The Politics behind Piketty

I think that this comments misses the force of Piketty’s inequality r>g. Even if intellectual property laws were weaker (and rents thereby smaller) and and labor laws and Keynesian policies stronger (and thereby g higher) and even if small savers had a bit higher rate of return, the Piketty inequality would still be in operation (and big savers would still have much relative returns), giving us the uncanny return of a rentier society.
In short, this comments seems to me to miss the force of the r>g inequality.

I don’t agree that Piketty ignores institutional changes or changes in property laws, e.g. the end of human chattel, the operation of war commissions, the evolution of minimum wage laws, the weakening of collective bargaining, and the “stakeholder” nature of Rhenish capitalism. Piketty is aware of all this, but he still reasons on the basis of his r>g inequality that the return of a rentier society is most likely except through a global tax on wealth. The principal reason: even if through institutional reforms r is reduced a bit, g is likely to revert to historical averages even with the right Keynesian policies. That gives us a r>g inequality great enough to yield an actual rentier society (not the petit rentier one we now have).

I’m sympathetic to the direction of this argument, but does a list so focused on the US provide an adequate explanation of a global phenomenon?

Hot off the presses, today’s example of rent seeking in trillion dollar markets: http://www.nytimes.com/2015/12/07/business/a-revolving-door-helps-big-banks-quiet-campaign-to-muscle-out-fannie-and-freddie.html?hp&action=click&pgtype=Homepage&clickSource=story-heading&module=first-column-region&region=top-news&WT.nav=top-news

see also work by Grusky and Weeden, who have been pushing the line that rents are ubiquitous throughout the labor market, and not just in the top 1%, for quite some time.

But, they are sociologists, so they are easily ignored by Stiglitz, Reich, and other economists who are trying to make rent-based arguments for rising income inequality.

Central banks across the OECD have practiced austerity

Whatever this is, it is not austerity.

What piketty does not analyze is nature of ideological hegemony in a rentier society. I already pointed to Bukharin’s critique of rentier ideology in the economic theory of the leisure class. It makes for a fascinating comparison

What piketty does not analyze is nature of ideological hegemony in a rentier society

As I read him, he doesn’t need to, because it’s irrelevant.

What Piketty’s numbers prove is that it wasn’t ideology or politics or unions or social movements and programs that gave us the Great Compression and decreased inequality but revolution, depression, and catastrophic war. Certainly history shows that every catastrophic war etc did not necessarily led to greater equality, but there is very little evidence for increases in equality without radical social disorder. Piketty explicitly says toward the end that moderate tax increases or redistributive social programs have had little effect, that the lower baseline after WWII was determining.

What is taken from the above can be up for discussion, perhaps the best can be done during peacetime is ameliorative efforts within a context of rising inequality, and ideology can help with those besides preparing for the inevitable collapse. But effective demand management will quickly fail for political reasons, see Kalecki.

If the above looks like Marxian praxis, it’s no coincidence. Piketty’s recommendation, taxing global wealth at confiscatory rates, should be understood as a practical recommendation. I think we all understand what it would take to tax away 40-50% of gross Saudi or Brunei or American wealth to distribute to Africa and South America, and Piketty surely was not unaware.

What struck me most about Piketty’s data was the near constancy of r over centuries. This suggests to me that it is not a matter of balancing supply and demand for capital, but a structural feature (perhaps the return necessary to sustain the hierarchy of production?). So r, in itself, has little to do with the distribution of return: it could be spread across a large middling to wealthy class, or concentrated in the 0.1%, as political factors dictated.

I will add that the underlying mental model in much of economics seems to be the gentleman’s estate. There is land, income for investment or consumption as prudence and virtue dictate, the lump sum in consols…with the ideal the improving landlord. That categories such as “capital” or “labour” do not stretch to countries does not seem to cross the imagination.

@18 If population is growing at a fast rate and therefore g as well, the fundamental inequality will be attenuated, and it will be difficult to see the long-term consequences of r>g in such a society. France gives us a better laboratory to see the likely effects of the fundamental inequality going forward than the US has hitherto provided.

@17 raises difficult questions. Some economists have claimed that r>g is just what you would expect from dynamically efficient economy, but this needs to be spelled out. Piketty has a complex section which I have not yet fully understood on why r being positive, and greater than g, cannot be explained in terms of a psychological theory of time preference. Perhaps another way of thinking about this would be: what would happen if r were to fall below g? Would there be mechanisms to restore Piketty’s fundamental inequality? Piketty, I think, is saying “yes”. So I shall re-read that section to get a better understanding of his argument.

A question for the more economically minded – Would one reason that r is reasonably stable over a considerable time frame be because it is determined not by the most wealthy holders of capital (who presumably could afford to take a lower rate of return on a long term basis), but by the less wealthy who depend on a higher rate of r as otherwise their smaller investments wouldn’t be financially rewarding?

For instance, in Australia workers have compulsory employer paid superannuation investments, and if the rate of return on these was lower I don’t know that the policy of moving people to self-funded retirement by superannuation as opposed to government pensions would be feasible?

I’m very sympathetic to much of the list of bad policies. I have a question about this though: “On the ideological front, several theories served to rationalized policy shifts in favor of increasing capital shares and top labor incomes. The stagflation of the 1970s was successfully blamed on Keynesian economics, fiscal irresponsibility, a bloated welfare state, militant labor unions, state regulation of the economy, and supposedly incentive-destroying high marginal tax rates on capital incomes and the rich.”

What should it have been blamed on?

[I’m very open to the idea that the lessons of the 70s were overlearned–i.e. just because too much inflation is bad doesn’t mean we should worry about it when it is below 5%. But this comment suggests that something else entirely was going on]

I am not an economist, but the source of the blame was political. I have heard that the primary causes of “stagflation” were “printing money” to cover the debts from the Vietnam War, increased oil prices and supply issues driving up costs, and economic competition from Japan reducing demand. The economic elites saw an opportunity to
take advantage of the crisis and blame it on policies they did not like. And push to replace them with policies that were advantageous to those elites. Ronald Reagan was a very successful salesman for this.

Piketty uses “capital” or “wealth” to refer to any asset which provides a stream of income. This is, in my view, correct. This is quite distinct from “capital” in the ordinary economic sense. Much – in fact most – economic capital does not yield income (roads, schools, food crops…) and so does not count. There is no reason to believe that wealth in the first sense does or should correspond to capital in the second sense. Our collective capital dwarfs wealth, while much wealth is simply extractive. To count a claim on tax revenues (a government bond) in the same class as a terraced field is a major mistake.

From the late C19 on much private “capital” was withdrawn into the public spheres (eg private tolls or offices), a move that accelerated in the wars. Since 1980 this trend has reversed. Discussion of the amplitude or scarcity of capital should note that it is a legal and political category subject to large arbitrary changes.

@Rakesh – but the whole r vs. g thing in Piketty, while central to his book, is also the part that makes the least sense. It’s made up, theoretically unsound, and with no evidence to back it up. It’s junk. An accounting relationship is not a “law”.

And it’s really Piketty’s single minded focus, based presumably on his desire to provide a grand “one size fits all” explanation for the phenomenon he’s discussing, which leads him to sideline all the possible institutional explanations, such as the ones enumerated above (not that I agree with all or even most of them)

I’ve argued before that the conclusion that the simple inequality r>g leads to unlimited inequality is wrong -or at best incomplete. There are multiple ways that concentrations of capital can be, and are dissipated (i.e. broken up into smaller bits owned by more people). Taxes, and “death-taxes” is only one mechanism to accomplish this. Having on average more than one inheritor is another. Think for example of the Saudi Royal family, which controls great deal of the wealth of the Kingdom. It isn’t all concentrated in one nuclear family, there are now thousands of princes, after not too many more generations a plurality of the country will be able to claim royal inheritance. Also there are other mechanisms, that can dissipate wealth concentrations, including luxury goods: Maserati is distributing some wealth from the super rich, to its shareholders and employees… Major donations to charity is any other. Still another comes from the application of the saying “a fool and his money are soon parted”: some of the progeny, will be separated from their inheritances. One can’t just use a simple theory of the evolution of the distribution of wealth and income, if you ignore wealth dissipation effects you will get a wildly wrong result.

So in order to control or reverse the tendency towards ever increasing inequality, there could be deployed multiple strategies, all of which are aimed at increasing the dissipation of concentrations of wealth.

notsneaky

My reading of this is:

consider r as the average rate of return on the things politics allows one to generate income from owing (land, slaves, government offices, army commissions, tax revenues, corporate stocks…). Piketty finds this to be a near constant 4% or so.

Piketty observes that long-run growth is generally less than this, that some part of r is plowed back into further wealth acquisition and that larger wealth-holdings earn higher returns and are, on the whole, more immune to negative shocks. So wealth concentrates, and takes a larger proportion of overall income until there is a re-set. This can be revolution, war, aggressive state redistribution or a redefinition of what is allowed to count as wealth.

It’s neither a law nor an accounting identity. It’s a historical trend.

My name links to my demonstration that Piketty is mistaken about his theory about the consequences of r exceeding g.

But that’s the point though. It’s not about r vs g. It’s about politics. r vs g could be doing whatever it is r vs g wants to do and capital’s share could be doing its own thing. So if we see capital’s share going up we shouldn’t say “it’s r vs g”. We should say “it’s politics”

No. Because the trend is there, inherent in the system. The politics is about limiting/reversing it. Unless, by “politics” you mean the structure of society.

If by “trend” you mean “r is greater than g” then that is neither a well established trend nor is it in any way (“inherently”) related to the degree of inequality. Not empirically. And theoretically, Piketty does not actually explain how it would be.

point 5 looks a bit weak.

– point 5 starts off with speculation and ends with illegality. They are separate. What exactly is your point here?
– fines capture only a small fraction of profits from illegal dealings where is your evidence for that?
– Where is your evidence that the amounts of money diverted in the scandals you mention are big enough to have resulted in measurable increases in global inequality?
– virtually no guilty bankers have been prosecuted for their roles in the financial crisis Tom Hayes has just been sentenced to 14 years, although he has an appeal. Your assumption that you know who is guilty without the need to go through a trial sounds like a witch hunt.

Why no mention of banks roles in Mergers and Acquisitions? These have reshaped ownership and control of many industries without any apparent benefit.

Why no analysis of regulation post-crash? Significant changes have taken place in Financial Markets, many of which left-leaning people should support. Are they working?

Omega Centauri brought up a point with the Saudi royal family. Wealthy families tend to burn out most of their money in a few generations at most – very, very few of them remain wealthy for longer than that. How does that work in a system supposedly dominated (or becoming dominated) by patrimonial capitalism? Just intra-elite competition in zero sum terms?

Brett @47
” Wealthy families tend to burn out most of their money in a few generations at most ”
That was true several decades ago, but is it still true?

17: “What struck me most about Piketty’s data was the near constancy of r over centuries.”

That struck me, too. In a dynamic, ever changing universe, Piketty’s claim to have found something akin to a constant of capitalism – without naming any mechanism that would explain this one aspect of capitalist economy to have stayed near constant for centuries, while everything else has constantly changed – should induce a healthy dose of skepticism.

I’m rereading an earlier thread on r>g (https://crookedtimber.org/2014/10/13/r-g/) and my impression (you can read my detailed arguments there) remains that hardly anybody is actually taking Piketty’s r>g theory seriously, in the sense of a scientific model supposed to describe reality and capable of being tested empirically. As I have shown, as a model (rather than a slogan) r>g doesn’t pass the reality test. It’s not consistent with the data Piketty himself presents. For example, Piketty reports r minus g of about 3.5% during most of the 19th century, which would imply a roughly 32-fold increase in the capital-income ratio over a century, yet he reports (http://piketty.pse.ens.fr/files/capitalisback/F3) that capital income ratio in the UK was *constant* at about 700% throughout the 18th and 19th centuries.

@52

Well yes, agreed, but Tom Hayes was convicted for LIBOR rigging. If that is not relevant to Elizabeth Anderson’s point why is LIBOR quoted in point 5?

Banking provides a vast and rich banquet of scandal, wrongdoing, and inappropriate behaviours. But if you want to make serious points you can’t just fill your plate with whatever is in front of you. You have to pick carefully, and join the dots with suitable evidence. I don’t see much of that in point 5.

Peter T: these factors are in direct contradiction to Piketty’s claim that the capital-income ratio remained constant from at least 1700 to 1900.

“I don’t know if these together explain why the wealth/labour proportion did not rise as much as might be expected” – if you are referring to the wealth-income ratio, it didn’t rise *at all* according to Piketty.

I have nothing to say about r>g. But something to say about “weak rawlsianism,” which is an interesting concept. What does the 99% get from the plutocracy? You can look at the Presidential primaries to see that: a promise of “safety” (and fear-mongering to make the general public feel that they “need” safety); a promise of “jobs” (and fear-mongering about minorities and immigrants who might “take” job). In neither case is there any serious thought about what “safety” might mean, or about whether “jobs” are meaningless if the pay is below poverty level. There’s no thought about whether proposed policies about either security or jobs might actually make the situation worse. If the situation becomes worse, that’s even better for the plutocrats, as long as the problem can be blamed on a minority.

“You hate what we hate; isn’t that enough?” It remains to be seen how well that will play out over the long term. Probably not well.

Peter, first we need to clarify what precisely we’re talking about (one of the annoying things about Capital20 is that Piketty never does this and then switches back and forth between different definitions of “inequality” committing various false equivocations and other fallacies in the process).

If by “inequality” we mean capital (or land’s) share in total income then in your example there’s nothing which actually affects what happens to it. That share could go up, could go down or it could stay constant. r vs g doesn’t explain anything about it.

If by “inequality” we mean concentration of ownership of capital assets then it’s possible that the process as you describe leads to higher concentration of wealth via “shocks which eliminate smaller” claims. BUT. The last part is not necessarily correct. It’s the fact that there’s random shocks which leads to capital ownership concentration, not anything to do with r vs g. Higher returns (higher r) may or may not affect how this process unfolds. Under some very implausible assumptions (both r and g are divinely determined) it could wind up like that. But as soon as you realize that r and g are actually related to each other, the logic breaks down.

There’s absolutely no explanation in Piketty’s book about how r greater than g should actually, logically, lead to higher inequality. There’s an assertion and some sketchy accounting. There’s a lot of claims about “inescapable logic of r vs. g” but no explanation of that inescapable logic. There’s a lot of discussion as to whether r is actually greater than g. But no explicit connection.

Empirically, we know that inequality – both in terms of capital’s share and in terms of capital ownership concentration – has increased. For some portion of the period, maybe r was greater than g (very debatable actually). So at best you have an empirical (very weak) correlation between a time of increasing inequality and r greater than g. But without an explanation of a casual link, this explanation fails. There’s a million other explanations/correlations that could be posited.

The implication is that there’s nothing “inherent” or “natural” about the increase in inequality that we’ve been observing. It was simply a consequence of policy choices which more or less redistributed income from labor to capital, and from small scale capital owners to large scale capital owners. We could very well have had r greater than g, a different set of policies and a different level of inequality.

So in general, the OP is correct here. Piketty is focused and determined to establish this r vs g thing, which isn’t even logically sound, that he misses the obvious roles of policy.

Here is Chuck Jones working through the logic of r vs g

http://pubs.aeaweb.org/doi/pdfplus/10.1257/jep.29.1.29

Here is Acemoglu and Robinson addressing both the theoretical and empirical weaknesses of the r vs g story

http://pubs.aeaweb.org/doi/pdfplus/10.1257/jep.29.1.3

I see an interesting discussion here about politics. It seems to me that neo-classical economics tried to Korzybskize political economy. At least in the sense proposed in The Manhood of Humanity. Which was to empiricize social science (which Korzybski referred as the pseudo-sciences. Ironic since Korzybski is pretty much now considered pseudo-science).
I do think it tells us something that they dropped the political part of the equation.
I suspose there was some intellectual honesty involved in that they were looking for
laws of economics outside of politics. However, I am of the opinion that everything involving human behavior is “political”. There is no “inverse square law” or “second law of thermodynamics” in human behavior. So I think making an empirical science of
political economy (or any other social science) is doomed to failure.

As I understand it, r>g is an empirical law, not a theoretical law, yet several commenters here seem to be making this mistake.

As to what causes it? I would guess that some of it is unintentional, but most of it is intentional, one way or another, and thus includes politics. Not merely includes politics, but animates much of politics, really.

Elizabeth Anderson’s list of political rent-seeking is a good one, and a keeper. But for me, her “money quotes” come at the end, after an implicit question: What to do about it?

Anderson observes, “…much of this has been peddled to the public…they feel strongly entitled to [their acquisitions]…reluctant to tax…need to scrutinize…getting this story out is critical…exposing the ways…”

Yet when we attempt to push further down this avenue, we crash into another empirical law:

Attempts to “get the story out”, to “expose the ways”, crash into a very potent combination of the following factors: mental inertia and cognitive limitations; personal time constraints on learning new information; the extreme informational complexity of the proper description; —

— and now, a rather new development: the explosive proliferation of new info-media, which has led to the complete disappearance of a common reference narrative to which people know that they can refer, for information that is reasonably true. Who is going where, to find out what? Our whole system is running on in-group narratives.

In short, we are already given a democracy, more or less, and thus we could fix things, if voters knew the facts as opposed to being driven by their emotions. Our real problem is an enormous RHETORICAL problem, with various facets to it. (I think there is a way to go here, and you can click on my name for a possible answer.)

However, I want to make a very different point, about where to go:

At the same time as we have exacerbated the era of rent-seeking, we appear to be moving into an era of post-scarcity and technological unemployment. I don’t think we should see it as a bad thing, although people often appear to be confused by two faulty objections: 1. that focus on technological unemployment puts aside the rent-seeking explanation for inequality (no, it doesn’t); and 2. that technological growth must cause environmental damage (no, it needn’t).

We should instead incorporate it into the way forward.

Therefore, I don’t think it will help anybody to fight the increasing capital share — to “raise g”, in other words — only to maintain the 30-40 hour work-week for everybody, and to continue with this ridiculous system of the phony scarcity of money administered by interest rates.

Instead we should head towards solutions that comport with the real abundance: 10 hour work weeks for everybody (then, they might have the time to learn what is happening to them!) and print the money for universal goods and services which have supply-and-demand characteristics that do not automatically cause inflation (e.g., education, healthcare, retirement security). There is no sense in coursing everything through the private financial system, just so they can take their share for no value-added. We will end up right back here, where we are.

I don’t really understand the criticism of r>g. If I understand correctly some are saying that P. is claiming that r>g when g is sometimes apples, and sometime oranges.
Some seem to be saying that any relationship between r & g is nonsense.
And some seem to be saying that P. is misrepresenting or misreading historical trends.

Are any or all of these criticisms legitimate.

notsneaky 61:

“Basically any economy (whether capitalist or not) which has a “steady state” will wind up with a constant r. (Malthusian economies might be exceptions)”

Now you are astonishing me. There are no “natural constants” in the economy and anybody who claims having found one is almost certainly a crank. And also, logically you cannot have a ‘steady state’ while capital accumulate faster than economic growth. Capital depreciation will end up swallowing the whole of GDP.

LAA 64: Piketty claims r>g as an empirical fact (or at least tendency) AND makes claims about the implications of r>g for inequality. Even though the latter aren’t really fleshed out as an explicit theory (as notsneaky says at 60), Piketty clearly claims (without demonstrating) some generizable correlation between inequality and the difference r minus g.

TM #69: “Piketty clearly claims (without demonstrating) some generalizable correlation between inequality and the difference r minus g.”

I don’t understand where you are going. Is your argument that Piketty thinks that the correlation between inequality and r>g is theoretical?

@65 “The way to fight an empirical law, in other words, may be to change the empirics.”

In that case it wouldn’t really be a law, would it?

(and anyway, it’s not even an empirical regularity. Sometimes r greater than g, sometimes g greater than r. Sometimes inequality goes up when r greater than g, sometimes it goes down. The correlation is weak)

“Now you are astonishing me. There are no “natural constants” in the economy and anybody who claims having found one is almost certainly a crank. And also, logically you cannot have a ‘steady state’ while capital accumulate faster than economic growth. Capital depreciation will end up swallowing the whole of GDP.”

Ehh. I don’t know if there are “natural constants”. All I said is that if an economy has a steady state (where output, capital, consumption, etc. all grow at constant rates) then it will have a constant r. That’s pretty much a definition of a steady state. Whether that constant is determined by time preference, tax policy, institutions, politics, technology or God is up for debate, but it’d still be constant.

By “accumulates faster than economic growth” I assume you mean that capital grows faster than GDP. That would indeed not be a steady state. That’s why I said *IF* an economy has a steady state.

I don’t know what “Capital depreciation will end up swallowing the whole of GDP” means.

Basically any economy (whether capitalist or not) which has a “steady state”

Like France, say?

The word “economy” in this sentence is really dangerously ambiguous in whether it refers to an actual economy (in which case it’s talking hypothetically about something which has never been observed and probably could never be), or to a mathematical entity (in which case it’s necessarily true). This isn’t just a problem of whether the model is accurate enough to be useful – the idea that this equilibrium property is relevant to Piketty’s book is an empirical claim (IMO an extremely strong and definitely incorrect one).

” the idea that this equilibrium property is relevant to Piketty’s book is an empirical claim”

I guess it’s empirical in the sense that we could open up Piketty’s book and check if he talks about economies and their steady states in there.

(or in other words, if you don’t like this approach, talk to Piketty)

75: “All I said is that if an economy has a steady state (where output, capital, consumption, etc. all grow at constant rates) then it will have a constant r.”

Sure, if your definition of steady state includes r constant, then any economy at steady state will have r constant. That’s a tautology.

Not quite. If steady state then r constant. But r constant does not automatically imply steady state. You’re denying the antecedent.

There are a series of logical and data issues surrounding the claim that r greater than g. Worth taking a look before weighing in on the meaning and technical merits of CIT21C. You can google Rognlie and find various high and low quality descriptions of the papers as well. But here are the originals and a discussion by DeLong.
http://www.mit.edu/~mrognlie/piketty_diminishing_returns.pdf
http://www.brookings.edu/~/media/projects/bpea/spring-2015/2015a_rognlie.pdf
and
http://delong.typepad.com/sdj/2014/06/over-at-equitable-growth-daily-piketty-matt-rognlie-has-a-first-rate-critique-thursday-focus-for-june-12-2014.html

Are people here seriously arguing that after-tax r may approximate g? I am not economist, but I don’t think we need to get into the intricacies of the Cobb-Douglas production function and neo-classical growth theory to grasp what is going on–see pp. 215ff of Piketty’s book . That r may not be greater than g is not the claim DeLong is considering–that involves the elasticity of substitution and whether any increase in Piketty’s β is at least counteracted by a fall in r so that Piketty’s α does not increase. But note again that Piketty thinks his β will increase due to reversion of growth to historical averages–this is key to his argument– so the increased volume of capital will counteract any possible declining r, resulting in his α trending upward.
Again I think Piketty would have been on stronger ground to abandon any theory based on the marginal productivity of capital and find theoretical support in the Cambridge Capital critique that he unpersuasively critiques.

Rakesh, I’m assuming you’re referring to those papers/critiques by Rognlie. That’s really a different argument then the one we’re having here, but yes, Rognlie is right.

If your production function is Cobb-Douglas and you have a fixed saving rate then whether r is greater than g depends on whether that saving rate is greater or less than the share of capital in income. However, whatever the case, that capital share is constant and r vs. g is unrelated to that kind of inequality.

If your production function is Cobb-Douglas and you have an endogenously varying saving rate then r is always greater than g (if consumption is increasing along with income, i.e. if you’re at or “below” the steady state). However, whatever the case, that capital share is constant and r vs. g is unrelated to that kind of inequality.

So you need a non-Cobb-Douglas production function. However, even with that, in steady state r and g will be constants, capital’s share will be constant and the steady state will look very similar to Cobb-Douglas. So instead, Piketty switches tack.

Rather than talking about the steady state (which is EXACTLY what he is assuming when he is discussing his alpha and beta) he waves some hands about the transitional dynamics. If you have a non-Cobb-Douglas production function and an endogenously varying saving rate then yes indeed, you can have that along the transition to steady state r is greater than g and capital’s share increases over time.

But, and this is what Rognlie and others point out (and once you get yourself unconfused by Piketty’s obfuscation, it’s sort of obvious), in order for that to happen you have to assume that capital and labor are substitutes. More substitutable than Cobb-Douglas. In fact, it must be possible to produce output with *only* capital or *only* labor. Piketty claims (though buries the claim) that this is indeed the claim. No one who has ever worked on this or related topics thinks this is true. Whether you estimate this substitution elasticity with macro or micro data, old data or new data, capital and labor are not substitutes. Piketty knows, or at least should know this.

(incidentally the Cambridge folks tend to assume the polar opposite, that capital and labor are perfect complements. Although I’m not sure how exactly Cambridge Capital theory would help Piketty out here))

It may be that the recent rise in α and β cannot be connected to Piketty’s mechanisms but to asset inflation in real estate. But again I think Piketty is getting a bad rap here. He certainly recognizes that his β can rise and fall as a result of bubbles and their bursting, but he also argues that s/g accounts for the long-term K/Y ratio.

“This is obfuscation–the capital share is not constant. Piketty shows that, so if your Cobb-Douglas function insists that it has to be–for reasons you could better specify–then you should ditch”

The point is that when we “ditch” Cobb-Douglas it actually gets *worse* for Piketty. In that case, if capital and labor are compliments (they’re both necessary for production to take place) then we should observe lower inequality when r-g is high, the opposite of Piketty’s whole thesis. And pretty much any serious study, from any corner of the political spectrum that’s been done comes to the conclusion that capital and labor are indeed compliments in production.

Now, Piketty at this point basically says “well according to my hypothesis inequality should should be when r-g is high, so therefore capital and labor must be substitutes”. In other words, he assumes his conclusion (just in a… obfuscated, way) rather than actually providing evidence for it.

No one’s arguing that capital’s share is constant (well…maybe, but anyway, that’s another argument, not this one) . The argument is that Piketty does not provide an explanation for why capital’s share has risen. At least not with this whole r-g thing.

if it’s about political struggle, then it’s not about r vs. g

I am afraid I do not quite see how that must be true.

@95 Trivial example. Suppose we live in a socialist utopia where workers own the means of production and all have equal shares in the economy’s output. For whatever reason r is greater than g. Is anything going to happen to inequality in this economy? (and if capital ownership is unequally distributed then there’s actually nothing about r greater than g that must lead to greater concentration)

@96 I’m a bit tired of trying to explain it. You can read those links provided by T above in 85. And keep in mind that when you say stuff like “There is nothing about production inherent in the accumulation of wealth.” you’re not arguing with me, you’re arguing with Piketty who’s the one that made the particular choice of this framework.

OK. We have Piketty’s “mysterious” reasoning that if those who enjoy a sharply disproportionate share of wealth are enjoying their wealth grow at a faster rate than the income of those who labor–that is r>g–then the capital/income ratio will tend to rise, the capital share of income will likely rise (though somewhat moderated by a fall in r), the concentration of wealth may well rise (those already with more wealth will be able to add to their wealth faster on account of their r being relatively higher than the average), the share of the wealth and income of the top centile and .1% will likely rise and the share of wealth that is inherited will also likely rise.

All this seems very mysterious to critics of Piketty who claim that there is no obvious connection between his fundamental inequality and inequality and that his having created the data to show that over two centuries r has tended to be greater than g and that inequality has tended towards disturbing and morally incoherent levels–except during times of war, revolution and political chaos–should not be much grounds for concern.

After all, it could be that in the course of accumulation, s, g and r–which are endogenous variables or variables in mutual relationship–could change in such a way that Piketty’s beta and alpha won’t rise as he expects.

No matter that Piketty tries to show that the best ranges that we can give for s, g and r on the basis of historical data painstakingly collected give us every reason to believe that the market left to itself will generate dystopian levels of inequality in the ownership of wealth and income.

Our economist model builders tell us that it is not necessary that things will work out the way Piketty thinks likely–r or s could sharply fall after all in the course of accumulation; g could miraculously reach Jeb-projected levels– and they rejoice at every admission of uncertainty Piketty makes of the future trajectory of market society.

Piketty after all does not claim to foretell the future. Though all Piketty does is let history set the range for the variables in his equations, he is accused of the same historicism with which Popper tagged the Marxists (we’ll leave aside the strangeness of Popper criticizing Marxists for predictions of cataclysm in a work written in exile from the Nazis).

All that said, notsneaky who I think is saying similar things to Acemoglu and thus really is no political bedfellow of Anderson of the OP writes: “if capital and labor are compliments (they’re both necessary for production to take place) then we should observe lower inequality when r-g is high.” Please explain why that would be the case, notsneaky.

notsneaky 83: Your *definition* of steady state includes the condition r constant. Therefore it’s a tautology to say (as you did) that every steady state economy has r constant.

75: “I don’t know what “Capital depreciation will end up swallowing the whole of GDP” means.”

1. A portion of production (GDP) goes toward capital replacement (depreciation) and a portion goes toward capital creation (net investment). These amounts are therefore not available for consumption.
2. If r>g and r is interpreted as the rate of growth of capital (or wealth), or a close approximation) (as Piketty does), then capital stock relative to GDP (the capital-income ratio) increases. (*)
3. Increasing capital-income ratio implies that an increasing portion of GDP is used for capital replacement and investment. If this process continued, there would be a point when nothing is left for consumption, which of course is physically impossible, but that is the implication of r>g, and with Piketty’s numbers (3-g about 3.5% over a period of centuries), that point would have been reached quickly. Of course this is NOT a steady state economy.

The argument in 2., which is the heart of Piketty’s r>g argument, makes superficial sense, but it really makes no sense when looked at closely. Piketty’s own empirical data (http://piketty.pse.ens.fr/files/capitalisback/F3) say that capital-income ratio was constant at 700% from 1700 to 1900, and has been steadyly increasing (from a much lower level) since 1950. But his r-g data (http://www.nybooks.com/articles/2014/05/08/thomas-piketty-new-gilded-age/ figure 1) are totally inconsistent with that picture – he says r was always much greater than g *except* in the 20th century, including the period sinced 1950. So empirically, nothing makes sense.

(*) Here is how Krugman explains Piketty, from the NYRB review:
“At the time [19th century], owners of capital could expect to earn 4–5 percent on their investments, with minimal taxation; meanwhile economic growth was only around one percent. So wealthy individuals could easily reinvest enough of their income to ensure that their wealth and hence their incomes were growing faster than the economy, reinforcing their economic dominance, even while skimming enough off to live lives of great luxury.” Inequality increases because the capital-income ratio increases, because capital grows at a faster rate than GDP (r>g). But again, Piketty says empirically the capital-income ratio stayed constant despite r>g (and it increased after 1950 despite r<g).

“Trivial example. Suppose we live in a socialist utopia…”

Well, my neoclassical example (see paper linked to by my name) is of pension capitalism, where retired workers live off their assets accumulating interest. And I have an asset that can yield a real rate of return (because of price changes), but does not function as an input into production.

I do not say this model is non-trivial, albeit I lay out the math in too much detail in appendices. I had fun figuring this out, especially stability.

Anyways, it is clear something more than r > g needs to hold for inequality to increase.

notsneaky And keep in mind that when you say stuff like “There is nothing about production inherent in the accumulation of wealth.” you’re not arguing with me, you’re arguing with Piketty who’s the one that made the particular choice of this framework.

I think Piketty did a supremely clever thing by confusing wealth and capital, but I am not confused. Without the confusion of wealth and capital, he cannot get a hearing from the mainstream economists, whose thinking is framed by Solow-Swan growth models. The struggle of economists over r > g is a struggle to come to grips with the shortcomings of a model of growth that features an aggregate production function and an accumulating capital, but does not distinguish wages from rents. Not Piketty’s model, so much as their own. Piketty does not have the answer; he has some facts, and he has cast those facts in a way that challenges the orthodoxy, by confusing them and drawing them into furious calculation and critique.

I appreciate that one of the shortcomings of Piketty’s exposition is the oversimplification he chose to make in not distinguishing rates of depreciation and reinvestment (the reproduction of capital) in his analysis. This oversimplification has consequences. That is what I get from T’s links @ 85.

Wealth and capital are NOT the same thing. Like I said, Piketty confounds the terms and concepts. His bad, I guess. But, in doing so, it seems to me he opened up the discussion to the political determinants of the distribution of income. In the full scope of Piketty’s vision, it is possible to see that private Wealth invests in rent-seeking; any investment in productive capital is purely incidental. The accumulation of private wealth can be a bad thing for society and the inexorable accumulation of wealth is a political force affecting the distribution of income. I would not want this obscured.

Bruce @105
Sorry, I see I have made pretty much the same point as you did. My answer referred to TM @101 .

I’m not sure why this is so confusing for some people.

reason 106, part of the difficulty is that Piketty’s use of terms like capital and income is not consistent. Nevertheless, I don’t see how the problems I point out at 101 go away by tweaking the definitions. After all, I am referring to Piketty’s own data concerning r, g and the capital-income ratio. These data are simply inconsistent with Piketty’s own interpretation. So please don’t tell me I should use a different definition. It shouldn’t matter.

“notsneaky 83: Your *definition* of steady state includes the condition r constant. Therefore it’s a tautology to say (as you did) that every steady state economy has r constant.”

A steady state of an economy is defined as a situation where output and capital (and population) grow at constant rate. If output and capital grow at a constant rate then r will be constant. If r is constant however that does not necessarily mean that the economy is or has a steady state (for example open economies with different time preferences and no adjustment costs to capital flows). So it’s not a tautology.

But if you like you can insist on it being a tautology. The point then would be that Piketty wasn’t the first to “discover” that economies can have steady states (i.e. constant r)

Rakesh, I’m sorry but you’ve gone off and started roughing up various strawmen, so I can’t really address that.

One more time. Piketty tries to stay firmly in the neoclassical framework. There’s absolutely nothing in the neoclassical framework which would link r-g to inequality. (There’s actually nothing in any framework I’m aware of that would link r-g to inequality but people are getting hung up on criticizing the neoclassical framework while defending Piketty – you can’t have your capital and eat it too ) He waves his hands. And confuses the issue. And uses some accounting identities to rewrite the same thing in different way and calls that a “law”

“2. If r>g and r is interpreted as the rate of growth of capital (or wealth), or a close approximation) (as Piketty does), then capital stock relative to GDP (the capital-income ratio) increases. (*)”

But r is not the growth of capital, it is the return on capital.

The growth rate of capital is (saving rate * output-capital ratio) – depreciation rate. Piketty actually does some redefinition here which cause a lot of confusion and obfuscates a lot. He rewrites the growth rate of capital as (output-capital ratio) *(saving rate – deprecation rate* capital-output ratio) and then calls that second term, (saving rate – deprecation rate* inverse of capital-output ratio), a … saving rate. So then you have growth rate of capital = (output-capital ratio)*(“Piketty’s saving rate”)

In steady state then (again, this is Piketty’s argument) this growth rate of capital should equal g (not r!!!!!). So we have g=(output-capital ratio)*(Piketty’s saving rate). Inverting we have capital-output ratio =(Piketty’s saving rate)/g

He then says “Look! If g is zero then capital output ratio will go to infinity!” which is what I understand you’re referring to when you say that depreciation will swallow up GDP.

But this isn’t true. The sleight of hand is hidden in the way that Piketty rewrote the saving rate.

Piketty’s saving rate = actual saving rate – depreciation rate * (capital-output ratio)

So note that if capital output ratio gets sufficiently large then actually Piketty’s saving rate will become zero. So his steady state condition is really zero/zero and there’s nothing here that will make capital output ratio go to infinity (it will actually be a constant)

It’s like one of those tricks that math students like to play on humanities folks where they prove that 1=2 by slyly dividing by zero.

(in Math:

dK=sY-pK

dK/K=s(Y/K)-p <– growth of capital, s is fraction of output reinvested, p is depreciation rate

dK/K=(Y/K)*(s-p*(K/Y))

dK/K=(Y/K)*s' 0 so that K/Y increases over time. Eventually we get to a point where K/Y=s/p. At that point s’=0. And at that point dK/K=0. So both Y and K remain constant and that’s your K/Y right there, a finite value)

(This was one of the instances in the book were Piketty genuinely started to piss me off)

Oh, and Robert, I like your example.

Not saving. K/Y

1. Well if you don’t hold them constant, you need to explain how they change. That’s why there is a long discussion in the book on the historical trends in r and g. Piketty makes a good case that g will fall and r will remain largely the same in the medium to long term, meaning the ratio will increase. He makes a mistake in connecting this discussion with neoclassical production theory, which is just a distraction in my opinion.

2. The capital income ratio is NOT identified with inequality. Instead a large section of Capital is taken up with a discussion of inequality of income from capital, inequality of income in general and the inequality of wealth. If the inequality of wealth and income from capital are increasing at the same time as the capital to income ratio is increasing, you get a rentier society.

115: “But r is not the growth of capital, it is the return on capital.”

The growth rate of capital is strictly speaking less than r because capitalists consume some of the profit rather than reinvesting it. But for Piketty’s argument, only the reinvested part is relevant and he assumes that only a small part is consumed. At least that is the only way I know how to understand the argument, and this is also how for example Krugman explicitly understands the argument, see 101. Inequality is increased not because rich people consume a lot but because they accumulate more wealth. If on the other hand capitalists consume so much that the growth of capital is reduced to g, then the capital-income ratio will indeed be constant and the distribution between labor and capital won’t change. A large difference r-g then means that capitalists get to consume an obscenely large share of income but that share remains constant and no implications follow for inequality.

Now btw your claim that under steady state, r must be constant, makes no sense any more, because there is no reason why the consumed fraction of capital income should be constant. Unless, of course, that too is presupposed. Forgive me but that kind of “economic law” – “if we make a lot of unrealistic assumptions, then some banal consequence can be deducted from accounting identities” – doesn’t impress me too much.

A simple way to understand Piketty:

1) Capital accumulation can occur in two basic ways: either through an increase in the total net stock of wealth (new valued added), or else by an amassment of wealth which is transferred, at the expense of other people. Usually both these modes of accumulation occur at the same time in varying admixtures, but one usually prevails over the other. In the boom, everyone can make gains, even if the gains are unequal, while in a serious slump, the gains of some are mainly at the expense of others.

2) The more equity you own, the more money you can make, at the very least because you can invest it at a higher interest rate, but also because you can borrow more money and use it to extract more profit. The effect is, that the concentration of wealth tends to accelerate (other things remaining equal), meaning that the more capital you own, the faster it will grow too.

3) Piketty assumes a very broad definition of capital, which includes the residential housing stock that grew enormously in the last half century or so. Consequently, his profit rate concept assumes the inclusion of the housing stock, and the income from housing. If however the housing stock and income from housing is excluded from the figures, then his equations do not work anymore.

@122. notsneaky writes: ‘But when he makes the “case that g will fall” he starts talking about *transitional* dynamics – what happens away from steady state.’

So Piketty is interested in what you guys may call the traverse or transitional dynamics–what exactly the problem here?. We are moving from one steady state to another as a result primarily of g likely falling from 3.0 to 1.5 percent as a result of the ending of the post-war boom, global catching up and demographic slow-down (so I won’t entertain your question of what would happen were g to fall to zero as this isn’t relevant to the projection).

This gives us a new beta and thus a new K/Y, perhaps climbing to 7.0 (10%s/1.5% g). Piketty would characterize this as patrimonial capitalism. Once that new K/Y is reached, it can enter an economic steady state, but Piketty thinks the problem will be sociological: we will have re-created patrimonial capitalism that is normatively out-of-synch with widely shared meritocratic values. He expects a social reaction or what Boltanski and Chiapello would call a sharpened social critique of capitalism.

Now perhaps you are arguing that as g stabilizes at a lower level, we should expect changes in s and r. Yes, they will doubtless change but all the data that Piketty provides gives us no reason to believe that they will change in such a way to counteract the uncanny return of a rentier society.

Larry Summers has already made a lot of these criticisms–Piketty simply assumes that the returns will be fully invested (wrong) and that he has set the elasticity of substitution too high due in part to his confusing gross and net savings. I really don’t find these criticisms compelling, but Summers does raise one concern that I share.

Even if Piketty is right about a slow transition from what he would characterize as a petit rentier to a rentier society in which the capital share of income rises to levels not seen since the end of the long 19th century and capital income becomes increasingly concentrated among the 1, .1 and .o1 percent of the population whose wealth comes to be mostly inherited–even if society evolves into such a disfigured state–there will be likely be other problems along the way that may destabilize society–high unemployment in protracted slumps, job displacement due to new technologies, popular anger at the bailout machinery, fascist scapegoating of immigrants, industrial conflict and of course ecological disaster.

Piketty himself raises the problem of the clash of temporalities or different time scales (p. 286ff). The return of rentier society is a long-term evolution, but there may be a lot of action in the short and medium term, and the prospect of a long-term evolution into a rentier society may have little salience or resonance in the face of more immediate problems.

Suppose one unit of capital produces two units of output. So Y/K=2. Out of those two units capital owner gets one unit and worker gets one unit. Capital owner saves 3/4 of their income. This turns into 3/4 units of new capital. Existing capital depreciates at 10%.

r=(Y-K)/K=1
Growth rate of capital = (3/4)*2-.1=(3/2)-.1 which is greater than 1

Specific units or assumptions don’t matter here. Just a simple way of illustrating that is not true that “The growth rate of capital is strictly speaking less than

“Capital accumulation can occur in two basic ways: either through an increase in the total net stock of wealth (new valued added), or ***else by an amassment of wealth which is transferred, at the expense of other people.*** ”

Not in the aggregate.

Yes, I agree, and I also agree that P should not have said s and g are independent (Steven Pressman criticizes but ultimately saves Piketty on this by arguing that s will not decline as much as g, so Y/K will rise with the decline in g). What I meant to emphasize (and I think P believes) is that during the transition or traverse there likely will be destabilizing social critique.

notsneaky @ 108: @98 Huh? Why not?

Because r, as Piketty explains (but then confuses by using the term “capital”) is the rate of return on wealth. Wealth is the present value of claims on income from ownership. No ownership of wealth, no r.

A point about r made at comments 17, 29, 30, 35, 44, 46, 84, 86, 96, 105, 106 and 126.

Think about the difference between “capital” as used in Jane Austen and Balzac and in economics texts.

@dsquared, well we’re not talking about the grand scheme of things, we’re talking about Piketty’s book. You might wish Piketty had written some other book but that’s a different conversation.

All I’m saying here is that Piketty’s whole “high r-g causes inequality” thing is nonsense within the framework he has chosen (and probably within any imaginable framework). And that is the major thesis/original contribution of that book.

I don’t think Piketty’s Jane Austen literary examples are Piketty’s definition of capital. They are just examples, which are suppose to illustrate something or other. Whenever Piketty starts writing down equation, including his “laws”, he’s squarely in the neoclassical definition of capital. True, he switches the definition back and forth (partly because at the end of the day you have to somehow measure “wealth” and return on capital so you got to make a choice of what is included and what is excluded), which just adds to the confusion.

But this is really semantics. You don’t like the socialist utopia example? Fine. Think instead of a capitalist utopia where the claims on capital (orchard) are equally distributed. Then here also it doesn’t matter what happens to r vs. g. You don’t like that example? Look at Robert’s example. You don’t like that one? Look at the standard growth model. There really is no framework out there which will give you that r-g affects inequality except for that one discussed in the JEP paper I linked above and there too there’s some implausible assumptions going on.

131: In your (somewhat far-fetched) example, let’s say K=100, Y=200, r=100% (nice), worker consumes 100, capitalist consumes 25 and reinvests (gross) 75, of which 10 go to depreciation. Net investment then is 65 and growth rate of capital 65%, which *of course* is less than r.

“that doesn’t not hold” unintentional double negative sorry

I am confused about why r should not be greater than g.

If r wasn’t greater than g it wouldn’t be worthwhile investing as you wouldn’t make significant returns. I looked at my Superannuation company and for 5 and 10 year investment streams the annual rate of return is at the lowest (except for one cash option which was much lower) more than 6% p.a. and at the highest almost 11% p.a. Whereas the growth rate this year has been between 2% and 3% which is mostly cancelled out by inflation as in the rises in the consumer price index.

I only have a small Superannuation investment, but if the rate of return was lower than the growth rate, why would anyone want to make investments? (Unless they just wanted to own part of a company and go to shareholder meetings or something like that.)

“If anyone could answer my question above @23, I would still appreciate it”

“Would one reason that r is reasonably stable over a considerable time frame…”

Ok, let me try. There’s couple stories you can tell for why the long run r is stable.

One is that each unit of physical capital produces a fixed amount of a consumption good. This means the return on physical investment (building factories, hiring some workers, producing the good, selling it) is constant. By arbitrage, and putting differences in risk aside, then the return on financial investment has to be equal to that constant. If it’s greater then people switch from building factories to buying financial assets. This bids up the price of these assets and lowers their return until the equality is restored. And vice versa. (This is the linear production model story)

Or maybe there’s diminishing returns to physical investment, so that each additional unit of capital produces less and less output. And people are impatient. If you give me 10000$ today, what is the minimum amount that you require in ten years to be willing to make that loan? The percent difference between that minimal amount and the 10000$ is your rate of time preference, a measure of your impatience adjusted for the fact you might be richer 10 years from now. If return on physical investment (building a factory, hiring some workers, producing some output and selling it) is greater than that rate of impatience, you build the factory. Which means more capital. But as the economy gets more and more capital, the most profitable investment opportunities are exhausted and by diminishing returns, the return to building a factory falls. Until it equals that rate of impatience. Arbitrage between physical and financial investment makes r equal to that rate of impatience too. Assuming there’s no long run swings in the rate of impatience, you get a constant r. (This is the neoclassical story)

Or another story would be simply that r is constant because central banks work really hard to keep it that way. (This is essentially New Keynesian story which doesn’t really work here)

K=400, income to capital owner = 250 r = 62%

2nd period
K=400-40+188=548
Y=(5/4)*548=685
g=37%
income to capital owner = 342.5 r= 62.5%
growth in capital 548/500

r=62% > g = 37%

The claim was that r is always going to be greater than growth of capital.

I cannot say I always follow the reasoning that employs these little toy models, but I can do arithmetic and hold a tentative definition of terms in my head for more a moment.

Err, sorry, your confusion is confusing me. The 62% is the income-capital ratio.

r is just ((5/4)-1)/1=25%

The coefficient (5/4) would be the capital to income ratio, I guess, if that makes any sense.

So what I am getting out of this discussion is that since Piketty has compromised his commitment to neo-classical economic theory by showing that actual historical evidence gives us little reason to accept the elasticity of substitution in the Cobb-Douglas production function, he will not be taken seriously in economics departments and will have the seriousness of historical results and projections better recognized elsewhere in the social sciences. It’s quite possible that the last person who would be surprised by this is Thomas Piketty himself.
Still perhaps the economists will still talk to him since after all he humbly used historical findings such as the rise in his alpha over long periods to criticize neo-classical economic orthodoxy. In this way he is in a much better place than if he had also used Cambridge Capital theory to make the case for why r would remain high enough for a rentier society to emerge; instead he trash talked those heterodox theorists, endearing himself back to the neo-classical economists whom he had just criticized.

After reading half of Piketty’s JEP response to the symposium on his book, I want to rewrite my critique. It provides a contrast by showing a case in which (1) all three of Piketty’s laws hold and (2) no dynasties inherit wealth and no shocks occur to different households in the same generations. Also, the types of assets that can be owned do not change and are excessively non-diverse, as compared to empirical reality.

Dan Kervick has some very good posts on his blog, Rugged Egalitarianism, that deal with why r > g is important and the issues notsneaky brings up. I tried to post a link but it got stuck in moderation.

From the post “Nothing Magical about Piketty’s Mathematics”:

“…the Second Fundamental Law of Capitalism is neither an identity nor or an approximate identity, but a long-term asymptotic law. We might therefore choose to write it less misleadingly this way:

β → s/g

The import of this law is that, for any fixed national savings rate s and fixed growth rate g sustained over some period of years, β will be moving in the direction of s/g during those years. If β is less than s/g, then the rate of wealth growth will exceed the rate of income growth, and β will increase. If β is greater than s/g, then the rate of wealth growth will be less than the rate of income growth, and β will decrease. Piketty employs this long-term law to explain why some countries which save a lot and grow slowly accumulate large stocks of capital relative to income, and how “small variations in the rate of growth can have very large effects on the capital/income ratio over the long term.” The law thus helps to explain “capital’s comeback” in recent decades…

When combining these theoretical conclusions relating to savings, growth and the capital-to-income ratio with further posits about the rate of return to capital in the description of a hypothetical economy, we need to impose some economically realistic further conditions, even in the case of extremely idealized models, if the posited rates are to describe a possible real-world economy. For example, since the total annual return to capital is rK, and that return can never exceed Y in any economy, then r must always be less than or equal to 1/β. Employing the Second Fundamental Law, another way of putting this is that it is that since 1/β continually approaches g/s, it is not possible to have even a fantasy economy with indefinitely fixed g, fixed s and fixed r, where r exceeds g/s. If these are the initial values, something would have to give eventually.

Nevertheless, for real world economies of the kind for which we have historical experience, rates of return on capital within the historically observed 4% to 5% range can be sustained indefinitely. Indeed, if an economy stabilized with a β of 6, and with relatively stable rates of growth and savings, it could sustain any return on capital less than 16.7%. Even an economy with a β of 10, a value far above the normal range for actually existing economies of the past few centuries, would permit a sustainable return to capital of 10%. Since Piketty observes a consistent 4% to 5% return to capital over this time, there is no tension whatsoever between his observed results and the mathematical model. Nor is there any mathematical reason to doubt that r can, and will, exceed g by a substantial amount in the future, leading to strong forces of income divergence and increasing inequality….

It is also important to note that Piketty’s inequality r > g is not responsible by itself for the strong forces of contemporary income divergence and growing economic inequality. Whether r > g is producing inequality or not depends on dynamics within the society. In a society, for example, in which every adult had an equal ownership stake in the society’s capital stock and capital income, then only differences in returns on labor would contribute to growing or shrinking economic inequality. What Piketty points out is that, given the unequal distributions of capital that actually obtain, r > g is a force for greater wealth and income divergence. And the greater r exceeds g, the stronger these forces will be. There are other factors driving inequality as well, including the rise of “super-managers” and their super-salaries, a phenomenon that Piketty argues is taking place mainly in the English-speaking world. Piketty’s full analysis of the structure of contemporary inequality, and its likely future evolution if the forces driving it are not altered by policy, is not derived mechanically from a couple of simple laws, but is developed over six chapters of the book.”

Obvious typo in that last sentence above; “pro” – > “anti”

I find this interview with Piketty truly remarkable.
http://www.potemkinreview.com/pikettyinterview.html

It is only useful if it is true and if it is a casual mechanism. I.e. r > g causes greater inequality. Piketty does not successfully explain how this would occur

This is a quite interesting looking-glass view. You’re making valid points about how “Piketty does not successfully explain how this would occur”, but kind of ignoring the large sections of the book in which Piketty explains how it *does* occur.

If the rate of return on wealth is higher than the growth rate of the economy, then if there’s an initially unequal distribution of wealth it gets more unequal. That is a law of motion, and it’s a locally very important one if conditions are similar to those which do actually obtain at the moment in a lot of important places in the world, including the ones we live in.

I don’t think notsneaky (and many other commenters) can abandon the notion that capital is something real that can be measured (albeit with some difficulty). Wealth – claims on income through title – can be. But wealth is only loosely tied to production.

Capital in the economics texts is a philosophic category, without testable empirical referent. One could, until the mid C19, legally invest in piracy or slaving (and that was capital). One can still invest in enterprises whose returns are based on the destruction of the environment, on the taxing powers of despotic regimes or on various forms of confiscation (and these are capital too). Conversely, many productive assets are unvalued: there are machines working away which have long been depreciated, whose book value is that of scrap. And not just machines – there are bridges, tunnels, canals, landscapes, footpaths and much more (and these are capital in the economic sense, but not accounted). And then there is intellectual, social, institutional capital…

Better to look at what can be measured, what measures play a socio-economic role, how what is counted changes and why.

FWIW (and maybe or probably someone has already made this point), if you want capital to earn less wrt labour, the easiest way is to decrease or limit the supply of labour. An empirical study in an environment where the working-age population is generally increasing exponentially, *should* show that capital is doing better wrt labour. Once population is controlled, labour will do better, and capital worse.

171: Good point, and worth pointing out that in Piketty’s sense, population stabilization is a bad thing because it depresses economic growth. Piketty thinks that the role of inherited wealth tends to dilute quickly in a fast growing population. There may be a grain of truth in this but trying to solve this problem with population growth rather than with an inheritance tax seems grotesque.

If I ever submit my paper somewhere, I am now thinking of using this as an abstract:

This paper presents a neoclassical overlapping generations model in which the rate of growth is positive, income distribution does not become more unequal in a steady state, and the effective real rate of return on savings exceeds the rate of growth. The existence of two assets in the model distinguishes between capital and wealth. In contrast to Thomas Piketty’s empirical results, no dynasties inherit wealth in the model, and no shocks occur to heterogeneous households in the same generation. Without such phenomena, the excess of the rate of return on wealth over the rate of growth need not drive increased income inequality.

I agree that Piketty’s narrative conflation of wealth and so-called productive capital was less wrong-headed than a number of professional economists seemed to think, especially when backed up with the reams of statistics that apparently made it so difficult to attack him on the grounds of a lack of professional seriousness. Jane Austen? Really? Yes, really.

It was refreshing to see economists forced to chew on something that those of us who are more familiar with the social and political effects of accumulated wealth than with economics have never been able to interest them in. When I look at what’s been happening to the European model of social democracy, and to the tattered remnants of the New Deal’s implied social contract in the US, my first thought has always been wherefore by their fruits ye shall know them. Call it an unbecoming Schadenfreude on my part, but it’s nice to see the pundits and experts confronted finally by an interlocutor far more formidable than I could ever be. The not-so-subtle references to Marx in Piketty’s title, and in his scene-setting, are just icing on the cake.

notsneaky 176, you are driving me nuts. The capital owner gets half the outout, that is half of 125%, so his rate of return is 62.5%. And re 178, look at the data. g has clearly not been constant. In any case, the question must be turned around: Why on earth should these economic parameters be constant? You cannot assume something to be constant just because you don’t know better. What kind of science is that.

Peter T @ 169

One of the several severe criticisms of the neoclassical use of the production function as a model is precisely that Capital conceived as an aggregate of “real” things — tools, location, reputation, ideas, inventories, organization, etc — cannot be measured, because there is no way to add it all up, without a common numéraire. Once you use money and financial value as a means of measurement, you have given up the concept of a distinct “real” economy — at least you should give it up, because it has no referent.

Capital investment in things, tangible and intangible, is distinctly a phenomena of creating sunk costs. The capitalist entrepreneur, the improving landlord is making irrevocable commitments in concrete, iron, management structure, advertising, because the aspects of the production process that require capital are the irrecoverable activities far in advance of consumption. Timing is everything and the thing about sunk costs is that they cannot matter to subsequent decision-making . . . or bargaining. Neither the actual, divers resources and efforts nor their financial costs ex ante matter to their value as capital ex post. The cost of building a structure or acquiring rights to a location do not affect subsequent negotiations over the rent. The capitalist will calculate in his speculations, of course; choosing what to spend based on expectations about the bargaining that follows. But, when and if a capital investment realizes any return, any income, that return will be in the nature of an economic rent. This is an aspect of capital’s factor income that the concept of the production function can lead analysts to overlook or distort.

One can imagine opportunities to invest are opportunities to do well by doing good in this best of all possible worlds, but the ability to invest with an expectation of return capturable as private income is tied not to resources that may be dedicated to the enterprise, but to an essentially political power to command an economic rent.

The tension in Piketty between neoclassical concepts of an accumulating and productive capital and competing forms of wealth such as government bonds with a more naked basis in political power rests on a stubborn refusal in mainstream economics to recognize even at the first analytic cut as a Krugman might say, income distribution is all politics all the time. Whatever income is realized on a sunk-cost capital investment in production is due to a political institution able to deliver an economic rent. Figuring out how to do this is what MBAs call, finding a viable business model in which to monetize innovation. It is not invisible except sometimes in our imaginations, when we are caught up with the familiar contours of the neoliberal argument.

In the neoclassical argument, money seeks out investment opportunities and as capital accumulates, marginal returns diminish. The accumulation of wealth is self-limiting, capital’s share of income tending toward a limit near a socially optimal structure of production and distribution of income. But, if money is seeking out political power and economic rents, to extract returns, it is not such a happy story and the limits ?

why would constant s and g NOT be a reasonable assumption in the long run?

Never has that Keynes quote seemed more apposite. The data’s in the book, and it covers a period of time long enough that not only are we dead, but over which countries, empires and entire political and economic systems have time to rise and fall. If Piketty is proved wrong in the long term but between times capitalist society has been torn apart by social tensions and ended in bloody revolution, I would consider that a Pyrrhic and moral victory at best, as I dangled from my lamp-post.

I’m actually surprised that people are questioning that the long run g can be thought of as constant. Go to google. Type in “real gdp xyz” where xyz is any developed country. Click the little “Images” thingy. Look at the picture.

NotSneaky: I think you are right about r-g and capital share. But what about Jones’ argument connecting increasing r-g, in certain sorts of models, with increasing wealth inequality? Is it too much of a special case, do you think?

What is the “long run g” of Germany, Britain, France, China? And, whatever your answer – how do you know? How do you decide what is a short term fluctuation as opposed to the long run trend?

I don’t think this debate is meaningful any more. You wish to discuss Esoterics, I happen to care about empirical reality.

d2, I’ll bite. As shown already many times, Piketty’s r>g theory doesn’t fit the data. What is the matter really? Why is it heresy to point that out?

“What is the “long run g” of …”

About 1.5% for the first three, we don’t know yet for China.

“how do you know?”

Same way we know anything, data and theory.

“How do you decide what is a short term fluctuation as opposed to the long run trend”

There’s some judgement calls there but how you decide mostly has implications for the fluctuations rather than for the long run trend. A non-constant long run g would show up some kind of secular swings (Kondratiev waves and the like) or g getting ever higher or ever lower. It’s pretty clear that for developed economies, that is not what’s happening.

“You wish to discuss Esoterics”

I don’t think the question of whether there is a long run growth rate g and what it is is esoteric. It’s sort of central to Piketty.

“I happen to care about empirical reality.”

90% of time when I see people say stuff like that it turns out to be code for “I’m just gonna make some stuff up out of thin air”

90% of the time someone invokes economic theory, it’s because they’ve decided to ignore the data.

Is non-constant g important to Piketty? (I read the book a while ago now, so if it is I don’t remember it at all.)

I think Charles Jones’ criticism of Piketty has been recommended more than once. I do not have his Macro textbook; does anyone know if he discusses wealth concentration, the distribution of wealth generally, and the capital income share in his textbook? I would guess that he mentions the wonders of compound growth in raising living standards, but is that discussed in relation to the growth and concentration of wealth? Have the Piketty concerns worked their way into textbooks; are his equations discussed along with Solow’s?

Got it. Thanks.

@198. “That’s an empirical question” – Not really. Empirical work can only tell you if there is a correlation. Without theory it cannot tell you if r is a function of g or if they’re co-determined by something else.

And no, Piketty did not do THAT empirical work, he did different empirical work (mostly data gathering, which is actually both underrated in general and quite important and very impressive in this case in particular)

I don’t think Piketty says that “historically there have been huge changes in g” (and if he does, he’s wrong). He might say that historically there have been huge changes in *the growth rate of output* (and/or capital) but that’s not the same thing.

g = long run growth

observed growth = g + transitional growth

For developed economies “transitional growth” = approx. 0

So there have been … large, changes in observed growth as economies develop. But as economies develop the transitional growth” part goes to zero. And at the end you got just that g. Which is pretty constant.

I think in the long run g is zero. If you look at Piketty’s graphs he has zero growth until 1700.

There would have been growth when agricultural civilisations began in some parts of the world , but he doesn’t look that far back.

The growth since 1700 would have been based on enclosure, colonisation, science and the industrial revolution etc

There is no reason to think the sorts of growth rates that were common over those 300 years would be long term, it’s more likely zero is the long term growth rate, with periods of higher growth due to paradigm shift style innovations like the development of agriculture and the scientific revolution

@203 That’s Malthus. We’re not there anymore.

@204 And which equations would these be, exactly?

Very helpful on connection between r>g and rising inequality. I should not have assumed that people already knew Branko Milanovic’s reply to Debraj Ray.
http://glineq.blogspot.com/2014/06/where-i-disagree-and-agree-with-debraj.html

Here is Debraj Ray’s response to Milanovic
http://debrajray.blogspot.com/2014/06/ray-on-milanovic-on-ray-on-piketty.html
“The second piece of Branko’s reasoning is correct. If we assume that capital incomes are more unequally distributed than labor incomes, and if we assume that the share of capital incomes in the total increases over time, then sure, total inequality will generally climb. But all these “ifs” are endogenous outcomes. Sure, they could be empirically what we observe. And as I have said many times: I fundamentally agree with the empirics. But please, don’t tell me that this is some deep theory of inequality when all the “ifs” in that sentence pretty much assume the answer already.”
So if it is not deep theory of inequality but mostly empirics…

I was disappointed that Jones’ JEP article did not use the terms “functional distribution” and “personal distribution” of income. I generally think mainstream economists do not draw on ideas arising decades ago.

I have come to believe Piketty draws conclusions not so much from his laws, but from his laws in a concrete setting.

Debraj Ray’s “r > g has nothing to do with any of this” repeated over and over becomes tedious in the extreme. I get that analytic thinkers like to make fine and “precise” distinctions. Sometimes, I like to do that myself. But, if you cannot concatenate your thoughts, you cannot see the world as it is. The world is a product of coincidence, of a combination of factors coming together.

Vautrin is a character from Balzac, not Flaubert. By the way, no number of extra tickets can make the parents go out if the poor-quality shows are not worth the price. Right now the shows suck.

Daniel, I do think it’s an important and significant book. I haven’t made up my mind if it’s a “good” book. There’s way too much irritating obfuscation and stuff that’s just plain wrong in it (in addition to the r vs. g thing, Piketty also manages to get Malthus, Ricardo and Marx wrong).

It’s not an original sentiment, many people much smarter than me have said it, but if he had just laid off the r vs. g and focused on the data, described the trends historically and provided context-specific explanations (“here wealth inequality decreased because the Bolsheviks refused to pay back Russian debt, here wealth inequality increased because of this housing law that was passed, here inequality increased further but it’s not clear what happened…” etc.) rather than trying (and failing) to uncover some arcane “laws of capitalism” it would’ve been a much intellectually sounder work. Probably wouldn’t have been a best seller though and probably wouldn’t be discussing it at this seminar.

(and let’s be honest, Cit21stC, as scholarly as it is, does have a whiff of those “How to Invest During the Coming Financial Apocalypse” books that show up in your sidebar if you don’t turn your adblocker on about it)

Milanvoic writes:

“The standard growth requirement that r>g is indeed a contradiction of capitalism because in capitalism, capital owners are private persons and they tend to be rich. And these rich people save more of their income, and gradually build up more and more of their capital stock, thus creating precisely the process of divergence of which Piketty speaks.”

notsneaky counters: “True premise. True premise. True premise. True premise. Irrelevant and unwarranted conclusion.”

Of course this is not Ray’s argument. He grants that Milanovic’s argument is valid. He asserts however that the additional probably true premises–about the concentration of capital, savings behavior and the savings coming from capital income–cannot be derived from the r>g inequality.

It is possible however that Piketty tries to show that the higher r-g, the more shocks are likely to concentrate capital ownership.

But leave that aside, Piketty is clear that given the concentration of wealth, the higher r-g (and it tends to be higher for the wealthy), the more likely it is that after rents are consumed and taxes paid that wealth will grow faster than income. See p. 351, 571

Add to this the competitive reduction of taxes and the slow down of growth from the petering out of catch up growth and demographic slow down and we are well on our way to rentier society.

And of course there are objections. How will labor relations have to be restructured to keep r high enough as more capital is accumulated and what kind of risky financial engineering will be used to create assets with the requisite returns. As Steven Pressman notes, all this make serious social, political and labor crises quite possible along the way to rentier society.

And yes there is a sense of incompleteness about Piketty’s theory because it is not a general theory of how the variables are related. Cooper with whom Kerwick is in dialogue gives a good example. If g falls near zero but r and s remain around 5 and 10%, Piketty’s theory gives us such a high beta that alpha or the capital share of income (which is r times alpha) would be more than the total income. Impossible. Either r or s would have to adjust. But Piketty does not give us a theory of how the adjustments could or would be made given the ways in which the key variables are related.

But still what Kervick is rightly saying is that Piketty gives us a reasonable historical range for these variables to play out, which gives us dynamics over the medium term; and it is the case in fact that nothing is standing in the way of a return to a rentier society.

If g falls near zero but r and s remain around 5 and 10%, Piketty’s theory gives us such a high beta that alpha or the capital share of income (which is r times alpha) would be more than the total income. Impossible. Either r or s would have to adjust.

it’s these adjustments which are the important thing, as Piketty does keep saying. It matters a lot whether the adjustment to r or s comes about as a smooth process of equilibration, or via something like the Russian Revolution. As I read it, the “laws” are really just meant to demonstrate that various kinds of conditions are unsustainable and therefore will, at some point in the future, stop.

“Piketty is going “look, the system can’t keep going on like this””

Piketty says nothing of the sort. What he says is that the system kept going for 200 years (from 1700 to 1900) with a stable C-I ratio of 700% and he expects capitalism (after that 20th century anomaly) to resume its old rentier mode of operation. This is what makes the debate so fruitless (sigh) – people keep imputing things that simply aren’t in the book.

in reply to @223. Somewhere, perhaps in a talk, Piketty says that he is quite Leninist about the Great War in that he believes that the social tensions of a rentier society found their outlet in the conflagration that changed everything. So I think dsquared is right about the system not being able to go on like this.

“And Milankovitch et al. insist on the point that how much of your income you save depends on how high your income is”

No, that’s what Raj says. Milanovic says that if it’s income from capital you save it, if it’s income from labor you eat it. That’s precisely what Raj critiques with the example of a subsistence farmer who owns a small plot of land (capital) – the fact that they get their income from this small piece of land is not going to make them save any more than if that subsistence income came from wages.

Not sneaky, are you writing r -g, instead of r > g, for any reason other than irritation over HTML trivia?

They (we?) are saying “r-g has nothing to do with it. The system can have a high r-g and be perfectly stable. The system can have a high r-g and low inequality. r-g is just completely irrelevant”

This is where Piketty often gets it wrong because he doesn’t take capital theory seriously, and where his critics encourage him to make the same mistakes as he does. It’s possible to construct all sorts of steady state examples of imaginary economies. But in the real economy living in real historical time, a short term local law of motion is that if r is greater than g, the proportion of output which is being claimed by capital holders has increased over the period. And, also in the conditions we currently live in, capital holders start the period at the top end of the distribution of wealth, and therefore over the period, the amount of output going to people at the top end of the distribution of wealth increases.

The issue then is “how short term” and “how local” this law of motion can be. The answer to the question “what happens in the very long term” depends on assumptions about what capital-owners do with the increment to their share of output, and on elasticities of substitution between factors of production. Piketty often forgets to have his head screwed on and gets into these debates. But actually, the important thing in the book is that “short term” can be “really quite a while, certainly long enough for very significant social pressures to build up”.

And therefore, that the question of the equilibrium properties of any given model is less interesting than you’d think – before anything can be brought back into equilibrium by the operation of marginal substitutability, it’s more likely than not that something like the Great War or the Russian Revolution will have happened, and rebased all the key ratios to a different set of values and a new set of conditions. Collin Street at #204 seems to be making this point – the “economist” critics of Piketty are concerning themselves with the equilibria, but actually the dynamics matter to. The equation mapping wealth distribution and the capital share at time T to their values at time T+1 is a difference equation, and if it’s a difference equation with destabilising positive feedback and damping mechanisms which are weak and/or slow, that’s really important to know.

@227, 228 I feel we are really arguing over rhetorical emphasis here.

If you and I start out with perfectly equal income, but mine comes from wealth and yours comes from labour, and we save the same amount out of our incomes in Period 0, then in Period 1 my income will be higher than yours if and only if r>g. Then I will: (i) save more, because savings rates increase with income; and (ii) have more wealth carried over from Period 0. So, with r-g still the same, our incomes in Period 2 will be even more unequal. And so on, to ever increasing inequality.

Is r>g the whole story? No. Is r>g completely irrelevant to the story? No again.

…@233 scratch that, actually, my example doesn’t work; I think I see the point now.

“And precisely what is Debraj Ray’s point? Does even Ray know? I doubt it.”

Umm, he’s pretty clear about it and even the passage you quote makes it explicit. The point is that r-g is irrelevant to inequality.

How can you both quote it and completely miss it simultaneously?

(Markus, I didn’t see your comment right after mine)

Take two individuals whose share of income from capital and labor is the same, but one has much greater total income than the other. Milanovic grants that r>g does not lead to widening inequality in this case, but if the one with larger total income, say 10x greater, had received his income only as capital income, inequality will widen if r>g. Milanovic makes this clear by making the income stream of the richer person entirely capital income. Now his income rises $100 rather than the $80 sum that would have kept the income of the richer person at the same multiple of the poorer one. Inequality increases by .1% in this example.

Check out his example.

This widening of inequality results because r is greater than g. If r was the same as g, say 4%, it would not widen inequality if the richer person were receiving all his income from capital or from some mix of capital ownership and labor. The reason that the switch widens inequality is indeed r>g

Now Debraj Ray responds to this example. But I don’t find his response responsive. Here it is:

“Oh dear, here we go again, a repetition of the very same error I’ve been trying to fix. Let me first make my point in words, and then we’ll see where Branko makes his mistake.

Here is the point: income is income is income, no matter where it comes from. Therefore, inequality will increase if the rich save more than the poor. It will stay constant if the rich save at the same rate as the poor. And it will decline if the rich save at a lower rate than the poor… “

???

“I think Piketty deserves more respect than Ray is giving him here, and Ray could show more humility.”

Piketty deserves a critical reading, and he deserves for his arguments, including the confused and the misguided ones, to be taken seriously, and when necessary to be refuted. I doesn’t seem very respectful to me to say that Piketty is vague and fuzzy but if we read him generously, reinterpret his arguments a bit to our liking and impute some stuff that isn’t actually in the book (e.g. 225 etc.) then he makes a bit of sense, or at least can be made useful to our political purposes. That is more or less what has happened to Marx btw.

I’m not sure what a “local law of motion” is

You are sure because it’s obvious – you just (correctly) don’t want to agree with all the awful mistakes Piketty makes about capital theory. But:

If we define W as the total “wealth” in the economy in the sense Piketty wants, including anything that produces an income, at the beginning of period t=1 (I’m starting at 1 because the font CT uses does zeros that look like os)

Define rt as the compoundable return on this stock over period t.

Define Y as the period t=0 output and gt reasonably normally.

For period 1, the ratio of the part of output claimed by wealth owners to the total is
P1 = (Wr1)/Y

For period 2, the ratio is

P2 = r2 (W(1+r1)) / Y(1+g1)

A bit of arithmetic manipulation and you get the ratio of P2 to P1 to be

(1+r1)r2 / r1 (1+g1)

Which if you then assume that all r’s and g’s are constant gives you

r+ r^2 / r+rg

So if r^2 is greater than rg (ie, r is greater than g), then P2 is greater than P1. But the “steady state” equation is a simplication – and as Piketty’s own evidence shows, not a very accurate one – of the version with all the time subscripts, which is what I’d call the “local law of motion”

But but but – if you define W in this way it isn’t possible to interpret it sensibly as “Capital”, and if you define r in this way you’re ignoring depreciation and the consumption of wealth owners, and the move from rt and gt to steady state is very underjustified. Yes, and Piketty makes all three of these mistakes. But the identity itself is an important one, because it’s telling you something important about compound returns and the importance of wealth in the economy. And equally clearly, the equation describing the evolution of Wr/Y in successive periods is a difference equation, and if you think rt is an increasing function of Wt-1 (which Piketty appears to think, I’m less than convinced myself), it’s going to be one with destabilising feedback.

It’s definitely simple, but it’s not a counterexample because in that trivial case, r can’t be greater (or less) than g.

In general, Yg is going to have an r*W part and another part which represents the increase in output which isn’t claimed by capital. And if r is greater than g, then the ratio of that r*W part to the total g is going to be greater than the previous period’s ratio of r*W to Y.

(Note that in Piketty’s definition, W includes things like government bonds, by the way; it certainly isn’t the case that an increment to r*W has to mean an equal increment to Y.)

I’ve never mocked anyone for making arguments from accounting identities, I don’t think. They’re often very useful.

@Rakesh, what I wanted is a term that, when multiplied by r, gives you 10*i. So the numerator is 10*i and the denominator just r.

OK I guess it does not matter whether r as 1.05 or .05, to use Piketty’s number.

I’ll just let r be what you want. Please define a and b, though
“The difference between our two incomes, in other words, went from 9*i to 9*i-g*i+(a-b)*r. Whether that’s more or less than the original 9*g depends on whether g*i is greater than (a-b)*r, where a and b are themselves complicated functions of our total incomes. ”

So you are saying that (a-b)r has to be greater than g*i for inequality to widen, but then saying that this does not show importance of r>g for widening inequality, though it points in that direction.

I guess it now depends on what a-b is, so please define a and b.

Or just differentiate between r and r*, the latter being defined as r-c-t.

c is marginal propensity to consume and t is taxes, as Steven Pressman most helpfully writes.

So the condition for widening inequality is r*>g; the net additions to the capital stock will exceed the growth rate. Or in Milanovic’s example we can see that if we switch the richer person’s income to capital income alone, inequality will widen due to r*>g.

At any rate, you are now disagreeing with S neaky N ot, and stand accused of making logical mistakes a freshman and an even more “rigorous” tenurable economist should not make, even if Piketty and Milanovic got away with it.

A lot of the drama in Piketty’s book is about why g will likely revert to a historical low level and why the competitive inter-state system will reduce t, which is part of the reason we are likely to get r*>g, which is a powerful tendency for growing inequality.

Good thing I’m not an economist then, even a freshman one at that!

I don’t really follow your comment, though; what are the logical mistakes? And, I’m not sure if I agree or disagree with notsneaky, Ray, or Piketty/Milanovitch; I’ve only worked through one simple example in which r>g seems to be *one* condition for widening inequality but far from a sufficient one.