. However, many people will disagree with the notion that case A is as good as case B. If you are a supporter of equality of opportunities and do not believe in perfect inheritability of personal characteristics, you must support a society that looks like case B.

The most important line in Alex's post is this one; "We might resolve the tie by adding more considerations to the model; for example, perhaps society Churn has more liberty (desert/justice etc.) and that is why it churns. In this case, I personally would break the tie in favor of Churn but then the deciding factor would have been liberty not mobility." In other words, you are coming to the same conclusion as he is for exactly the same reasons.

The hard thing about Alex's example is the attempt to distinguish between liberty and mobility, since the former seems to be a precondition of the latter.

I don't think left concerns about mobility can be divorced from concerns about inequality. The desire for mobility is not just a desire for place swapping. It's a desire for convergence. Income convergence also generates income mobility. Relative income mobility can occur through either relocation (one for one place swapping) or repartitioning (redefining the places) or both.

To do that, one needs to account for not just mobility relative to the income of other families (place swapping/relocating), but mobility relative to the income of one's own family (repartitioning).

Society Static Convergence (Strictly Repartitioning):
Fam: Gen 1 Gen 2
A 100 75
B 50 60
C 25 40
Total 175 175

Society Rank-Churn Convergence (Repartitioning + Relocating)
Fam: Gen1 Gen 2
A 100 40
B 50 75
C 25 60
Total 175 175

Once you make the model more complex by populating the strata with multiple individuals contained within an income strata, the importance of the repartitioning aspect of income mobility becomes even more apparent.

It's silly to treat incomes as if they were simply ordinal ranks. We're not talking about going from (1, 2, 3) to (1, 2, 3) or (2, 3, 1). The quality of the ordinal ranks also changes.

Ugh, the tables broke.

The relevant patterns are as such:

Static Rankings, Converging Ranks: Going from (100, 50, 25) to (75, 60, 40)

Churning Rankings, Converging Ranks: Going from (100 50, 25) to (60, 40, 75)

By contrast, Alex offered (Static Rankings, Static Ranks) and (Churning Rankings, Static Ranks). One could fully spell out the possibility by adding in (Static/Churn Rankings, Widening Ranks).

The main idea, I guess, is that changes in relative income inequality are a form of income mobility.

Alex: I am pleased to see you lay this all out clearly in simple language. Your interpretation of what Tyler is saying is the same as my original interpretation, and I thought Tyler was making a good point. (One that could be argued with, but good nevertheless.) And I thought that Paul had totally missed the point. So it needed to be repeated clearly and simply, the way you just did.

As others here have suggested, I suspect Krugman and DeLong see churn as a proxy for equality of opportunity, which I think everyone involved in the discussion agrees is a good thing.

With only two families it's a bit hard to see, but Bayesian analysis would show a strong relation between the two.

Equal opportunity is the key point.

In a society with equal opportunities for everyone, there is churn. However, churn could also have other causes.

careful there. True equality of opportunity requires equality of conditions, no?

You gave a really poor example to prove your point. Churn is always a better society than Stasis unless this churn is dramatically high as in the example you give. The very fact that Stasis has no churn directly implies only two possible state of affairs. The society is heavily loaded against those who already have money or the society has reached such an advanced state of perfection that genes are all that matter and nothing else matters. Both are not worthy goals for any society.

But broadly the point is that mobility needs to be close to its natural level. What this natural level is a difficult question. Higher or lower means an inefficient and/or unjust society. It is plainly because this natural level is an impossible calculation that both sides can continue to rant and go home thinking they have won the argument.

For example Mr. Krugman's main grudge with America today is Inequality. That it has gone up. But it has gone up everywhere including in countries with statist and capitalist policies. In fact Inequality has fallen dramatically the most in guess which country.


Normally we draw altruistic family dynasty utility functions such that the goods are additively separable (u(income 1) + beta x u(income 2)). But my understanding is that this is done for model convenience, not necessarily because we believe the world is really like this. If the utility function is drawn in other ways (u(income 1, income 2)) then it's certainly possible to prefer churn if you want to maximize aggregate utility. This would be particularly true if there are declining marginal rates of utility type effects that push towards preferences for a diversity of goods, ie u(income 1,income 2) = (income 1+beta x income 2)^0.5

Isnt the reason that Churn it is better than Stasis is that shows that there can be movement - i.e, it isnt a class structure that perpetuate itself, but the actual working of meritocracy? Am I missing something?

OMG you guys, I would love to move to either of the societies Alex described. Either of them would be amazing!

Instead, the reality is more like this:

Family Generation 1 Generation 2
A 60 70
B 30 28
C 10 5

"Top 1% incomes grew by 11.6% while bottom 99% incomes grew only by 0.2%. Hence, the top 1% captured 93% of the income gains in the first year of recovery..."

Now redo this test following individuals instead of income classes.
Poor young people are always poor, and getting poorer (as universities+lost income absorbs most of the value of a low end 4 year degree). And rich old people are heavily subsidized by the state.

Yes, Yes, Yes

Doc, your argument that young people are poor is such a poor argument that I am surprised you made it.

Think about this: We were all young once, and we grow older with time.

That means the young poor of 10 years ago are wealthier today, and they are replaced by new poor young people, who become.... As long as there is no bulge at the young end of the distribution (suddenly MORE young people than there were, percentagewise at a different generation) his argument makes perfect sense.

Turing test attempt: Similar to how many on the right may think that if the poor remain poor, it's their own fault, I wonder if many on the left tend to think that if the rich become poor, it's their own fault. That would be a theory for why Churn would seem better than Stasis... society gives the poor a chance to become rich, and if the rich become poor (after ostensibly inheriting wealth) it's not society's problem because it shows they didn't deserve their wealth anyway.

I think it depends on how exactly they became poor. A few years ago a lot of people became poor because of George Madoff.

Some commenters seem to be assuming that Churn society values hard work more than Stasis society. That is not implied in the model at all. Imagine a Churn society where A-class generation 1 families work hard and still lose their fortune to become the poorest in generation 2.

Equality of opportunity was never part of the model. Everyone likes equality of opportunity.

Question: Churn and Stasis societies are identically unequal. But Churn provides inter-generational equality through the richesrags process. Has someone studies this kind of ergodic equality in which cross-sections are unequal, but generational averages seem more or less equal. We could create a new index, something like the ratio of the average of income inequality over time divided by the inequality of the average income over time.

Again, your thought experiments appear to actual data free and certainly do not use any comparisons and contrasts with actually existing societies in the historical record. The actual data for the last 12 years would be something like this for the U.S.:

Society Redistribution Upward Stasis/LowGrowth

Society Growth
Family Generation 1 Generation 2
A 100 175
B 50 00
C 25 50
Total 175 350

Both "sides" of this argument seemed determined to be as obtuse as possible, thus reflecting much of the "mood affiliation" that makes our national politics so nauseating.
On one side we have Tyler and Alex and others who state "We will only look at this in aggregate; in aggregate the numbers add up the same for stasis and churn, therefore you can't say one is better. We will ignore the fact that either stasis or churn involves real individual humans and policies that may lead to undesirable outcomes that aren't measured by our numbers".
Then you have Krugman and DeLong who jump up and down and scream and cry and say "Immobility is so terrible. It is so obvious that it is terrible that we will not try to explain why. We will not try to present any actual data that this is terrible, we will just resort to ad hominems."

Society X
Family Generation 1 Generation 2
A 100 300
B 50 50
C 25 25
Total 175 375

Society Y
Family Generation 1 Generation 2
A 100 125
B 50 100
C 25 75
Total 175 300

Which society is better? Which society will have higher Growth in Generations 4, 5, and 6?

Those are not questions that can be answered based on the information provided

When is an evaluative question ever capable of being answered on the basis of the information provided?

While I appreciate the attempt to clarify the discussion with some creative examples. They reinforce two major problems with this point of view. 1) ignoring the social value of liberty seems pretty drastic, I thought it was pretty important to almost every other argument i have heard this blog make. And 2) The world is nothing like churn, static or growth. The choice we are faced with is between static with modest growth for the wealthy and static with modest growth for the deserving.

What this debate is really about is leftist economists throwing in the towel. Their policies when implemented strangle growth, so the only thing left is zero sum game arguments.

It has been fascinating to see how the left almost in lockstep abhors the situation in Canada. A young person with any skill can do very well and become firmly middle class. Wages are very good, social programs can be funded adequately. And we have all the center left to left political parties working to put an end to it. The latest argument is that it ruins the economy.

I'm willing to accept the admission of defeat. No use wasting any more time on the subject.

The Left abhors Canada? In what alternate Universe? In this one the Left routinely holds Canada up as a model for the US.

The canadian left.

I think churn is probably good and probably inevitable in a free market system.

Increasing government intervention in the economy inevitably reduces churn because rent seeking and regulatory capture by existing incumbent interests kills competition to incumbent enterprises before they become a competitive threat.

Ironically more government intervention and the policies Krugman and DeLong favor are going to reduce churn. While less government intervention and the free market policies Tyler favor will increase churn.

It would be interesting to see more discussion on how government policy influences amount of churn.

This is a good economist blog arguement, neatly divorced from whatever real world growth and distribution we actually have. 50 years ago there was growth and Group B did relatively well. Now there less growth and all of it goes to Group A. That's PK's point and has been for a while. Nothing wrong with saying it because group B and C have all the wrong skills but lets not pretend he meant something different.

Churn/Stasis and growth are not independent situations. The entire discussion becomes purely academic (irrelevant) if you make that assumption.
A society without churn is one that is : a) probably controlled by elites b) has limited creative destruction. This will surely lead to lower growth.

Krugman is being his usual obnoxious self. Tyler's point was said without malice and was meant to be read in the context of an academic discussion. Two lessons :

i) Don't engage with Krugman.
ii) Keep it real. Have discussions that are not tenuously connected with reality.

It seems to me that growth doesn't eliminate the churn/statis dynamic.

Churn/stasis would (does) exist in an rising and declining economy. In fact, that dynamic may be even more important in a declining economy.

I think the lesson for all the players in this spat comes out of the comments to TC's last post. Commenters here (couple exceptions—you know who you are) are sharp and very good at keeping one of TC's feet in the door of honesty. Here he complains about Krugman being himself. Tyler should (1) ignore Krugman, or (2) call him the dick that he is—but definitely not (3) praise Krugman while getting upset when he acts exactly the way Tyler knows or should know he would.

From behind the veil of ignorance, I choose Churn. I'm shocked that so many Libertarians disagree with this. Tyler and Alex, I urge you not to persist in this silliness.

I don't get why anyone would choose Stasis either. For the rulers, maybe because it means less upheaval. But for the players in the game I don't see why Stasis ought to be any better than Churn.

Agree. But it's because I think the relevant veil of ignorance scenario is which dynasty to be the founder of.

If you don't know which family OR which generation you'll be born into, then I agree with others that under the veil of ignorance scenario you should be indifferent between Stasis or Churn.

Might churn be, in and of it self, evidence for liberty? A property you state is inherently valuable? Perhaps this is the source of Krugman & DeLong's desire to see churn in American Society? It's a proxy measurement for other valuable properties.

We appear to be talking around the point.

"There is no difference in expected utility between Stasis and Churn"

We know incentives matter. When people believe that hard work is likely to result in increased wealth/status, they will work harder. They will invent things. They will create. Expected utility will be higher.

"Churn" is the necessary consequence, or symptom, of a society that rewards hard work with wealth. It is not an end in itself (the point I think Tyler was making), but a symptom of a functioning capitalist political-economy.

On the other hand, we can easily identify the problems with a "stasis" regime: Every wealthy dynasty will eventually succumb to financial mismanagement. So, to maintain the "stasis" over multiple generations, society must actively subjugate the less wealthy cohorts, taxing them (implicitly or explicitly) in order to maintain the status of the wealthy families. This causes a pervasive sense of unfairness, a countervailing incentive that is a net drag on utility/productivity.

"Animal Spirits" by Shiller and Akerlof is the best book that I know to validate these points.

This is only true if the curn is not random. ...If people are "getting what they deserve."

That's not true. The evidence suggests that society will accept a fair amount of randomness in the actual results as long as the system is viewed as "fair".

"fair amount of randomness "

Without defining what a fair amount is, I don't think your statement really tells us much. Is a fair amount closer to 1%, 50% or 99%?

I'd say I'm decently pro-churn. Mostly because I don't think churn and growth are as independent as you present them. However, I'd say churn is a symptom, not the driver of a healthy economy.

While I'm light on numbers, I at least have some decent theory. We are unable to determine where innovation and productivity gains come from ahead of time. There is no formula, nor does it's potential appear tied to any economic class. Therefore, if you are seeking to maximize the amount of innovation and incentivize innovation through tangible returns, then you should expect innovation across the economic spectrum, which should lead to what looks a like like churn as those who innovate move up the economic ladder.

"We are unable to determine where innovation and productivity gains come from ahead of time. There is no formula, nor does it’s potential appear tied to any economic class"

This seems a very unlikely statement. I'd say that there is a far more likely chance for an economically innovative idea to come from a random member of the upper 5% than from a random member of the lower 5%. If for no other reason than it's pretty easy for a talented individual to rise out of the lower 5% fairly quickly.

Alex writes:
"In economics, however, we try to evaluate outcomes with more than our aesthetic preferences or moods ..."

What would those higher "economic" evaluations be but more aesthetic sensibilities? -- (We hope more responsible, less partial.)

I'm sorry, I don't see this model as measuring anything meaningful. Yes, I think we will all agree that in economic terms growth is better than no growth, we can also agree that water is wet, but neither conclusion is anything more than stating the self evident. Growth happens not solely a result of any single individual's efforts, but is the result of an individual interacting in a larger society (would Microsoft or Apple exist today if Bill Gates and Steve Jobs were born in Nigeria, or born women, for that matter?). Clearly individual effort has to be rewarded, but just as clearly a society that puts all the rewards of economic growth in the hands of a small subsection of the population, and then gives that subsection license to financially dominate the political process, is foreign to the idea of remaining a functioning democracy.

Churn really isn't the issue. It doesn't matter if it's the same 10,000 people, or if they turn over x percent per year. What matters is deciding if we want to live in an oligarchy or a democracy.

In a larger social context, churn does equal growth. You can't have growth without destruction, and ossified societies will generally lack the legal and social mechanism that underpins destructive growth. It's not an accident that Silicon Valley happened where it did. Smart, motivated people are everywhere, but an environment that allows (in fact, actively seeks out) ideas that will disrupt the current status quo, and contains both the hard and soft social infrastructure necessary to bring such ideas to fruition, are exceedingly rare and non consistent with a static social structure.

In an economically active society growth is connected to risk taking behavior, people taking a risk on business and or other enterprises increases the over-all standard of living through increased competition and presumably better services/goods/products/productions methods/scale/etc.

Risk-taking includes both possibilities of success and failure, as an example most small businesses either fail or remain small businesses forever, some make it big. Churn is an indicator that risk-taking behavior is taking place, that the economy is active, and that there is confidence in the economy.

Furthermore, assuming that all parts of the economy does not grow synchronously, inter-generational churn will be a natural side-effect of growth or lack of the same. As one group of people earn more money they move up a quintile, consequently another moves down. An economy in stasis could indicate that: there is little or no growth in any economic group, that all quintiles of income earners are growing harmoniously within themselves in a high growth situation, or that all the growth is happening within the top quintile which indicates possible systemic problems with the economy.

The reason churn is seen as a positive is that it indicates healthy economic activity across the economy. To answer the question why churn-causing economic activity is better than static economic activity, you will have to refer to subjects of a more political nature. Tyler mentions habit formation and frame of reference effects, two things that do play a part in diminishing the happiness acquired from increased economic status, but similar biases are the motivator for people to desire an increased economic status at all (referential preferences), and inter-generational churn tells us that our economy is working in a way that lets people act on those motivators.

Perhaps churn isn't as important as the illusion of churn.

Which would explain why poor red staters - who have no real hope in hell of ever being rich unless scratch ticket odds change immeasurably at some point in the future - keep voting Republican.

I know plenty of poor red staters who made it rich.

Oil, the great equalizer.

Which group of semi-organized gangsters they vote for doesn't have any effect on the chances that they'll become rich and they know it. They're more interested in the outcome of the Texas-Oklahoma game, the Daytona 500 and American Idol.

It's funny that people seem to think that the benefits of economic growth in the developed world are actually shared with the average family. How about we redo those models above to reflect the growth in inflation adjusted wages for the mean wage earner? Also, Churn would presumably have some non-zero level of growth, though potentially lower than Stasis. The real question isn't overall growth numbers, but rather in which situation the median wage earner is better off.

To play devil's advocate, aren't you just conveniently eliminating the possibility of the bottom tier rising faster than the top tier without impoverishing the top tier, and in so doing ignoring the traditional Rawls' argument for social justice? In other words, at least under Rawls' framework, wouldn't adding some Churn to Growth be preferable if it resulted in a distribution something like:

A - 125
B - 100
C -75.

While this would have less aggregate wealth than Growth, the least wealthy would still be in a better position than in any other scenario. At least under Rawls' theory of justice, this would be a superior outcome. Now, I think there is a viable utilitarian response to Rawls, but it seems like you have just pretended as if the leading liberal political philosopher of the last 50 years didn't defend a model in which resources were distributed in a manner that did not advance growth at all costs. If you are going to dismiss the liberal position, I think you have to address it rather than just pretending like utilitarianism is the only viable way to measure a successful outcome.

I increasingly think the framing of the options here is misleading, as only the "growth" example offers an example of a qualitative change in the positions, even though a zero sum situation can also produce qualitative changes in the positions available - by immiserating one position to the benefit of another. You can have absolute income mobility locally but not in aggregate (there can be absolute mobility within a zero sum system), even when relative mobility is zero.

If you're going to count growth as a form of income mobility (absolute mobility), then you also need to count contraction as a form of absolute income mobility. Both positive sum (universal upward mobility) and negative sum (universal downward mobility) changes are examples of absolute mobility. (And, of course, universal is a simplification. A positive sum change need not be pareto efficient). This means that redistribution is a form of absolute income mobility/churn.

Once you count redistribution/repartitioning as a form of income mobility (absolute mobility), and hence a way of churning, churn becomes much more interesting.

But churn has to be qualified. Income divergence is also a variety of absolute income mobility and hence a variety of churning.

Relative churn is just position swapping.
Absolute churn includes convergence, divergence, uniform growth, and uniform contraction.

So if we're going to count growth, or absolute mobility, as a variety of income mobility, then income inequality is subsumed under income mobility.

Then the left position becomes much clearer: it's not just an aesthetic preference for immiserating the rich and enriching the poor and the movie Trading Places. (Absolute) income mobility/churn is also a necessary feature of an income convergent society.

It doesn't matter if the economy is contracting, stagnant, or growing. If there is no absolute churn, there is no convergence of incomes.

I must be missing something in this debate, because I don't see what there is to debate. Tyler and his critics must be talking past each other.

A society with growth is better than a society with no growth, almost always. You always take the 350 society over the 175 society. There are only two exceptions to this rule. The first is a case where any one of A, B, or C (its almost always A) takes the additional growth in the 350 case AND takes what the other two classes already have, so you get something like A = 300, B = 25, and C = 25. Other than this nightmare scenario, the other exception is possibly the one commentator sry123 above raise, a static society which a small loss for the top class and a small rise for the bottom class.

Really, the interesting questions start happening when the total wealth of society contracts.

Egalitarian is a virtue in and of itself. For one thing, if too much of the wealth goes to one class they can crowd everyone else out of the market for everything. In the A = 300, B = 25, and C = 25 example, A can use their purchasing power for example to bid up the prices of houses, education, and politicians past what B and C can possibly say. So egalitarianism has a value,but unlike growth its a punctuated equilibrium. As long as inequality is kept within bounds growth should provide benefits, and its a continuum so a small increase in growth may well be worth a small increase in inequality.

Actually stability is another virtue, I think commentators are underestimating how well people, including poor people, adjust to their situations and develop workarounds as long as the situations are stable. I would put stability third behind growth and inequality, and I think a better argument with growth vs. inequality is that they differ in that small increases or decreases in growth matter to an extent that small increases or decreases in equality often don't.

It seems obvious to me that adding politics to the scenarios changes them considerably. Without some Churn the governing class will trend towards generational entrenchment.

Total income after 2 gens for a,b,c respectively

Stasis: 200, 100, 50

Growth is best for a and b, but churn is best for c.

If minimizing the worst case is the goal of society then churn is best. Otherwise go for growth.

It is hard to keep implicit assumptions about the social correlates of these idealized income distribution/growth discussions. Mine are that generation after generation of no-churn, no growth would lead to a caste-like society (in which Krugman’s poem would be apt) with feelings of resentment by lower income people and airs of superiority from higher income people and that such a society would be inferior to a pure churn. Some of these effects would be likely to persist even with growth and no mobility. Since slow growth is thought to contribute to lack of mobility, however, I fail to see why the two are place in opposition here.

When I first saw this post, I thought that Krugman and DeLong had engaged Tyler in a debate on this topic. But when I read their linked replies, I realized that they had done no such thing. Tyler's post was reasonable and put forward in the spirit of open-minded inquiry. Their responses were juvenile and condescending, not even bothering to muster an argument. Apparently they consider opposing views as being so wrong-headed and wrong-hearted that no effort must be made in countering them.

If churn is *unambiguously* better than stasis, then there should be some values of negative growth churn that is *equal* to stasis, perhaps

Family Gen A Gen B
A 100 24
B 50 50
C 25 99
Total 175 173

Take the limit over time to see what DeLong and Krugman are really advocating.

Have to disagree with the statement:

"Again, no go, there is no difference in expected utility between Stasis and Churn from behind the veil of ignorance."

With any concave utility function in which parents care about their child's welfare, and allowing inter-generational transfers, Churn will have families which smooth consumption across negative income shocks and raise overall utility. I think this is a crucial reason why Churn should be preferred to Stasis ceteris peribus.

Tabarrok and Cowen are living in a hermetically sealed ivory tower if they think that income mobility and growth can be considered as independent variables. Societies with high churn are more dynamic, more entrepreneurial, and more meritocratic. Societies with high stasis experience hereditary poverty, which breeds all of the social ills that depress growth. If poverty is expected to be transitory with a time frame of a generation or two (or less), you get better outcomes. Think incentives. That T&C don't engage with this basic feature of all human populations, and instead suggest that stasis may be preferable because the rich have formed rich habits and will be sad if they can't enjoy the same luxuries a decile or two lower*, is more offensive to my intellect than my aesthetics.

* TC: "More upward — and thus downward — relative mobility probably means less aggregate happiness, due to habit formation and frame of reference effects."

As the expected values of each individual's income in the two societies is the same, if there is constant relative rsik aversion willingness to pay for income insurance [having a welfare state] in the two societies is the same for all individuals. DeLong and Krugman, Alex and Tyler seem to be chasing an irrelevancy.

From Derek:
“Their [“leftist” economists’] policies when implemented strangle growth, so the only thing left is zero sum game arguments.”

Could we have an example of what Derek thinks are policies of "leftist" economists being implemented and growth being strangled? I'm thinking of the Clinton application of the Keynesian (generally thought of as "leftist") prescription of budget surpluses during good times with no evident strangulation of growth. On the other hand, low NGDP growth does seem to be strangling growth, but I don't attribute that policy to "leftist" economists.

Alex knows that churn is preferred because we think it reflects that things are working right.

I think libertarians can see this point intuitively. Suppose we had a list of Fortune 500 companies and we could have either churn or stasis. At first glance we don't really care because market cup is the same in either case. But we know that is the Fortune 500 never changed something is wrong with our economy. There are barriers to entry like regulation or predatory tactics or plain on thuggery keeping entrants and innovation out. This is bad.

If we don't see any social mobility then it's hard to believe we have anything close to equality of opportunity or we're getting optimal growth. You're wasting a ton of potential from the lower classes because of [insert many market failures].

And of course everyone really does love a riches to rags story.

good comment. and we're not above a bit of schadenfreude either, particularly when it happens to the rich, no?

Now you are just trying to filibuster.

I suspect Krugman has moved on.

The original Tyler piece was a defense of stasis (and status).

Reading comprehension people...the original point was not about churn as it is in the real world. It's about churn *WITHOUT* growth. Musical chairs. Churn without growth implies that someone must be getting the short end of the stick. Why is that a good thing again? It's all about whether you think we can make the poor better without making the rich worse off. Apparently some people can't shake their zero-sum mentality.

Churn/stasis and growth/stagnation are not unrelated variables. Tabarrok tries to beg the question with his toy models but it's not an impressive or enlightening effort. This is really easy stuff: consider two industrialized, rule-of-law-abiding societies. In the first, the poor have little chance of rising out of poverty and the privileged have little risk of losing their wealth. In the second, the poor have a reasonable chance of clawing their way to the middle class and the rich have a credible risk of going broke. Now think through the incentives: which society will foster more growth? A couple of years ago this would have been right in Marginal Revolution's wheelhouse and I'm not sure why things have changed around here.

Now think through the incentives: which society will foster more growth?

You're reinforcing Alex's point, not rebutting it. You're arguing for mobility on the grounds that it fosters growth. So you're agreeing with Alex that what really matters is growth, not mobility itself.

Cowen's original post argued that income mobility was over-rated and that we should be concerned about "slow growth" instead. Nowhere did he make the obvious connection between the two, and neither did Tabarrok. They have both consistently treated churn/stasis and growth/stagnation as independent variables. Nice try, but I'm not buying that "you have low growth - stop focusing on low income mobility!" is the same as "you have low growth - your low income mobility is probably contributing to the problem!".

The obverse of this alleged 'zero-sum mentality' is the mentality that believes

1. a distributional pattern which maximizes/optimizes growth is the best pattern


2. there is only one distributional pattern which maximizes growth.

A wide variety of distributions can produce the same aggregate level of wealth. There is not one best (with respect to growth/production) possible world. Among the best possible productive worlds, some worlds are better than others. Among all possible worlds, the generally best ones may not always be the most productive ones.

A spherical chicken in zero gravity is clearly superior to a spherical chicken at 1 G. Discuss.

What do you mean? An African or European chicken?

I feel like this discussion totally missed the important points.

The first important point is, money is the reward for directing talent toward valuable activities. One job pays more than another because it is important to give a person with the talent to to both jobs to do the one that pays more. "Importance" here relates to increasing the overall productive output of society.

The second important point is, talent is not conveyed from parent to offspring in a manner that consistently preserves the relative payoffs mentioned above. That is, the child of a lawyer might serve society best as a tattoo artist, or the child of a school-teacher might best be an business executive. Moreover, the current allocation of talent is far from ideal: many business executives would be better placed in lower-paying positions, being replaced by people in lower-paying positions, had everyone's talents been fully developed.

And so, the expectation is, as we become better at fully developing talent, we should find there is a lot of movement among income ranges as we survey families from one generation to another.

I thought this was the whole point. The above discussion seems to make no reference to it.

Economists on the Left often do not give enough respect to the general good that economic growth can create.

Everyone pays too much attention to Paul Krugman.

You are forgetting that parents buy their children stuff, give them gifts and often give them an inheritance. Therefore, going from riches to rags means they can still get support from the parents. Not so if your parents are rags and you are in rags as well.

If our concern is an efficient allocation of human capital then we should be concerned to the extent that the allocation of resources does not incentivize the cultivation of innate individual talent into economically beneficial skills. A caste or "stasis" society is only ideal if a child's innate abilities are perfectly correlated with those of their parents. The extent that there is variation between the innate ability of parents and their children is the extent to which "churn" is economically beneficial. We want to reward and cultivate individual ability to incentivize individual, familial, and societal investment in one's human capital. No one is advocating churn for churn sake: a world in which the children of the rich are automatically made poor is just as absurd as a world in which the children of the rich are automatically granted their parents position in the economic stratum. Growth is not a separate model, rather it is a product of some degree of churn. Absent churn, there is little reason for intelligent but poor children to invest in their individual human capital.

Thanks for the numerical example, this is helpful.

But maybe I'm missing something. I think that "churn" is unambiguously better, I guess from a forward-looking veil of ignorance argument. As long as I care about the welfare of future generations, then I would much rather be the founder of Dynasty A in the "static" society than the founder of Dynasty C. The "churn" society is much more equitable.

How did generation 2 in Stasis get there?

How did generation 2 in Churn get there?

What does this tell us about the prospects for generation 3?

Churn is only unambiguously better than stasis when the churn is associated with compensating persons according to their marginal revenue product regardless of their initial endowment of wealth or ability. Otherwise, by most objective criteria, churn is no better or worse than stasis. The simplistic of the welfare measures being the Kaldor Criterion.

Income mobility is the result of a competitive free market, not a desirable quality to be manufactured unless there are barriers to entry. The problem is that the left doesn't believe in property rights and voluntary intergenerational transfers. They see it as a source of inefficiency and inequity. It may be inefficient to endow your genetically and motivationally deficient kid with your wealth legacy, but to alter this robs the original wealth earner of property rights and the incentive to earn wealth. They will adjust their behavior around your redistribution scheme. The barriers to entry are also not as high as some think they are.

Stasis is only unambiguously better than churn if you are on top regardless of you or your children's ability. Otherwise, it's shit. (Even if you are wealthy stasis may not be optimal if your head is being lopped off by angry peasants.)

Oh, come on.

Utility is not income. Income is sometimes used as a proxy (an imperfect one). In this case, it is highly imperfect. The ability to have choices and freedom in life (which wealth gives) is valued by people.

This is silly argumentation. Re-read Amartya Sen. - "So when Cowen talks about economic mobility not mattering much 'for a given level of income', or when Tabarrok talks about 'some simple societies' with fixed levels of income, they’re taking the variable in the equation and they’re turning it into a constant. What they should be doing is looking at two societies, equal in all respects except that one is high-stasis and the other is high-churn, then fast-forwarding to see which one turns out better. The answer, of course, is the high-churn society — which means, working backwards, that if you want growth, you also want social mobility."

How did generation 2 in Stasis get their wealth?

How did generation 2 in Churn get their wealth?

What does this tell us about the prospects for generation 3?

This is what Tyler wrote in the original mobility post:

" Just look at income growth for non-wealthy families and that is more useful than all the mobility measures put together."

There is no possible interpretation of Krugman and Delong that does not make THEM ass*oles (more specifically, being guilty of kinder-garden reasoning coupled with sophomoric moral outrage), in light of the quote above.

I think Tyler already defended himself quite ably. His point is understood. That said, this post seems to raise more questions than answers. With standard Econ 101 theory of decreasing marginal utility, and allowing for intergenerational transfers, Society Churn seems quite obviously strictly better from a maximization of social utility perspective. Tyler's arguments for habit formation and frame of reference effects would seem to hold much less sway when we are talking about multiple generations as Alex is here.

Even ignoring this point, I think you and Cowen assume that the factors which create "Churn" and "Stasis" are completely exogenous to growth. That is not consistent with the argument that orthodox liberal economists like Krugman and DeLong make, so it seems like you are knocking down a strawman here. Krugman and DeLong might argue that the mobility in Society Churn will create additional growth, or that the stasis in Society Stasis leads to stagnant incomes for middle and working classes (B and C) while upper classes (A) reap the majority of the income gains. It's hard to argue with that point given we've seen it play out over the last several years. In other words, they would likely reject the major assumptions of this model.

You and TC are some seriously smart guys, so I'd have to assume you are discarding these basic points intentionally, but I can't see why?

" I’d have to assume you are discarding these basic points intentionally, but I can’t see why?"

Agreed. The assumptions here are highly restrictive, why do that? (Other than to defend the somewhat indefensible).

Oh, come on, this seems silly.

Income is not utility. There is utility from having freedom to shape your own destiny. Higher social mobility, judged by income, gives greater freedom of choice, even if aggregate income does not change.

(If there's greater social/income mobility, you have the freedom to work harder and receive more for your efforts. That choice gives you more freedom, and higher ex-ante utility). - "So when Cowen talks about economic mobility not mattering much 'for a given level of income', or when Tabarrok talks about 'some simple societies' with fixed levels of income, they're taking the variable in the equation and they're turning it into a constant. What they should be doing is looking at two societies, equal in all respects except that one is high-stasis and the other is high-churn, then fast-forwarding to see which one turns out better. The answer, of course, is the high-churn society — which means, working backwards, that if you want growth, you also want social mobility."

This looks to me a bit like Arrow-s Theorem about conflicting sets of priorities among voters.

Is it not the truth that everyone, not just Krugman, secretly wants a kind of blend of Churn and Growth where the poor get richer, some rich people get punished, and whoever is speaking ends up better off?

Since everyone clearly cares so much more about relative income than absolute income, we should start admitting that lots of economic viewpoints are really social-status disputes. Arguments about best routes to economic prosperity are simply the 19th-and-20th-century version of disputes over aristocratic rank or religious virtue. We pretend this is objective this time, but it is really all about private grudges over relative status of certain groups disguised as public debates over absolute benefits to the whole community.

The idea is that in generation 2 {100, 50, 25}, {50, 100, 25}, {50, 25, 100}, {25, 50, 100}, {25, 100, 50}, and {100, 25, 50} are all equally likely -- that wealth itself does not lead to wealth in later generations. That would be a 1/6 chance for the status quo.

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