Is The Big Problem r < g or r > g?

Two different memes about secular stagnation seem to be circulating in the econoblogosphere recently.

The first says that r < g, or will be in future, therefore the economy is dynamically inefficient, and we need government to fix this problem.

The second says that r > g, or will be in future, therefore inequality is increasing, and we need government to fix this problem.

Is this a moral panic?

[Update: soon after I posted this, Stefan Homburg emailed that he had noticed the same thing. His working paper (pdf) is now online. Stefan's figures 1 and 2 are especially interesting. It is land values that are rising, not capital. Theories of secular stagnation need to pay a lot more attention to land.]

[Make sure you put a space either side of < and > in comments, otherwise Typepad thinks it's a link.]

Comments

[Sandwichman]

Could you give some cites for the r < g meme? Haven't seen it.

[Edited to put a space each side of < , so Typepad doesn't think it's a link. NR]

[Sandwichman]

The "greater than" and "less than" symbols (which are also html tag brackets) are going to reek havoc with you comments!

[Sandwichman]

Anyway, the "big problem" (as summed up by Fred Block and Gene Burns, citing Harry Magdoff from the 1930s) is people relying on composite indexes and summaries as if they were true (rather than contingent) measures of reality. Piketty also makes this point with reference to the Gini coefficient and offers similar critiques of Cobb-Douglas, the Kuznets curve and representative agents. Taken out of context r greater than g and r less than g are meaningless.

[Tom Brown]

Nick, this is the easiest puzzle you've laid out yet: the answer is obvious! Government simple need to make r = g. :D

[JW Mason]

You are right that there is a tension, perhaps a contradiction, between the Piketty and sec stag stories. But I'm not sure this is the best way to describe it.

First of all, "dynamic inefficiency" is a story about a suboptimal consumption path. But neither of these stories are framed that way. They don't talk about utility at all. The sec stag story is that a fall in desired investment relative to consumption requires a lower interest rate to maintain S=I at full employment. If the interest rate fails to fall, the output gap will have to rise instead, until desired saving falls to a level that can be absorbed. So you can't tell this story in terms of a generic "r" -- profits are too low, but interest is too high. In Piketty's story, r covers all kinds of asset returns, and there is no independent investment function or financial intermediation -- all capital income is automatically invested. The problem in his story again isn't dynamic inefficiency (in my opinion, the concept of "utility" has nothing to contribute to this conversation, but I don't expect to convince you of that) but the changing functional and/or household distribution of income.

Despite these disagreements with your way of putting it, I think you are onto something inportant here. In sec stag, higher profits and investment would be a solution to the problem. In Piketty, they would make it worse. This contradiction deserves more attention than it's gotten.

[Avon Barksdale]

No, this is nonsense. The claim is markets work only over sets of measure zero. Come on, there is no serious discussion one can have with such a starting point. And no, we don't need to solve inequality. I am vastly unequal to Roger Federer when it comes to tennis. Society pays him very well for his efforts, and this hurts no one. He plays tennis and people voluntarily pay to watch him. Looks to me like it's win-win. There is no sense in which the world is a better place by trying to make me more equal to Roger Federer. Skills premia should not be "rectified" by some leftist clap-trap excuse. Either you think markets are a good way to organize economic behaviour or you don't.

(BTW, dynamic inefficiency requires a driving term in a differential equation to maintain the fix point. At heart it arises because there are an infinite number of agents in overlapping generation models (necessary but not sufficient for DI).There is no reason to think that the economy is dynamically inefficient just 'cause. You need a model, man!)

[Nick Rowe]

Sandwichman: the original(?) statement of the r < g problem is Samuelson 58. The most recent blogosphere discussion has been around the Eggertsson and Mehotra paper, discussed for example here by Paul Krugman. Earlier blogosphere r < g discussion was on Larry Summers.

Yes, there are lots of different r's, depending on term to maturity, risk, liquidity, etc. And lots of different g's too. And it's only in a simplified model that both are defined precisely. But I will leave it to the r < g people to argue it out with the r > g people.

[Nick Rowe]

JW: I disagree with you a little here: "The sec stag story is that a fall in desired investment relative to consumption requires a lower interest rate to maintain S=I at full employment. If the interest rate fails to fall, the output gap will have to rise instead, until desired saving falls to a level that can be absorbed."

With a high enough inflation target (or with a tax on currency, which is equivalent) we can get real interest rates low enough to eliminate the output gap. But that still leaves the problem of dynamic inefficiency, if r < g.

Avon: "No, this is nonsense." My post? Or the "r < g is a problem" people? Or the "r > g is a problem" people?

[JW Mason]

Nick-

You might be right formally, but that's not what anyone else in this conversation is talking about, I don't think. The important point is that lower real interest rates are required to reach full employment.

[JW Mason]

The "original statement" of secular stagnation is of course Alvin Hansen. Replacing the original argument with Samuelson is your own innovation.

[JW Mason]

ither you think markets are a good way to organize economic behaviour or you don't.

So we must either want state-owned airlines, or to shut down the FAA? Yet curiously, in every existing society, the fraction of economic activity organized through markets is strictly greater than zero but strictly less than one. I wonder why?

[Sandwichman]

Nick: the different r's that would seem to me to matter the most would mainly have to do with the degree of inequality of wealth. If everybody has a piece of the pie -- not necessarily the same size piece, but within reason -- then return on investment is not going to drastically concentrate wealth. What Piketty seems to be concerned about is the confluence of wealth inequality and income inequality.

Avon Barksdale: Can we extrapolate from your Roger Federer model to Donald Sterling?

[Nick Rowe]

JW: "You might be right formally, but that's not what anyone else in this conversation is talking about, I don't think. The important point is that lower real interest rates are required to reach full employment."

Hmm. You may be right. There does seem to be some muddled talk out there. But if that was the only secular problem, a higher inflation target (or NGDP target) is an easy solution.

Theories of secular stagnation go back at least to Malthus/Ricardo. But they were talking about low g. They didn't worry about r < g, IIRC. And I thought Hansen was worrying about low r, rather than r < g. AFAIK, Samuelson was the first who said that r < g is a problem, regardless of r and g.

[JW Mason]

Hmm. You may be right. There does seem to be some muddled talk out there. But if that was the only secular problem, a higher inflation target (or NGDP target) is an easy solution.

I would say that people are formalizing the problem differently from you, not that they are muddled. But I'm hardly in a position to criticize aggressive rhetoric.

I think the sec stag people think some combination of (a) higher inflation is not achievable in practice, (b) higher inflation has real costs, and (c) actuvity is not very interest-sensitive in any case. I think you are right that in a model where the interest-elasticity of expenditure was a non-issue, where inflation had no real effects, and where the central bank could always hit its NGDP target, there would be no problem of secular stagnation.

[Kevin Donoghue]

Isn't this the same question Brad DeLong is addressing when he asks: Are Piketty and Summers Reconcilable?

http://equitablegrowth.org/2014/04/12/notes-finger-exercises-thomas-pikettys-capital-twenty-first-century-honest-broker-week-april-12-2014/

[Nick Rowe]

Kevin: It is rather similar. A bit more emphasis on the question of whether r is too low or too high, than on the question of whether r < or > g.

[Min]

Well, there is more than one "r" being talked about these days. Can you specify which one you mean?

Thanks. :)

[Min]

"reek havoc"

I like it. ;) But the school marm say it's "wreak havoc". :)

[Sandwichman]

Min: those reeking havocs sure do stink, though!

[Sandwichman]

"there is more than one "r" being talked about these days."

Just wait until talk like a pirate day...

[Min]

Nick Rowe: "Theories of secular stagnation go back at least to Malthus/Ricardo. But they were talking about low g. They didn't worry about r < g, IIRC."

Gee, if they were talking about low g, that suggests that g < r. ;) And if g < r leads to a caste society, then we can get centuries of stagnation with both r and g low, can't we? (It's been done, hasn't it?)

But anyway, if a complex system has two different growth rates, especially if they affect different parts of the system, then that is potentially unstabilizing, eh?

[Nick Rowe]

Min: I would rather let the "r < g!" people argue it out with the "r > g!" people, about what precisely they mean by "r" (and "g"), and just watch from the sidelines.

[BS Economist]

This post is just really confused for at least two reasons.

First, the secular stagnationists don't think that the problem is r < g... they think that R (=0) is too low at i. Which means that raising i (or increasing demand at R) will drive down r and drive up g at R. Moving toward a situation (not necessarily getting there) in which r < g is the point. The only time when r < g in practice seems to me to be when there is explicit financial repression.

Second, there's a long run/short run confusion here. Not necessarily that you are making this mistake, but someone reading the post probably would: most interventions that people imagine in this space would tend to steepen the yield curve, but that's because they forsee growth returning and bringing r along with it (not that higher r is a goal)... the sign of r-g doesn't need to flip for that to be the case, even in the long run. To put the problem in another way, you're post is confused because it is trying to reason from a change in interest rates, which is something that in other contexts you're warning others not to do.

[Min]

Nick Rowe: "I would rather let the "r < g!" people argue it out with the "r > g!" people, about what precisely they mean by "r" (and "g"), and just watch from the sidelines."

My impression, FWIW, is that they are talking about different "r"s. In that case they may have nothing to argue about. In fact, it is quite possible to have both high inequality (r1 > g) and economic stagnation (r2 < g), isn't it?

[JW Mason]

A bit more emphasis on the question of whether r is too low or too high, than on the question of whether r < or > g.

That's right -- in the sense that a lot is a bit more than none. :-)

Min - that's right. But in any case, there are no r less than g people.

Nick is arguing that the people who are worried about secular stagnation, really *should* be worried about dynamic inefficiency. Which is potentially a useful contribution! But it seems a bit unfair of him to then turn around and criticize the stagnationists on the basis that if they adopted his proposal (which they haven't), that would put them in contradiction with some other view.

[Mark A. Sadowski]

I was getting worried that I was the only one in the entire econblogosphere who thought there might actually be a contradiction between the two memes.

https://www.youtube.com/watch?v=wlMegqgGORY

"But I will leave it to the r < g people to argue it out with the r > g people."

I think that would be a very interesting argument (provided you can get it going) because I am under the general impression that they are often the same people.

[Nick Rowe]

Mark: I had an email from Stefan Homburg very soon after posting this. He had noticed it too, and sent me a draft of his working paper that will be coming out soon.

There is something weird going on in the Zeitgeist. Especially maybe in the US? "Moral panic" is the best I can do to describe it, though I'm not sure if that is 100% accurate. Something Must Be Done. About Something. This is Something. Therefore we should do it.

[Karsten]

Nick,

I suspect there's less of a problem than you imagine. What matters for the second meme (Piketty's rising inequality) is the return, R, on the market portfolio. As far as your first meme goes, I don't know if there is a single statement of the dynamic inefficiency hypothesis (restating the definition of dynamic efficiency was one of the points of Abel et al), but certainly, if r (the risk-free rate) is less than g asymptotically, we can increase G (government consumption) via debt financing without Ricardian consequences. In fact even without raising G, if r is less than R, government can carry out a statistical arbitrage by borrowing at r and investing at R. In the limit, such a sovereign wealth fund makes a profit with probability 1. I.e. it is almost surely efficiency improving.

Tobin and others long ago pointed out that in an overlapping generations framework, R is greater than r. And empirically (i.e. in the past 100 years, in the developed world) we have R>g>r. Who knows about the future but certainly market measures of the future risk free rate (government long bonds) are lower than most people would expect for nominal growth and much lower than expected returns on real assets.

The "market risk premium" is the difference between R and r. In general equilibrium, a rising risk aversion will drive R up and r down (with g down but somewhere between the two). So high risk aversion is exactly what is required to explain both Piketty's capital-driven inequality *and* the existence of "dynamic inefficiencies" (which may or may not be curable by government intervention).

So rather than a conundrum, I looks to me like your two memes have a single, relatively well explained and understood, common cause.

[SvN]

Karsten:
Are you sure that R > g > r? My impression was g > r is a good characterization of US economic history, but not that of many other countries. Would you have a source?

[Nick Rowe]

Karsten: maybe, but I would like to see it modelled.

1. If Moneybags the capitalist is investing at R, and reinvesting all his interest rather than consuming some, and bequeathing his wealth to his heirs, who do the same, forever and ever, then won't R fall, and r fall, and R-r fall too? And g rise? It's like that old puzzle, of $1 being invested at interest in 0 AD, which would now be worth umpteen quadrillion dollars, and more than the total world's wealth. No it wouldn't be, because r would have been reduced, and g would have been increased, if that had been done.

2. If all the Moneybags as a class can get richer and richer with certainty, even if individual Moneybags dynasties lose their wealth, why can't a financial intermediary replicate the portfolio performance of the pooled moneybags and make arbitrage profits off the spread between R and r?

3. How come the government can borrow at r and invest at R, but financial intermediaries can't do the same? Governments and voters don't like risk either.

4. Demographics are changing in a big way, and it looks like it might be permanent. More people planning to retire for longer. I can see a secular story like that causing a secular drop in both R and r. I don't see any similar secular story explaining why the spread between R and r should permanently increase.

5. Compare the media (and the econoblogosphere is a medium) reception of the r > g meme to the media reception of "The Son also Rises". The latter had a much more stunning conclusion. But it made much less of a splash. This looks to me like a moral panic.

[Karsten]

SvN,

In the past I have looked at UK, Canada and the US, and the trends seemed remarkably similar. r was lower than g until 1980 or so, then above for a couple of years, followed by a long period of roughly r=g (and then the recent period of r much less than g). So on average r was less than g, and even during the Great Moderation I'd argue that r was above its equilibrium value (that's why we got the disinflation). I haven't looked at other countries, and I don't know the literature. (I wouldn't accept any argument from non-sovereign issuers though: that's just a banana republic way to run an economy).

Nick,

First, disclaimer: I haven't read Piketty. This is just how *I* see it.

1. "won't R fall, and R-r fall too, and R-r fall too"

As Krugman pointed out in a recent post, eventually there will be equilibrium between R and the Wastrels, so K/Y will stabilize as will R-r.

2. "why can't a financial intermediary replicate the portfolio performance of the pooled moneybags and make arbitrage profits off the spread between R and r?"

Anybody with sufficient access to borrowing at r can do the arbitrage. Moneybags is *already* doing the arbitrage to the extent that they can safely do it given their access to borrowing.

3. "How come the government can borrow at r and invest at R, but financial intermediaries can't do the same?"

Good question. I'd say governments can credibly claim some fixed fraction of Y indefinitely, whereas current capital represents a declining claim on future profits. The totality of all future claims on Y of current capital is finite, whereas the totality of government claims on future Y is infinite. Most future capital will be created and owned by humans who aren't even born yet, but that doesn't stop government from staking a claim to the resulting future output today. As a result, private agents are fundamentally more credit constrained in carrying out the arbitrage. There are no welfare theorems in the presence of borrowing constraints.

4. "I don't see any similar secular story explaining why the spread between R and r should permanently increase."

There is one secular force I can think of: if more capital is offshore/tax sheltered, that significantly advantages bond holdings which would tend to increase R-r. But the biggest issue keeping the risk premium high right now, I suspect, is not secular. It's that 2008 is still a recent memory for investors, especially those with fixed future liabilities.

5. "This looks to me like a moral panic."

Maybe. I have no idea. But I think the dynamics are real enough, and if you add in the inevitable secular rise in robot IP rights, land rents, etc, along with increasing off shore capital holdings, the upper bound for wealth concentration seems extremely high (assuming you can deal with the Wastrel problem via trust agreements, etc).

[Nick Rowe]

Karsten: I think the big secular picture is an interacting mix of retirement, robots, and land. As Tyler Cowen(?) said, retirements and robots will partly offset each other. Land prices are rising as r falls. This increases the wealth/income ratio, but land rents as a share of income could go either way.

"(I wouldn't accept any argument from non-sovereign issuers though: that's just a banana republic way to run an economy)."

I tend to agree. But Germany and France might be upset! ;-)

[Karsten]

Nick,

"I would like to see it modelled"

The model is in Abel et al 1989: http://abacus.bates.edu/~daschaue/abel89.pdf

See especially the simple model starting on page 12.

I could have stated point 3 more clearly...

The private sector only has its capital to borrow against. Maybe you can leverage a position in the market portfolio 2-3 times, but beyond that it gets very risky. Government can do that too, but additionally has its tax asset (which is much bigger than current K) to borrow against.

"Germany and France might be upset!"

Some people need to learn the hard way...

[Nick Rowe]

Karsten: thanks for the link to Abel et al. Looks like a tough but interesting paper. I will try to get my head around it. (But no land in their model? Tut tut!)

[Karsten]

Nick,

"land rents as a share of income could go either way"

This is further out, and very speculative, but then the asymptote matters a lot, even now...

Once wages fade as a share of income, I'd think Land rich countries like Canada would have an interest in ignoring most IP laws (just like Labour rich countries do today), and just copy the robots for free. The competitive international equilibrium is all land rents. Sooner or later the Georgists will make a comeback.

"Looks like a tough but interesting paper."

Section III is not too bad, and contains almost everything of relevance. (I suspect it's one of those papers where the initial basic model and argument (section III) were too simple for a big journal, and so it had to be dressed up and obfuscated.)

"But no land in their model? Tut tut!"

Indeed! Dynamic efficiency is all about the long run, and the long run is all about land...

[Mandos]

5. Compare the media (and the econoblogosphere is a medium) reception of the r > g meme to the media reception of "The Son also Rises". The latter had a much more stunning conclusion. But it made much less of a splash. This looks to me like a moral panic.

It is a "moral panic" in the sense that the establishment of a high-tech feudal dystopia on a planet of slums is a "moral panic".

[Herbert]

@Karsten and Nick:

Abel et al. (1989), a classic paper in the field, argue that for assessing dynamic inefficiency only the risky rate (R) matters. The riskless rate (r) is immaterial.

This is the very essence of the paper. I believe, Karsten, that you got their message wrong. Their intuition is simple: The return on the market portfolio measures the decrease in GDP induced by public deficits. Hence this risky rate is the adequate measure of the social opportunity costs of public spending. The fiscal attitude of watching the safe rate masks the level of these costs.

[Nathanael]

Don't get confused by Piketty's usage of "capital". By "capital" he means accumulated wealth.

Most of that is in the form of
(1) land (collecting rents)
(2) copyrights, patents, trademarks, etc (collecting rents)
(3) government-granted licenses and franchises (collecting rents)
(4) natural resources of a land-like character (collecting rents)
(5) paid-off equipment which continues to be useful for long periods with low maintenance: this behaves like land in the 50-year timeframe (collecting rents)

Etc. Most of Piketty's "capital" is stuff which collects rents, in economic terms.

[Karsten]

Herbert,

"The return on the market portfolio measures the decrease in GDP induced by public deficits."

What does this mean? If we have no deficits, markets will return 0%? Or maybe the risk free rate? The way I see it, expected market returns can be anything depending on risk aversion, whether you have a government or not...

"I believe, Karsten, that you got their message wrong."

No, I read the spin loud and clear. Just that their models (which I think are excellent) don't support it. In particular, the argument against social security with the flippant reference to Samuelson '79 is completely bogus. In fact, the Abel analysis supports a social security intervention, and even more so, a sovereign wealth fund. Also, their dismissal of the test "r less than g", in favor of the test "new investment less than consumed investment returns" strikes me as arbitrary (and very vulnerable to the existence of rents). At best they found some conflicting evidence on dynamic efficiency, and their model suggests all kinds of statistical arbitrage opportunities available to government.

[Andy Harless]

JW and Nick,

Larry Summers does specifically talk about the importance of r < g as an issue in secular stagnation. His argument isn't entirely clear to me, but I think the idea is something like this: When r < g, a stable Ponzi game is more profitable than real investment. Therefore, when r* < g, you get either (1) stagnation or (2) central bank policy that encourages Ponzi games (bubbles). He's a little wishy-washy, I think, about what "r" means exactly. Maybe he thinks that wishy-washiness is inherent in the way financial markets work IRL. IOW, risk isn't as well-defined as economists would like it to be. If the return on real capital is close to the growth rate, then there's an incentive to create a Ponzi game and convince people that it's less risky than real capital. And it's not always clear whether it may actually be less risky (e.g. land can be like a Ponzi game, and Nick and I will argue about how risky it is; indeed I will argue with various people, taking opposite sides of the debate depending on my mood).

[Andy Harless]

BTW I had a more succinct version of Nick's post a few weeks ago. :)

[Nick Rowe]

Andy: And I though my post was succinct. Yours is even succincter!! But yes, you beat me to this one.