Piketty’s Capital: II

Thomas Piketty’s Capital in the Twenty-First Century is well-written and well-researched, as I have indicated already, but it has some fundamental problems with the way it depicts capital.

Piketty says “the first fundamental law of capitalism” is that the share of income going to capital, α, is equal to the return on capital, r, times the capital/income ratio, β, or in equation form, α=rxβ.  I can accept this as an accounting identity, although even then with minor issues.  I have more of an issue with the way Piketty uses this to describe the interrelationships among the three variables.

The minor issue is that β measures capital as an aggregate monetary value, whereas in fact capital is a heterogeneous collection of producer goods that, combined with labor, produce output.  So already, there is an oversimplification by aggregating a heterogeneous stock of capital and calling it equal to its money value.

A larger problem is that Piketty assumes capital earns some rate of return, r, so the share of income going to capital, α, is determined by the value of capital times the return it earns.  This is exactly backwards.

Capital does not have some value, which then earns a return to provide income to the owners of capital.  Rather, capital consists of productive assets that generate a return, and the value of the stock of capital is determined by the return it generates, rather than, as Piketty depicts it, the return being determined by its value.

This makes a difference because it misrepresents how capital owners earn their incomes.  In fact, capital must be allocated to productive uses in order to generate a return, and the job of the capital owner is to allocate that capital as productively as possible.  Successful owners of capital will earn higher returns, and unsuccessful owners may lose their investment altogether, and see the value of their capital drop to zero.

This is apparent even in the stock market.  Stockholders do not just own capital and receive r as their rate of return.  They look for promising investments, trying to buy into companies that will produce value for the economy, which will enable the company to earn income, leading to a higher stock price.

The challenge is similar (perhaps greater) for managers of firms, who make investment decisions regarding building new plant and buying equipment, producing new product lines, and so forth.  Capital does not just earn a return.  The return is determined by how productively it is used.

The people who are making those decisions, whether they are management who make the decisions directly, or stockholders who delegate the decision-making to those managers, are working in a competitive environment in which, if they make poor decisions, can end up with a negative return, and ultimately to bankruptcy, so their capital becomes worthless.

Piketty’s equation, α=rxβ, aggregates all these individual decisions so that while it is accurate in an accounting sense, it is misleading in an economic sense.  Piketty makes it appear that because capitalists have β, they get α.  That is not true.

This can be illustrated with an example from Piketty’s book.  He says the long-term return on capital, r, is around 4-5% per year, and gives an example (p. 54) of a Paris apartment that is valued at 1 million euros and “…rents for slightly more than 2,500 euros per month, or an annual rent of 30,000 euros, which corresponds to a return on capital of only 3 percent per year… This type of rent tends to rise until the return on capital is around 4 percent. … Hence this tennant’s rent is likely to rise in the future.”

As the example shows, Piketty assumes that the value of capital, β, determines the amount it earns, α.  But surely the reverse is actually the case.

Piketty uses the relationship α=rxβ, but a more accurate way to depict the economic relationship is β=α/r.  The expressions are mathematically equivalent, but Piketty’s way of showing it assumes that the value of capital determines its return, rather than the more economically accurate depiction in which the return produced by the capital determines its value.

The rent on an apartment will be determined by the supply and demand for apartments, so α in this example is 30,000 euros a year, which is market-determined.  If r = .04 as Piketty assumes, then because β=α/r, β=30,000/.04=750,000 euros.

The rental rate is determined by the supply and demand for apartments, so following Piketty’s assumptions about the annual rent and the rate of return the landlord will earn, the apartment is worth 750,000 euros and will fall in value.

The value of the apartment is determined by the rent it can command, and not the other way around.

This general idea that capital does not just earn a rate of return, but has to be employed in productive activity by its owner, plays no role in the way Piketty analyses his extensive data set on inequality.  Piketty makes it appear that earning a return on capital is a passive activity in which, by virtue of owning capital that has some value β, capital owners receive a flow of income α.  Capital has value only because it provides a flow of income to its owners, and it only provides that flow if the owners employ it productively.

Capital produces income only if it adds value to the economy.  Wal-Mart has done this, and provided a return to its owners.  Circuit City did not do this, so the value of its capital fell to zero.  The value of capital is determined by the income it produces, so capital has value only because it adds value to the economy, which benefits everyone.

Piketty laments the increase in inequality since 1980, but setting aside inequality for the moment, anyone who has lived in a capitalist economy since that time can see the increase in the standard of living that everybody — not just the economic elite — has enjoyed.  That increase in the general standard of living has been due to the employment of capital in productive uses by its owners, but this economic function of the owners of capital plays no role in Piketty’s analysis.

Sorry, readers, this post is already too long.  I will post again with additional analysis of Piketty’s Capital.

Randall G. Holcombe is Research Fellow at the Independent Institute and DeVoe Moore Professor of Economics at Florida State University. His Independent books include Housing America: Building Out of a Crisis (edited with Benjamin Powell); and Writing Off Ideas: Taxation, Foundations, and Philanthropy in America .
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