r > g

I have to admit that formulas leave me befuddled…

http://www.dailykos.com/story/2014/05/31/1303402/-Piketty-for-Dummies

Economics crosses my eyes, so this is a helpful post.

I think if you add some numbers to your penultimate paragraph, as you did for your third paragraph, things would be clearer.

John,
I followed up until this sentence:
“This in turn means that the ratio of capital income to non-capital income must rise, both because the capital stock is getting bigger in relative terms and because the rate of return, r, is increasing.”

Why is r increasing at this point? It seems to come from nowhere.

I understand this part of the argument fine. What I would like to know is why Piketty thinks r>g is close to inevitable for the foreseeable. That’s how it was in the 19th century, and the last 6 years seem headed in that direction is not much of a argument, and our society and economy are clearly more like the 20th century than the 19th, so I would like to see why he thinks we are fated to return to the earlier period. The majority of the population working in agriculture and related fields is also a very strong pre-20th century norm, but I don’t see it returning unless industrial civilization collapses.

piketty also needs one last element: capital has to be so effective that the real economy will substitute labour for capital even as the rental rate r increases. without this, the rate of return r in r > g will fall so fast that it will rapidly once again be equal to g, and the impact on the equilibrium K/Y ratio much reduced

that is the horror being invoked, after all – that capitalists will sit about pursuing wealth via dynasty formation rather than via employing people.

this is why arguing for an alternative interpretation of r as claims on real income streams more generally is problematic – how would one sustain the intuition of substitution?

I understood him to think that the return on capital does not increase. Rather that the return is extremly constant over time, while growth varied in the past due to wars, population growth etc. and is expected to approach a rate at or below 2%, at least in the developed world.

On consumption, my interpretation was that he thinks theres a tendency to keep consumption constant in relative terms at the top, which leaves lots of room for further accumulation without any particular skill or effort/behavioural change.

So, is the conclusion that r is relatively constant, while g varies?
I would think that relationship would be more complex. However, as far
as economics goes, I am Sargent Schultz. As I understand it in my limited way,
the capitalist argument is that r feeds back into g and as long as r increases, g will
follow. At least that seems to be the supply-side argument.

the last 6 years seem headed in that direction is not much of a argument

Martin, he’s talking about the last 50 years or so. He showed how the 20th century’s wars and policy decisions interrupted a process that resumed in 1970 or so.

I think it’s a bit strong to say that he regards r>g as “inevitable.” I’d characterize his view as: there’s nothing that stops r>g until the point JQ mentioned in the original post:

This can only stop if the stock of physical capital becomes so large as to bring r and g back into line

And, of course, Piketty also explicitly discusses how history/policy can intervene to keep this from happening.

As mbw notes, the Kos summary is also nice. I’m grateful for this line:

The first part of the book, told with numbing repetitiveness,

Piketty gets lots of praise as a writer that, at least as translated into English, seems largely undeserved. (Though his deployment of Balzac and Austen is fun and illuminating.)

We ought to at least consider the effect of “Limits to growth” on “g”. Recessions tend to be triggered by oil price spikes, which are themselves a function of oil’s declining availability.

(Note that fracking isn’t easier, it makes oil and gas available that was previously inaccessible but it also consumes more oil in the extensive drilling required.)

every equation reduces the readership by a factor of x

The econ textbook my mother used for her one economics course has no math at all. I have looked and looked and can find no numbers or formulas, nothing except a long excursion on graphs (which, incidentally, are not graphs (in the accepted sense of the term) at all–though, worse, I think there is a long excursion on the standard algebraic use of Cartesian coordinates, followed by another on the standard econ non-graph graphs–so let’s let the OP call “r > g” an equation, I say, there seems to be no reason not to). Of course, that was community college, I’m sure Harvard’s Econ 101 has a lot of real math in it, and that above the sophomore year or so economics students start using math exactly the way people in other fields do.

Piketty has more than one equation. He claims to have discovered two “Fundamental Laws of Capitalism” from which he derives his conclusions: α= r x β, and β=s/g. The inequality r>g seems to be an empirical observation, not one of the Fundamental Laws.

Six months ago, on this blog, I explained why I was skeptical.

https://crookedtimber.org/2014/04/05/piketty-on-capital-a-footnote/

I am still skeptical.

Piketty’s supporters appear to pass over the two Fundamental Laws in silence, which is to me a signal that perhaps they are not as persuasive as he thinks. Krugman’s NYRB article, for example, never mentions them.

Reviewers who discuss them are not persuaded,

e.g., James K. Galbraith,
http://economistsview.typepad.com/economistsview/2014/05/unpacking-the-first-fundamental-law.html

Justin Wolfers,
http://users.nber.org/~jwolfers/papers/Comments/Piketty.pdf

George Cooper,
http://georgecooper.org/2014/04/29/does-pikettys-r-g-hold-in-a-low-growth-world/

The blogger Matt Breunig tries to “explain” Piketty’s r > g by introducing another factor, savings – in effect concluding sub silencio that Piketty’s own explanation doesn’t make much sense.

I hasten to say that I am not remotely an economist and I have no way to judge who is right or even who is worth paying attention to and who is a crank. I take my economics a lot like I take my evolution and my climate science (and my views on dinosaurs and why airplanes stay up, for that matter) – I recognize that I personally have no business having an opinion other than one based on respect for authority and the most simplistic popular explanations.

Piketty, based on my very limited ability to understand, hasn’t made it into the group of people whose authority I tend to respect. I say this with full appreciation for the extraordinary empirical work he’s done on inequality, which has altered the debate significantly and hopefully irrevocably. But the theoretical structure he’s built on that work is not something I’m as yet willing to incorporate into my own understanding of the world.

Is r>g on a worldwide basis? I’d guess that r<<g for China, no? Does it make any difference if all parts of the planet are equally developed?

If there were a jubilee and everyone became a capital owners, would "r" be meaningful? Or must there always be people who borrow, except maybe the borrowers are only the people who happen to be corporations?

“I was speaking loosely”? On an econ-related thread, that seems to be a pretty harsh accusation. I do really like how you’re sure there really was some math in the textbook, which you have not seen and I have. This is OT though and I’m done.

I followed most of this, but then you hit me with

if the capital-income ratio goes from 4 to 6 and r goes from 2 to 5, then capital incomes goes from 8 per cent of non-capital income to 30 per cent

and I feel like I’m halfway through a logic puzzle – and the phone’s ringing. So the mathematician lives next-door to the owner of the zebra, who… damn!

The annoying thing is that I can see that the maths isn’t hard – it’s barely even maths, just some arithmetic with substitutions. I used to think I needed to learn calculus some day; I’m starting to think what I really need is just to spend a few days doing algebra worksheets, “express x^2 = 4r + 9 in terms of r”, that kind of thing. If I could look at a problem like that and think “well, obviously…”, I sense that economics would hold no fear for me.

@ John Quiggin

Thanks.

We’re there other such vast destructions of capital – before 1914-1945? Pre-industrial capital was basically land. I’m sure there was some destruction of wealth from past wars, and resulting periods where g was higher than r. Doesn’t seem to be the case over the long run. Piketty’s data doesn’t go back that far, of course, but the rationale for his estimate of g seems reasonable.

43:Kondratiev waves, short somewhat accepted, long more controversial?

If the cause of the post-WW2 prosperity was just the destruction of wealth that preceded it, did other vast destructions of wealth have similar effects?

If I remember my Piketty, been six months now, it wasn’t just the destruction of wealth, which started at WWI (Russian revolution), but the change in political dynamics and players that the destruction of existing wealth enabled. In the case of WWII, for historical and contingent reasons (Communism), the lack of a secure wealth/power base enabled egalitarian and social democratic forces. So maybe it would be a new set of oligarchs, but I could probably go through every wealth destructive epoch and tell a similar story.

But you were talking about prosperity rather than equality? The 15th Century in Europe after the Black Plague and 100 years war? The 17th century after Sengoku in Japan? Ming after Yuan?

Maybe it has to be catastrophe instead of slow decline, and resources have to be available, but you can find plenty of scholarship talking about cycles and creative destruction.

I think this was a useful post. In place of my usual rant, I thought I might offer a modest extension of the finger exercise.

Suppose that we start out in Year 1, with $400 in capital earning 5% and total income, $100, so that people net $80 of total income for consumption, and $20 (5% of 400) goes to accumulating additional capital. The capital to income ratio is 4. The growth rate of total income is 2%.

In Year 2, total income is $102, accumulated capital wealth is $420, income available for consumption is $81, while $21 is being diverted to add to capital.

In Year 20, total income is $146, accumulated capital is ~$1000. Income available for consumption has grown to $95. Capital’s claim on income (still fixed at 5%) is ~$50.

In Year 20, the Capital to Income ratio is approaching 7. The proportion of income diverted to capital accumulation has risen from 1/5th in Year 1 to 1/3rd in Year 20.

These numbers, in isolation, lay out the basis for a story of very gradual change, and not a story of immiseration. Consumption is higher after 20 years, even if a substantially larger part of income is being diverted to the further accumulation of capital.

One might ask, what do capitalists eat? (What follows is not clearly delineated in Piketty; it’s just a matter of exploring the logic of the exercise in numbers.)

If one imagines a division of society between capitalists and workers, in which the former draw on capital income for their consumption, before committing their “savings” to further accumulation (that 5%), then we ought to account for that.

Let’s imagine that the capitalists draw 2% off the top for consumption — that is, the return on wealth is actually 7%, and 5% is the income from capital dedicated to accumulating more capital.

In Year 1, everything is as before, but the capitalists take 2% of $400, or $8 for their consumption, as opposed to workers’ consumption. So the total $80 for consumption in Year 1 is divided: $8 for capitalists and $72 for workers. Capitalists are taking 28% of total income, but only 10% of total consumption.

In Year 2, capitalist consumption rises to $8.40, an increase of 5% over the previous year, in line with the increase in accumulated capital. Workers’ consumption rises, too, from $72 to $72.60 — a rise of less 1%; workers’ consumption lags behind overall growth in income.

In Year 20, capitalist consumption is ~$20.00, a bit more than 21% of total consumption, up from 10% of total consumption in Year 1, and it continues to increase in line with the accumulation of capital, at 5% per year. Workers’ consumption is ~$75 in Year 20, an increase from $72 in Year 1, but Workers’ consumption peaked around Year 12, and is on a downward trend, declining by a bit more than half a percent per year. Of nearly $150 in total income, capitalists take not quite half.

Layman, well, the bulk of the wealth of the old South was in slaves, that was completely abolished with the stroke of a pen, and much of the other wealth was destroyed in the process. Other than natural resources, mostly of value to moderns, the value of land tends to be a function of what is built on and around it, and wars do tend to be destructive of that, burning cities to the ground being a pass time that goes back to Old Testament times at least.

Bob, yes, I’m aware that there are historical examples of rapid bounce backs following partial collapses, but there are also many counter-examples, so I’m not seeing the basis for a causal inference. At the least the causal inference would have to look at other factors than the destruction of wealth itself, whether we are talking about prosperity or equality. That said, disasters obviously can increase equality. Level the city with a tidal wave, and rich as well as poor will be sifting through the ruins.

I agree that pressure from Communism helped create space for Social Democracy.

JQ: “g is defined to be the rate of income growth.”

No, g is for all practical purposes defined as GDP growth. Economists lazily identify GDP with income but it just really isn’t. Piketty actually has an interesting technical section where he explains these things, but he then goes on to ignore them. Nowhere does he come up with plausible estimates of actual income, as opposed to GDP derivatives. To just quote one example, he says that capital depreciation must be deducted from aggregate production – but then all he does is deducting a constant percentage. This is of course nonsensical given that his argument is based on the accumulated capital increasing faster than GDP – it would necessarily follow that capital depreciation must increase as a share of GDP, and in fact given r>g it wouldn’t take long until all of GDP would be swallowed up by capital replacement. That is clearly a nonsensical result and to me undermines the whole argument. If we (economy-wide) were really spending so much more on capital replacement, wouldn’t anybody have noticed?

It was earlier noted (A H 33) that r>g rests on the assumption that capitalists save all their income, obviously an unrealistic assumption but also one that would lead to the problem explained above, that depreciation becomes way too expensive. Contrary to A H (and Piketty), capital accumulation at rates much higher than g cannot give rise to any kind of steady state.

In math,

r=(m/s)*g, where m is capital’s share. s is saving rate.

r-g=((m/s)-1)*g.

K/Y=s/g.

Initially r=g, so we have m=s. Then get r>g. So either s went down or m went up. If m went up, capital’s share has increased. Done (although we could’ve just assumed that, we don’t need anything about K/Y here). If s went down then K/Y decreased but we observe K/Y going up. Contradiction. Hence, capital’s share went up.

Now the other way. If K/Y went up then either s went up or g went down. If g went down and initially r=g, then m=s, so r-g=0 doesn’t change. But now we’re supposed to have r>g, so it can’t be g going down (at least not by itself).

So it has to be s going up. So all this inequality is caused by the saving rate going up (note it doesn’t matter what assumptions you make about who saves and who doesn’t, that’s extra), at least assuming you start with r=g.

I blogged a similar analysis about r>g, with more numbers and a few graphs:
http://gropingtobethlehem.wordpress.com/2014/05/01/spreadsheeting-rg/

It includes a look at the impact of capitalists’ consumption on the balance between wages and rents.

Also, I think that outside the case where initially r=g (?, in a bit of a hurry, have to think about it), the initial K/Y will matter, and it ceases to be a “must” increase, but becomes a “may” increase.

Suppose initially
capital’s share = .16, K/Y=4, g=.03, s=4*g=.12, so r-g=.01

Then
capital’s share=.16, K/Y=6, g=.006667, s=6*g=.04, so r-g=.02

So we can have a case where K/Y is going up, r-g is going up, but there is no change in capital’s share (of course can adjust to make it go down)

Off the top of my head, I think you might be thinking of Herman Kahn, who is mostly known as a military strategist and futurist, but whose ideas concerning economic growth were very much like those you describe.

“Layman, well, the bulk of the wealth of the old South was in slaves, that was completely abolished with the stroke of a pen, and much of the other wealth was destroyed in the process.”

True, and I imagine the result was decreased income inequality across the population of the old South.

“Ronan, if the only way to increase equality is light the torches of war or pray for natural disaster, we really have to ask whether that game is worth the candle.”

You don’t need the war, or a natural disaster. Just a mechanism for prying some of the wealth away, and redistributing it. Piketty suggests a wealth tax.

And if you let me change the saving rate, then we can have inequality decrease, even if K/Y is going up, r-g is going up and initially r=g.

Initially: r=g=.1, K/Y=4, capital’s share is .4, which is also the saving rate.

Then: r=.06666, g=.033333, K/Y=6, capital’s share is still .4 (easily tweaked to make it less), and the saving rate is .2 (calibrated to the long run condition that K/Y=s/g, which is of course another assumption we could drop giving us even more degrees of freedom)

There just isn’t a “must” here anywhere. Almost.

IF r goes up and K/Y goes up then capital’s share goes up. Of course, that’s just restating the definition of what a capital share is.

Ok. IF initially r=g, K/Y goes up, r-g goes up, we keep saving rate constant AND assume steady state, then capital’s share must go up. But that’s a lot more than just “if r-g goes up, capital’s share goes up”.

AH@33 “The annoying part about about r > g being so important is that it rests on two assumptions that are rarely made clear. These assumptions are 1) that capitalists save all their money and ..”
This does not seem to be the case. 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.”

Seth Ackerman in his Jacobin review calls r ‘raw’ rate of return and says that it has been steady for centuries. Browsing through ‘A nation deep in debt: the financial roots of democracy’ I find on page 93 ‘Then in 1482, Venice attempted to revive the old idea 0n a clean state,… Interest rate was again set at the magic rate of 5%…”. Can somebody comment on this 5%?

43: this is interesting, but I don’t believe in the bit about building up technology in periods of low aggregate demand – I’d rather expect the opposite. Investment is precisely what you need if you’re an inventor, and productivity gains are more likely to happen when you’re working near capacity (if you’re not, why bother?).

In general, I don’t buy the “wealth destruction” thing either. You couldn’t have a fortune based on motor buses in the UK in 1914 because that wasn’t a thing; you could in 1922 and people were all het up about the hordes of dangerous drivers and the brash nouveaux-riches who employed them. The 1920s saw a long productivity surge based on the high technology of the time. You couldn’t have a fortune based on radar or jet engines in 1935 because neither of them existed yet; by 1945 you most certainly could and some people did. Who ended up with the capital investments and technological achievements, well, there’s a whole other question, but the point isn’t *which* capitalists, though, is it?

“The history of all hitherto existing society is the history of class struggles” is like the important first step toward understanding.” I do not wholly disagree, but the history of inequality is also the history of states trying (often failing) to keep a balance between the wealth-owners and the rest. r may be larger than g for most of history, but it mostly never quite runs right out of control because some political limit is imposed. Usually by either periodic forced redistributions or be keeping some large share of capital out of the market. The books focus on the catastrophes, but the periods in between when the balance was more or less kept are just as instructive.

#62 Ze Kraggash

Productivity is the game. It’s close to “technological advance”, but it can be achieved without any technological advance, just by ways of organizing production, creating incentives, etc.

Yes. I think he has only part of the story. If you find improved ways to organize production at a constant rate, but sometimes you don’t get to actually spread them through the economy because something stops you, then when you actually get the chance to increase productivity then you can increase fast for awhile. But then you start running out of ideas, and productivity growth slows to the rate that you actually come up with new stuff as you go.

If you get a new way to organize production that works in one area, you can spread it wherever it works — when the economy is ready to improve. It isn’t just technological gadgets.

#67 Alex

this is interesting, but I don’t believe in the bit about building up technology in periods of low aggregate demand – I’d rather expect the opposite. Investment is precisely what you need if you’re an inventor, and productivity gains are more likely to happen when you’re working near capacity (if you’re not, why bother?).

I thought the theory was a bit weak there. The evidence I remember was a bunch of lognormal graphs of national GDPs, that appeared to be straight lines with occasional deviations downward, that then rose back to the straight line. Never a deviation above the line that then drifted back down to it. But the data from communist economies was likely falsified. There may be a psychological tendency to see graphs that way. The author may himself have consciously or unconsciously falsified his graphs a bit. It doesn’t have to be true just because he printed it.

How much of our productivity improvement depend on big expensive innovations, and how much on lots of little things? Recently we have paid attention mostly to the big breakthroughs. A new graphics card that for $200 gives you graphics better than ever before. Prius. Iphone. Fracking.

But a normal chemical engineer, running the same chemical plant week after week, may increase productivity by 1% to 5% per year, just doing his job. That sort of thing adds up. And he doesn’t stop improving things just because the plant isn’t running at full capacity. It’s his job. He’ll keep doing it until he’s fired.

Just maybe it’s the big expensive projects that tend to be cancelled or delayed in bad times, and often they don’t pay off in the short run even when they proceed to completion. But attempts to improve efficiency and reduce waste don’t stop in recessions — if anything they might intensify.

I can’t argue that he’s completely correct, but as a first approximation it might fit better than you’d expect.

Thanks to JQ and the various commenters here. A good review/aid to my understanding.

One question – If we accept r>g does it follow then, that if I’m a “non-wealthy” person, my best path to wealth creation is simply to comsume less than I earn, which would mean over some period of time I should benefit from r>g at a compounding rate as I continue to save.

Collectively, obviously this is impossible, but individually it seems to suggest thrift as a path to wealth, which isn’t really un-true but its not affirmatively true either.

Trader Joe @ 1:33 pm

Piketty gloss on history suggests that the effective path to wealth is inheritance: choose ancestors, who own appreciating wealth claims and can leave them beneficially to you.

@78 BW

Yes, that follows, since its the power of compounding that’s doing most of the heavy lifting in wealth creation.

That said, someone has to be the “zero” ancestor who dies with something to pass along and that person must have done so by consuming less than they earned….it could be they innovated and earned excess rents from their labor or skill, it could be he was a miser and consumed little – whatever the cause, someone has to provide the first inheritance that subsequent generations can compound.

In Piketty’s framework, the capital to income ratio β will rise whenever it is less than s/g, where s is the rate of saving and g is growth rate. That phenomenon has nothing to do with the relationship between r and g. Piketty misleadingly introduces this fact in the form of an equality, β = s/g, which he calls the Second Fundamental Law of Capitalism, but in the extended discussion of the law in the pages that immediately follow its introduction, he makes it clear that the 2nd Fundamental Law is a long-term asymptotic law about the direction in which β is headed, not an equality. It would be better if he had abbreviated it as “β → s/g”, since in many circumstances the equality β = s/g will not even be approximately true.

Contrary to the assertions of a few of the participants on this thread, Piketty does not assume that capitalists save all of their income, nor that it is necessary for them to save all of their income in order for inequality to grow along several dimensions. The idea that Piketty assumes 100% capital income savings is a really bad misreading that seems to have been started by Lawrence Summers in his badly botched review of Piketty’s book. In fact, Piketty analyses historical examples of rising inequality in which capitalist savings rates more on the order of 25% are estimated, and that is the magnitude he uses in developing his projections for the future.

And leave us not forget the glorious promise of the (non-tradeable) service sector: portfolio manager, bodyguard, personal trainer, courtesan, Walmart associate. The opportunities are endless.

One equation? What about Beta = alpha / r ? How about by = mu m Beta ? And if you’re willing to have some fun with differential equations, you can derive his conclusion that B goes to s/g in the long term. And the relaxation time works out to 1/g. Jolly good fun.

One equation! Sheesh.

JQ 72: I don’t think your joke is very good. Call me humorless but the thing is, I actually take seriously what Piketty says. I take him seriously as somebody who claims to have made a significant discovery in economics, namely that three simple formulas are all you need to explain life, the universe, and everything (now I’m joking but only slightly). If that is the case, we should be able to compare the predictions implied by his formulas with empirical measurements. That’s what mathematical models are for. I’m not impressed with attempts (including yours) at illustrating his model with simple examples that are neither here nor there. (don’t we all love those dumb context-free economics cases where supposed “economic laws” are illustrated at the example of an “economy” consisting of one producer and one consumer of one product, or the like). Piketty isn’t talking about a debtor accumulating interest, he is talking about capital accumulation. Why not for Pete’s sake take it seriously.

And to expand on my argument in 50. Let’s take r to be the rate of capital accumulation, and g the rate of income growth, as Piketty does most of the time (*). Then it is obvious that r-g is the rate of growth of the capital-income ratio, which is really the cornerstone of Piketty’s argument. For example, if r=5% and g=3%, the capital-income ratio would grow eight-fold each century. That’s the model. Does it conform to empirical data? Nope. Piketty reports roughly a doubling of the capital-income ratio during the 19th century, reaching levels up to six or seven by WWI. According to Piketty’s data (figure 1 at http://www.nybooks.com/articles/archives/2014/may/08/thomas-piketty-new-gilded-age/), in fact g-r was 3.5% during the 19th century, which would have yielded a roughly 32-fold increase. That’s simply out of bounds of the empirical data. I guess I’m a party-spoiler for pointing that out but I can’t help it – I take this stuff seriously.

Interestingly also that his data for 1950-2012 indicate rg argument would be pointless.

[Oh something with the html parser – very funny]

Interestingly also that his data for 1950-2012 indicate r less than g, but precisely that period has seen inequality increase dramatically. So Piketty’s model predicts way more inequality than observed in the 19th century, and way less than observed in the second half of the 20th century. And we should accept the model why exactly?

(*footnote) Although there is ambiguity that he never really resolves how to deal with the part of capital income that is not reinvested – see the discussion in 33 and 64. Piketty implies, and every reviewer I have read seems to have understood him thus, that r is fairly close to the reinvestment rate, otherwise his whole r greater g argument would be pointless.

And JQ, I would appreciate your technical opinion as to how realistic current income (as opposed to GDP) estimates are. You correctly point out in the OP that depreciation must be deducted from GDP, but why 20%? Is that just a guess or has it been measured? Do you agree that if the capital-income ratio increases, the deduction for capital replacement must also increase? Do we actually have reliable measurements of the capital-income ratio? If yes, references would be appreciated.

Piketty pretends that capital replacement is a constant fraction of GDP

Uh, I think he assumes that capital replacement is a constant fraction of the capital stock (or wealth). Or are you referring to the fact that he’s using national income rather than GDP?

JT: Capital is a stock and GDP a flow. A portion of what is produced each year (GDP) goes to replace degraded capital (depreciation), and a portion goes to capital accumulation (net investment). There seems to be agreement that capital replacement is not part of income so income is production minus depreciation (*).

Let’s say capital depreciates over 20 years (i. e. 5% p.a. on average). If capital stock is three times GDP, 15% of GDP must be dedicated to replacement. Now Piketty says the capital-income ratio (**) goes up, say to 6. Then 30% of GDP is swallowed by depreciation. If the ratio increases further, as implied by the r>g law, then eventually all of GDP will be swallowed once capital stock reaches 20 times GDP (which apparently doesn’t happen empirically but it would happen if capital accumulation exceeds economic growth for a long enough time).

Now consider that net investment is also included in GDP – it counts as income, the income of the capitalist class, but is not consumed. At a net investment rate of 5% (which is about what Piketty describes), when capital stock increases to 6 times GDP, 60% of GDP is depreciation and investment and only 40% are left for consumption. Let capital accumulate a little more and there is nothing left of GDP. Now there are economies where the rate of consumption versus investment is low (I think China is a case in point) but the US for example, despite high inequality, doesn’t appear to fit the model. Also it is unclear to me how, if at all, public investment is accounted for in Piketty’s model. We (let’s say, liberal and leftist Keynesians) tend to think that investment in public infrastructure is a good thing, not a bad thing. But that should increase the capital-income ratio, which Piketty says is bad (I think Piketty simply ignores publicly owned capital, which would be another shortcoming of his model).

Notes:
(*) It makes sense that for example when I replace the roof of my house, that is negative income – I spent money to keep my capital stock constant. The money I spent provides income for the laborers whom I hired. But there is no economic statistic that I am aware of that actually deducts the cost of roof replacement from my income (while also adding the benefit from house ownership to my income). Adjusting GDP to reflect actual income is quite tricky and I doubt that we have any reliable statistics.
(**) Piketty says that he adjusted GDP to get actual income but his adjustment is simply a constant percentage deducted. For all practical purposes, he uses GDP and income interchangeably.

94: “I think he assumes that capital replacement is a constant fraction of the capital stock.” No he doesn’t. he subtracts a constant percentage (I think 10%) of GDP.
95: Piketty does theoretically distinguish s and r but his catchphrase is r>g, not s>g, and that is because for practical purposes he doesn’t distinguish between the two. Folks, read the actual book.

What I said above wasn’t precise. The rate of capital accumulation is s*Y/K. So the capital-output ratio grows at s*Y/K-g. This is why any economic model which has a steady state will give you K/Y=s/g in the long run, whatever other assumptions are in there. As far as I can tell, Piketty believes in models/economies with steady states.

I’ll confess that I’m a bit confused as to how Piketty treats depreciation, as it is a bit non-standard, and I’ll have to look it up again. I was originally puzzled by how high he assumes this rate is. Most work which estimates capital depreciation has a number that’s at least half (in % points) of his. So maybe there’s something to what you’re saying.

The standard way would be to write dK/dt=sY-bK, where b is the rate of capital depreciation, measured as % of capital stock. But Piketty wants to stick that b inside of the s somehow. Rewriting dK/dt=Y[s-b(K/Y)] where now the whole term s-b(K/Y) is how Piketty measures the “net saving rate”. So Piketty’s depreciation rate is b(K/Y) which could account for both why usually when people talk of depreciation (when they mean just b) they quote numbers that are much lower, and your confusion. And mine. I’m guessing that that’s what he’s doing but I would have to look it up again.

Or to clarify a bit more, Piketty assumes that b is a constant fraction (of capital), he does not assume that b*K is a constant fraction of Y. His whole (well, one of them) point is sort of that it isn’t.

I guess I’m a party-spoiler for pointing that out but I can’t help it – I take this stuff seriously.

Intrepid warrior for Truth battles confederacy of dunces…

Billikin: The Civil War destroyed a great deal of the wealth of the American South, and it is still a poor area of the country.

Bruce Wilder: It was a poor area before the Civil War; the poverty was just distributed differently.

Really? I always heard that the ante-bellum South was richer than the North because of cotton exports. Then industrialization made the North richer than before, and the Civil War destroyed much of the South’s wealth (not including the nominal loss of wealth in slaves).

#107 Actually not. The usual wealth-per-capita figures divide by total population, not by “free population”. But Bruce Wilder in #99 is (sort of) right.

Umm… ante-bellum the notional market value of slaves constituted over 80% of the value of the total U.S. capital stock. Now obviously slaves should be accounted as labor and the northern industrialists and farmers didn’t get accounted for their employment of labor as capital. However, slaves could be used as collateral for financial borrowing, in a way that northern labor couldn’t, and that both contributed to a quasi-permanent bubble in slave prices and the perceived wealth and power of the plantation “aristocracy”, as well as their ability to rapidly expand into new lands. After the Civil War, there were massive bankruptcies.

John, I don’t disagree (except maybe about the “quasi-permanent bubble part”. If it’s permanent, then how can it be a bubble?). Just pointing out that Collin’s reason given in 107 is not the right one.

greg, look up stuff by Gavin Wright. Like Table 2.4 here:
http://books.google.com/books?id=k_ZJrhZ2coEC&printsec=frontcover#v=onepage&q=wealth&f=false

notsneaky @ 109: The average white man in the South in 1860 was roughly twice as wealthy as the average northerner. The South had a poor record of achievement in education. Its road network was poor, its rail network lagged and was poorly integrated; river navigation was only middling. There was no financial sector to speak of, little in the way of a commercial or professional establishment or merchant marine, very little manufacturing or mining, only one large city.

jch @ 110: ante-bellum the notional market value of slaves constituted over 80% of the value of the total U.S. capital stock

That doesn’t seem even facially plausible to me. There’s got to be some qualifier missing?

JBTW, I’m interested if the slave economy affected the wages of free labor in the antebellum South. It seems (to me) as though slavery should have driven down the wages of free white labor.

I suspect this would be hard to measure. It affected the wages of free labor compared to what?

When I try to think about it theoretically I get mixed up. On the one hand, when slaves were being imported that sent money out of the nation. That would tend to make all other imports more expensive, and make exports more profitable compared to producing for the domestic market. This is a clear difference between paying foreigners for slaves versus allowing an equivalent number of wage-slaves to immigrate.

There was not much of a financial system. A textile manufacturer in the north could get a factor to give him a short-term loan to pay his wage-slaves, and pay it off when the cloth was sold. The south had nothing like that. Slavery helped to get past those problems, and wage labor in the south would face them head on. Which led to such things as sharecropping after the war — if neither side had money until the crop was sold, they had to rely on personal promises until then.

I plain don’t see how to theoretically simplify it into something tractible. Maybe somebody else will see how to ignore some of the important variables.

Layman, in comment 37, I asked whether Piketty had done comparisons to other eras that had vast destruction of wealth. In comment 40 you wrote, explicitly in response ”Pre-industrial capital was basically land”. My response in comment 48 was very obviously a response to that specific assertion – pointing out that slaves were the main form of capital in the old south, and that the value of land tends to be mostly the value of improvements on and around it. Responding to that by saying the abolition of slavery increased equality is, at best, a non-sequitur.

My response to Ronan in the same comment refers, of course, to the material Ronan linked in 41. This paper states that it “seeks to document – in as much as it is possible to prove a negative – the general absence of comparably effective non-violent mechanisms [to war, plague, and other major disasters as reducers of inequality]”. Piketty may think non-violent solutions are possible, but the author Ronan linked was specifically trying to rule them out. One can agree or disagree – I disagree – but simply asserting the contrary and pretending it is a rebuttal is “is so – is not” level of argumentation.

@116:

The 80% figure is cited in numerous sources, including Picketty. But that gets into the question of @121, as to what is accounted as capital. If you think of capital as a produced means of production, “physical” capital, as opposed to land and labor, then slaves as capital is perverse, but there you have it, by the standards of the time. We’re probably talking about something like marketable equity, at a time when the banking and financial system was limited and unstable, when there wasn’t as yet any limited liability, etc. The value of a slave would presumably have been the NPV of its life time product (minus subsistence costs). In contrast, in the north the value of capital would have been limited by its labor costs, with wages likely relatively high, due to the availability of land and other resources for subsistence (e.g. passenger pigeons), productivity would have been relatively low, by modern standards, and tight liquidity constraints would have limited its value. By contrast, the additional value of slaves as collateral would have boosted their value above the value of their output.

#122 John Halasz

If you think of capital as a produced means of production, “physical” capital, as opposed to land and labor, then slaves as capital is perverse, but there you have it, by the standards of the time.

Wouldn’t it be the same logic as that with horses? Any farmer with a female horse could breed it if he chose, for female slaves that was even easier since male slaves were not castrated as a rule and owners were the same species.

#119 Greg

The supply of slaves was intentionally restricted, since, as capital, this made them more valuable,

I knew that slave importation got restricted and I attributed that to abolitionists. Southern slaveowners agreed to it because it made their existing slaves worth more?!

Did slaveowners have a sort of cartel, where they agreed to reduce the reproduction rate of their slaves so they could keep the value up? That seems like astounding forward thinking. Not what I’d expect from people who drifted into a war they must inevitably lose.

JT @ 124:

The importation of slaves was banned in 1807, as part of the original constitutional compromise. Nonetheless, the population of U.S. slaves grew steadily, as slave-holders had an incentive to both care for (sic!) and breed their slaves. (There were actually agronomic manuals published dealing with the care and breeding of slaves, exactly like domestic animals). Mortality rates for imported slaves in the tropics, by contrast, were drastically high.

J Thomas @ 124:

From Gavin Wright, (notsneaky’s reference) (p71) “…The antebellum slave South was not a “cheap labor” economy; it was a society whose economy and polity revolved around the scarcity and high price of slave labor.”

…

(p72) “The policy most directly aimed at augmenting slave prices was the federal closing of the African slave trade. Though this 1807 measure is commonly considered part of the antislavery agenda, having been proscribed for twenty years in a compromise between northern and southern states at the Constitutional Convention, when the deadline arrived, the South acquiesced with little objection….most representatives from both regions actively favored the ban.”

Note: The price of slaves tripled (nominally) in the period from 1810 to 1860. Of course, each slave owner was interested in breeding his slaves, since this would increase his own capital. So no, I don’t think they were that forward thinking. Self interest would call for banning the importation of slaves, but would also motivate the increase in slave population due to breeding. Hmm. That sentence from my post @119 is perhaps poorly worded.

From Gavin Wright (p73): ”…the issue was considered so politically charged that candidates for office avoided any hint of association with it. This hypersensitivity was closely tied to the awareness that reopening the African slave trade would undermine the value of slave property. As H. S. Foote of Mississippi argued in opposing the proposal: “If the price of slaves comes down, then the permanence of the institution comes down…the permanence of the system depends on keeping the prices high.””

re Martin Bento’s comment at 129, I agree that r is not the driving force behind the current rise in inequality. But here is where a little history and sociology would benefit economics. The major economic form of our day is the corporation – it is this that provides the primary frame within which wealth manoeuvres, as the landed estate did up to a century or so ago. And the modern corporation is owned not by single major stockholders (as in the 20s) but by pension funds, universities, other corporations and similar. As such, it is office rather than ownership that is the prize. In some ways, the modern set of corporations resembles the Ottoman or Mameluke power structures – in which also office was the prize, open in theory if mostly not in practice to a merit defined by the corporate hierarchy (the Mamelukes were technically slaves owned by the corporation they in turn managed). My impression is that in the US political and corporate office-holding have become closely entwined, while they mostly remain more distinct in Europe.

But it appears that in most cases the managers are, for all intents and purposes, the owners. And shareholders are mere speculators. And the way managers/owners extract wealth has little to do with the ROC.

“He sees this period coming to an end.” – How?

I have never met Peter K.

If you want r < g, then have fewer workers. The 19th century, with its rapid population increase, was more the exception than the rule.

Ze, I hadn’t realized your comment was a response to me. Managers being owners for all intents and purposes is a complicated question. First of all, high level executives are largely, sometimes almost solely, compensated in stock, so they are also shareholders. There are a lot of complexities around how ownership of companies has developed, but if it is just that the managers are the real owners, then we are no longer in capitalism as traditionally understood, since the managers did not buy the companies, (nor necessarily did they create them, though sometimes so), so their “ownership” is not a function of their capital.

As for how this era will end, I gather Piketty thinks growth will decline while r stays the same, or at least declines less, so returns on r will again be the main game in town. As I think I’ve made clear in this thread by asking basic questions, I haven’t read the book, so why he thinks growth will decline so much is probably a question for someone else, though I would guess it has to do with declining (and eventually negative) population growth, aging population, and perhaps environmental constraints.

MB 138, Piketty says – correctly I think – that high economic growth rates of the past one or two centuries are a historical anomaly and that there is no reason to expect they will continue. It is unclear to me why r should be assumed to be a historical constant when g clearly isn’t.

notsneaky 105: Thanks for that link – the chart book only adds to the confusion. In the Capital book in the early chapters, Piketty talks about the capital/income ratio increasing in the 19th century (consistent with the large r – g differential, though not to the extent one would expect). But according to figure 3 (http://piketty.pse.ens.fr/files/capitalisback/F3), UK capital income ratio was constant at 700% throughout the 18th and 19th centuries, then declined to 200% and from 1950 on steeply increased to now exceed 500%. None of this is consistent with his Capital in the 20th century narrative and his r and g data. In the US (figure 12), there was again little increase in the 19th century and little fluctuation overall.

Did you read the link?
As I said, I havent read all the book. And Im not an economist, although Im assuming his argument is overall more sophisticated than you make out.
You say:

“According to the r > g (or s > g if you wish) model and Piketty’s own data, we shouldn’t have expected inequality to increase in the second half of the 20th century. ”

who cares ? does Piketty say it’s the *only* factor that might increase inequality? Or that in its absence inequality will not increase ?
From the link:

“Piketty’s Capital in the Twenty-First Century never suggests r>g is the main reason behind the recent rise of inequality. Rather, it theorizes that, in the absence of government intervention, r>g ensures the future concentration of income and wealth. ”

and from his own mouth:

“I think the book makes pretty clear that the powerful force behind rising income and wealth inequality in the US since the 1970s is the rise of the inequality of labor earnings, itself due to a mixture of rising inequality in access to skills and higher education, and of exploding top managerial compensation (itself probably stimulated by large cuts in top tax rates), So this indeed has little to do with r>g”

ie, pro rich policy has increased inequality ?

So it doesnt appear *everybody* has misunderstood, but perhaps you have ? Or what am I missing?
to add, Im not saying anything about r>g. I have no opinion one way or the other on,or even fully understand, it. But are you not arguing a strawman here ?

144 “Rather, it theorizes that, in the absence of government intervention, r>g ensures the future concentration of income and wealth.”

‘It theorizes’ would be a good description for “the tendency of the rate of profit to fall”, while the r>g thing is based on (dubious) empirical observations, and none of the observed periods is of “the absence of government intervention”.

The cult status of this idea seems so weird. The only explanation I can imagine is that it presents the rise in inequality as some neutral apolitical phenomenon.

Martin Bento, having clearly misunderstood you earlier, for which I apologize, I’ll limit my further comment to simply saying that many of your questions about what Piketty says and means might best be answered by reading him.

TM @ 143

Really, what are you going on about?

From Piketty’s introduction, on the conclusions of the book:

“The first is that one should be wary of any economic determinism in regard to inequalities of wealth and income. The history of the distribution of wealth has always been deeply political, and it cannot be reduced to purely economic mechanisms. In particular, the reduction of inequality that took place in most developed countries between 1910 and 1950 was above all a consequence of war and of policies adopted to cope with the shocks of war. Similarly, the resurgence of inequality after 1980 is due largely to the political shifts of the past several decades, especially in regard to taxation and finance. The history of inequality is shaped by the way economic, social, and political actors view what is just and what is not, as well as by the relative power of those actors and the collective choices that result. It is the joint product of all relevant actors combined. The second conclusion, which is the heart of the book, is that the dynamics of wealth distribution reveal powerful mechanisms pushing alternately toward convergence and divergence. Furthermore, there is no natural, spontaneous process to prevent destabilizing, inegalitarian forces from prevailing permanently.”

So, there are economic mechanisms which tend to increase inequality, but they are not solely to blame, because there are also political mechanisms which impact inequality. In the absence political action to counteract the economic mechanisms, inequality tends to grow.

Piketty’s entire point with r > g is that it is an economic tendency which can only be managed through political means; means which are harder to enact when the wealthy wield disproportionate political power.

Layman,

Piketty’s entire point with r > g is that it is an economic tendency which can only be managed through political means; means which are harder to enact when the wealthy wield disproportionate political power.

Nicely done.

It’s all political.

Politics may reach everywhere, but it isn’t everything.