Bob Rowthorn questions two of Piketty’s central assumptions

26 Jun, 2014 at 17:38 | Posted in Economics | 5 Comments

Piketty uses the terms “capital” and “wealth” interchangeably to denote the total monetary value of shares, housing and other assets. “Income” is measured in money terms. We shall reserve the term “capital” for the totality of productive assets evaluated at constant prices. The term “output” is used to denote the totality of net output (value-added) measured at constant prices. Piketty uses the symbol β to denote the ratio of “wealth” to “income” and he denotes the share of wealth-owners in total income by α. In his theoretical analysis this share is equated to the share of profits in total output. Piketty documents how α and β have both risen by a considerable amount in recent decades. He argues that this is not mere correlation, but reflects a causal link. It is the rise in β which is responsible for the rise in α. To reach this conclusion, he first assumes that β is equal to the capital-output ratio K/Y, as conventionally understood. From his empirical finding that β has risen, he concludes that K/Y has also risen by a similar amount. According to the neoclassical theory of factor shares, an increase in K/Y will only lead to an increase in α when the elasticity of substitution between capital and labour σ is greater than unity. Piketty asserts that this is the case. Indeed, based on movements α and β, he estimates that σ is between 1.3 and 1.6 (page 221).

assumptions-analysis1Thus, Piketty’s argument rests on two crucial assumptions: β = K/Y and σ > 1. Once these assumptions are granted, the neoclassical theory of factor shares ensures that an increase in β will lead to an increase in α. In fact, neither of these assumptions is supported by the empirical evidence which is surveyed briefly in the appendix. This evidence implies that the large observed rise in β in recent decades is not the result of a big rise in K/Y but is primarily a valuation effect …

Piketty argues that the higher income share of wealth-owners is due to an increase in the capital-output ratio resulting from a high rate of capital accumulation. The evidence suggests just the contrary. The capital-output ratio, as conventionally measured has either fallen or been constant in recent decades. The apparent increase in the capital-output ratio identified by Piketty is a valuation effect reflecting a disproportionate increase in the market value of certain real assets. A more plausible explanation for the increased income share of wealth-owners is an unduly low rate of investment in real capital.

Robert Rowthorn

It seems to me that Rowthorn is closing in on the nodal point in Piketty’s picture of the long-term trends in income distribution in advanced economies. As I wrote the other day:

Being able to show that you can get the Piketty results using one or another of the available standard neoclassical growth models is of course — from a realist point of view — of limited value. As usual — the really interesting thing is how in accord with reality are the assumptions you make and the numerical values you put into the model specification.

(h/t Erik Hegelund)


  1. “The apparent increase in the capital-output ratio identified by Piketty is a valuation effect reflecting a disproportionate increase in the market value of certain real assets”

    Another strawman argument. The important thing is the fact and not its causal interpretation. After all, causality can be “streched.”. Increasing inequality is a fact. Any framed hypothesis about its causes is a strawman argument. If you want to decrease inequality, you need to start by taxing automation producers at 80% or even more.

  2. I continue to be impressed by how effective this very simple move — equating wealth with capital — is in provoking a dialectic that usefully re-examines both concepts and facts. I’m not sure I have enough of an intuitive grasp of optics to know what it means to be a nodal point, but Rowthorn seems to be noticing something little discussed, which has been observable for some time, to wit the extent to which dis-investment can account for increased capital income.

    If we re-think what it means to derive income from ownership, and ask, critically, what the composition must be of that income and that wealth (i.e. what’s owned), then, it seems to me, that we have to admit usury and financial insurance as well as “productive capital” into the ambit of wealth. It cannot all be robots.

    In a world of uncertainty and risk, it may be that wages are equal to the marginal product of labor, but that is only because management makes it so. Meanwhile, the ability of wealth to earn income is limited only by its ability to lend at interest, which simply isn’t the same thing as investing in “productive” capital.

  3. Call “K” the amount of capital, “Y” the national income, and “P” the amount of profits. Piketty’s first law can be written as:


    “K” cancels, and this is just an accounting identity.

    Now call “S” savings, and “I” investment. The rate of saving “s” is equal to S/Y.
    If we assume that there is not an unusual instability of the capital-income ratio, the rate of growth of income cannot be too far apart from the rate of growth of capital for too long. The rate of growth of capital I/K is then equal to rate of growth “g”. Piketty’s second law (Harrod-Domar) can be written as:


    Since S=I, this is again an accounting identity.

    As for the corollary r>g, which is the central conclusion Piketty reaches, in the notation above it can be written as:


    “K” cancels, and this leaves us with:


    Which must be true since profits are not spent only on investment, part of it is spent on luxury goods. So it all comes down to the classical idea that the surplus can be reinvested or used in luxury, that is, only part of the surplus is used in productive investment. Piketty argues that both Marx and Kuznets are wrong, because inequality is not deterministic, it depends on institutions. But in the neoclassical theory Piketty uses (and Mankiw also uses when criticizing Piketty), distribution is determined by the marginal productivity of capital and labour. If Piketty follows his logic until the end, he must reject neoclassical theory, and adopt a circular flow of income theory, such as the Physiocratic, Classical, Marxian or Post-Keynesian approach, in which the distribution of the surplus depends upon institutions (rather than on marginal productivities), and P>I because not all profits are reinvested (some is spend in luxury goods). The Cambridge controversies in the theory of capital, which Piketty neglects, are essential to understand all this.

  4. Here is what I found to be a good discussion of the topic of capital and other things.

  5. All of this is interesting but ironically has been criticized from moving away from neo classical model assumption on capital and savings. I’m a bit baffled!

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