In Capital in the Twenty-First Century (hereafter C21C), Thomas Piketty concludes that the everyday activities of capitalism are brewing a crisis for the global economy. The historical tendency for returns to capital to exceed overall growth, fully manifest today, concentrates wealth and distorts choices in ways that harm economic performance in the long run. If he is right, only unprecedented international cooperation can avert it. If he is wrong, market forces and existing institutions will suffice to correct the imbalance. The stakes of an author’s thesis are seldom so high. Maybe that is why C21C is such a publishing phenomenon.

Piketty argues (by now, famously) that the logic of capitalism implies that economic returns to capital (r) exceed the economy’s growth rate (g), necessarily reducing returns to labor and resulting in ever-greater inequality of incomes and wealth. Less famously but more portentously, he also claims that capitalism has a backward looking bias that, barring international cooperation to counter it, compromises the future. His case rests on original data, a reinterpretation of standard macroeconomics, and a consideration of how politics, culture, and demography affect the economy.

Piketty became well-known among social scientists studying inequality a dozen years before C21C. With Emmanuel Saez, Anthony Atkinson, and others, he compiled a database of anonymized tax records from rich countries, covering decades and, eventually, centuries. Tax records have fewer errors and more detail than most social science data on incomes and wealth. Standard sources are statistical samples that support calculations about the deciles of a population; they are too imprecise for the study of smaller groups. In a 2001 working paper from the National Bureau of Economic Research, published in 2003 in the Quarterly Journal of Economics, Piketty and Saez identified “fractiles” of the top ten percent, zooming in on both the top one percent and the top 0.1 percent. They discovered “the one percent” in that paper and showed that American income inequality from 1913 to 1999 rose and fell according to the fortunes of the top earners. Their term “the one percent” crossed over into public discourse.

C21C is Piketty’s explanation of how and why the one percent matter so much. He reinterprets standard macroeconomics by focusing on two economic principles: (1) The share of income from capital (α) equals the simple product of the rate of return to capital (r) and the ratio of capital stock to annual income flow in the economy (β). (2) The capital to income ratio (β), in turn, equals the ratio of savings (s) to real growth (g). The first principle is a mathematical identity, true by definition; the second is true in equilibrium. Equations like these—a quantity of interest equals the product (or ratio) of two other things—aid analysis if we can say in advance how one of them behaves. Then we put the known out of mind for the moment and focus on how one unknown relates to the other. In physics, e = mc ² yields insight because c is a constant, implying that the ratio of energy to matter must also be constant. In social science, Marxism can be formalized as a statement that returns to capital (r) decrease over time. Twentieth-century American economists switched the focus to α; short time series implied that α was a constant, which they understood as the proposition that markets push a high r down by prompting investors to use more capital and push a low r up by rewarding saving. British economists countered that technology determines β, implying that growth (g) depends on savings (s) under a given technology and its associated β.

Piketty rejects both arguments. His data show that both α and β fluctuate over time (C21C, Figure 10.8). If α and β are not constants, then markets are not self-correcting. According to Piketty, capitalism with varying α and β is a race between returns to capital (r) and growth (g). Generally, r > g, but the gap between r and g varies, and inequality varies with it. Since the 1970s, r has been high, and g has been low in rich countries. Consequently, inequality of incomes and wealth have increased.

When r gets too far ahead of g, capital is making money without producing goods and services. Finance prospers while wages race to the bottom. This situation has bred bubbles in the past—Japan through the 1990s, the American dot-com bubble a little later and, most disastrously, the mortgage-rate bubble that collapsed in 2007 and almost took the world financial system with it. Markets can avert trouble if r declines following a rise in β, but r and β have been rising together since 1975, taking α up with them. Markets cannot stop the spiral under these conditions. The problem is systemic, not the consequence of bad actors. Policy must intervene.

Savings (s) were once thought to be the key to stimulating growth (g), but Piketty has already accounted for savings in his second principle. Invention can create new wealth, but “the logic of r > g implies that the entrepreneur always turns into a rentier” (p. 395). Thus manipulating the economic variables r, g or s will not suffice as an explanation or solution. Piketty marshals politics, culture, and demography to account for how r – g rose from 1830 to 1929, fell during the Great Depression and World War II, leveled off, then rose again from 1977 to now. He asserts that the demography of aging populations will keep r up and g down for the foreseeable future. Savings behavior reflects r to some extent, but cultural differences matter, too.

In short, Piketty argues that the capitalist economy is brewing a crisis of concentration that markets can neither avoid nor correct on their own. Political intervention will be required to avoid an unsustainable degree of concentration. Unfortunately, globalization pushed the problems beyond the reach of current political institutions. Capital moves around the globe with ease, and people take pains to move, too. Nation-states acting alone cannot corral capital. So Piketty prescribes a worldwide tax on capital. Workers of the world unite to save capitalism from itself (again).

So is Piketty right? His argument rests on original data, formal economic analysis, and a social-political analysis. I will take each in turn. Piketty has the best data available on this subject. He, Saez, and Atkinson have increased knowledge by compiling and integrating a truly amazing database which they make available to all for free download. Some of the time-series are more complete than others, but no social scientist can bring better evidence to the discussion of inequality.

Their income data is better than their capital data. That will always be true. Income is more specific as to value and timing. Somebody did something for money and got paid. Both the amount and the date can be recorded to any desired level of precision (Piketty repeatedly thanks governments for requiring people and corporations to report those transactions). Capital, on the other hand, is a stock of useful objects and rights that capitalists and their agents use to make goods or provide services. Its value cannot be counted directly; it might be imputed from the price of similar objects that were recently sold, but capital can never be known the same way income is known. Ascribing the value of capital to a particular time is even more difficult. Capital persists, but its value changes. Some objects, like laptop computers, depreciate over time; other objects, say a shop on a “hot” corner, appreciate.

Piketty’s data on capital are mostly estate tax records. They sum the deceased person’s accumulated wealth. But, in a time-series, what year do we assign the sum to? The tax collector links it to the holder’s date of death, but that inserts some serious time-shifting into the core of the data analysis. Piketty uses age distributions of wealth holding to adjust his data, but mostly he relies on the tendency for the estate tax records to correlate very highly with other kinds of assessments when those assessments become available. As he shows, (pp. 391-393, 401-403), his calculations depend on the ratio of bequests to total wealth, not on the absolute level of wealth. So he is probably right about the long-term trends in r.

I have a question for Piketty that he does not address in the book or online appendix: Do we double-count capital stock when a dead man’s estate passes to his wife and then hers to their children?

Inheritance (Piketty sometimes calls it “patrimony”) is crucial to the r – g gap. We hear from free-market enthusiasts that technological innovation could disrupt patrimonial capitalism, suggesting that the historical evidence in C21C is simply out-of-date. New calculations by Lisa Keister and Hang Young Lee (as yet unpublished) show that inheritance remains significant despite the tech sector’s recent disruptions. Americans in the top one percent of the wealth distribution were twice as likely as the rest of the wealth distribution to have inherited money (45 percent of the wealthiest one percent had some inheritance compared to 20 percent of the rest of the wealth distribution). And heirs in the one percent inherited eleven times the wealth of other heirs—a median inheritance of $550,000 compared to just $49,000. So Piketty is not only right but still relevant.

Moving from data to math modeling, though I must leave the task of assessing the technical details of Piketty’s macroeconomic analysis to the macroeconomists, I can say that he makes fewer assumptions than do most analysts who work with these equations. He rejects Marx who said r inexorably declines over time. He rejects the twentieth-century economists who assumed that either α or β was constant. He is left with the empiricist’s fate: when data contradict others’ assumptions, the analyst must move on without them. He shows that only untenable assumptions result in the model implying that inequality will decline on its own before it becomes a problem. If the model implies trouble, then he is absolutely right that avoiding trouble requires going outside the system that the model describes. He advocates political intervention in the form of a universal capital tax. In that he encounters the dilemma of a failed model: failure of the model implies that the solution lies beyond its parameters but it says nothing about where “outside” the solution resides.

Nonetheless, Part Four of C21C merits close reading for its interesting theory of what he calls “the social state”. Ever data-driven, Piketty begins his discussion of the social state with data on tax revenues as a share of GDP in Britain, France, Sweden, and the United States from 1870 to 2010. In the late 1800s, tax revenues were only seven or eight percent of GDP in all four countries. Between 1920 and 1980, all increased state spending to between thirty and fifty percent of GDP; the United States stopped at thirty, Sweden at fifty. Regulation of economic institutions complements spending. Piketty’s most telling point here is that the social question is less whether tax collection is progressive or regressive than whether spending and regulation are progressive or regressive. France uses a modestly regressive sales tax to fund a progressive health care system. The United States from 1950 to 1986 used a very progressive income tax for such a wide variety of purposes that, despite accounting for thirty percent of the economy, redistribution amounted to just one percent of revenue (pp. 474-479).

Tax rates matter as incentives as well as revenue sources, of course, as Piketty’s discussion of executive pay (pp. 508-514) makes clear. “[T]he countries with the largest decreases in their top tax rates are also the countries where the top earners’ share of national income has increased the most.” He counters the claim that rising productivity among executives caused CEO salaries to rise, and concludes that the lower marginal tax rate simply increased the incentive for top earners to seek more pay since they would be able to keep it. The executive pay section would have been better if Piketty had read Neil Fligstein’s Architecture of Markets (Princeton University Press, 2001). Fligstein roots the “shareholder value society” in regulatory changes that ended up making stock prices the dominant index of executive performance. Executive pay and job security depended on stock prices and little else. With less new data to work with in this part of the book, Piketty offers some of his best one-liners, including “Although data on this are sparse, it also seems US politicians of both parties are much wealthier than their European counterparts and in a totally different category from the average American, which might explain why they tend to confuse their own private interest with the general interest” (p. 514).

Piketty doubts that states can control capital accumulation on their own anymore. The land-based economy of the eighteenth and early nineteenth century bound capitalists to the nation their land was in. Today’s financial capitalism leads directly to the politics of “corporate inversion”, whereby companies pick where to pay their taxes without regard to where economic activity actually occurs. Piketty calls for global (or at least pan-European) capital taxes because companies act this way. Twenty-first century nation-states lack the span of control to outmaneuver them. Without coordinated international action, the crisis of concentration Piketty sees coming will arrive.

Capital in the Twenty-First Century is a challenging tour de force. As dense as it looks, it is every bit as important as it looks.