Thursday, September 11, 2014

Piketty and the Money View

I recently picked up Capital and the 21st Century again. And what's striking to me, on revisiting it, is the contrast between the descriptive material and the theory used to make sense of it.

Piketty’s great accomplishment is the comprehensive data on wealth he has compiled, going back to the 18th century. He deserves nothing but praise for making that data easily accessible. (You could think of his project as an iceberg, with most of the substance hidden below the waterline in the online appendixes.) I have not seen any serious doubts raised about the accuracy of this data; and the descriptive generalizations he draws from it, while not above criticism, are obviously based in a deep study of the concrete historical material. But the connections between this material and the theoretical claims it's mixed in with -- r > g and all that -- are tenuous at best.

It’s important to remember that all the underlying data is in nominal terms. All the empirical material in the book relates to stocks and flows of money. But when he turns to explain the patterns he finds in this data, he does it in terms of physical inputs to physical production. The money wealth present in a country is assumed to correspond to the physical capital goods, somehow converted to a scalar quantity. And the incomes received by wealth owners is assumed to correspond to a physical product somehow attributable to these capital goods. I am hardly the first person to suggest that this is not a sensible way to explain trends in private wealth as measured in money, and the money-income derived from it. But what I haven’t seen people say — even people who jump at the chance to revisit the Cambridge Capital Controversies — is the remarkable difference in the attitudes of Piketty the historian and Piketty the economic theorist to data. Shifts in the scale and distribution of private wealth are described on the basis of years of meticulous study of the tax records of various countries. But the production processes that are supposed to explain these shifts are described without any data at all, purely deductively.  You would think that if Piketty believed that the share of property income in total income depends on physical production technologies, returns to scale, depreciation, etc., then at least half the book would be taken up with technological history. You’d think he would spend as much energy studying the inputs and outputs associated with different degrees of mechanization of major production processes, how long is the useful life of different kinds of buildings in different eras and how much annual maintenance they require, and so on. After all, these are the kinds of factors that he believes — or claims to believe — drive the money-wealth outcomes the book is about. In fact, of course, these topics are not discussed at all. Terms like “production” and “depreciation” are black boxes, pure mathematical formalism. You would think that Piketty, who presents himself as a historian and is admirably critical of the deductive character of so much of economics, would have hesitated before staking so much on deductive, evidence-free claims about physical production.

Because when you take a step back and think about it, this is what Piketty has done:  He has carefully described the historical evolution of monetary wealth, and then postulated an imaginary physical reality that exactly matches that evolution. It’s a kind of economic preformationism, or like the folk psychology that tries to explain your actions by imagining a little homunculus in your head that is choosing them.  The “real economy” in Piketty is just a ghostly mirror-image of the network of money payments and money claims that is actually observed.

* * *

Let me give a concrete example. Piketty shows that around 1800, the wealth-income ratio was relatively low in the United States -- about 300% of national income, compared with 600-700% in England and France. About half of this difference was the lower value of agricultural land, which totaled about 150% of national income in the US and over 300% in both England and France. Piketty suggests that this is because the great abundance of land in the New World meant that its marginal product was relatively low. This sounds reasonable enough -- but it flies in the face of Piketty's larger argument about the capital share. His big theoretical claim is that the capital share is determined by the growth rate of cumulated savings relative to the growth rate of income. And this only works if the return on "capital" is relatively insensitive to its scarcity or abundance. (This is the question of the elasticity of substitution between capital and labor, which has dominated economists' debates about the book.) If having more land makes the share of land rents in national income go down, why won't the growth of "capital" similarly push down its return?

This isn't meant as a gotcha. Piketty frankly acknowledges the problem. He suggests two possible solutions: First, constant returns might only apply over some range of capital-output ratios. Beyond that that range, further accumulation might make capitalists as a group poorer rather than richer. Second, it might be easier to substitute between labor and modern capital goods, than between labor and agricultural land. Both these assumptions sound reasonable, altho I think they are both more problematic than they seem at first glance. But that's not the argument I want to have right now. The point I want to make now is that Piketty just takes it for granted that behind the smaller flow of money going to land owners in US circa 1800, there must have been a smaller physical flow of output coming off the marginal piece of land. Of course this isn't logically necessary -- the money-value of agricultural land will also depend on the legal rights associated with land ownership, the terms on which new land can be acquired, the ease with which land can be sold or borrowed against, etc. Presumably the same physical mix of land, tools and people would have led to a different share of money income being claimed as land rents if frontier land in the early United States had been owned by a few large landlords, instead of being freely distributed to white families by the government. But these types of explanations are not even considered. For Piketty, behind each flow of money there must be an identical flow of stuff.

The other strange thing is that, despite his insistence that money flows are fully explained by physical conditions of production, Piketty shows no interest in investigating those conditions. The numbers on the level and composition of money wealth in US are meticulously sourced and documented. The claims about physical production conditions, on the other hand, are entirely speculative. There is no shortage of material you could turn to if you wanted to ask whether whether land was really more abundant, in an economically meaningful sense, in the early US than in France or Britain, or if you wanted to know if adding an acre to an 1800-era American farm would increase its output proportionately less or more than adding an acre to a similar-sized British or French farm. But Piketty doesn't even gesture at this literature.

* * *

I draw two conclusions. First, it's hard to say anything sensible about the book until you realize it consists of two distinct, almost unrelated projects. There is the historical data on money wealth and money incomes. And then there is the whole rigamarole of "laws of capitalism." The book is mostly written as if the latter somehow distill or summarize the former, but they are really very loosely articulated. Let me give one more quick -- but important -- example. You might think that with all the huffing and puffing about r > g, the data would tell a story in which the share of wealth in national income rises in periods when r is relatively high and g is relatively low, and falls when g is high and r is low. But the data tell no such story.

The great fall in the capital share took place between 1913 and 1950, according to Piketty. But his own data show that this was the period of the highest returns to capital, and the lowest growth rates, in the whole 240 years the book covers. I've reproduced his graph of r in the UK below; the figures for other Western European countries look similar. Meanwhile, he gives an average growth rate for Western Europe over 1913-1950 of 1.4%, compared with 1.8% in the high-capital share 19th century, and 2.1% in the period of rising capital shares since 1970. This is exactly the opposite pattern that we would expect if r and g were the central actors in the story.

Of course Piketty has an answer for this too: The fall in the capital share in the first half of the 20th century is explained by the World Wars and the destruction of the old social order in Europe. No doubt -- but if factors like these dominate the historical trajectory of wealth and income, why not tell your story in terms of them, instead of a few dubious equations from the orthodox growth model? Unfortunately, discussion of the book has been almost entirely about the irrelevant formalism. I think that is why the conversation has been so noisy yet advanced so little. To return to the earlier metaphor, it's as if everyone is ignoring the iceberg and talking about a little igloo built on top of it.

My second conclusion is that the disconnect between the two different Pikettys shows, in a negative way, why what I've been calling the money view is so important. The historical data assembled in Capital in the 21st Century is a magnificent accomplishment and will be drawn on by economic historians for years to come. Many of the concrete observations he makes about this material are original and insightful. But all of this is lost when translated into Piketty's preferred theoretical framework. To make sense of the historical evolution of money payments and claims, we need an approach that takes those payments and claims as objects of study in themselves.

LATE UPDATE: A friend forwards the following (verbal) comment from Joe Stiglitz:

"There is a confusion in Piketty on valuation and physical stocks. In France, the main 'increase' in wealth is because of higher prices of land. Do we really think that France has become wealthier (using Piketty's physical understanding of wealth in his model) because while the manufacturing capital stock has declined, the Riviera has become more expensive?"


  1. Interesting post. Something came to mind while I was reading. Dunno if it is relevant, but I do like to share...

    "If having more land makes the share of land rents in national income go down, why won't the growth of "capital" similarly push down its return?"

    I.11.8: Rent, it is to be observed, therefore, enters into the composition of the price of commodities in a different way from wages and profit. High or low wages and profit, are the causes of high or low price; high or low rent is the effect of it. It is because high or low wages and profit must be paid, in order to bring a particular commodity to market, that its price is high or low. But it is because its price is high or low; a great deal more, or very little more, or no more, than what is sufficient to pay those wages and profit, that it affords a high rent, or a low rent, or no rent at all.
    [Adam Smith]

  2. An amateur take from one who hasn't even read the book yet, just the discussion it has provoked:

    The "laws" of capital he puts forward aren't really laws but correlations or tendencies. Policy can change things, like if his proposal for an international wealth tax was put in effect.

    The history he lays out is that r is always pretty constant but g varies given government policy (and the usual demographic and technological variables). This is the orthodox growth theory stuff. Leading up to the World Wars and Great Reset, growth was slower and government policy wasn't great so the wealth to income ration was high. You had high inequality and government malfeasance which lead to the Great Depression (and before that the Long Depression of the late 90s.) Inequality high, wealth-income ratio high and politics bad.

    This changed with the World Wars and destruction of capital. Inequality was lower as was the wealth-income ratio. Politics and policy was better. (Maybe partly in reaction to Lenin and Communism?) High taxation, unionization, regulation, full employment, etc. But as time wears on, inequality increases, good polices to keep g and growth up are done away with, the wealth-income ratio increases and you get the Reagan/Thatcher/neoliberal revolution.

    The 30 years after WWII has higher growth and less inequality than the 30 years beginning in the 70s/80s. Sort of makes sense that the wealthy can spend some of their surplus income on extracting rents, on politics, and on propaganda.

    But I think Piketty admits it's not an iron law and things aren't destined to get worse. Government policies can be changed. The issue I wonder about is the euthansia of the rentier. Demand management policies of the government (monetary, fiscal, currency) need to do at least the minimum to avoid escalating deflation. That may involve the euthanasia of the rentier as liquidity becomes abundant. There's only so much the credit-worthy want to borrow and the rest will have to be lent out to those with spottier credit reports for the financial industry to make any money. There's a push to loosen credit standards.

    For me it's an open question.

  3. My two cents:

    I think that there are 4 different kinds of capital assets (though in reality most capital assets are a mix of the four kinds).

    1) There are some capital goods that are stuff that is materially produced, such as factories. This stuff has a cost of production, that arguably has some relationship with its "value". This is what I would call "real" capital. The ambiguity in Piketty comes from the fact that he speaks as if all capital is "real" capital, and as if every money flow translates in "real" capital.

    2) There are some assets that are a finite resource that someone controls, like land. In fact, classical economists distinguished between "capital" and "land". The value of land can't be linked to the "cost of production" of land, because said cost doesn't exist. So arguably the value is just the cashflow derived from the asset divided by the normal rate of profit. I'd call this kind of assets simply "land".

    3) While land is certainly something that exists, there are some assets that have an economic value but that don't relate to something that clearly exists or that can be produced: for example, ownership on patents, or a famous brand that has an high market penetration and visibility etc. I think that these assets have dinamics that are similar to land, although they are mostly non material.

    4) Finally, there is credit. Credit also is a non material thing, and is different from all the 3 previous classes of capital for these reasons:
    4.1) It doesn't have a "cost of production";
    4.2) It isn't related to any fixed resource, something that differentiates credit from both 2 and 3;
    4.3) It has a fixed nominal value (which implies that the currency provider can literally print it out of existence).
    4.4) It usually has a nominally fixed interest rate, something that can obviously cause chain bankruptcies.

    My problem with the "monetary view" is that it sounds like if assets of the 2 and 3 classes all are just a "montary" thing, as opposed to a "real stuff view" that sees all assets as if they were of the 1 class.
    In fact there is a lot of "financial value" that is not credit (nominally fixed), but assets of the 2nd and 3rd class IMHO.

    1. Insightful comment as usual. I am writing a reply, but I'm afraid it is going to have to be a very long reply. Hopefully up tonight.

    2. I posted a response as new post.

  4. I need to think about this but my first impression is that you're being a bit unfair. For example, you say: "Piketty suggests that this is because the great abundance of land in the New World meant that its marginal product was relatively low." What I find him saying on pgs 150-151 is that the price of land was depressed by its abundance. Am I looking in the wrong place? When he mentions marginal products he mostly gets things right. (Though I don't like the way he defines the MPK on page 213, conflating it with the marginal efficiency of capital.)

    I've been thinking about how one should assemble the simplest possible model capable of doing justice to the book's theory. A two-sector model (C & I) seems to suffice. A one-good model won't do because changes in the value of the stock of capital are important. If P is the price of the capital good in terms of the consumption good, Piketty's beta = PK/(PS+C). Obviously S=I, there's no place for Keynesian complications in a model which is designed to describe events which take generations. In the short run variations in P matter a lot, but in the long run beta is determined by s/g. It's realy just a merger of Solovian growth and Tobin's Q. AFAICT the theory hangs together quite well.

    Enough already. If you're working on another post I may as well wait for that before sounding off.

    1. Kevin-

      There are several distinct claims to consider here. First is that the money value of capital is proportional to a well-defined physical quantity of capital. Second is that the physical quantity of capital depends on the cumulated savings. Third is that the price per unit of capital is equal to its marginal product. Now, for one and three to both be true, we need also four, the marginal product of capital does not vary with the quantity of capital. This last proposition is the one that has been subject of most of the debates about the book among economists, at least that I've seen. Piketty admits that it does not apply to land in the early US. But I don't see any systematic questioning of the third proposition, that capital has well-defined physical units and a technically determined marginal product and that the price of one unit of capital is equal to its marginal product. Yes, he says that the price of land was low in the early US because it was so abundant -- because its abundance meant that its marginal product was low. Or is there a passage I've overlooked where he talks about a systematic divergence between the price of land and its marginal product?

      I think your minimal theory captures the argument of the book pretty well. And as you say, he stipulates that P doesn't vary in the long run -- a claim that doesn't seem to be supported by either theory or evidence. (Most of the rise in the capital share since 1970 looks like an increase in P.) So, where is "r > g" in that minimal theory?

    2. Proposition 1 will be sort-of-true in any simple model, whether P & K are scalars or vectors. Proposition 2 is just an identity if depreciation is just the evaporation of a percentage of the physical stock of capital. Of course if depreciation is largely a matter of obsolescence or the like things get complicated.

      With Proposition 3 you lose me completely. Why should P=MPK? I see no reason why it should, nor does Piketty assume it AFAICT. I see him as a user of standard neoclassical concepts, but until proven otherwise I assume he doesn't make silly mistakes. So let's suppose he's thinking like an educated neoclassical. If K can be increased over time until a steady-state is reached, the MPK settles at a constant which must just cover depreciation and time-preference. P also settles at a constant which matches the slope of the production possibility curve at the point where Total K-good produced = (K x rate of depreciation) + (K needed to match population growth). I can't see why P=MPK in that situation. Nor can I see why theory should lead us to reject a constant P in the steady-state. In fact, if P doesn't converge to some limit it's hard to see how a steady-state can be reached.

      "Yes, he says that the price of land was low in the early US because it was so abundant -- because its abundance meant that its marginal product was low."

      Cheap land is not sufficient to ensure that the marginal product is low. For a colonist farmer, the return had to cover interest costs which incorporated a pretty stiff risk premium I'd imagine. There was a high probability that better land would be grabbed by competitors out West, driving down the value of his investment. The MP of land needed to be high enough to compensate for this. Certainly Piketty says the price was low, but I can't find any sign that he reasons from the price to the marginal product.

      If Proposition 3 is a dud, as I believe, then Proposition 4 ( the marginal product of capital does not vary with the quantity of capital) doesn't follow. Piketty assumes a high, but not infinite, elasticity of substitution. So the MPK must fall, albeit rather slowly, as K increases.

      "Most of the rise in the capital share since 1970 looks like an increase in P."

      I'm not sure what you mean by this. For Piketty, as a rule capital gains are not included in income (except for the fraction attributable to companies' retained earnings, which is included). When capital gains are included he makes a point of mentioning that. The way in which Piketty tests for the long-run constancy of P is to compare his beta with s/g, in Chapter 5, pages 183-191. As he notes, there are anomalies which he tries to deal with. But the "rebound in asset prices" will only be fatal to his theory it fails to generate real capital accumulation as per his "Tobin's Q" reasoning.

      "So, where is r > g in that minimal theory?"

      That's where I struggle because Piketty doesn't commit himself to any particular theory of r. He mentions time-preference theory in a disparaging way, but mostly he just says saving is complicated. Clearly he needs the demand for wealth to stabilize as it accumulates, in such a way that P will approach a limit.

    3. Will reply to the rest later but this last point is important. Despite all the noise, it's quite unclear what role, if any, "r > g" plays in the dynamics Piketty describes. I can't find anywhere in the book a clear statement of the form "if r > g, then this will happen; if g > r, then something else will happen instead." Nor can I find, either in the book or online, a table or chart showing r and g together for different countries and periods.

      you are right that the obvious link is via s but Piketty explicitly disavows this and it is not easy to come up with a simple function for s = s(r) that would imply two distinct regimes in the way the text suggests. Alternatively, and I think more plausibly, r > g might be important not for the capital-labor split, but for the distribution of capital income across households. Piketty has a coauthored paper (I don't have the cite handy) that does develop a formal model like this. But the model in that paper seems quite different from the implicit model of K21.

  5. I don't like the way he defines the MPK on page 213, conflating it with the marginal efficiency of capital.

    Agree. But unlike you, I don't think this is a misstatement or unfortunate choice of words. I think it's a very clear statement of the basic theoretical orientation of the book. And I don't agree with your statement (on your blog) that MPK and MEK are just two terms for the same concept. One is ratio of two quantities of physical stuff, the other is a ratio of two quantities of money.

    1. Here's what I wrote: "The MPK should be understood as units of additional output per unit of additional input, while the MEC is akin to an interest rate (it can be thought of as an internal rate of return). It's important to avoid confusion because the two terms often rub shoulders in a discussion."

      So I'm not saying they are 2 terms for the same concept. I'm saying Piketty uses the term (marginal productivity of capital) incorrectly in that passage on pg 213. For now though I'll give him the benefit of the doubt and say it's an isolated slip.