"Piketty’s World Formula"

Hans-Werner Sinn

Anti-Piketty - Capital of the 21st Century, 2017, pp. 215-218

Thomas Piketty’s book (2014) on inequality hit a sensitive spot with Americans. It channeled the mounting dissatisfaction in a country that lacks a robust welfare system and a more progressive tax system. His book has a whiff of Karl Marx, with his style of writing. And he resorts to a theory similar to Marx’s when he decries the increasing inequality that results from an ever higher ratio of wealth to national income. Marx predicted the increase in this ratio with his law on the growing organic composition of capital. Piketty attributes the growth in inequality to the r > g formula, one of the few formulas that have made it to the international daily newspapers and which by now has attained a hallowed status among journalists akin to Einstein’s E = me2. Piketty’s formula states that interest in the form of the average return on capital, r, is persistently higher than the growth rate of the economy, g.
The consequence, according to Piketty, is that the wealth of an economy accumulates faster than the growth in economic output. The formula is a hot topic of discussion everywhere. In fact, the formula has been known for quite a long time now; it denotes a fundamental implication of the neoclassical theory of economic growth. Indeed, over the long run, the rate of return to capital usually lies above the growth rate of the economy, as Piketty asserts. If that were not the case, land prices would be infinite, there would be excessive consumption, and growth would eventually end. But the formula does not imply that wealth grows faster than economic output. Such a conclusion would only be warranted if the savings of an economy could be set equal to the economy’s capital income, so that the rate of economic growth is the same as the interest rate. But that is not the case. Rather, savings are consistently smaller than the sum of all capital income. The wealthy consume substantial parts of their income, and the savings from labor income usually is small. Thus, the growth rate of wealth lies significantly below the interest rate; the fact that the interest rate exceeds the rate of economic growth in no way implies that wealth grows faster than the economy. Indeed, a central finding of economic growth theory states that the interest rate of an economy, dependent on the savings rate, settles over the long term at a level in which the growth of capital equals the growth rate of output. The consequence is the longterm persistence of the ratio of wealth to economic output. The long-term constancy of the ratio is a basic ingredient of all growth theories. Behind the long-term persistence of this ratio stands a simple mathematical law. If an economy saves a given portion of its income, the wealth resulting from the accumulation of those savings will increase in the long run at the same rate at which national income grows. Thus, the ratio of wealth to income cannot increase permanently. The law is based on the fact that every increasing quantity can grow over the long run only at the rate at which its accretion grows. An example is the heaping of earth into a mound. Assume that in every period, a further spade of earth is added, and that the size of the spade itself grows at a given rate from one period to the next. The growth rate of the amount of earth in the mound converges toward tire growth rate of the spade size. If we substitute the current savings of an economy for the amount of earth in the spade and wealth for the size of the mound, we obtain the long-run constancy of the ratio of wealth to income when a fixed share of income is saved.

It must be stressed that this law applies over the long run, over several decades. Wealth can well grow faster than the economy at given times. Piketty could then have a point. But even when such is the case, there is hardly any reason for apprehension. When it comes to distributional issues, the important element is less the ratio of wealth to national income than the ratio of capital income to wage income, that is, the proportion of capital and wages in national income. The distributional shares of national income, as first observed by the left-leaning economist Joan Robinson in her 1942 book, An Essay on Marxian Economics, have remained fairly stable over time and follow no discernible trend. Much more important than Piketty’s theory of everything is the question of how many people share in the wage and capital income. If the number of wage earners increases faster than the number of wealth owners, a less desirable distributional pattern could emerge despite the constancy of the ratio of capital to wage income. That could be the case in the United States, with its large number of immigrants, and could be the reason for the current dissatisfaction among the populace. But there is no evidence to support this as a general law. And if the risk should indeed exist that the number of people sharing the capital income grows too slowly compared with the number of people sharing the labor income, the best medicine is to improve the chances of upward mobility. The more people share the wealth and capital income, the smaller the distributional problem. It helps for this reason if the rich have more children than the poor, since their wealth will eventually become spread among their heirs, solving the distributional problem at a stroke. A family income splitting system such as France’s is one of the policy measures that a society might consider if it fears an undesirable concentration of wealth. Regardless, a progressive taxation system is needed to check the growth in net income among the upper income echelons. Even in the absence of a fundamental trend toward greater inequality owing to the theory formulated by Piketty, inequality within the wealthy group can increase because some dynasties accumulate ever more wealth at the expense of other dynasties. Whether action is needed in this regard in Europe is open to debate, since progressive taxation is already present it will be hard to make the case for even more of it. My conclusion is that Piketty, like Marx, caters to a longing, simmering among the people, but that he tries to underpin his policy proposals with a theory that does not substantiate what he asserts.