Imagine that you’re a person who is obsessed with airplanes. Naturally you’re excited when everyone starts talking about this big new book, Aviation in the 21st Century. You get your copy and start reading. Just as you’d hoped, there’s a detailed discussion of the flight characteristics of a vast variety of plane types and a comprehensive record of different countries’ commercial fleets, from the beginning of aviation until today, plus a few artfully chosen illustrations of classic early planes. But long stretches of the book are quite different. They are devoted to the general principle that, in an atmosphere, heavier objects fall faster than light ones, building up to the universal law that lighter-than-air objects will float. Finally, in the conclusion, you find some bleak reflections on the environmental consequences of air travel – hardly mentioned til now – and a plea for the invention of some new technology that will allow fast air travel without the use of fossil fuels. How do you feel, when you set the book down? You would be grateful for the factual material – even if the good stuff is mostly relegated to the online appendices. You would be impressed by the rigorous logic with which the principle of buoyancy was developed, and admire the author’s iconoclastic willingness to break with the orthodox view that all motion takes place in a vacuum. You probably share the author’s hopes for some way of eliminating the carbon emissions from air travel. But you might also find yourself with the uneasy feeling that the whole is somehow less than the sum of its parts.
You’re probably not into airplanes. But reading Capital In the 21st Century, you may have experienced a similar unease. You know the great social change the book is motivated by is the long run trajectory of income distribution – high in the 19th century, declining through much of the 20th century, and rising in recent decades. You understand that the central theoretical claim of the book is that “r>g” creates a secular tendency for income to concentrate. But it’s hard to find an account of how the universal logic accounts for the concrete history. (It’s striking, for instance, that the book does not contain a table or figure comparing r and g historically.) In contrast to the comprehensive account of the evolution of wealth shares in a dozen countries, the evidence linking this evolution to the supposed underlying dynamics is sparse and speculative.
The fundamental source of this disconnect is the two different senses in which Piketty uses the term “capital.” In the historical material, it is the observable aggregate of property claims, measured in money. But in the theoretical passages, it is a hypothetical aggregate of physical means of production. As a result, the theory and the history don’t really connect.
In treating capital as a money value when he measures it, and a physical quantity when he theorizes about it, Piketty follows the practice of most economists. I am far from the first one to point to problems with this approach. Heterodox critics who focus on this choice often invoke the Cambridge capital controversies, and suggest there is something logically inconsistent about the idea of a quantity of capital. In my opinion, these criticisms do not quite hit the mark. “K” and the formal models it is part of are tools for abstracting away from some aspects of observable reality in order to focus on others. Joan Robinson was certainly right that growth models of the kind used by Piketty cannot be derived from generic assumptions about production and exchange. But so what? The question to ask about a model is not whether it is logically derivable from first principles, but whether it gives a good description of the phenomena we are interested in. There is no reason in principle that a model of capital as a physical stock cannot capture important regularities in the behavior of capital as observable money wealth. It just happens that for for the central questions of Capital in the 21st Century, it does not.
Probably this is familiar to most people reading this, but let’s recap Piketty’s formal argument. He begins with two laws. The first decomposes the profit share into the rate of return on capital and the ratio of the capital stock to national income: alpha = r beta. Alpha is the share of capital income in total income, r is the average return on capital, and beta is K / Y, the capital stock (K) as a share of total income (Y). This “law” has been criticized as vacuous on the grounds that it is an accounting identity – an equation that is true by definition. Again, I think this is unfair. Yes, it is an accounting identity, but an accounting identity read in a particular way. It says that there is a given stock of capital, which produces a certain stream of income; this can then be compared to total national income to give the capital share. We could write the identity in other ways. The same identity could be read in other ways, for instance, K = alpha Y/r. Formally this is the same but it means something different. It means that a certain share of output is first claimed by a class of capital owners, and then their tradable claims on this income are assigned a value based on a discount factor r.
The loose articulation between Piketty’s historical material and his formal analysis comes from his decision to interpret the identity in the first way and not in the second. Starting from a quantity of capital leaves no room for valuation effects or distributional conflict in explaining the wealth ratio W/Y. instead, Piketty is forced to explain the ratio by focusing on the increase in the capital stock attributable to saving (s) relative to the growth of income (g). The problem is, these variables don’t do much empirical work in explaining the data. Almost all the historical action in the wealth share is in the changing value of existing wealth, not the pace at which new wealth is being accumulated.
Piketty’s second law states that in the long run, the ratio of the capital stock to national income converges toward the ratio of the savings rate to the growth rate. This second law is the equilibrium condition of a “zeroth law” (Yanis Varoufakis’ coinage), which says that the change in the capital stock from one period to the next is equal to the output from the previous period that is saved rather than consumed. (Minus depreciation of the existing capital, but Piketty somewhat idiosyncratically defines saving as net of depreciation, a choice that has been criticized.) This zeroth law is usually implicit, but it is critical to the question of whether we should treat capital as a physical stock. If a value is stable over time except for identifiable additions and subtractions, we can usefully treat it as a physical quantity, whether or not it “really” is one. If we assume that the evolution of the capital stock follows this zeroth law (i.e. that capital is cumulated savings) and also assume that savings and growth rates change slowly enough for the capital stock to fully adjust to their current values, then the capital output ratio will converge to the value given by Piketty’s second law. [^17] This apparatus – which is basically the growth theory of Harrod and Domar via Solow – is Piketty’s preferred tool for analyzing changes in the capital share over time.
So the question is, do these laws describe the historical trajectory of the wealth ratio? The answer is pretty clearly no.
Piketty, I should be clear, poses this question clearly – not so much in the book itself, where the Harrod-Domar-Solow framework is mostly taken for granted, but in articles like this one (with Gabriel Zucman). There they ask: How much of the variation in alpha and beta – over time and between countries – can be explained in terms of cumulated savings and income growth rates – that is, by treating capital as a physical stock? Unfortunately, the answers are not very favorable. Piketty’s critics on the left have not done ourselves any favors with our fondness for deductive proofs that any use of “K” is illegitimate. But it is true that, applied historically, this method can only explain that part of the variation in income and wealth distribution that corresponds to different rates of accumulation relative to output growth. And the problem is, most historical variation is not explained this way, but precisely by the features Piketty abstracts from – changes in the flow of output going to owners of existing capital claims, and changes in the valuation of future capital income.
There are many ways to see this. Here are a couple of examples, using data from his online data appendixes. [^19] First, let’s look at the change in the wealth ratio beta in various countries since 1970. This rise in the value of capital relative to current output is one of the central phenomena Piketty wants to understand, and underlies his claims about the increasingly skewed distribution of personal income. The horizontal axis shows the change in the wealth ratio implied by observed savings and growth rates. This is the change in wealth ratios that can be explained by differential accumulation and growth. On the vertical axis is the actual change.
As you can see, there is not much of a relationship. It’s true that slow-growing, high-saving Italy has the biggest increase in the wealth-income ratio, just as the capital-as-quantity approach would predict, and that fast-growing, low-saving United States has the smallest. But that’s it. German savings have been nearly as high as Italian,and German income growth nearly as slow, yet the growth of the wealth ratio there is close to the bottom. In the UK, the behavior of savings and income growth implied that the wealth ratio should decline; instead it rose by over 200 percentage points. Cumulated savings and growth rates explain only about 20 percent of the variation in wealth ratio increases across countries; 80 percent is explained by changes in the value of existing assets. If we want to know why the capital share has increased in some countries so much more than others over the past 40 years, the Harrod-Domar-Solow approach is not much more helpful than the principle of buoyancy would be to analyze the flight performance of different aircraft.
Next let’s look at the evolution of the US wealth ratio over time. The second figure shows the historical path of the US capital output ratio and two counterfactual paths. The counterfactuals are what we would see if wealth followed the “zeroth law.” The first counterfactual simply shows the wealth ratio under the assumption of standard growth theory that the value of capital stock in one year is equal to the value in the previous year, less depreciation, plus saving. All of Piketty’s formal analysis is based on the assumption that, on average, this is indeed how the capital stock behaves. The second counterfactual is based on capital gains fixed at their average for the full period, and again historical savings rates. (It also follows Piketty by treating quantity changes as saving, but this is not qualitatively important.)
What do we see? First, the cumulated-savings trajectories are quite different from the historical trajectory, even over the long run. As Piketty notes, the Harrod-Domar-Solow approach assumes that over the long run, the value of assets rises at the same rate as the price level in general. But in the US (as in other countries), this is not the case – over the full 140-year period, real average capital gains are 0.6% annually. This might seem small, but over a long period it has a decisive impact on the trajectory of the wealth ratio. As the figure shows, in the absence of these capital gains the US wealth ratio would follow a clear downward trend, from a bit over 4 times GDP in 1870 to a bit less than 3 times GDP today. In the US, in other words, the growth of the capital stock through net saving has consistently been slower than the growth of output. Under these conditions, the Harrod-Domar-Solow framework predicts a declining wealth ratio.
The capital-as-quantity framework also does not fit most of the medium-term variation in the wealth ratio. True, it does match the historically observed rise in the wealth ratio during the 1930s and the fall during World War II, which are driven by changes in the denominator (GDP) not the numerator. But it suggests that the only significant postwar recovery in the wealth ratio should have come in the 1970s, when in fact the wealth ratio reached its nadir in this period. And the more recent rise in the wealth ratio has come in a period when Piketty’s framework would predict a sharp decline. During the decade before the Great Recession, savings were low but capital gains were high; in a Harrod-Domar-Solow, framework, that implies a decline in the value of wealth relative to output. The message of Piketty’s data is clear: If “capital is back,” it is entirely because of an increase in the value of existing assets, not, as the book suggests, because accumulation has been outpacing growth. [^20]
So treating capital as a physical stock fails to capture either the long-run trajectory of capital-output ratios or the variation in wealth ratios across countries and between different periods. All of the developments Piketty describes in his historical material, is driven by the valuation changes that he abstracts away from in his formal analysis.
With a moment’s reflection, this should not be surprising. After all, a significant fraction of the wealth stock is land, which is not produced. If land prices did not consistently rise faster than the general price level, then land would have long since declined to a trivial fraction of total wealth. The problem land poses for Piketty’s story is emphasized by Matt Rognlie among others, whose critique of the book is in some ways parallel to the argument I’m making here.
If we can’t make sense of the changes in the wealth ratio by thinking of the incremental accumulation physical stock of capital, how else can we think about it?
Let’s go back to Piketty’s First Law. As I suggested, there are different ways to interpret this accounting identity. We can think of it as Piketty and most other economists do, as saying that there is a stock of capital goods; these goods generate a certain amount of output, which is received as income by the owners of the capital goods; that stream of income can then be compared to the national income to find the share of capital owners. From this point of view, the stock of capital is the real sociological fact and the shares are secondary. Alternatively, instead of starting from an endowment of capital goods, we could start from the process of social production. The output of this process is then divided up according to various socially recognized claims, which we call wages, profits, taxes, and so on. Some claims are marketable; these claims will have a price. The price of profit-type claims on output is related to the flow of income assigned to them by r, now understood as the discount factor applied to an income stream rather than the income generated by an asset.
It’s the same identity, the two stories are formally equivalent. The effort to turn this formal equivalence into a substantive identity – to reduce money values and distributional conflicts to the technical problem of allocation of scarce resources – have yielded two centuries’ worth of tautological circumlocutions. But at the end of the day we are left with a choice of ways of looking at the same observable phenomena. In the orthodox perspective favored by Piketty, we ask “why is there more capital than there used to be?” and “what is the product of each unit of capital?” In the second perspective – which following Perry Mehrling we might call the money view – it’s the distribution among rival claims that is the real sociological fact, and the value of these of claims as “capital” that is an after-the-fact calculation. From this point of view, the relevant questions are “how much of the output of the firm is appropriated through property claims?” and “what value is put on each dollar of property income?” In which case, we should expect to see higher wealth ratios not in times and places where cumulated savings have outpaced growth, but in times and places where the bargaining process has shifted in favor of holders of capital claims, and where financial markets place a higher value on ownership claims relative to current output.
What does this mean concretely? Piketty himself gives some good examples. There is a short but interesting section in the book on the abolition of slavery in the US. Here we have a drastic (though short-lived) reduction in the wealth ratio and capital share in the US. Clearly, this has nothing to do with any change in the pace of accumulation of physical capital. Rather, what happened was that a share in output that had taken the form of a tradable capital-type claim ceased to be recognized. Piketty presents this as a special case, an interesting excursion; he might have done better to treat it as a signpost to the main road. Slavery is only one possible system in which which authority over the production process, and a share of the surplus it generates, goes to the holders of particular kinds of property claims.
Another, perhaps more directly relevant case, is the case of Germany. Germany, by income one of the richest and most equal countries in Europe, has among the lowest and most unequal household wealth. In addition – and not unrelatedly – German corporations have unusually low stock market valuations. Among the major rich countries, Germany consistently has the lowest Tobin’s q – shares of a company with given assets and liabilities are valued less in Germany than elsewhere. The first puzzle, that of low and highly skewed market wealth, is largely explained by low levels of homeownership in Germany. Compared with most other rich countries, middle-class Germans are much more likely to be renters. This does not mean that their housing is any lower quality or less secure than in other countries, but it does mean that the same physical house in Germany shows up as less market wealth.
The lower valuation of German corporations also reduces the apparent wealth of German households. And why are German firms valued less by the stock market? Piketty and Zucman offer a suggestive explanation:
the higher Tobin’s Q in Anglo-Saxon countries might be related to the fact that shareholders have more control over corporations than in Germany, France, and Japan. … Relatedly, the control rights valuation story may explain part of the rising trend in Tobin’s Q in rich countries. … the “control right” or “stakeholder” view of the firm can in principle explain why the market value of corporations is particularly low in Germany (where worker representatives have voting rights in corporate boards). According to this “stakeholder” view of the firm, the market value of corporations can be interpreted as the value for the owner…
In other words, one reason household wealth is low in Germany is because German households exercise more of their claims on the business sector as workers rather than as wealth owners. Again, this is treated by Piketty as a sideline to the main narrative. But given that almost all the rise in wealth ratios is explained by valuation changes, this sort of story about the strength of shareholder claims under different institutional arrangements probably has more to say about the actual evolution of the capital share than the whole apparatus of growth theory.
When I’ve made this argument to people, they’ve sometimes defended Capital in the 21st Century by saying that we should take its title seriously. Despite appearances, this is not fundamentally a book about the historical evolution of wealth and income in various countries, but about what we might expect to happen in the future. But it seems to me that our interpretation of the historical record is going to shape our judgements about future prospects. In Piketty’s story, there seem to be two different kinds of forces at work. There are valuation changes and revisions of property rights, which operate episodically; these explain the mid-20th century declines in the wealth ratio and capital share. And there is the ongoing dynamics of accumulation, which operates all the time; this explains the convergence of the wealth ratio and capital share to high levels both in the 19th century and more recently. (Or explains the increase of the wealth ratio without limit, if you prefer that reading.)
When we split things up this way, it’s natural to base our predictions for the future on the continuous process, rather than on the historically specific episodes – especially if those episodes all coincide with major wars. The continuous process, furthermore, implies a tight link between growth and the wealth share. The same acts of saving and investment that allow society to increase its material production, also ensure that an increasing share of that production will be claimed in the form of capital income, even while the great majority of us continue to depend for our income on labor. So it’s futile to try to change the distribution of income directly; all that can be hoped for is redistributive taxes carried out by the deus ex machina of a global state.
But when we realize that changes in the value of existing assets are central not just to the decline in wealth ratios in the mid-20th century, but to their whole evolution – including their rise in recent decades – then the mid-20th century decline no longer looks like a special case. It’s bargaining power, it’s politics, all the way down. The same kind of redistributive projects – the decommodification of basic services like healthcare, pensions, and education; the increased bargaining power of workers within the firm – that were responsible for the fall in the capital share in the mid 20th century were responsible, in reverse, for its rise since 1980. In which case we can learn as much about our possible futures from the 20th century decline in the claims of property over humanity, as from their recent reassertion.
[^17]: I’m emphasizing the “zeroth law” here, but it’s worth noting that the conventional practice of treating s and g as “slow” variables and beta as “fast” is also open to question. If you look at the historical data, national savings and growth rates are much more variable than the capital-output ratio, and they don’t appear to be stationary around any long-term average. So it seems a bit nonsensical to talk about the capital-output ratio as converging to a long-run equilibrium defined by a fixed s and g.
[^19]: Piketty’s presentation of his data online is superb, both in content and organization. Even if the book were otherwise worthless – which is very far from the case – these appendixes would be a huge contribution.
[^20]: Another problem is that Piketty’s narrative suggests that r, the rate of return on capital, is constant or increasing, while his data unambiguously show a long-term decline. As a result, the rise in the wealth ratio has not been accompanied by a rise in the capital share, at least not everywhere. In the UK and France, there is a clear downward trajectory from a capital share of 40 percent in the mid-19th century to around 25 percent today.