Aaron Hedlund on Piketty

He writes me in an email:

I feel comfortable saying that his extensive documentation of inequality– it’s trends, composition, etc.– is a big contribution that should drive future research.

…the thesis that r > g is the explanation for inequality or an ominous predictor of future inequality is, to be blunt, ridiculous.

1) Consider the most basic economic growth model: the Solow model where households arbitrarily follow a constant savings rate rule. In that model, the long-run growth rate equals the rate of technological progress, and the rate of return to capital is constant and completely independent of that growth rate. Therefore, you could have r > g, r = g, or r < g, simply because there is NO relationship. In that model, the capital/output ratio is stable in the long-run, again regardless of what r is relative to g.

We could beef the model up a bit by allowing households to actively choose how much to save (rather than impose a constant savings rate rule on them). In that model, the economy will also get to a point with stable long-term growth where the growth rate is determined purely by technological progress. In that model under log utility, 1 + r = (1 + g)*(1 + rate of time preference). As long as people are at all impatient, the implication is r > g. Therefore, the economy will have r > g, stable growth, and a stable K/Y ratio.

The flaw with both of these models, of course, is that they are representative household models where there is no inequality. Therefore, we can go a step further and add uninsurable risk to the model (whether that be health risk, earnings risk, or any other important source of economic risk). In *these* models, households also engage in precautionary savings, so in equilibrium r is lower than it is in the rep agent models. In fact, the greater amount of risk, the more wealth inequality and the SMALLER the gap between r and g.

2) Another huge fallacy is to translate “r > g” as “the return to capital is greater than the rate of return to labor.” The notion “rate of return” indicates an intertemporal dimension: for example, if I invest $1, how much do I get back in return a year later? The growth rate of the economy is not the return to labor. In fact, the “return” to labor is static: I give up x units of time in exchange for y dollars.

The RELEVANT comparison would be to compare the rate of return on capital to the rate of return on investing in human capital (ie you go to college and then reap labor market rewards in the future). The rate of return on human capital is most definitely not just “g.” In fact, the college premium is at an all-time high, which suggests that the rate of return on human capital is quite high and very possibly higher than the rate of return on physical capital.

3) The r > g –> inequality thesis is also based on ignoring the fact that r and g are both determined in equilibrium. Here’s what I mean: it is bad economics to say “Look, r > g, therefore IF people behave in such and such manner, their wealth will grow at a higher rate than g indefinitely.” The reason it is bad economics is because you can’t take the “r > g” as given and THEN impose whatever behavioral assumptions you want. The fact is, people’s behavior affects r and g. In the heterogeneous models I mentioned above, r > g, inequality is STABLE, and the behavior of households is determined by their desire to maximize utility. If I were to go to the model and arbitrarily force the households to behave differently, then the equilibrium r would change.

Here is Hedlund’s home page.


I am unqualified to assess the merits of his argument, but his intemperance is worrying. He is an assistant professor at a third rate economics department yet he feels that his economic understanding is so far above that of many of his peers (many from first-rate departments with Nobel prizes to their name) that what they found either convincing or on balance unconvincing, he found "ridiculous". If he wants to be taken seriously he should at the very least modify his tone.

I believe you are advocating what Paul Krugman calls pulling rank. Piketty's book has revealed the intellectual bankruptcy of the left. Even Robert Solow has been hodwinked at it took someone like Hedlund to come along and show him that Solow's VERY own model disproved Piketty. It is like the child showing the Emperor has no clothes. Solow frankly has become a bit of a disgrace to the profession despite his pedigree.

I especially liked how Krugman coined that term in a post where he did it. I wonder if his memory is better than mine because he has a nobel prize or because he did better in high school.

I've seen enough to know that no one is immune and we know about the us/them hit to IQ.

I don't understand any of the points above, but I do think we just added 2 billion workers to the economy and lots of immigrants and free trade agreements not to mention a full decade and a half of constant jobless recovery from recession and a rare financial crisis. I wonder if the empirical trend underlying the market for such a book has something to do with labor supply.

The US has a critical undersupply of labour right now, not nearly enough skilled workers to do all the important new jobs in the new economy, Google or Facebook ad placement optimization for instance. The new workers added from India and China have been a godsend however the US desperately needs more immigrants to have a hope of staying competitive.

By the way I find it hard to believe Krugman even GRADUATED from High School. His intellectual level is on par with a typical 15 year old.

So the labour supply needs to be as small as possible, otherwise retarded racists like Steve Sailer lose their sh*t.

My only question would be - why blame furriners ? Why not blame high-school graduates who go out looking for jobs ? Aren't they just inflating the labour pool and making like harder for the rest of us ?

Yes I DO in fact blame the American graduate, they have wholey unrealistic assumptions on pay and career advancement which has caused employee pay to skyrocket in recent years. More immigrants to compete with these people would knock some sense of reality back into the system.

Your existence must be sad and lonely.

Yes I DO in fact blame the American graduate, they have wholey unrealistic assumptions on pay and career advancement which has caused employee pay to skyrocket in recent years. More immigrants to compete with these people would knock some sense of reality back into the system.

Thank you! I agree completely! Cannot be stated loudly or frequently enough!

Right, the size of the supply of labor is obviously a central question. One reason why Piketty's book is bigger in America than in Europe is because in Europe voters are very concerned about the size of the labor supply. Voters who understand the law of supply and demand have articulate political spokesmen like Marine le Pen and Nigel Farage.

Here in the U.S., in contrast, bipartisan elites have largely shut down public discussion of supply and demand for labor as being racist. So, Piketty's book manages to thread the needle of what's allowed to be talked about.

The US establishment thankfully understands that to compete in this new world economy we need the best and the brightest here. The typical lazy US employee needs a wake up call. Europe is being left in the dust because of increasingly anti-immigrant sentiment.

America has to get serious about efficiency if we have any hope of competing. That's why I'm releasing a disruptive new smartphone app tomorrow: Hotbunk!

In the digital sharing economy of the 21st Century, why should your bed go unused for 2/3rds of each day? With Hotbunk, you can rent out your bed for the 16 hours per day you don't need it. It's a futuristic digital marketplace for shift workers needing a mattress while you are at work.

The good thing about the sharing economy is that it turns consumption into production so employers can pay lower, more fair and competitive wages. There is hardly any need to purchase anything outright anymore you can always share consumer goods amongst others. I think this gets us back to the more realistic world in which actual ownership is reserved for the truly productive people.


Using Paul Krugman against progs/liberals is always good tactic in a rhetorical game. This move silences and embarrass them, because of... # cognitivedissonance

Accusing thoughtful, well-informated bloggers of playing a silly rhetorical game is...........#moodaffiliation

This is getting so confusing... you are not a blogger. Tyler is the blogger. Tyler did not mention Krugman... right??

Ha - the MR meta-comments are becoming even better than the real thing. JAMRC - your tone is getting uncannily close to target. I love that even Steve Sailor is jumping in. Thanks guys!

I'm not sure what you mean by "the real thing" but I am thinking about starting my own blog where I write many posts about how I possess an IQ rather to the far right side of the bell-curve. I will also include many post extrolling the virtues of having a high IQ and bemoaning the lack of discussion of IQ in the popular media. I believe a blog of this sort will be unique.

And it goes without saying I will spend a consideriable number of posts either directly or covertly chastising those who did not make the wise choice of chosing to have a high IQ and demanding that they be reduced to a state of bare subsistance, or possibly not even that.

I will start my own blog recommending affirmative action in favor of those with low-IQ. Followed by posts recommending affirmative action for those with the misfortune to be born with criminal misbehavior problems, and also the unattractive and unathletic, for whom life is so unfairly challenging.

Do you think we could be cobloggers like a Hannity and Colmbs type deal? It could be an interesting team up.

@Jonathon : It's very straight forward in economics for one economist to find a work "ridiculous" and for another to be "unconvinced" and for a third to find it "important". In apolitical topics It's usually a question of focus and self interest. Every work has flaws but the trick is to see if it has the potential to teach you something new about some corner of the economic universe. As a young economist, it is easier to focus on everything a paper/book gets wrong and all the contexts in which it is inapplicable. Usually when junior people referee papers, they reject at a higher rate. The hard part is to see what a paper gets right and to see that potential and see if you learned something from it.

If some new work supports an economists ideas and prior work, they will look slightly favorably upon it. That's just human nature. If some new work supports your politics then you can be damn sure you will support it because nothing evokes religious passion like political ideas.

Hedlund may be at a low ranked school but if he types up a note and sends it to AER or JME or similar journals and if it has sufficient merit, it will make it thorough the review process in spite of which school he is from and what credentials he has.

I disagree a bit. Something that is, on balance, incorrect, does not automatically become ridiculous. To be ridiculous an argument or line of reasoning has to not be just wrong but "invite derision or mockery; be absurd". Hedlund implies that Piketty is not just wrong but so obviously and painfully incorrect that he, and by implication Krugman, Stiglitz, Solow and just about every other reviewer, should be openly mocked for not realising it. Hedlund manages to at once elevate himself to the status of guru for seeing that which no-one else saw, and simultaneously denigrate the intellectual capacity of people who are very, very good at this stuff for not having seen it. That's both obnoxious and dangerously arrogant, regardless of whether he turns out to be correct or not. Any person with the least humility would have enough reasonable self-doubt that they would be cautious in their tone for fear they had made a mistake.

Well he *was* an assistant professor at a third rate economics department. He is leaving for mizzou this fall and will be missed by his third rate colleagues very much!

Don't worry, I'm sure you're both very clever. But so are your colleagues at other institutions so it's probably polite to give them some credit too.

Well you shouldn't assume I'm clever as I didn't say I was. I will say though that Aaron did not call Piketty ridiculous. Nor has he ever said anything pejorative to me (for whatever that's worth) about Piketty. His conclusion that a particular theoretical claim like the r>g one is based entirely on the kind of theoretical reasoning that Tyler reproduces above. Ultimately, I don't see why being you're concluding that because X person at Y esteemed university agrees that r>g causes wealth inequality that therefore everyone else is obligate to take that face value even though you yourself acknowledge you can't actually evaluate a criticism (like Aaron's) due to your ow lack of familiarity with the macroeconomics being referenced. Why even say anything at all since by your own admission you don't have the background to evaluate the argument?

Whining again.

So, you are "unqualified to assess the merits of his argument", but you still are certain that his conclusions are inappropriate. Why? Because he's "an assistant professor at a third rate economics department". Great line of reasoning!

You misunderstood what I wrote. I made no comment about the merits of his argument.

Yes, you did. You're saying that you understand the argument well enough to be certain that the conclusion "ridiculous" is inappropriate.

>He is an assistant professor at a third rate economics department

Ah, the competence from prestige argument.

So, actually, I'd argue given the audience Hedlund is presumably reaching (conservative economists) for I would instead assume that _in order for him to be taken seriously_ he needs to be engage in histrionics lest his mood affiliation be questioned.

That said, I disagree with your ad hominem. It troubles me that in a field where the total research tool outlay are a handful of journal subscriptions, a few hundred dollars worth of computer time per annum and an RA or two that arbitrary university rankings should stand in as any objective measure of a scholar's intellectual capacity.

"Voters who understand the law of supply and demand have articulate political spokesmen like Marine le Pen and Nigel Farage."

That was just hilarious. The correct phrasing is of course "voters who believe the economy is perpetually fixed in size have wildly populistic spokesmen like Marin le Pen and Nigel Farage".

Have you ever met anyone who votes for these parties? If you talk to them about supply and demand, what do you thnk they would say?

Because voters for mainstream parties are so well versed on supply and demand among other basic economic principles.

Piketty's book has more holes than Swiss cheese

Oh I never eat the stuff, the hole in Swiss cheese make me sneeze - no wonder I feel a strong reaction to this Piketty dreck. Funny though a Frenchman wouldn't consider writing on a nice sensible Camembert.

Read the Democrat's Apostle's Creed. Every "I believe..." covers ALL the ASSUMPTIONS made by Piketty.

Most theories do, including those of his critics. What none of them address is the implications of his research showing that capital to national income ratio of a country does not change much except during world wars and the years following them as countries pay down the debt they incurred fighting them.

So please explain exactly what r and g have to do with his other stats on inequality. I don't care which side you're on. Please give me a clear link using Piketty's own theoretical framework (Solow model).

I have not read his book , but I have looked at the data he presents online and there is nothing there about inequality or even r and g, just historical capital to national income ratios which the is new information that has cause all the uproar. Solow makes the connection clearest between the ratios and r and g but you must make a lot of assumptions to get from there to income inequality which am not sure I believe.

Please, I don't believe those kinds of words are really appropriate for this environment. That's gutter language.

There is no such thing as a balanced growth path. The Solow model is obviously too simple to imply anything about these patterns, but you can write a model that does carry this prediction (I'll give you a hint: it involves the elasticity of substitution between capital and labor, and skill biased technological change). But this is missing the point. The r g stuff is based on historical data and accounting, neither of which requires an economic model. The tendency of economists to fall back on babbling about theory no one outside economics understands when they see an argument they don't like is the reason people don't think our field is a science. Piketty says the same thing, and if you look at his body of work it's clear that he understands economic theory. It is a historical fact that when r is bigger than g, we see very high levels of inequality and inherited wealth. That's not a leftist statement that's a fact. And it's a new fact.

"It is a historical fact that when r is bigger than g, we see very high levels of inequality and inherited wealth. That’s not a leftist statement that’s a fact."

Have any of Picketty's critics been able to demonstrate that, as a historic matter, this is false?

Up until a few years ago, it was still common to be told in economics classrooms that the capital labor split was high immutable. I know I was told this. Obviously this has been shown to be buncombe and it is a black mark on the ability and interest of conventional economic modelling to get at distributional issues.

Rather than try and poison the well about the poison the well about the powerful new time series Piketty is producing, we should be trying to explain the time series before we congratulate ourselves for having destroyed Piketty's hypothesis. The onus is on conventional modellers to prove they have something useful.

If someone is wrong, we should not point that out until we have the right solution? I guess that's a little like mathematical proofs? Can't disprove someone else's until you prove your own? The "onus" is on us to solve the unsolvable math problems and until we do we should not comment on others' supposed proofs?

I don't want to get into a muck throwing fight here, but my original message to Tyler Cowen was a personal e-mail which I gave him permission to reproduce. To add context, I preceded my comment about the "ridiculous" r > g inequality mechanism with the following:

"I feel comfortable saying that his extensive documentation of inequality-- it's trends, composition, etc.-- is a big contribution that should drive future research."

Perhaps the word "ridiculous" was overly strong, but my underlying thoughts still stand. Piketty's book is an important work that we should take seriously. However, the thesis that r > g is the DRIVER of inequality is something that has to be justified with more than just hand waving about "rich get richer" dynamics or anything of that sort. The fact is, many workhorse macroeconomic models generate endogenous wealth distributions that do not automatically explode to limitless inequality whenever r > g.


It is perhaps unsurprising that a popular press book does not have a planner's optimal control problem in it. Have you read Piketty's other work? I'm thinking of his 2013 Econometrica article on inheritance taxation, or the 2012 one on capital taxation, etc.

More importantly, do you think anything he says in the book is inconsistent with those formal models?


Critics who haven't read the book are actually criticizing someone else's summary or interpretation of the book. Such critics should preface their remarks with "I am criticizing not Piketty's book itself (which I have not read), but what the New York Times book review says is Piketty's argument" or something to that effect.

I'm reluctant to take such criticisms very seriously.

Aaron may well have read Piketty, but it's not clear from the excerpts of his email that Tyler posted or from Aaron's comment above.

But it seems pretty clear that most of the commenters here haven't read Piketty but are predisposed against the ideas they think are in the book.

Response to Aaron:

Preface: I haven't read Piketty yet (my copy is on backorder), but I am responding to Aaron's points, not to anything others have said might be in Piketty.

Point 1: If I have $100 million in stock and the real interest rate is r, then my $100 million grows at rate r. In neoclassical growth models, the real wage grows at rate g. Hence, r > g implies real income paid to owners of capital grows faster than real income paid to owners of labor. This is true despite the ratio of physical capital to real GDP being constant.

Point 2: Any growth model that uses the Cobb-Douglas production will have a constant steady-state share of capital in national income. But the use of Cobb-Douglas is an assumption, an assumption that leads to the conclusion that inequality between capital and labor income cannot be widening.

Point 3: As Aaron aptly notes, the conclusions of macro models depend on assumptions and how the models are set up. I'm a huge fan of macro models. But I'm not sure it would be wise to use the conclusions of macro models to critique statements about inequality that are based on this new carefully constructed dataset. That said, I'll reserve judgment until I read Piketty. Perhaps others should, too.

Point 4: Aaron says the relevant comparison is between the rates of return to physical and human capital, the latter of which Aaron equates with the college premium. True, if the only inequality you care about is inequality between income paid to owners of physical capital and income paid to college-educated workers. But people who worry about inequality also care about income paid to workers lacking college education.

On Point 4: The college premium may never have been higher, but I'm not sure that proves what Hedlund wants it to prove.

That is, let's say that H1 is the median high-school educated worker's wage in 1970, and H2 is the median high-school educated worker's wage in 2014. C1 and C2 are the median college-educated workers in 1970 and 2014, respectively. The college premium has never been higher means: C1 - H1 < C2 - H2

Okay, sure. But isn't this largely because H2 C1, or at least not massively greater. On an absolute scale, if you compare "how well will I do if I go to college in 2014" to "how well will I do if I go to college in 1970," and you assume you will not be in the top 10% or so of college grads, then the answer could be "not much better."

>But people who worry about inequality also care about income paid to workers lacking college education.

So this inequality stuff is a diversion, changing the subject. Funny thing is that if someone with investment money builds an asset in the US, they employ these people. Why are people with investment money not investing in this way, in the US?

Unfortunately the answer to that question is hard, rather uncomplimentary to the political power structures on both sides of the aisle, in fact would challenge the money flows that are now going to the folks that are complaining the loudest about inequality. So it is easier to blather on about r and g than doing something that would solve the problem.

Point 1: Your $100 million grows at r only if you save 100% of it and don't consume anything from it. This is empirically false, and if the top 5% or 1% truly behaved like this in the aggregate, the impact on total capital would be enormous, thus driving down r.

Point 2: Having a steady-state capital/income ratio is not dependent on Cobb-Douglas. Having a time series for the capital/income ratio that is ALWAYS constant *is* dependent on Cobb Douglas. This distinction is key. If r > g is the CAUSE of greater inequality, then the very existence of a balanced growth path (which does not depend on Cobb Douglas) implies that r > g does not cause the K/Y ratio to explode. It's entirely plausible that some other structural factor simultaneously causes low-frequency movements in the (r - g) gap and the degree of inequality, but then we should be investigating what that factor is.

Point 3: People can completely agree with Piketty's data documentation, but you need more than just correlations to talk about causality. An internally consistent model or some other econometric analysis is therefore required.

Point 4: I was simply explaining that labor doesn't really have a rate of return. Investments have rates of return, whether that investment is in physical capital or human capital.

Similar arguments were made here:


One thing that I have found lacking in these basic solow type models is that technology and capital are considered independent from one another. In reality, when a company conducts R&D this is often done by accessing financial capital markets. Technological advancement is in part I think a function of savings or financial capital investment. I know there are other endogenous growth models that try to take a stab at this, but how do these kinds of models explain something like the huge returns to early investors of Facebook and PayPal? The owners of the financial capital yielded a huge return but not because what we would normally consider r was very large. Rather the return is due to a new technological innovation, not because of more physical or even human capital.

To clarify, the returns to owners of financial capital are not just the returns to physical capital. Rather the owners of financial capital also have a claim to the returns on new technological innovation, which often times requires savings/financial capital.

Am I missing something here?

I'm astounded by the number of people who not only *assume* that 100% is saved, but they don't even bother to state that they are assuming it. And besides "consuming" it you also have the possibility of giving it away to charity, or paying a big chunk in estate taxes when you die.

On Point 1 above, Piketty says in Chapter 10, page 351,"For example, if g=1%, and r=5%, saving one-fifth of the capital from income (while consuming the other four-fifth) is enough to ensure that capital inherited from the previous generation grows at the same rate as the economy. If one saves more, because one's fortune is large enough to live well while consuming less than one's annual rent, then one's fortune will increase more rapidly than the economy, and inequality of wealth will tend to increase even if one contributes no income from labor."

I am sorry to see Aaron Hedlund back off a bit from his original characterization of Piketty's argument as "ridiculous" because he was right. Indeed, Piketty's mistake is so elementary that one has to wonder if it really is just a mistake or if in fact it is outright dishonesty.

Every 1st-year PhD student in economics learns the Cass growth model, in which there is an interest rate that is above the growth rate but in which the economy exhibits balanced growth with everybody's income growing at the same rate. That right there is enough to disprove Piketty's assertion that r > g implies that capital's income share necessarily grows faster than average income. One counterexample is sufficient to disprove an hypothesis. In general, on the transition to the steady state capital's share may grow faster or slower than labor's share even with r > g the whole time. However, with a Cobb-Douglas production function, capital's share is constant at all times, including during the transition. The same conclusions hold for the more sophisticated endogenous growth models.

There is no way that Piketty was unaware of the foregoing points. They are simply too basic. Draw your own conclusions about him and his intellectual honesty. However, even putting that aspect of the matter aside, it remains true that Piketty's mistake is the kind that would earn him a failing grade on an examination in a 1st-year PhD macro course. Given the elementary nature of the mistake, it is quite accurate to label Piketty's argument as ridiculous, precisely as Aaron Hedlund did. The fact that some prominent economists choose to ignore the problem is a comment on them as serious scientists, not on Hedlund or his argument or his conclusion of what label to use. A distressing aspect of the economics profession is the readiness with which so many well-known economists abandon what their science tells them when the science conflicts with their political preferences. We have an example of it here.

Hmm is anyone else encountering problems with the images on
this blog loading? I'm trying to determine if
its a problem on my end or if it's the blog.
Any responses would be greatly appreciated.

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