This is a huge book, and I do not mean just the length. It is social science at its best and boldest, attempting to explain the long sweep of history. Piketty's book is reminiscent of Marx's Capital (of course the title invites that comparison) or Durkheim's The Division of Labour in Society in that regard. The book is the culmination of a research program on top income shares based on tax records initiated by Piketty 20 years ago. Anthony Atkinson, the dean of income distribution studies, Emanual Saez, and Facundo Alvaredo joined Piketty in this enterprise and it resulted in a series of books and articles, first by Piketty on France in 2001 and an article by Atkinson on the UK in 2002, and by the other PIs on the US, the rest of Europe and some emerging economies in the subsequent years. The dataset that resulted from this collaboration, World Top Incomes Database (http://topincomes.parisschoolofeconomics.eu/) contains data from 29 countries, with a time series as much as a century long. The database itself is a major contribution to social science.

Piketty's goal is to examine the development of income and wealth inequality over the very long run. He focuses on three dimensions of inequality: household income, capital and labour shares of national income, and the ratio of wealth to national income. Piketty defines K as the stock of capital but he does not mean productive capital but all wealth; he uses wealth and capital interchangeably in the book. He defines national income in a given year as Y (following convention) and the ratio K/Y as β. He argues that “β does measure the overall importance of capital in a society so analysing this ratio is a necessary first step in study of inequality” (p. 51) and he spends the first third of the book on this task. The time series for France and the UK stretch back to 1700. He shows that β follows a U shaped curve in the two countries as it is fairly steady at 700% (that is K is 7 times Y) throughout the 18^th and 19^th centuries and this falls precipitously from the eve of World War I to the close of World War II to 300%, then back up to 550–600% by 2010. The time series for Germany, which begins in 1870, shows a similar pattern. In the new world countries, the U shaped pattern also appears but β is only circa 500% in the 19^th century and does not decline so much in the first half of the 20^th century nor does it rise so much thereafter. Piketty shows that the U shaped pattern of β is a general pattern in four other countries for which he and Gabriel Zucman were able to assemble data.

Piketty defines r as the real rate of return on capital after tax; g as real growth of GDP; s as the savings rate; and then α as the capital share of national income. He calls the identity α=r*β, the “first fundamental law of capitalism” but it is not really a law; it is true by definition (p. 52). He then argues that in the long run β=s/g (“the second fundamental law of capitalism”) and since r is the primary determinant of s (again in the long run) that as long as r > g, β will increase. Here we see the core of his explanation of the U curve. He states that an empirical regularity is that g has been 1 to 1.5% for most of history (p. 93); the Trentes Glorieuses, the period of rapid growth after World War II, was very much the exception. The two world wars and the Great Depression caused massive destructions of capital, both physical destruction of capital and bankruptcies, very low savings rates, and policies, above all high marginal taxation, which greatly reduced K and thus β (p. 148). The rapid growth in the Trentes Glorieuses then served to suppress the rise of β. I found this explanation quite convincing.

It seems that this analysis would imply that there would also be a U shaped pattern for capital/labour shares of national income and the share of national income of the top 1% of income households, the other two dimensions of income inequality which Piketty examines. He shows that there is evidence for this for capital/labour income shares (p. 200–01), though the U pattern is not nearly as marked as for β. However, for top 1% income shares (and top 0.1% shares), the elegant and parsimonious explanation he developed for the wealth/income ratio, β, does not work very well. While it is true that some countries do show the U shaped pattern, many do not and the ones that do are not necessarily the ones which show the sharpest U pattern for β. For example, top 1% income shares rose more steeply in United States in the past three decades (from 10% to 23%) than any other country, while in France they hardly rose at all, yet the β rose much more sharply in France than in the US, where the rise is modest, as I noted previously.

My colleagues, Evelyne Huber and Jingjing Huo, and I have analysed the determinants of the top 1% income share and that analysis sheds some light on this puzzle (https://kellogg.nd.edu/publications/workingpapers/WPS/404.pdf). In a pooled time series analysis of 18 countries for the period 1960–2010, we do not find that β explains variations in top income shares. In fact, it is wrongly signed (though the zero order correlation is correctly signed but very weak, r=.16). We find that secular centre and right government, union density, union centralization, veto points, stock market capitalization, top marginal income tax rates, and education spending, in that order, are the most important determinants of variations in top income shares. The first three variables are characteristics of the Anglo-American or liberal welfare states which explains why it is those countries that experienced the largest increases in top income shares.

The World Top Incomes Database and the articles and books that emerged from it are primarily responsible for publicising and politicising the rising income shares of the top 1 and 0.1% of households. No doubt many readers will be disappointed, as I was, that Piketty's elegant explanation for the U shaped pattern of β does not explain the rise in the top income shares in Anglo-American democracies. Piketty knows this, of course, and presents the data showing this, without directly commenting on it. However, going forward in the 21^st century it is likely that the logic of his argument will play itself out and that we will see a return of the preponderance of inherited wealth, a return of “patrimonial capitalism” as he calls it. It is very likely that r > g inequality will continue to hold, indeed, that r will be substantially higher because population growth is unlikely to return to the levels of the Trentes Glorieuses as fertility rates are far below population reproduction in most post industrial democracies, and we are not likely to experience another one off increase in productivity like the one experienced in the transition from agricultural to industrial society.

Thus, it is likely that we will see a return of β to 6–700%, and that level of wealth concentration is bound to result in further rises in top income shares across a broader range of countries unless policy counter measures are introduced. The last 100 pages of Piketty's book are devoted to this topic. Recall that r is after tax and Piketty presents evidence that high marginal income taxation installed to pay for the two world wars and retained, until the Thatcher/Reagan neo-liberal revolution brought them down, decreased top income shares. Piketty favours the re-introduction of very high marginal income tax rates (circa 80%) as well as increases in capital and inheritance taxes. He is worried about the effect of capital mobility so he proposes global taxes, if possible, if not then regional (e.g., EU) taxes. Even that seems utopian, but the conversation has to start somewhere.