r > g

by John Quiggin on October 13, 2014

A standard piece of advice to researchers in math-oriented fields aiming to publish a popular book is that every equation reduces the readership by a factor of x (x can range from 2 to 10, depending on who is giving the advice). Thomas Piketty’s Capital has only one equation (or more precisely, inequality), at least only one that anyone notices, but it’s a very important one. Piketty claims that the share of capital owners in national income will tend to rise when the rate of interest r exceeds the rate of growth g. He suggests that this is the normal state, and that the situation prevailing for much of the 20th century, when r was less than g, was an aberration.

I’ve seen lots of discussion of this, much of it confused and/or confusing. So, I want to offer a very simple explanation of Piketty’s point. I’m aware that this may seem glaringly obvious to some readers, and remain opaque to others, but I hope there is a group in between who will benefit.

Suppose that you are a debtor, facing an interest rate r, and that your income grows at a rate g. Initially, think about the case when r=g. For concreteness, suppose you initially owe $400, your annual income is $100 and r=g is 5 per cent. So, your debt to income ratio is 4. Now suppose that your consumption expenditure (that is, expenditure excluding interest and principal repayments) is exactly equal to your income, so you don’t repay any principal and the debt compounds. Then, at the end of the year, you owe $420 (the initial debt + interest) and your income has risen to $105. The debt/income ratio is still 4. It’s easy to see that this will work regardless of the numerical values, provided r=g. To sum it up in words: when the growth rate and the interest rate are equal, and income equals consumption expenditure, the ratio of debt to income will remain stable.

On the other hand, if r>g, the ratio of debt to income can only be kept stable if you consume less than you earn. And conversely if r < g (for example in a situation of unanticipated inflation or booming growth), the debt-income ratio falls automatically provided you don’t consume in excess of your income.

Now think of an economy divided into two groups: capital owners and everyone else (both wage-earners and governments). The debt owed by everyone else is the wealth of the capital owners. If r>g, and if capital owners provide the net savings to allow everyone else to balance income and consumption, then the ratio of the capital stock to (non-capital) income must rise. My reading of Piketty is that, as we shift from the C20 situation of r ≤ g to one in which r>g the ratio of capital to stock to non-capital income is likely to rise form 4 (the value that used to be considered as one of the constants of 20th century economics) to 6 (the value he estimates for the 19th century)

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, has increased as we move from r=g to r>g. For example 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[^1]. This can only stop if the stock of physical capital becomes so large as to bring r and g back into line (there’s a big dispute about whether and how this will happen, which I’ll leave for another time), or if non-capital owners begin to consume below their income.

There’s a lot more to Piketty than this, and a lot more to argue about, but I hope this is helpful to at least some readers.

[^1]: Around 20 per cent of GDP is depreciation, indirect taxes and other things that don’t figure in a labor-capital split, so this translates into a fall in the labor share of all income from a bit over 70 per cent to around 50 per cent, which looks like happening.

{ 154 comments }

1

Joe 10.13.14 at 5:54 am

That’s no equation…

2

MPAVictoria 10.13.14 at 6:10 am

I have to admit that formulas leave me befuddled…

3

mbw 10.13.14 at 6:20 am

A somewhat more complete discussion, still short, may be found at .

4

mbw 10.13.14 at 6:21 am

5

John Quiggin 10.13.14 at 6:23 am

@Joe Pwned! An inequality about inequality is too confusing to talk about, but I’ve added a parenthetical correction

6

Anderson 10.13.14 at 7:27 am

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

7

Joe 10.13.14 at 7:36 am

Thanks for sating my enormously tedious inner pedant, John. One day I hope to be able to resist it.

8

Billikin 10.13.14 at 8:09 am

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

9

John Quiggin 10.13.14 at 8:44 am

@Billikin OK, I’ll have a go at this

10

reason 10.13.14 at 9:51 am

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.

11

John Quiggin 10.13.14 at 9:57 am

Ok, I’ve tried to clarify this. The point is that initially r=g, but then r > g. Some of that shift might come from a slowdown in g (as Piketty suggests) but the big factor is an increase in r.

12

Martin Bento 10.13.14 at 10:08 am

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.

13

Peter T 10.13.14 at 10:22 am

I think the question of why Piketty’s r rarely falls below 5 per cent is best explained by seeing it not as a return on capital as investment, but as the return on a claim on other income streams. There is a difference between living off the return on an investment in, say, a factory or a set of houses, and off the return on, say, government bonds. The benchmark middle and upper class investment in the C19 was British government debt (“consols”), which paid around 3 per cent. This was a claim on the tax income of the British state; the debt had long since been spent, mostly on the Navy and subsidies to allies in the Napoleonic Wars. The ability to claim a share of income is more political than related to the abundance or otherwise of physical assets.

“Capital” read as “the worth of current claims on primary income streams” makes more sense, as what counts as capital depends on what incomes can be claimed against. The article linked to above notes that governments’ net capital is mostly zero, but governments have immense amounts of physical capital (roads, parks, buildings…) – just few claims on income other than taxes. Piketty makes nods in these directions, but does not analyse his categories in real detail.

14

david 10.13.14 at 12:20 pm

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?

15

TM 10.13.14 at 12:29 pm

Piketty’s g is not a per-capita growth, but an aggregate one. So one argument for a decreasing g in the future is simply demography.

16

hix 10.13.14 at 12:32 pm

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.

17

Bruce Baugh 10.13.14 at 1:29 pm

Thanks, John and commenters. This was really helpful to me.

18

jake the antisoshul soshulist 10.13.14 at 1:59 pm

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.

19

Layman 10.13.14 at 2:14 pm

“So, is the conclusion that r is relatively constant, while g varies?”

I think Piketty reports that even g is relatively constant at a very low value, 1-2% over most of the period of his estimates – once you eliminate the growth (g) due to population growth, and certain special circumstances like the growth following the destruction of capital during the period 1914-1945.

Over the long run, r=5% and g=2%, with the resulting consequences for concentration of wealth. The era of strong growth (g) from 1946 was an aberration, and without some action we’re heading back to economic feudalism – which has been more or less the human condition since the invention of agriculture.

20

politicalfootball 10.13.14 at 2:42 pm

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.

21

politicalfootball 10.13.14 at 2:45 pm

So, is the conclusion that r is relatively constant, while g varies?
I would think that relationship would be more complex.

That’s a bit oversimple, but yeah, this is basically what he’s saying. I found it surprising also, but he appears to have done his homework.

22

politicalfootball 10.13.14 at 2:59 pm

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.)

23

Evan 10.13.14 at 3:46 pm

I guess I happen to fall into your target group. Great post!

24

Pete 10.13.14 at 4:09 pm

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.)

25

Omega Centauri 10.13.14 at 4:55 pm

Isn’t there a hidden assumption, that income from R is totally reinvested? If so, and if the capital owners decide to party with some of the proceeds, then the equation would change. I suspect as r lowers, the incentive to party versus re-invest changes as well. And I suspect there may be other mechanisms that operate to disperse the ownership of capital, which a simple binary (creditor/debtor only) model doesn’t cover.

26

bianca steele 10.13.14 at 5:09 pm

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.

27

Kiwanda 10.13.14 at 5:28 pm

“The econ textbook my mother used for her one economics course has no math at all”.

“math” =/= “formulas”

28

Bloix 10.13.14 at 5:31 pm

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.

http://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.

29

bianca steele 10.13.14 at 5:38 pm

“math” =/= “formulas”

I’m sure you’re right. It couldn’t be that this is a textbook for people who have not (or barely) passed algebra. It has to be that I just don’t really know what math is. How could I possibly?

30

Kiwanda 10.13.14 at 5:38 pm

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?

31

Kiwanda 10.13.14 at 5:43 pm

“It has to be that I just don’t really know what math is.”

I’m sure you know what math is, and was just speaking loosely. But “equations” became “inequalities”, so.

32

bianca steele 10.13.14 at 5:57 pm

“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.

33

A H 10.13.14 at 6:08 pm

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 2) that everybody else saves none.

This means that capital income (r) is equal to yearly savings. An economy will reach a steady state capital to income ratio (K / g) when K/g is the same as the savings rate to income ratio. Because of the above assumptions, r is equal to the savings of the economy, and therefor the steady state is equal to r / g.*

Therefore if r is greater than g, the steady state amount of capital relative to g will need to rise and this will obviously cause increased power of capitalists vs workers. Though r > g than g isn’t really that important, the important thing is that if r and g are spreading apart it implies increasing inequality.

*Robert Solow’s review of Capital has a good run-through of how this steady state works.
http://www.newrepublic.com/article/117429/capital-twenty-first-century-thomas-piketty-reviewed

34

Phil 10.13.14 at 6:47 pm

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.

35

TM 10.13.14 at 7:26 pm

r>g is unconvincing because it is terribly confused and JQ adds to the confusion. To state the obvious, the analogy of r with interest rates and g with income growth is wrong.

36

Billikin 10.13.14 at 7:42 pm

@ John Quiggin

Thanks.

37

Martin Bento 10.13.14 at 8:06 pm

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? The Napoleanic Wars? Genghis Khan? The French Revolution? The fall of Rome? Sure, in absolute terms WW2 was bigger than any of those, but the world population was much bigger and richer, and the conflict was more global. But it would seem that if burning the loot of the wealthy were the secret, then burning the loot of the wealthy in an economic area where the bulk of its economic activity was internal to it would be the same for that area as burning it globally, and WW2 was not the first such fire we’ve seen. Does Piketty do any comparisons to other eras that saw massive destruction of wealth?

38

John Quiggin 10.13.14 at 8:21 pm

TM @35 This is the kind of comment (not unusual) that I find to be utterly unhelpful. I have no clear idea what your objection is, and I fear that the attempt to discover it will lead down a rabbit warren.

But, I’m going to try to respond. First, there is no “analogy” here. r is defined to be the interest rate and g is defined to be the rate of income growth.

You can of course, object that there is more than one interest rate, interest rates are not the only return to capital, income growth is not uniform across the population etc etc. That raises problems for the argument, but not, in my view, fatal ones. In fact, as Piketty points out, the rich are likely to have higher returns to capital, so this only strengthens the key point.

Maybe that’s what you’re on about in which case you ought to spell out why you think this is a fatal problem. Or maybe you’re just blowing smoke. I really can’t tell.

39

John Quiggin 10.13.14 at 8:23 pm

I’m not really convinced by the wealth destruction story. The obvious problem is that wealth and capital stock grew rapidly over the decades after 1945, while inequality remained low or declined from the historically low levels that followed the Great Wars and Depression.

I want to write on this later. For the moment, I’m just trying a bit of exposition of the way the r>g claim works.

40

Layman 10.13.14 at 8:24 pm

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.

41

Ronan(rf) 10.13.14 at 8:28 pm

Martin Bento- I dont know the answer to your question, but came across this recently which *might* be relevant

http://www.stanford.edu/~scheidel/Leveler.pdf

42

John Quiggin 10.13.14 at 8:53 pm

AH @33 That’s a good point, but it’s only precisely necessary when r is very close to g. With r well above g, we can have non-capitalists doing some saving, but not enough to prevent the debt/income ratio from growing, and capitalists doing some, in fact much and obvious, consumption, but still getting richer.

43

J Thomas 10.13.14 at 9:21 pm

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?

There was an east-european economist who had a clear interesting idea about this, and unfortunately I can’t remember his name. Maybe he was russian. He wrote in a communist context, as he had to at that time and place.

First he made the simplification that technological advance was mostly constant. Like in the days when quality of computer chips increased linearly — if all you need is to make incremental advances, and you make the next increment when you see the results of the last increment, you can keep advancing even when sales are very low. If you can afford to build the next prototype, that tells you what you need to know to build the next prototype after that.

Second, he supposed that economic advance was linked to technological advance. If you can do things more efficiently then you can do more.

Third, he supposed that in times of low investment or low consumption, we developed a store of unused technology that we could draw on later.

So he concluded (supposed) that after something like the Great Depression or europe recovering from WWII, or the USSR recovering from the Revolution and disorders, for a time the economy grows very fast and then it slows down when it reaches the level it would have reached if the delays did not happen. He had data and graphs that tended to fit his conclusion, which he took as support for his assumptions.

He claimed that the USSR had a higher base growth rate than the Czarist empire, which he attributed to structural improvements and he pointed out that there was a lot of suffering involved in the transition.

I thought the idea was clear and plausible. It was of course oversimplified, but any economic idea you can understand with less than 10 years concentrated effort will be inevitably oversimplified.

44

bob mcmanus 10.13.14 at 10:09 pm

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.

45

Abbe Faria 10.13.14 at 10:40 pm

“Around 20 per cent of GDP is depreciation, indirect taxes and other things that don’t figure in a labor-capital split..”

GDP by definition doesn’t include depreciation, because it’s not production. Indirect tax can be included or excluded, depending on whether GDP is measured at factor cost or producer price, but it’s just a cash transfer – not production. I don’t know what the other items could be…

This is important because if your capital is tied up in a factory, eventually the factory will fall apart and your capital will be worth nothing – hence the depreciation charge. That’s relevant to AH’s point about the assumption that capitalists save all their money.

“First, there is no “analogy” here. r is defined to be the interest rate and g is defined to be the rate of income growth.”

I thnk the point is r is defined to be the rate of return to capital. Analysing it as an interest rate ignores physical and property wealth, which is the majority of wealth.

“In fact, as Piketty points out, the rich are likely to have higher returns to capital, so this only strengthens the key point.”

What the logic here? The marginal returns on capital for the poor are enormous, you give someone a bike or some eyeglasses and it can transform their productive capability. While much physical capital – like jewelry or housing – isn’t deployed productively.

46

Bruce Wilder 10.13.14 at 10:42 pm

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.

47

TM 10.13.14 at 10:43 pm

JQ: ” r is defined to be the interest rate”

Piketty does not define r to be the interest rate . If you define it as such, you are saying something different from what Piketty is saying.

48

Martin Bento 10.13.14 at 10:46 pm

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.

49

Bruce Wilder 10.13.14 at 11:04 pm

Abbe Faria @ 10:40 pm: r is defined to be the rate of return to capital. Analysing it as an interest rate ignores physical and property wealth, which is the majority of wealth.

Piketty’s “Capital” might better be termed, “wealth”. If you imagine the two sides of a balance sheet, with assets on the left and equities and liabilities on the right, Capital, in the sense of the things, money and investments needed to do business in all their variegated glory, are on the left side of the balance sheet, but the legal claims on ownership and income are all on the right side of the balance sheet, and Piketty is toting up the right sides of every balance sheet he can lay hands on. The capital stock is not some differentiated subset of things on the asset side; it is the total of claims on the right side.

A purist would say that the Land on the Asset side of the balance sheet is not really and strictly speaking capital, but Piketty isn’t making such a distinction. If owning land earns an income, it is capital income.

So, if a particular Capitalist is a loan shark, with a claim on income from usurious loans, the loan shark’s capital is in the giant pot earning its part of the aggregate 5% . . . (where marginal productivity comes into it can be left as an exercise).

I’m not sure if that’s the point Abbe Faria intended to make, but it seemed worth expanding upon.

50

TM 10.13.14 at 11:05 pm

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.

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Martin Bento 10.13.14 at 11:10 pm

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. I’m not willing to stipulate that it is the only way and I think pre-modern societies are different enough from ours that I hesitate to define our possibilities by their experience.

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notsneaky 10.13.14 at 11:30 pm

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.

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notsneaky 10.13.14 at 11:36 pm

Actually s going up by itself doesn’t work either, does it? You need s up AND g down by the right amounts.

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Bill 10.13.14 at 11:57 pm

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.

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J Thomas 10.14.14 at 12:07 am

#50

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.

I’m not sure I followed that. Could you maybe make up some numbers to show what you mean?

It doesn’t make sense that capital depreciation would be a constant fraction of GDP, if physical capital creation increases faster than GDP. It would make more sense for capital depreciation to be a constant fraction of physical capital. It would make even more sense for capital depreciation to have an age structure, so it would be a smaller fraction of physical capital when physical capital is increasing fast, and a larger fraction of an aging capital structure. But that’s more complicated and maybe not helpful at this level of abstraction.

If capital depreciation is a constant fraction of, well, almost anything then it isn’t going to swallow up all of GDP, because whatever it is a constant fraction of will swallow up all of GDP first.

Or maybe I’ve misunderstood.

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notsneaky 10.14.14 at 12:20 am

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)

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J Thomas 10.14.14 at 12:53 am

#44 bob mcmanus

No, it wasn’t Kondratieff. This guy wanted to assume that technological innovation mostly averaged out, he wasn’t thinking about a few grand innovations that could not be predicted but which transformed society, he instead thought about the cycle of iterative improvement — you don’t know how to make the next improvement until you actually make the current improvement and see how to improve it. That takes time, and the rate you can do that determines the maximum rate that new innovations can be produced. He thought that each society had a sort of intrinsic rate of growth, and he didn’t have much explanation why a given society had a given intrinsic rate. But he believed that any time something delayed growth, that (given the chance) the delayed economy would speed up until it got to where it otherwise would have been, and then slow down to the intrinsic rate. In some ways opposite of Kondratiev.

I have found no trace of his work with a quick search. It would be classed somewhere around endogeneous growth theory and unified growth theory.

I have the impression a lot of innovative work came out of eastern europe that has been mostly ignored.

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Bruce Wilder 10.14.14 at 1:03 am

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.

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Peter T 10.14.14 at 1:47 am

I’ll come back to the distinction between wealth and capital, because I think this is where both Piketty and a lot of economics gets confused. A story might help:

A town gets it’s living from fishing. The harbour, wharves, drying sheds and roads, built over many generations, are all kept up from taxes. No-one draws incomes from them. Boats and houses can be bought, sold and rented, and one class of people own them and draw income from them. In this case, boats and houses are wealth, but the whole complex of assets and knowledge is capital, and contributes to the town’s income. The boundary is political. It may be that the fleet is taken into communal ownership, in which case wealth is diminished, but not capital. Or it may be that, say, the sheds are sold into private ownership, in which case wealth increases but not capital. And not all forms of wealth contribute to productivity: maybe the harbour-masters’ perquisites are in private hands, and shares bought and sold. This is wealth, but not capital (ancien regime France and Babylonia both had a lot of this sort of claim, IIRC).

Piketty’s diminution of wealth 1914-1970 seems to me to have more to do with redrawing the boundaries of wealth than actual destruction. A great deal of wealth was nationalised in Europe, or subject to regulation in the US (as an example the formation of the TVA removed half or more of the value of the region’s power companies). The largest single transfer Piketty highlights was the end of slavery in the US – an enormous destruction of wealth, with no loss of productive capital. Piketty’s r is the return on wealth – it’s total value reflects both the politically-negotiated boundary of wealth and the minimal acceptable return to the owners. The relationship to capital as a factor of production is highly elastic, and should not be taken for granted.

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Layman 10.14.14 at 3:21 am

“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.

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Helen 10.14.14 at 4:16 am

John, I’ve been wondering how Piketty’s theory, if true, affects thinking on steady-state or “degrowth” economies , which you also discuss on your own blog.
If the only thing which will save us from excessive income inequality, which we know is socially damaging, is eternal growth, we know we’ll eventually kill ourselves like bacteria in a jar. Seems as though we have the choice of socially damaging inequality or environmentally damaging growth, if Piketty is right. Perhaps (or likely) I’ve misinterpreted?

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notsneaky 10.14.14 at 4:32 am

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”.

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Ze Kraggash 10.14.14 at 6:58 am

43 “Second, he supposed that economic advance was linked to technological advance.”

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. And conversely, a huge technological breakthrough in building some super bomb may not affect productivity. All other things equal, economic growth is a consequence of the rise in productivity.

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gaddeswarup 10.14.14 at 7:34 am

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.”

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notsneaky 10.14.14 at 7:52 am

Capital’s share is by definition r*K/Y.

Any economy which has a steady state will have K/Y tending towards s/g.

Hence the capital share will tend towards r*(s/g), or s*(r/g).

If the *ratio* (r/g) increases *and* saving stays constant, then capital’s share will tend to go up. I don’t know why he chose to frame this in terms of r-g, rather r/g, since you can in fact have one go up and the other go down. r goes from 3 to 5, g goes from 1 to 2. r-g goes up from 2 to 3, r/g goes down from 3 to 5/2. Keeping saving constant, r-g goes up, but capital share falls. This has been both confusing and annoying. Of course *if* you start with r=g, then they both conditions, r-g, and r/g, will move in the same direction (as long as g>0).

But this isn’t really a “theory”. It’s an accounting relationship + a long run condition. To the extent there is a theory here, it’s just “assume the economy has a steady state”. That’s it. For it to be a theory you’d need to specify how r and g are related (and s, too, but that may be asking too much). Otherwise, given your assumption of the long run condition, saying “r/g” went up, is equivalent to just saying “inequality (i.e. capital’s share) has increased”. Which we already knew (sort of, for US there isn’t much of an increase until very recently). There’s no explanation for *why* it increased.

One possible, and plausible, explanation, is that r/g went up because of whatever the “natural” relationship between r and g, the tax rate on capital returns has gone down. This actually fits very well. But this is a statement purely about the effects of policy, not about any “inherent” tendency of capitalism. If you tax capital more, capital has lower share. If you tax capital less, capital has higher share. Yes. True. But nothing to do with capitalism or K/Y or the “natural” rates of r and g (those in absence of tax policy).

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gaddeswarup 10.14.14 at 8:51 am

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%?

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Tom Womack 10.14.14 at 8:53 am

The thing that absolutely fascinated me about Piketty was an aside, which I’ve not been able to find citations to anywhere else other than in Piketty’s other publications:

“At the same time, in 1945, the provisional government decided to implement a one-shot tax on capital holdings, with rates up to 20 percent on top fortunes (and 100 percent on those fortunes that experienced substantial nominal increases during the war!)”

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Alex 10.14.14 at 9:41 am

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?

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bob mcmanus 10.14.14 at 9:52 am

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.

Pointedly skips the non-trivial step of implementation, politics, making the wealth tax happen. The idea of a wealth tax does not bring us equality, anymore than the idea of a natural disaster. The politics of re-distribution or rebalancing have historically been preceded or accompanied by catastrophe…which word I prefer to disaster, for example the effects of the silver mines of America on the global economy.

Peter T up at 13 captures much of the story for me: “The ability to claim a share of income is more political than related to the abundance or otherwise of physical assets.”

r > g because the rich had/have the political power to make it so, and by accumulating gain more power and more accumulation. There are interesting questions as to limits on the power or process, but “The history of all hitherto existing society is the history of class struggles” is like the important first step toward understanding.

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Peter T 10.14.14 at 10:01 am

“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.

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John Quiggin 10.14.14 at 10:48 am

Abbe Faria @45 “GDP by definition doesn’t include depreciation, because it’s not production.”

As you may be aware, I do this stuff for a living. That doesn’t mean I’m always right. It does mean that, before asserting that I’ve got a standard definition wrong, you ought to spend the two minutes necessary to check. The “Gross” in Gross Domestic Product refers to the fact that it includes depreciation. There are good reasons why GDP is headlined in the quarterly national accounts (it’s the most reliable short-term measure of economic activity) but it’s a lousy measure of income and economic welfare.

As an aside, “Domestic” refers to the fact that we are talking about activity undertaken within a given jurisdiction, rather than by residents of that jurisdiction (the alternative value is “National”), so it includes production by foreign companies. “Product” refers to the fact that it is a product-based and not an income-based measure. This leads up to my favorite bon mot on the subject. “There are only three things wrong with GDP: it’s Gross, it’s Domestic and it’s a Product.” The number we should look at for most purposes, including those of the OP, is Net National Income. Sadly, reporting in terms of GDP is so common it’s necessary to make the adjustments referred to in the footnote.

I await your retraction and apology (only joking!).

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John Quiggin 10.14.14 at 10:50 am

@TM I’ve used the definitions of r and g that make economic sense, and shown that they yield Piketty’s conclusion. I regard this as clarifying his argument for the benefit of readers here. But if, as you assert, Piketty defines these terms to mean something different, which does not yield his conclusion, then you should be congratulating me for correcting the errors in his analysis (only joking!).

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mattski 10.14.14 at 11:03 am

Bloix,

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’m curious who you are talking about here?

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J Thomas 10.14.14 at 11:04 am

#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.

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Charles 10.14.14 at 1:15 pm

Great post, Professor Quiggin. Though I like Piketty’s book, my big complaint about what he does is that he inadequately engages in a dialogue with Marxian and Keynesian insights. As a result he gives the impression that modern economies “naturally” behave in a certain way (with a fairly stable r and a g tending to become low), rather that such behavior being the product of complex forces such as technological innovation, the structure of economic institutions, and the character of political struggles. True, he freely acknowledges that government in contemporary societies seems to be run on behalf of the one per cent, and that when g has been relatively high and r relatively low it has been through governmental intervention such as occurred in the postwar period, such as high taxes on capital income and social democratic policies that increased labor’s share of national income. But gaps in his analysis are also striking: he doesn’t discuss the Keynesian point that government spending, by increasing effective demand, can both elevate g and also favor a larger share of national income going to labor. Nor does he mention the labor theory of value or say much about class struggle, Marxian theories which would encourage us to see a relatively stable r as not a natural characteristic of modern economies, but as the result of the character of market-based economic structures and arising from political struggles that allow capitalists to exploit labor while limiting redistributive state policies. My hope would be that progressives could take the generalizations Piketty makes and build on them with sharper theoretical insights drawn from Marxian and Keynesian traditions to build a more full understanding of contemporary economies.

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Trader Joe 10.14.14 at 1:33 pm

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.

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Peter K. 10.14.14 at 1:48 pm

Haven’t read the book, but have obsessively followed the discussion and I pretty much agree with Quiggin’s take on it. The equation is more political economy and history than New Keynesian economics even though it has growth rates and interest/return rates.

For some reason r, the rate of return on wealth, has been constant throughout modern history (which is what, since the 16 or 17th centuries? Or later I’d guess?) This is a political function or institution arrangement not some law of economics. Maybe it’s sort of a vague fact about political economy. At a higher r rate, societies cease to function and capital gets the highest rate it possibly can?

Growth is what has varied. In unequal societies of the 19th century, growth was at 2 percent and with r at higher rates, wealth accumulated and rising inequality helped cause societies to implode (which is why Piketty see rising inquality as a bad thing and something to be countered with or helped to be countered with by an international wealth tax.)

Matin Belto’s view (@12) that inequality has risen only in the last 6 years is something of a howler. It’s been going on noticeably since the 70s and 80s, and even the wealth ratio was already rising again in the 1950s. What has happened since the 1980s is that policy and politics has moved to the right along with outcomes that include rising inequality and slowing growth levels, in a vicious circle. What the last 6 years have shown is that this can lead to some really bad outcomes (which reminds us of the roaring 20s and Great Depression) and that there’s hasn’t been a significant political reaction to counteract the rightward drift. There has been some however. This may be why K21 struck a chord. The trends don’t look good.

But Piketty freely admits it’s not all preordained. He isn’t teleological. As we move forward, my interest lies in Keynes’s conception of the euthanasia of the rentier. K21 is history and political economy and is at odds with New Keynesianism and the “objective” economics of equilibrium and supply and demand. However I do wonder what will happen as Capital become more and more plentiful and governments are forced to continually reduce interest rates (and raise inflation rates?) in order to keep up aggregate demand and keep the whole thing from going under. Will oversupply reduce the political power of Capital?’

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Bruce Wilder 10.14.14 at 1:50 pm

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.

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Peter K. 10.14.14 at 1:55 pm

Internationally, it’s as if the U.S., Europe and Japan are on the cutting edge and other countries will follow as they develop. Europe and Japan’s growth rates are very, very slow but lately Japan has made a push to speed up with its rival China breathing down its neck.

China could divert more income and create a middle class as the US and Europe did during the golden years, but a quickly growing middle class would make more political demands (see Hong Kong) and they are using money to buy US Treasury debt in order to keep their export sector competitive and economy growing.

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Trader Joe 10.14.14 at 2:08 pm

@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.

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J Thomas 10.14.14 at 2:37 pm

#76 Trader Joe

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.

That might work, but you must be far more frugal than most people are willing to.

Consider for example the problem of medical payments. If you do not have insurance then it is predictable you will get a catastrophic medical bill which will wipe out all your savings. You must have health insurance.

However, health insurance will not reduce your average medical expenses in the long run. You can expect to pay more on average for health insurance than you would have paid for the catastrophic bill. Insurance gives you a predictable income drain rather than a sudden catastrophic one.

You must save so much of your income that if you didn’t have health insurance, you could pay your medical bills anyway and still have savings left over.

I recommend becoming a Christian Scientist. If you refuse all medical treatment and die when God wants you to, you are more likely to have savings you can pass on to your children. Alternatively, become a Seventh Day Adventist. They try to eat healthy food and probably as a result they live longer and healthier lives than most, and also pay less medical bills.

As a second issue, savings will probably not work for you. To keep your money you need tax advantages and those are mostly not available to people with small incomes who save. You do better on average to invest. The best investment is probably your own business. There are statistics that 80% of small businesses fail within 4 years. But these statistics are biased. The IRS requires new businesses to make a profit within 5 years, so 4 years is the right time for a business to fail if it was started in the first place as a tax dodge. There are also other reasons not to trust the numbers. Anyway, do not start a business you think will plausibly fail in 4 years, or that you intend mainly as a tax dodge. Look for some special angle that will let your business succeed. If it is profitable, but others with more capital don’t find out how profitable it is, you have a good chance they will not come in drive you out of the business. Ideally you want a business that looks like it’s marginal, and that is good at supplying customer needs. You want your customers to be glad you provided your product or service so cheap, and you want them to vaguely wonder how you can possibly squeak by.

You might also invest in your friends’ small businesses. But then you take the risk that you lose them as friends when you find out they have been cheating you.

And you might set aside some of your savings to gamble on the stock market. Before you do that, look for ways that the government through its tax structure etc will subsidize you to play the stock market. If you can get a big enough edge from the government paying you to gamble, that can more than offset the fact that you are likely to lose on average, combining the occasional catastrophic losses with the steady gains.

If you look carefully, you may find other ways that a small investor can make money. I knew a man who carefully investigated what land his local airport would need when it expanded. Then he bought his new home in the perfect spot. He had noise from airliners arriving and departing, but sooner or later his land would be condemned. He built a deck, using cheap materials and his own labor. He built a cheap backyard swimming pool. He built a sauna. He put in a new cheap bathroom. Everything he did to increase the value of his home would pay off when he sued the city for taking it and undervaluing it. I lost track of him before they expanded the airport, but no doubt he made out like a bandit.

Whatever you do, don’t sell drugs. It is a mug’s game. Your suppliers will demand too much, and your competitors and customers will report you to the police. There’s not nearly enough money in it for the risk. Find a business opportunity that hasn’t gotten so much attention.

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Dan Kervick 10.14.14 at 2:43 pm

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.

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Bruce Wilder 10.14.14 at 3:00 pm

J Thomas @ 81

:-)

Don’t sell drugs; sell pharmaceuticals!

Also, see The Best Way to Rob a Bank Is to Own One

And, of course, the tried and true: buy real estate with other people’s money.

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William Timberman 10.14.14 at 3:34 pm

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.

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mjfgates 10.14.14 at 3:39 pm

The way that people get that first generation worth of wealth is to do stupid things and be the lucky bastard who gets away with them. Whether you’re a Celtic tribesman who gets into all the cattle raids and actually comes out ahead in cattle, the one merchant who manages to dodge all of the bandits between Venice and China, or the guy whose garage business actually takes off rather than devouring your life’s savings, the pattern is the same. Sane risks just don’t generate a high enough rate of return to create wealth out of one lifetime’s work.

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John David Stanway 10.14.14 at 7:33 pm

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.

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TM 10.14.14 at 7:59 pm

JT 55, your argument is precisely what I am saying. Piketty pretends that capital replacement is a constant fraction of GDP, which can’t be right. Under the assumption that C/GDP is increasing (exponentially!), capital replacement has to increase as well (roughly at the same rate), which means that its share of GDP must increase, logically until it swallows up the whole of GDP. That’s the contradiction I am pointing out.

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TM 10.14.14 at 7:59 pm

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.

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TM 10.14.14 at 8:02 pm

[oops – 88 continued]

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

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TM 10.14.14 at 8:04 pm

[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.

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Abbe Faria 10.14.14 at 8:15 pm

“It does mean that, before asserting that I’ve got a standard definition wrong, you ought to spend the two minutes necessary to check. The “Gross” in Gross Domestic Product refers to the fact that it includes depreciation.”

The Gross is there because it’s aggregate production.

I do see how you could look at the formula GDP – depreciation = NDP on wikipedia and think depreciation is a component of GDP. But think through the accounting. You’re making chips and add $(100) of value to your potatoes [GDP], in doing so you get $20 wear on the machinery [depreciation], the difference is $(80) profit [NDP]. The $20 expense is not part of your $(100) production, it’s entirely possible for depreciation to be greater than production.

Depreciation is a debit and is included in NDP not GDP. You can rearrange to GDP = NDP + depreciation, but that’s not the definition of GDP and depreciation is not a component of GDP, this is just a calculation trick. You can’t have positive depreciation anymore than you can have a negative number of deaths. Depreciation is inherently something subtracted from production not included within it.

This obviously abstract, but in terms of income distribution the importance is rather than netting down GDP before getting to the labor-capital split, depreciation is an expense which will only hit capital owners.

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TM 10.14.14 at 8:23 pm

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.

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J Thomas 10.14.14 at 8:57 pm

#87 TM

Under the assumption that C/GDP is increasing (exponentially!), capital replacement has to increase as well (roughly at the same rate), which means that its share of GDP must increase, logically until it swallows up the whole of GDP. That’s the contradiction I am pointing out.

OK, it doesn’t particularly make sense to me to assume that capital replacement is a fixed share of GDP. That could happen, if it turned out that with improving technology and increased capital goods, the stuff just lasts longer and that improvement comes at about the rate that increasing capital goods outpaces GDP. But it seems ad hoc to assume it.

Instead the ad hoc assumption that capital replacement is a fixed percentage of capital goods would be more sensible, though still wrong.

But I don’t see how you get capital replacement swallowing all of GDP. Wouldn’t that only happen if capital goods first swallow all of GDP? Capital replacement doesn’t get its chance to swallow all of GDP until GDP has already been swallowed and thoroughly digested by something else. Have I made a wrong assumption? How do you figure it yourself?

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notsneaky 10.14.14 at 9:49 pm

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?

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notsneaky 10.14.14 at 9:51 pm

Let’s take r to be the rate of capital accumulation

r is the return on capital (wealth). s, the saving rate, is the rate of capital accumulation.

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TM 10.14.14 at 9:52 pm

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.

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Billikin 10.14.14 at 9:55 pm

Martin Bento: “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?”

Was the Black Death one cause of the Renaissance? I dunno. It seems plausible.

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

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TM 10.14.14 at 9:56 pm

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.

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Bruce Wilder 10.14.14 at 10:04 pm

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.

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

Peter T @ 59 is a useful comment, worth reading again.

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notsneaky 10.14.14 at 10:05 pm

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.

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notsneaky 10.14.14 at 10:06 pm

And he most certainly distinguishes between s and r.

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notsneaky 10.14.14 at 10:12 pm

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.

103

notsneaky 10.14.14 at 10:21 pm

If he does assume that b*K is a constant fraction of Y then that would indeed be problematic, since it would be equivalent to assuming that the (actual) capital depreciation rate always varies inversely with the capital-income ratio, and since he’s all about how that can change dramatically, he’d be forced to argue that the (actual) capital depreciation rate changes dramatically (and in “just the right way”), which would be hard to swallow.

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mattski 10.14.14 at 10:31 pm

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…

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notsneaky 10.14.14 at 10:39 pm

I looked it up in Piketty’s US Table 12c. Here, in USAxls:

http://piketty.pse.ens.fr/fr/capitalisback

“Piketty’s depreciation rate” varies between 11% and 15% for 1950-2010. If at the same time we have K/Y varying between 4 and 6 then the actual depreciation rate (as % of capital, b) could maximally vary between 1.83% and 3.75%. These are numbers much closer to what’s in the literature and aren’t crazy. So it’s a weird way of doing things but I don’t think it’s incorrect. To know for sure I’d have to know exactly how he computes that depreciation rate, rather than just guessing at it, and he doesn’t really provide that info. Maybe it’s buried somewhere.

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Billikin 10.15.14 at 12:58 am

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

Collin Street 10.15.14 at 2:43 am

Really? I always heard that the ante-bellum South was richer than the North because of cotton exports.

No, it’s a statistical artefact: the southern population included a quite large group of people who played a large role in the economy but who weren’t accounted as part of the population when generating wealth-per-capita figures.

108

notsneaky 10.15.14 at 3:01 am

#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.

109

notsneaky 10.15.14 at 3:10 am

(he’s right in the sense that the amount of inequality was much higher, which entailed more poverty as well. But per capita wealth or income was higher in the antebellum south)

110

john c. halasz 10.15.14 at 3:16 am

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.

111

greg 10.15.14 at 4:36 am

john @110: I’m interested in the period. Useful and accessible references, esp. about relative wealth and income? Thanks.

112

notsneaky 10.15.14 at 5:55 am

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

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John Quiggin 10.15.14 at 6:08 am

AF, it’s clear from this and our previous discussion (when you claimed that “ban” meant the same thing as “restrict”) that we speak different languages. I can’t see any further point in engaging with you.

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John Quiggin 10.15.14 at 6:14 am

@TM Your example makes it clear why we shouldn’t be using GDP in our discussions. That’s why I talked about national income as does Piketty (contrary to your claim )

http://piketty.pse.ens.fr/fr/teaching/10/25

I only mentioned GDP in the footnote because the most easily accessible measures of the labour share use GDP as the denominator. It may be that at some points Piketty refers to GDP for similar reasons, but national income is the relevant variable.

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John Quiggin 10.15.14 at 6:19 am

@TM In response to your question, depreciation is always a guess (though it can be an educated guess). That’s why GDP is used as a quarterly measure of economic activity: it doesn’t require such a guess.

But for the issues we are talking about, it’s always correct to focus on net income rather than gross product.

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Bruce Wilder 10.15.14 at 6:24 am

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?

117

greg 10.15.14 at 6:56 am

Thanks, notsneaky. A good start. 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. Certainly it reduced social capital, such as education and infrastructure.

118

J Thomas 10.15.14 at 7:28 am

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.

119

greg 10.15.14 at 8:03 am

J Thomas: “I suspect this would be hard to measure. It affected the wages of free labor compared to what?”

Which helps makes the problem interesting. An increase in the supply of labor, free or slave, would reduce the wage free labor could demand. But, slave labor was apparently not cheap. The supply of slaves was intentionally restricted, since, as capital, this made them more valuable, (and their owners wealthier,) but then the return on their labor had to cover their capitalization. And free immigration tended to concentrate in the North, so even with slavery there was not a ‘surplus’ of labor.

I’ve just started on notsneaky’s reference.

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Martin Bento 10.15.14 at 9:30 am

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.

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Peter T 10.15.14 at 10:42 am

The material linked by notsneaky at 112 illustrates my point perfectly. BW at 116: ” The average white man in the South in 1860 was roughly twice as wealthy as the average northerner”.

The average white man in the South was not a slave-owner. Per capita (including both slave and free), the South was much wealthier than the North. Table 2.4 of the link puts it at $569 as against $482. But in non-slave wealth per capita, the North was much wealthier: $482 for the North as against $292 for the South. Most of the wealth of the South was in slaves. This was real wealth – one could sell slaves in the South, take the money and buy farmland or houses in the North. In doing so, one translated wealth into capital. The reverse transaction would translate capital into wealth. The boundary could be – and was – adjusted at the stroke of a sword.

Of course, not all the North’s wealth was actual capital, and much of the capital was not wealth. It’s just that the boundaries were drawn differently. Today, a change in the bankruptcy or copyright legislation can do nearly as much as war accomplished then. This would be comforting if the boundary were shifting against wealth but. alas, it seems to be moving the other way.

Piketty’s central argument pertains very much to wealth, hardly at all to capital.

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john c. halasz 10.15.14 at 4:32 pm

@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.

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Bruce Wilder 10.15.14 at 6:54 pm

jch @ 4:32 pm

The reference to Gavin Wright given by notsneaky @ 112 appears to me to be conventional enough, and there, in table 2.4, slaves are about 20% of total U.S. capital-wealth stock in 1860: $3 billion slaves out of $16 billion total. 80% of capital stock would be not-slaves.

There were about 4 million slaves, out of a total population of 31 million.

The capital value of the slave has to relate to some value for per capita output and the value of per capita output has to relate to the total size of the economy. If U.S. GDP in 1860 was in the range of $4 billion to $6 billion, the capital value of commercial equipment and inventories alone would have to approach the value of annual output. I just don’t see how the numbers could possibly work out that would make the value of slaves 80% of U.S. capital stock in 1860.

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J Thomas 10.15.14 at 8:02 pm

#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.

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john c. halasz 10.15.14 at 8:22 pm

B.W. @123:

The 80% figure doesn’t just come from Picketty; I’ve read the same figure cited in many different sources over the years. The tables cited by notsneaky are a modern economist’s reconstruction in modern accounting terms. (Needless to say, there was no such thing as GDP and the like then). So my suggestion, (aside from just what counts as or is accounted as “capital”, so that, e.g., raw land or houses are wealth, but not capital), is that what is being referenced by the figure is liquid, tradeable forms of capital, by the standards of the time, rather like stocks and other such financial assets. Perversely, slaves were precisely such “assets”, whereas as a lot of fixed capital investment, infrastructure, and even land might not have been readily tradeable, and had only imputed value. For example, I read several years ago, that the value of total global financial assets outstanding in 1880 was 30% of the value of total global output and rose to 50% by the eve of WW1, (obviously a reconstructed estimate). Nowadays it’s +300%. Similarly, there was a claim a while back that German household wealth was much lower than that of Spain , Italy and the like, despite the fact that Germany has a much higher per capita GDP, though the report was quickly discredited as due to artifacts of accounting, (since Germany has a much lower home ownership rate, less than 50%, and a higher level f government benefits). The additional point, is that because of their additional function as collateral, the value of slaves were inflated above the value of the total output of slaves, (whereas the opposite effect would apply to fixed capital). Also antebellum the U.S. was still overwhelmingly an agrarian economy, and most of its output would have been agricultural output, much of which would be consumed rather than traded.

Sorry, that the best I can do, in making out that oft cited claim.

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john c. halasz 10.15.14 at 8:29 pm

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.

127

Bruce Wilder 10.15.14 at 10:57 pm

jch

Reading the relevant portion of the Gavin Wright book, which notsneaky linked to, I could see where, maybe, it might be possible to argue that the value of unimproved land and slaves together approached 80% of capital in the deep South. That would not be an unimportant factoid, since it would indicate to some degree the extent to which slavery and plantation agriculture as a system tended to extinguish investment along other lines, and with it, advanced economic development.

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greg 10.16.14 at 3:44 am

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.””

129

Martin Bento 10.16.14 at 5:57 am

Peter K., what I said was not an assertion about inequality. It was a question about increasing inequality due to r > g. Treating the two as equivalent is only valid if r > g is the only possible source or inequality, which is not. Treating it as assertion about inequality since 1970 is only possible if it is the sole cause of increasing inequality during this period, which it clearly was not. First of all, r was not greater than g during this period, overall, though perhaps the last few years have been an exception.The inequality is primarily because this is a period that saw a great deal of increase in wage inequality. It saw large decreases in the progressivity of the tax system. It saw people like Gates and Ellison amass great fortunes starting with little. As I understand it, Piketty calls this the “period of the supermanager” – by which he means basically high-level executives – people who are being compensated for what they do, not for how they invest. He sees this period coming to an end. Reviews of Piketty, for example Krugman’s, also seem to indicate that he is arguing that r>g is where we are headed more than where we have recently been, though the political changes that set the stage occurred earlier. Indeed, Piketty himself says ““in all the English-speaking countries, the primary reason for increased income inequality in recent decades is the rise of the supermanager in both the financial and nonfinancial sectors” (Chapter 9, pg. 315, at least according to this blog).

130

Peter T 10.16.14 at 6:49 am

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.

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Peter T 10.16.14 at 6:51 am

And I would add that these people are not “compensated for what they do”. They are compensated for what they are.

132

Ze Kraggash 10.16.14 at 8:03 am

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?

133

Martin Bento 10.16.14 at 9:25 am

For the record, are Peter T. and Peter K. different people or was that just a typo? I like to know if I’m conversing with the same person.

I agree “compensated for what they are” is more accurate, since it usually seems to have little to do with performance.

134

Peter T 10.16.14 at 10:12 am

I have never met Peter K.

135

Martin Bento 10.16.14 at 11:04 am

Nor have I met Martin Bento, but I take it you mean no, you are not the same person.

136

dax 10.17.14 at 1:20 pm

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

137

notsneaky 10.17.14 at 1:27 pm

@136 Piketty says the opposite.

138

Martin Bento 10.17.14 at 8:16 pm

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.

139

TM 10.17.14 at 11:31 pm

JQ 114: “@TM Your example makes it clear why we shouldn’t be using GDP in our discussions. That’s why I talked about national income as does Piketty (contrary to your claim )”

Contrary to which claim? I wrote: “Piketty actually has an interesting technical section where he explains these things [that GDP isn’t income], but he then goes on to ignore them.” It is a bit rich of you to misquote me in such a strawman way when my precise point is that Piketty does talk about national income but then still for all practical purposes uses GDP as if it were the same thing.

JQ 115: You are simply confirming what I said: that we don’t have any reliable estimates of net income as opposed to gross product. So we are using GDP instead because it “doesn’t require guessing”. But as I have shown (and you seem to acknowledge), we cannot get correct answers about the development of the capital-income ratio if we don’t have reliable estimates of net income. Piketty says explicitly that he estimates income by deducting a constant percentage from gross income. And frankly, what else can he do if he doesn’t know either the value of the capital stock or the amount of depreciation? But then how can we empirically test his model?

And a propos, nobody has refuted my point in 88/90. 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. That is a real oddity – after all, Piketty became famous for his meticulous empirical work about inequality rising in that period. How strange that he then proposes a model of inequality that fails for precisely that period (*), and how strange that this fact has simply been ignored in the debate (but then, who wants to discuss boring empirical data if you can instead pontificate how a simple formula explains the Universe and Everything).

(*) I would argue that it also fails for other periods. As shown in 88, the 19th century r-g differential of 3.5% according to Piketty should have led to a much higher capital/income ratio even allowing for a net investment rate somewhat smaller than r. On the other hand if the investment rate is much smaller than r, then it was pointless to dwell on r as the alleged driver of inequality in the first place.

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TM 10.17.14 at 11:37 pm

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.

141

Ronan(rf) 10.17.14 at 11:43 pm

139 – I havent read it all but is this not his argument

““Well,” he told me in an email this morning, “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.””

http://www.slate.com/blogs/moneybox/2014/10/15/piketty_igm_forum_economists_did_not_just_reject_capital_in_the_21st_century.html

142

TM 10.17.14 at 11:53 pm

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.

143

TM 10.17.14 at 11:55 pm

Ronan 141: What is “his argument”? That inequality “has little to do with r > g”? You mean, everybody has completely misunderstood Piketty’s big book?

144

Ronan(rf) 10.18.14 at 12:22 am

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 ?

145

Martin Bento 10.18.14 at 7:57 am

I’m glad we’re all now in agreement that Piketty does not attribute the recent rise in inequality to r>g. Peter K. owes me an apology for calling my comment on this a “howler”.

I have a problem with treating the 20th century as a simply anomaly though, precisely because it is an anomaly in innumerable ways, most of which seem unlikely to reverse. The way we live today, due primarily to technology, and the way the system works is drastically different from anything pre 20th century. If we expect r>g just to return because that is historically “normal”, do we expect most people to return to the farm because that, too, is “normal”? Do we expect the return of unowned land in the developed world? I’m not saying Piketty is necessarily wrong, but modernity is so exceptional I don’t see reversion to long-term historical norms as a strong argument.

146

Ze Kraggash 10.18.14 at 9:22 am

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.

147

Martin Bento 10.18.14 at 10:33 am

Ze, I think implicit in the whole idea is that the rate of profit does not necessarily tend to fall and has not historically. The Marxists and neo-classicals both have theoretical reasons why it should, but, according to Piketty as I understand it from hearsay, this does not stand up to experience.

148

Layman 10.18.14 at 2:15 pm

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.

149

Layman 10.18.14 at 2:31 pm

TM @ 142: “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). “

Piketty, Capital in the 21st Century, page 115: “We find, to begin with, that the capital/income ratio followed quite similar trajectories in both countries, remaining relatively stable in the eighteenth and nineteenth centuries, followed by an enormous shock in the twentieth century, before returning to levels similar to those observed on the eve of World War I. In both Britain and France, the total value of national capital fluctuated between six and seven years of national income throughout the eighteenth and nineteenth centuries, up to 1914.”

This is in the opening if his section on the capital / income ratio.

150

Layman 10.18.14 at 3:44 pm

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.

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martin bento 10.18.14 at 10:53 pm

Layman, thanks for the apology. I wasn’t expecting one from you. Sure,I would get the answers by reading piketty, and i may do that,but blog threads are a good way to get the bottom line of something as you decide where to put it in the reading queue, I think.

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mattski 10.19.14 at 1:57 pm

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.

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Ze Kraggash 10.19.14 at 2:26 pm

“Piketty’s entire point with r > g is that it is an economic tendency”

How’s that an economic tendency? When g gets high, the central bank will jack up interest rates to bring it down, to keep unemployment rate high, and so on. It’s all political.

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mattski 10.19.14 at 3:24 pm

It’s all political.

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

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