Finance and capital in the 21st century.

• Author: Jones, Robert C.
• Position: Critical essay

In Thomas Piketty's controversial, ambitious, but ultimately flawed book, Capital in the Twenty-First Century, he claims that: (1) the return on capital (r) has exceeded the growth rate of the economy as a whole (g); (2) this relationship (r > g) has produced ever-greater concentrations of wealth and income; and (3) raising taxes, especially on capital, is the best way to reduce these inequalities. He concludes with an impassioned plea for economics to aspire to a higher "political, normative and moral purpose," while lamenting modern efforts to treat it as a science.

Because finance is essentially the study of capital and capital markets, this article evaluates Piketty's claims from the perspective of financial theory, using the scientific method. Is Piketty's theory of capital internally consistent? Does the data support his hypotheses? What are the policy implications? To briefly preview, I find that his theory of capital confuses cause and effect, the data do not support his hypotheses, and his policy prescriptions would likely prove counter-productive.

Why Is r > g?

In financial theory, the internal growth rate (1) (g) is a function of the return on capital (r) and the reinvestment (or savings) rate (s):

(1) g = r*s

where s = (1 - t) * (1 - c).

The reinvestment rate (s) is the percent of income that gets saved and reinvested--that is, what's left after taxes (t) and consumption (c). This reinvested income earns the marginal return on capital (r), resulting in additional income, or income growth. Equation 1 is an accounting relationship that holds for a company, an investment portfolio, or the economy as a whole. (2)

Taxes are clearly a net loss for individuals, companies, and (taxable) investment portfolios, reducing their reinvestment and growth rates dollar for dollar. Conversely, for the economy as a whole, taxes represent a transfer of wealth within the economy: If they are reinvested at marginal returns above those available to the original owners--a really BIG if--they may even contribute to overall economic growth. If, however, they are invested poorly, or consumed, the economy will have less capital accumulation and slower economic growth--but, perhaps, more consumption spending and higher standards of living for the recipients.

Clearly, however, since no company, portfolio, or economy reinvests all of its income every period, g will necessarily be less than r, often quite substantially (ignoring random changes in price-to-book ratios). This is not unusual, problematic or, as Piketty claims, a "fundamental force of divergence" or "the fatal flaw of capitalism." Instead, the math dictates that the return on capital is and always will be greater than the economic growth rate (except for short-term variations caused by changes in the price-to-book ratio). It's not the return on capital--but its growth and use--that matters.

Note that Equation 1 is identical to Piketty's "second fundamental law of capitalism": [beta] = s/g. In Piketty's terminology, [beta] is the capital/income ratio, the primary metric he uses to assess inequality (a high ratio implies more inequality). But the inverse of the capital/income ratio is simply the return on capital (r = income/capital), or the amount of income an economy generates from its capital base. Since Piketty's savings rate (s) is equivalent to the reinvestment rate, or what's left after taxes and consumption, Piketty's second fundamental law is a simple rearrangement of Equation 1. (3)

Piketty's has the algebra right, but the dependent variable wrong: he confuses cause and effect. In Piketty's second fundamental law, an economy's savings rate (s) and growth rate (g) are independent variables that jointly determine its return on capital (since [beta] = 1/r, the fundamental law also says that r = g/s). In Equation 1, the return on capital (r) and reinvestment rate (s) are the independent variables that jointly determine an economy's internal growth rate (g). Equation 1 is more consistent with accounting theory and economic logic: An economy's return on capital (r) reflects its technology--how much income it can generate from its capital base--which logically determines its growth rate, not vice versa.

Piketty also confuses cause and effect when he speaks of the return on capital (r) and growth rate (g) as if they were independent, exogenous variables that together create inequality (via r > g). In accounting theory, g is a function of r and the reinvestment rate (s, which itself is a function of r). Thus, contrary to Piketty's assertion that r > g is a "contingent historical proposition," in financial theory, it's an accounting necessity.

Testing Piketty's Hypotheses

Piketty offers two main hypotheses, but never formally states or tests either, so I will do so here.

Piketty's First Hypothesis

Piketty's first major hypothesis is that, due to r > g, capitalism inevitably produces ever-more concentrated pools of inherited wealth. He believes that the United States may be entering an era of "patrimonial capitalism" with rigid class structures and plutocratic government that "looks like old Europe prior to 1914." He fears we are headed toward a Dickensian future in which "a small group of wealthy but untalented children controls vast segments of the US economy and penniless talented children simply can't compete." (4)

Piketty's fears are misguided for two reasons: (1) He mistakes the return on capital (r) for the growth of capital (g), as discussed above; and (2) he fails to account for differential returns (r) and reinvestment rates (s) across generations and types of investors. The returns on large pools of private capital are often taxed three (or more) times: at the corporate, personal, and estate levels. Across generations, they are also "consumed" through poor stewardship, fragmented inheritances, and charitable giving. Accordingly, per Equation 1, the growth of private inherited capital will likely be slow or negative across generations.

The data confirm that inherited wealth is a relatively small percentage of total wealth, and is declining in importance. Wolff and Gittleman (2011) find that inherited wealth declined from 29 percent to 19 percent of total U.S. capital between 1989 and 2007. Looking at just the top 1 percent, inherited wealth fell from 27 percent to 15 percent of capital over the same period. (This may reflect the accelerating pace of "creative destruction," as new capital makes old capital obsolete.) In addition, since inherited wealth is a greater percentage of total wealth outside of the top 1 percent, it actually reduces inequality. There is no reason or evidence to suggest that private, inherited pools of capital will grow faster than national income or wealth, even if r > g (as it must be in equilibrium). (5)

Conversely, the last half-century has seen the emergence of a new class of dominant investors: public institutions. These include sovereign wealth funds; private, public, and union pension funds; and foundations and endowments. The largest of these institutions dwarf the largest private capital pools: The wealthiest individual in the world is Bill Gates with roughly $76 billion in net worth as of 2013 (most of which he has pledged to charity), while the largest pension fund, the Government Pension Investment Fund of Japan, is $1.3 trillion (17 times larger). In addition, there are 35 pension funds and 15 sovereign wealth funds that control more capital than Bill Gates. If capital is becoming increasingly concentrated, it's doing so in the hands of public institutions.

Importantly, many of these institutional pools are semi-permanent (i.e., they don't naturally dissipate over time), tax exempt, well diversified, and managed by professional fiduciaries for the benefit of workers, charities, universities, governments, and the general public. Given their lower levels of consumption (c) and taxes if), plus their professional stewardship (higher r), these institutional pools are likely to continue to grow much faster than private pools over the decades ahead. It's no accident that the Carnegie, Ford, and Rockefeller foundations live on long after the personal fortunes of their creators.

Rather than producing an ever-more concentrated cadre of rentiers and wealthy plutocrats, then, Western capitalism is producing ever-greater concentrations of wealth in pools that are managed by professional investors for the benefit of the public at large. It's these technocrats, not Piketty's plutocrats, who finance our economy, allocate capital, pick winners and losers, and ultimately fund the research, innovations, businesses, and entrepreneurs who...