Capital in Pikettys Capital

Capital in Piketty's 'Capital'

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An important but perhaps under-discussed aspect of Thomas Piketty's Capital in the 21st Century is Piketty's definition of capital itself, and the implications this has for his thesis and its critics. Capital is a notoriously tricky to define concept, and many have taken issue with Piketty's definition and the framework he builds around it. Typically, the implication is that a more Correct understanding of capital leads to vastly different conclusions to Piketty's, especially with regards to his conclusions on inequality.

We should first be clear about Piketty's definition of capital. He provides this at the beginning of the book, defining (non-human) capital as "all forms of wealth that individuals (or groups of individuals) can own and that can be transferred or traded through the market on a permanent basis." The 'non-human' qualifier is especially important, as reviewers such as Arnold Kling have argued that, since we all own our own skills and abilities - which economists sometimes call 'human capital' - there's no need to make a distinction between those who own capital and those who don't. The result is that Piketty's contention that 'capitalists' will become richer is nonsensical and empty, since we are all capitalists of one form or another.

However, Piketty explicitly rejects a definition of capital which includes human capital, primarily on the grounds that unlike the former, the latter "cannot be owned by another person or traded on a market" ( he notes the exception of slave societies). Furthermore, apart from conceptual considerations, he gives empirical reason to maintain the distinction:

"...skill levels have increased markedly over the past two centuries. But the stock of industrial, financial, and real estate capital has also increased enormously. Some people think that capital has lost its importance and that we have magically gone from a civilization based on capital, inheritance, and kinship to one based on human capital and talent...but I have already shown enough to warn against such mindless optimism: capital has not disappeared for the simple reason that it is still useful—hardly less useful than in the era of Balzac and Austen, perhaps—and may well remain so in the future."

In other words, if we are to understand the dynamics of inequality, the returns to non-human capital remain a major and distinct factor that require separate investigation. If we conflate human capital with other types of capital, we lose an important analytical nuance.

Capital confusion

Another typical charge directed at Piketty is that he relies on an overly homogeneous conception of capital itself, and this causes him to miss  the dyanmics that result from capital heterogeneity. But Piketty actually takes great care to point out the nuances hidden by aggregates and averages:

"As important as it is, this evolution of the overall capital/income ratio should not be allowed to obscure sweeping changes in the composition of capital since 1700...In terms of asset structure, twenty-first-century capital has little in common with eighteenth-century capital...we can see that over the very long run, agricultural land has gradually been replaced by buildings, business capital, and financial capital invested in firms and government organizations."


"Obviously, the rate of return can vary widely, depending on the type of investment. Some firms generate rates of return greater than 10 percent per year; others make losses (negative rate of return). The average long-run rate of return on stocks is 7–8 percent in many countries. Investments in real estate and bonds frequently return 3–4 percent, while the real rate of interest on public debt is sometimes much lower."

Thus it is clear that when Austrian economist Peter Klein claims Piketty "understands “capital” as a homogeneous, liquid pool of funds, not a heterogeneous stock of capital assets", he's simply wrong. Piketty does not claim there exists something called 'capital' which automatically and mysteriously yields a return: he explicitly references the historic rates of return on particular forms of capital and the capital accumulation that results. Austrian meanderings about entrepreneurship and capital heterogeneity are simply irrelevant to this point.

A similarly themed - though far more comprehensive and informed - critique of Piketty came from Jamie Galbraith. Galbraith (correctly) argues that Piketty has misunderstood the Cambridge Capital Controversies (CCC) and so does not appreciate the implications of treating capital as a homogeneous substance. The main issue raised in the CCCs was that you cannot derive the rate of return on 'capital' - measured as Piketty does in monetary terms - without first knowing the relative distribution of income (between wages, profits, rents etc.) Galbraith contends that, contra Piketty, a return on capital higher than the return on growth is not an inevitable "law", but can be politically managed to avoid increasing inequality.

While I have always sided with the post-Keynesians over both the correctness and theoretical relevance of these debates, the frequency with which they are referenced can become  rather tiring, particularly where they are just not relevant - as is the case with Piketty's book. Since Piketty's main aim is to understand how financial capital is accumulated over time, there is no reason to be concerned with classic capital aggregation problems. In fact, Piketty's use of market value to measure this type of capital is exactly the type of analysis where it is most relevant, as market valuations reflect the actual nominal returns or capital gains being made by holders of capital. The problems arise when financial capital, a la Piketty, is conflated with physical capital, a la neoclassical production functions. By reading Galbraith, one could easily get the impression Piketty is explicitly using a workhorse version of the latter:

"The basic neoclassical theory holds that the rate of return on capital depends on its (marginal) productivity. In that case, we must be thinking of physical capital—and this (again) appears to be Piketty’s view. But the effort to build a theory of physical capital with a technological rate-of-return collapsed long ago, under a withering challenge from critics based in Cambridge, England in the 1950s and 1960s, notably Joan Robinson, Piero Sraffa, and Luigi Pasinetti."

But Piketty does not use or rely on the marginal productivity theory of capital (he questions its relevance at several points in the book). Instead, he simply notes the historical regularity of a 5% average return on capital: this could be attributed to exploitation, marginal productivity, political, social and institutional circumstances, or any other number of factors. He does not claim that the empirical regularity he has found is a logical necessity or that it cannot be changed - on the contrary, he states that "the inequality r > g is a contingent historical proposition, which is true in some periods and political contexts and not in others". Galbraith builds his entire argument about a largely irrelevant debate just to point out something Piketty would not dispute: that r - and other key variables in Piketty's framework - can be changed from their historical averages.

The Rise of Capital?

If Galbraith misses the mark by recasting Piketty's framework purely as a neoclassical production function, then attacking his framework from without, a recent (and good) critique of Piketty by Matt Rognlie misses the mark by recasting Piketty's framework as a pure neoclassical production function, then attacking his framework from withinRognlie's major contention is that as capital's share of income increases, diminishing returns will set in and hence the return to capital will fall, so inequality need not increase. Rognlie makes a number of arguments to support his hypothesis, mostly centering around the value of the 'elasticity of substitution between labour and capital', which is a technical term for how readily firms can switch between capital and labour. The higher the elasticity, the easier it is to substitute and the lower the likelihood of diminishing returns.

Now, although Piketty relates his framework back to the neoclassical production function, it plays only a supporting role (he refers to Cobb-Douglas somewhat disparagingly as a 'simple story'), and his conception of 'capital', as defined above, is far more general than a literal interpretation of the production function might suggest. While Rognlie's argument takes the estimates of the elasticity as central, referencing research that dispute's Piketty's own estimate, Piketty only references elasticity estimates for support, and actually stakes most of his claim that diminishing returns will not become a problem on historical observation:

"On the basis of historical data, one can estimate an elasticity between 1.3 and 1.6. But not only is this estimate uncertain and imprecise. More than that, there is no reason why the technologies of the future should exhibit the same elasticity as those of the past. The only thing that appears to be relatively well established is that the tendency for the capital/income ratio β to be sure, it is likely that the return on capital, r, will decrease as β increases. But on the basis of historical experience, the most likely outcome is that the volume effect will outweigh the price effect, which means that the accumulation effect will outweigh the decrease in the return on capital."

This is not to say that Rognlie's arguments are not worth considering, and he makes some good points contra Piketty. He argues that the returns to new, IT-based technologies are not especially high, owing to their rapidly declining prices and high depreciation rate. He also points out that, absent housing housing bubbles, capital's share of income has declined in many countries over the past few decades. 

There are a couple of immediate counterpoints to these arguments: first, Piketty does not single out IT-based technologies as a source of returns, and may instead be expecting other (potentially uninvented) forms of capital to counteract diminishing returns. Second, it's not clear why we should single out asset bubbles for elimination from the returns to capital: they seem to be all too frequent, and there's also no reason to expect that the returns to other forms of capital would have followed the same trajectory had asset bubbles not occurred. Most important, though, is that Rognlie's focus on aggregate returns to capital causes him to miss an essential point in Piketty's argument: the distribution of capital ownership. 

Matt Bruenig has previously argued that Piketty actually identifies two major mechanisms for increasing inequality: first, the increased capital/income ratio, which Bruenig dubs the 'Capital Concentration Effect'; second, the increased inequality of ownership, which Bruenig dubs the 'Capital Share Effect'. Rognlie focuses only on the former, but even if capital's share of income stays roughly the same, an increased concentration of capital ownership can still increase overall wealth inequality. Furthermore, as Chris Dillow has pointed out, financial wealth is far more unequally distributed than property wealth,  so the housing bubble may well have dampened the the rise in inequality of capital ownership (which Piketty notes has only increased slightly). The result is that even if the returns to non housing capital (such as new technologies) are relatively low, their concentrated ownership may explain the rise in wealth inequality observed by Piketty over the past few decades. 


Piketty's definition of capital is well formed to address the major themes of his book. He avoids many of the common pitfalls in this area, and is careful to justify his approach at every step. More often than not, reviewers who criticise Piketty for his poor definition of capital are either attacking a straw man or do not engage directly with the reasons he gives for this definition. It's important that we retain Piketty's nuanced understanding of capital if we want to know if, why and how inequality under capitalism changes over time.


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