April 22, 2015 | by Anthony de Jasay Print

The people gathered to see the emperor, who had magnificent new clothes and would show them off presently. The palace grounds were packed full of courtiers and the simply curious, waiting excitedly. The door opened and the emperor stepped out. Although he was stark naked, the public was breathless with admiration and oohs and ahs. Only a little boy was unimpressed. “But the Emperor has no clothes!” he declared.

It takes only a little acumen to notice that the emperor’s new clothes form a close parallel with Thomas Piketty’s bombshell book Capital in the Twenty-First Century. The book comprises three components. By far the largest is an ambitious account of the quantitative evolution of capital in the main countries of the Western world from the 18th to the 20th century. One may doubt the feasibility of measuring capital, let alone capital in a distant past, but the effort is a herculean feat by a research team led by Sir Anthony Atkinson. This, in itself, at least deserves respect.

The second component is a commentary on this history by Piketty, linking it to his abstract theory. This commentary is plausible while seeking to support the theory, but a different commentary not supporting the theory could be no less plausible. Of two mutually contradictory commentaries, one is not more “true” than the other. As Karl Popper warns in his book The Poverty of Historicism, projecting trends out of data does not make for empirical laws of history — however impressive the data-gathering may be. The sheer weight of the assembled data, however, serves to persuade the lay reading public that the accompanying theory rests on a firm scientific base, or is indeed “proven.”

The third component, a kind of theory of capital, is what Piketty clearly intends to be the heart of the book and his claim to originality. For him, unlike for other theorists of capital and growth, everything originates in the inequality of the rate of growth of total output g and the return on capital r. Although r is durably higher than g, Piketty does not explain why — or, indeed, why capital has any return at all. In any case, capital is almost fully reinvested. The effect of this is that the stock of capital has the same rate of growth as its rate of return. To choose a reasonable estimate from the book’s data, the long-term average return on capital could be 4.5 percent, the rate of growth of capital also 4.5 percent, and the growth of total output 1.5 percent per year. So far so good. Our simplification, which assumes that all return on capital is reinvested, offends reality only negligibly.

From here on, the model proceeds to destroys itself. With r permanently higher than g (with r=4.5 and g=1.5), it will outgrow g inexorably. In our example, the catch-up occurs after 60 years, a medium-term range for Piketty. The catch-up means that all the output in that year is absorbed by the increment in the stock of capital. The workers all starve because they are made to produce only tools, machines, vehicles, and building materials, but no consumer goods. After the 60th year of the life of the model, everything stops and all the workers have been devoured by the ogre of capital.

It is strange that Piketty, a mathematician by training, did not immediately see that his model necessarily produces this absurdity. It is even stranger that none of the star-studded economists who reviewed his book (“Nobel material,” as one of his most eminent critics has judged it) seems to have noticed this elementary and decisive mistake. Most of the criticisms, such as they are, introduce qualifications or escape clauses, which all amount to suggesting — without openly saying so — that if the theory were different than the one Piketty presented, it might be correct.

There is, however, more to reject in Piketty’s opus than the fairly obvious blunder of putting both a large and a small exponent, r and g, in the same exponential function and expect them peacefully to coexist. Here, we are dealing with elementary logic and not with method or judgement. Yet a particular method permeates the work and must leave any economist readers ill at ease. Economists may well admit that some people are irrational some or even all the time, yet they build theories in which people purposefully seek to serve their preferences and interests — i.e., they maximize. This is how economics deals with orderly minds whose choices make sense within “incentives and resistances.” In Piketty’s book about the ogre of capital and its victims, however, the objective of maximising a desired result seems to play no role in behavior. Incentives are absent or too well hidden to be perceived.

This absence, felt throughout the book, becomes quite striking when Piketty reaches what his title declares to be his central subject, the 21st century. Albeit with caution and modesty, he makes forecasts about this century with the central feature that economic growth will be slower than at present, and the capital intensity of the economy will just about double. This means that workers will have twice the productive help as before, in terms of equipment and other capital, but will turn it to only half as much productive use. It also means that, despite the manifest failure of additional capital to elicit greater productivity, capitalists will furiously accumulate capital until the capital:output ratio in the 21st century is about twice as high as the average from the 20th. Mercifully, we are not asked to think about how this story would continue in the 22nd century, but it promises to be very strange indeed.