Picking on Piketty (12) Robert Rowthorn

One of the best critiques of Piketty’s theoretical explanation has been presented by Robert Rowthorn from the University of Cambridge (UK) in his Note on Thomas Piketty. He explains that Piketty uses the standard neoclassical theory of factor shares.

This theory establishes a link between the capital intensity of production and the share of profits in total output. The nature of this link depends on the elasticity of substitution between capital and labour. When this elasticity is greater than unity, an increase in the capital-output ratio leads to an increase in the share of profits. This, in essence, is Piketty's explanation for the increased share of wealth-owners in national income. Thus, the shift in income distribution is due to the over-accumulation of capital: there has been too much real investment.

The above explanation has two related flaws. Piketty's assumption regarding the elasticity of substitution is not correct. There is considerable evidence that this elasticity is less than unity. Moreover, Piketty's method for measuring changes in the capital-output ratio is misleading. He fails to allow for the disproportionate increase in the market value of certain real assets, especially housing, in recent decades. This leads him to conclude, mistakenly, that the capital-output ratio has risen by a considerable amount. In fact, conventional measures of this ratio indicate that it has been either stationary or has fallen in most advanced economies during the period in question. This would suggest that the basic problem is not the over-accumulation of capital, but just the opposite. There has been too little real investment.

The increase in the capital/income ratio measured by Piketty is the result of price effects.

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).

Thus, 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.

Rowthorn shows that K/Y has been falling in the United States since 1981 and has been roughly constant in most of Europe. This implies that the income share of wealth owners is rising because of a low rate of real investment and a falling capital–output ratio.

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.