The Economist, in its “The Economist Explains” column, offers a terse four-paragraph summary of Thomas Piketty’s Capital in the Twenty-First Century. The summary is useful on the whole. However, on two important points, I believe, the benefit of terseness has been purchased at the cost of accuracy.

The Economist begins by outlining the historical elements of Piketty’s monumental study:

“Capital” is built on more than a decade of research by Mr Piketty and a handful of other economists, detailing historical changes in the concentration of income and wealth. This pile of data allows Mr Piketty to sketch out the evolution of inequality since the beginning of the industrial revolution. In the 18th and 19th centuries western European society was highly unequal. Private wealth dwarfed national income and was concentrated in the hands of the rich families who sat atop a relatively rigid class structure. This system persisted even as industrialisation slowly contributed to rising wages for workers. Only the chaos of the first and second world wars and the Depression disrupted this pattern. High taxes, inflation, bankruptcies, and the growth of sprawling welfare states caused wealth to shrink dramatically, and ushered in a period in which both income and wealth were distributed in relatively egalitarian fashion. But the shocks of the early 20th century have faded and wealth is now reasserting itself. On many measures, Mr Piketty reckons, the importance of wealth in modern economies is approaching levels last seen before the first world war.

The statement that “high taxes, inflation, bankruptcies, and the growth of sprawling welfare states caused wealth to shrink dramatically, and ushered in a period in which both income and wealth were distributed in relatively egalitarian fashion” is very misleading, and does not represent Piketty’s account very well, since it creates the mistaken impression that all four of the cited factors were responsible for both a reduction in wealth and its more egalitarian redistribution. But high taxes, inflation and welfare states caused a redistribution of wealth, not its destruction. In some cases the redistribution went from private hands to other private hands; in other cases, the redistribution took the form of a conversion of private wealth to public wealth. But since the emergence of the social state in the mid-20^th century, national wealth has grown consistently in both Europe and the US. Whether the social state was responsible for a slower rate of wealth accumulation, or in fact supported higher rates of wealth accumulation, is a matter about which people may disagree, but there was no aggregate wealth destruction during this period. The outright destruction of wealth was caused earlier in the 20^th century by war and depression. The other factors, combined with strong postwar growth, were responsible for slowing the return of pre-20^th century levels of inequality in the distribution of wealth and income as wealth continued to grow.

The Economist then turns to Piketty’s theoretical explanation of the forces driving these observed historical trends:

From this history, Mr Piketty derives a grand theory of capital and inequality. As a general rule wealth grows faster than economic output, he explains, a concept he captures in the expression r > g (where r is the rate of return to wealth and g is the economic growth rate). Other things being equal, faster economic growth will diminish the importance of wealth in a society, whereas slower growth will increase it (and demographic change that slows global growth will make capital more dominant). But there are no natural forces pushing against the steady concentration of wealth. Only a burst of rapid growth (from technological progress or rising population) or government intervention can be counted on to keep economies from returning to the “patrimonial capitalism” that worried Karl Marx. Mr Piketty closes the book by recommending that governments step in now, by adopting a global tax on wealth, to prevent soaring inequality contributing to economic or political instability down the road.

This paragraph contains a mistake. Piketty does not argue that “as a general rule wealth grows faster than economic output,” and that is not the dynamic captured by the expression r > g. Nor does his argument require a rate of wealth growth higher than income growth in order for the forces of divergence to predominate and produce greater inequality. What he argues is that, for a given savings rate s and national income growth rate g, the wealth-to-income ratio will tend to stabilize around the ratio s/g. If the wealth-to-income ratio is less than s/g, then wealth will grow more rapidly than national income. But if the wealth-to-income ratio is greater than s/g, then wealth will grow more slowly than national income.

So assume a savings rate of 10% and a growth rate of 2%. Only if the wealth-to-income ratio were less than 5 would wealth be growing faster than income. But that’s neither here nor there, since it will stabilize near 5 in any case over the long run, and the capital share will stabilize at rs/g. Whether or not wealth is growing faster than income is not what drives growing inequality. What drives increasing inequality of capital ownership, as I understand Piketty’s argument, is that some individuals save at a higher rate than the national savings rate, and other save at a lower rate; and the savings rate for individuals is likely to be higher in proportion to the amount of previously accumulated wealth they already possess. As a result, even in an economy with a stable wealth-to-income ratio and stable capital share, the rate of change in the proportion of the capital share flowing to a given possessor of wealth will tend to vary directly with their wealth. The rich don’t just get richer; they get richer at an increasing rate depending on how rich they already are. This part of Piketty’s argument is captured on page 351 of Capital in the Twenty-First Century:

This fundamental force for divergence, which I discussed briefly in the Introduction, functions as follows. Consider a world of low growth, on the order of, say, 0.5-1% a year, which was the case everywhere before the eighteenth and nineteenth centuries. The rate of return on capital, which is generally on the order of 4 or 5 percent a year, is therefore much higher than the growth rate. Concretely, this means that wealth accumulated in the past is recapitalized much more quickly than the economy grows, even when there is no income from labor.

For example, if g = 1% and r = 5%, saving one-fifth of the income from capital (while consuming the other four-fifths) is enough to ensure that capital inherited from the previous generation grows at the same rate as the economy. If one saves more, because one’s fortune is large enough to live well while consuming somewhat less of one’s annual rent, then one’s fortune will increase more rapidly than the economy, and inequality of wealth will increase even if one contributes no income from labor. For strictly mathematical reasons, then, the conditions are ideal for an “inheritance society” to prosper – where by “inheritance society” I mean a society characterized by both a very high concentration of wealth and a significant persistence of large fortunes from generation to generation.

Note also, that these portions of Piketty’s argument only deal with issues related to inequality of capital ownership. But there are other factors driving inequality. Piketty tells a very complex and nuanced story about the forces tending toward inequality in wealth and income, a story spread over six chapters of the book. The story weaves together three factors: inequality in capital ownership, inequalities in labor income, and inequalities related to the way in which the first two factors interact. He also stresses that he does not rely on one single synthetic index of inequality, such as a Gini coefficient, but that inequality is a multidimensional phenomenon, and that it is best to examine and understand these dimensions separately.

Note that, for a given rate of return to capital, a higher national income growth rate will tend to result in a greater significance for the labor share of income in national income, and in wealth-building. But that force for income convergence can be offset to some degree if there are extreme differences in labor income. Thus, Piketty devotes a chapter to trends in the inequality of labor income, particularly the rise of the supermanagers, and their super-compensation, in Anglo-Saxon countries after 1980.