Tag: anti-Piketty

Piketty Post at Crooked Timber

Crooked Timber is having a book event on Piketty’s Capital in the 21st Century. My contribution is here. A few supplemental bits:

First, I need to point out a problem in my post. I write: “It’s striking, for instance, that the book does not contain a table or figure comparing r and g historically.” But of course, as David Rosnick points out in email, this is not true. There are three figures in chapter 10 that purport to give historical values for r and g. The inadequacy of these figures to bear the weight put on the r > g apparatus is, I think, evident. Why are there no cross-country comparisons? Why the odd periodizations? Why so much emphasis on the data-free values invented for the distant past and future? Perhaps most damningly, what about the fact that r > g is no more true in the increasingly unequal second half of the 20th century than in the increasingly equal first half? But none of that changes the fact that my sentence, as I wrote it, is wrong.

Some people may be interested in other things I’ve written relating to Piketty on this blog over the past couple years:

A Quick Point on Models

Posts in Three Lines

Piketty and the Money View: A Reply to MisterMR

Piketty and the Money View

Wealth Distribution and the Puzzle of Germany

Mehrling on Black on Capital

Three Ways of Looking at alpha = r k

With respect to the Crooked Timber piece, I should say — should have acknowledged in the post itself — that it all comes out of conversations I’ve been having with Suresh Naidu over the past year or so. Suresh himself has written various things about Piketty; he’s working on a piece now on these same themes of capital, Piketty and the money view that should move the conversation significantly forward.

I should also have pointed out the Real World Economic Review’s superb special issue on Piketty. Jamie Galbraith’s, Merijn Knibbe’s, and Yanis Varoufakis’ contributions made many of the same points I tried to make in the Crooked Timber post. Knibbe’s piece in particular is a tour de force, everyone interested in these debates should read it.

Finally, I should say: I’ve been reading Crooked Timber since it began, in 2003. For a long while I was a regular commenter there, most of that time pseudonymously as Lemuel Pitkin. Now twelve years is a long time in internet time. Not so long in real life but still long enough  for me to go back to graduate school, get my PhD and various teaching jobs, and to start this blog. Crooked Timber was probably my main inspiration to try to write in this format. So I can’t deny it, I’m thrilled to finally have a post up there.

 

 

Piketty and the Money View: A Reply to MisterMR

The last post got some very helpful comments from MisterMR (the regular commenter formerly known as Random Lurker) and Kevin Donoghue. Both of them raise issues that are worth posts of their own. I’ll reply to MisterMR now, and perhaps to Kevin Donoghue later. Or perhaps not — the biggest thing I’ve learned in four years of blogging is: Never make promises about future posts.

* * *

MisterMR is coming from what I hope he won’t mind my calling a classical Marxian perspective — a perspective I’m simpatico with, tho I haven’t been taking it here. One aspect of this perspective is the idea that capital can be understood in physical terms, as embodied labor. Now I agree that Marx does clearly say this, but I think this can be seen as a concession he is making to the orthodoxy of the day for the sake of the argument. Capital is subtitled “A Critique of Political Economy,” and I think we should take that subtitle seriously. In effect, he is saying to Ricardo: OK, let’s accept your way of thinking about capital, the system based on it is still conflictual, exploitative and in contradiction with its own conditions of existence.

I’m not sure how widely this view is held — that Marx adopts the labor theory of value ironically. Anyway, that’s not the argument I want to have here. What I want to do is clarify the perspective I’m offering in place of the labor theory. It’s more in the spirit of the other core Marxian idea about capital, that it is a social relation between people.

MisterMR writes:

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.

My response is that the money view is not a substantive claim about the nature of particular assets, but a way of looking at assets in general — “real” capital goods as much as the more vaporous claims in categories 2 through 4. It does imply some kind of ontology, but in itself, the money view is just a choice to focus on money payments.

But I do want to explain the broader view of social reality that, for me at least, lies behind the money view.  Here’s the way I want to look at things.

* * *

On the one hand, there is the human productive activity of collectively transforming the world and maintaining our conditions of existence, along with the conditions that make that activity possible. When you sit down and write a blog post, you are engaged in creative activity with the goal of building up our collective knowledge of the world, and you are also maintaining the network of social ties through which this kind of activity is carried out. Your ability to engage in this activity depends on a great number of objective conditions, ranging from your physical health to the infrastructure that communicates your words to the rest of the world. Many of these conditions are the result of past human activity.

Under capitalism, a subset of human productive activity gets marked off as “labor.” Labor has a number of special characteristics, most obviously that it is carried out at the direction of a boss. But for current purposes, the most important distinctive characteristics of the activity that we call “labor”  are (a) it carries a price tag, the “wage,” with labor that is somehow similar carrying a similar wage. And (b) labor becomes substantively more similar over time, with the disappearance of specific skills and increasing interchangeability among the human beings performing it; it follows from this that the wage also become uniform. To the extent that (a) is true, we can attribute a “cost” to some particular set of conditions and to the extent (b) is also true, that cost will correspond to the hours of labor expended maintaining those conditions. Of course all productive activity additionally requires many conditions, both natural and social, that are not reflected in labor hours. In particular, a great deal of passive social cooperation is required for any productive activity, especially when there is an extensive division of labor.

Even in the pure case, where labor is completely homogeneous and all production is carried out for profit, under identical conditions and with no barriers to competition, there will not in general be a unique mapping from labor hours to costs or relative prices. The best we can do is to reduce all the infinite possible sets of relative prices to variation along a single dimension, with one set of relative prices corresponding to each possible profit rate. (I think this is Sraffa’s point.)

So the description of assets in group 1 is correct — but only with respect to one particular way of describing one particular way of organizing production, not as statements about reality in general. The productive activity that takes place in a factory does, of course, require the past activity that resulted in the existence of the factory. But it requires lots of other activity as well, much of which is not counted as “labor.” And the fact that “labor” is a measurable input at all only holds to the extent that the productive activity has been deskilled and homogenized, a sociological fact that is never completely true and is not true at all in most historical contexts.

The think you have to avoid is believing that quantities like “value” or “cost” have any existence outside the specific social relations of capitalism.

The next question is what it means to “own” some conditions for productive activity, like a factory. The beginning of wisdom here is to recognize that ownership is a legal relationship between persons, not a relationship with a physical object. To own a piece of land means you have certain legal rights with respect to other people — to exclude them from the use of that land, to receive some equivalent from them if you do permit use of the land, to transfer those rights to someone else — and that no one else has those rights with respect to you. However, that’s only the first step. Next, we have to recognize that what constitutes “use” of piece of an asset is not a physical fact, but a social one. (As in the old story, the baker can exclude others from eating his rolls, but not from enjoying the smell of them.) So it would be more accurate to say that ownership of a piece of property is simply a form of social authority — a bundle of rights over other people. Indeed, if we want to relate the world of money flows to broader social reality, the most fundamental fact is probably this: The person who receives a money payment labeled “profit” gives orders, and the people who receive money payments labeled “wages” have to follow them. To say you own a piece of property is simply to say there is a set of commands that, if you issue them, other people are compelled to obey. Those rights are metonymously referred to by a label which bears a picture of some tangible good, just like the insignia on an officer’s uniform bear a picture of a leaf or a bird.

So:

When you say, here is a means of production, a factory, with a certain cost, you have already chosen: to ignore all the various conditions that make a certain form of collective productive activity possible, and let the existence of this one tangible object, the factory, stand in for all the rest; to ignore all the various forms of productive activity and social coordination that were necessary to bring the factory  (and the rest of the conditions of production) into existence, except for those we class as wage labor; to convert that wage labor to some common quantitative standard by measuring it in wage payments;  to assume some exogenously given profit rate, to give you the discount rate you need to add up wage payments made at different dates. Only then can you say the factory has a cost — and even then, this money cost is calculated by adding up a certain set of money payments.

At that point we have MisterMR’s category (1) as a concrete social reality. We still have to establish the profit rate, since it cannot be reduced to a marginal physical product. Only then do the issues specific to the other three categories come into play.

I should be clear: the money view is not a complete account of the sphere of social reality we call the economy. (And again, I’ve adopted the term from Perry Mehrling, it’s not my invention.) The money view is defined by making the atomic units of analysis bundles of money payments. I would argue that it is logically consistent to think of any capital good as simply a bundle of income streams contingent on different states of the world, in a way that it is not logically consistent to think of it as a physical object producing a stream of physical outputs.

The fact that this is a logically consistent account doesn’t mean it’s sufficient. Obviously the money view doesn’t give a complete story, since we don’t know why the income streams attached to different assets are what they are, or why they change over time, or why assets in the monetary sense are attached to tangible goods or production processes, or for that matter why anyone cares about money payments in the first place. But by adopting a consistent story about money payments and assets, we get a clearer view of these other questions. We distinguish the questions that can be addressed with the formal techniques of economics from other questions that require a different approach. This is a step forward from the perspective that mixes up questions about money flows with questions about tangible productive activities and so can’t give a coherent story about either.

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?”

Mehrling on Black on Capital

In a post last week, I suggested that an alternative to thinking of capital as quantity of means of production accumulated through past investment, is to think of it as the capitalized value of expected future profit flows. Instead of writing


α = r k

where α is the profit share of national income, r is the profit rate, and k is the capital-income ratio, we should write 
k = α / r
where r is now understood as the discount rate applied to future capital income. 
Are the two rs the same? Piketty says no: the discount rate is presumably (some) risk-free interest rate, while the return on capital is typically higher. But I’m not sure this position is logically sustainable. If there are no barriers to entry, why isn’t investment carried to the point where the return on capital falls to the interest rate? On the other hand, if there are barriers to entry, so that capital can continue to earn a return above the interest rate without being flooded by new investment with borrowed funds, then profits cannot all be attributed to measured capital; some is due to whatever privilege creates the barriers. Furthermore, in that case there will not be, even tendentially, a uniform economywide rate of profit. 
In any case, whether or not we have a coherent story of how there can be a profit rate distinct from the discount rate, it’s clearly the latter that matters for corporate equity, which is the main form of capital Piketty observes in modern economies. Verizon, to take an example at random, has current annual earnings of around $20 billion and is valued by the stock market at around $200 billion. Nobody, I hope, would interpret these numbers as meaning that Verizon has $200 billion of capital and, since the economy-wide profit rate is 10%, that capital generates $20 billion in profits. Rather, Verizon — the enterprise as a whole, its physical capital, its organization and corporate culture, its brand, its relationships with regulators, the skills and compliance (or not) of its workers — currently generates $20 billion a year of profits. And the markets — applying the economy-wide discount factor embodied in the interest rate, plus a judgement about the likely change in share of the social surplus Verizon will be able to claim in the future — assess the present value of that stream of profits from now til doomsday at $200 billion.  
Now it might so happen that the stock market capitalization of a corporation is close to the reported value of assets less liabilities — this corresponds to a Tobin’s q of 1. Verizon, with total assets of $225 billion and total liabilities of $50 billion, happens to fit this case fairly well. It might also be the case that a firm’s reported net assets, deflated by some appropriate price index, correspond to its accumulated investment; it might even also be the case that there is a stable relationship between reported net capital and earnings. But as far as market capitalization goes, it makes no difference if any of those things is true. All that matters is market expectations of future earnings, and the interest rate used to discount them.
I was thinking about this in relation to Piketty’s Capital in the 21st Century. But of course the point is hardly original. Fischer Black (of the Black-Scholes option-pricing formula) made a similar argument decades ago for thinking of capital as a claim on a discounted stream of future earnings, rather than as an accumulation of past investments. 
Here’s Perry Mehrling on Black’s view of capital:

As in Fisher, Black’s emphasis is on the market value of wealth calculated as the expected present value of future income flows, rather than on the quantity of wealth calculated as the historical accumulation of savings minus depreciation. This allows Black to treat knowledge and technology as forms of capital, since their expected effects are included when we measure capital at market value. As he says: “more effective capital is more capital” (1995a, 35). Also as in Fisher, capital grows over time without any restriction from fixed factors. 

… 

For Black, the standard aggregative neoclassical production function is inadequate because it obscures sectoral and temporal detail by attributing current output to current inputs of capital and labor, but he tries anyway to express his views in that framework in order to reach his intended audience. Most important, he accommodates the central idea of mismatch to the production function framework by introducing the idea that the “utilization” of physical capital and the “effort” of human capital can vary over time. This accommodation makes it possible to express his theory in the familiar Cobb-Douglas production function form: y = A(eh)^α(fk)^(1-α), where y is output, h and k are human and physical capital, e and f are effort and utilization, and A is a temporary shock (1995, eq. 5.3). 

It’s familiar math, but the meaning it expresses remains very far from familiar to the trained economist. For one, the labor input has been replaced by human capital so there is no fixed factor. For another, both physical and human capital are measured at market values, and so are supposed to include technological change. This means that the A coefficient is not the usual technology shift factor (the familiar “Solow residual”) but only a multiplier, indeed a kind of inverse price earnings ratio, that converts the stock of effective composite capital into a flow of composite output. In effect, and as he recognizes, Black’s production function is a reduced form, not a production function at all in the usual sense of a technical relation between inputs and outputs. What Black is after comes clearer when he groups terms and summarizes as Y=AEK (eq. 5.7), where Y is output, E is composite utilization, and K is composite capital. Here the effective capital stock is just a constant multiple of output, and vice versa. It’s just an aggregate version of Black’s conception of ideal accounting practice (1993c) wherein accountants at the level of the firm seek to report a measure of earnings that can be multiplied by a constant price- earnings ratio to get the value of the firm. 

… 

In retrospect, the most fundamental source of misunderstanding came (and comes still) from the difference between an economics and a finance vision of the nature of the economy. The classical economists habitually thought of the present as determined by the past. In Adam Smith, capital is an accumulation from the careful saving of past generations, and much of modern economics still retains this old idea of the essential scarcity of capital, and of the consequent virtue attached to parsimony. The financial point of view, by contrast, sees the present as determined by the future, or rather by our ideas about the future. Capital is less a thing than an idea about future income flows discounted back to the present, and the quantity of capital can therefore change without prior saving.

In comments, A H mentioned that Post Keynesian or structuralist economics seem much closer to the kind of analysis used by finance professionals than orthodox economics does. I think one reason is that we share what Mehrling calls the “money view” or, here, the “finance vision” of the economy. Orthodoxy sees the economy as a set of exchanges of goods; the finance vision sees  a set of contractual money payments. 
Mehrling continues:

In The Nature of Capital and Income, Irving Fisher (1906) straddled the older world view of economics and the emerging world view of finance by distinguishing physical capital goods (for which the past-determines-present view makes sense) from the value of those goods (for which the future-determines-present view makes sense). By following Fisher, Black wound up employing the same straddle. 

Piketty may be in a similarly awkward position. 

Three Ways of Looking at alpha = r k

Piketty’s “first law of capitalism” is the accounting identity

α = r k

where α is the share of capital income in total output, r is the average return on capital, and k is the aggregate capital-output ratio.

As accounting, this is true by definition. As economics, what kind of economic behavior does it describe? There are three ways of looking at it. 

In the standard version, the profit share is determined by a production function, which is given by technology. The profit rate r* required by capital owners is fixed by technology in combination with time preferences. In this closure, k is the endogenous, or adjusting, variable.  Investment rises or falls whenever the realized profit rate differs from the required rate, thus keeping k at the level that satisfies the equation for r  = r*. 

In Piketty’s version, r is fixed (somehow; the mechanism is not clear) and k is determined by savings behavior and (exogenous) growth according to his “second law of capitalism”: 


k = s/g

That leaves α to passively accommodate r and k. Capitalists get whatever the current capital stock and fixed profit rate entitle them to, and workers get whatever is left over; in effect, workers are the residual claimants in Piketty’s system. (This is the opposite of the classical view, in which wages are fixed and capitalists get the residual.)

In a third interpretation, we could say that α and r are set institutionally — α through some kind of bargaining process, or by the degree of monopoly, r perhaps by the interest rate set in the financial system. The value of the capital stock is then given by capitalizing the flow of profits α Y at the discount rate r. (Y is total output.) This interpretation is the natural one if we think of “capital” as a claim to a share of the surplus as opposed to physical means of production. 

This interpretation clearly applies to pure land, or to the market value of a particular firm. What if it applied to capital in general? Since claims on the surplus — including claims exercised through nonproduced assets like land — are not created by reserving output from consumption, aggregate savings would be a meaningless accounting construct in this case. (Or we could adopt a Hicksian view of saving in which it equals the change in net wealth by definition.) Looking at things this way also puts r > g in a different light. Suppose we think of the capital stock as a whole as something like the stock of a firm, which entitles the owners to the flow of profits from that firm. If the profits today are α Y and output is expected to grow at a rate g, what is the value of the stock today? If we discount future profits at r, then it is the sum from t=0 to t=infinity of α Y (1 + g)^t / (1 + r)^t, which works out to α Y / (r – g). So if we can take the rate of return on capital as the discount rate on future profits, then r > g is implied by a finite value of the capital stock.

We shouldn’t ask what capital “really” is. It really is a quantity of money in a process of self-expansion, and it really is a mass of means of production, and it really is authority over the production process. But the particular historical questions Piketty is interested in may be better suited to thinking of capital as a claim on the social surplus than as a physical quantity of means of production. Seth Ackerman has some very interesting thoughts along these lines in his contribution to the Jacobin symposium on the book.