Piketty’s Capital

May 25, 2014

No graphs this week!  Awwww!

A few months ago, Thomas Piketty, a French economist, released Capital in the 21st Century, a book that I mentioned to readers back in January before its publication.  Piketty’s book has aroused much interest, praise and denunciation.  What could arouse such fire in the hearts of men, you ask?  Inequality.  We humans are a social bunch and, like our chimpanzee cousins, are especially sensitive to inequality.  “She got more chocolate milk than me!  It’s not fair!” is a familiar lament to many parents.

To understand Piketty’s thesis, let’s review some fundamental concepts of capital and income.
“Income is a flow…the quantity of goods produced and distributed in a given period…Capital is a stock…the total wealth owned at a given point in time.” (p. 50)  Piketty’s thesis is based on a ratio of the capital of a nation to the national income.  His definition of capital is so encompassing that my immediate suspicion was the accuracy of estimates of the total wealth of a nation, a flaw that Piketty acknowledges.

The main thesis of Piketty’s book is: as the capital wealth of a nation accumulates, capital’s share of annual national income increases.  For long periods, the rate of growth of accumulated capital is larger than the growth of the economic output/income of a nation.  The process is self-perpetuating, so that capital takes an ever increasing share of national income.  The higher the capital/ national income ratio the more inequality of wealth and income.  Piketty estimates that, in 2010, the capital/income ratio was 450% for the U.S., a bit above Germany and Canada’s ratios, and far below those of France and Great Britain. Piketty proposes a solution to this inexorable process:  a progressive tax on wealth.  Mount up your steeds, men!  The Marxists are coming!

Wealth = Capital

I’ll begin a review of some criticisms of Piketty’s methodology with a brief primer on some measures of capital.  Economists and accountants often analyze the flow generated by a store of capital, but it is capital that can be more easily counted. In finance, there is a metric called Working Capital Turnover Ratio which calculates the flow of sales from the working capital of a firm, and is used to assess both the value and liquidity of a firm.   Piketty rarely uses the term liquidity in his book, but I think it may be an unstated implication of his work.

ROIC, or Return On Invested Capital, is frequently used to measure how well a firm uses the capital and debt invested in the firm to generate a profit.  These measure net after tax profits as a percentage of the stock of capital and debt in a business.  Piketty also measures flow but it is sales, not profits that is his primary focus.  Profits are of course an intrinsic component of sales since they are that portion of sales income that is left over after all expenses.  The change in real GDP is the percent change in that flow.  Piketty’s concern is the accumulation of the residual of past economic flows, the stock of wealth that he claims earn a greater rate of return than the increase in the annual flow of economic activity.  Capital is a key component of economic growth but Piketty raises concerns that Capital can become too large relative to the flow of economic activity.
Hopefully, this brief background will enable the reader to appreciate the criticisms of Piketty’s thesis.  Charles Gave is a forty year veteran of investment management and cofounder of the international investment firm GaveKal.  Coming from the world of finance, Gave understands capital as meaning invested capital or working capital. Keep that in mind as you read Gave’s denunciation of Piketty’s thesis:

The extraordinary thing is that Piketty’s analysis is based on a massive logical error. His thesis runs as follows: if R is the rate of return on invested capital and if G is the growth rate of the economy, since R is greater than G, profits will grow faster than GDP, and the rich will get richer and the poor poorer. This is GIGO (garbage in, garbage out) at its most egregious. Piketty confuses the return on invested capital, or ROIC, with the growth rate of corporate profits, a mistake so basic it is scarcely believable. [Gave’s emphasis]

On page 46 of his book Piketty writes: “In this book, capital is defined as the sum total of nonhuman assets that can be owned and exchanged on some market.”  While this includes invested capital, it is not solely invested capital, for it includes residential real estate, government capital, land and natural resources, some of which are very difficult to value.

In short, Gave read “invested capital” when Piketty wrote just “capital.”  Gave read “corporate profits” when Piketty wrote “return on capital, including profits…” (p. 25).

The economist James Galbraith takes issue with Piketty’s all inclusive  definition of capital: “he conflates physical capital equipment with all forms of money-valued wealth, including land and housing, whether that wealth is in productive use or not.”

Piketty anticipated his critics: “some definitions of ‘capital’ hold that the term should apply only to those components of wealth directly employed in the production process…Capital in all its forms has always played a dual role, as both a store of value and a factor of production.  I therefore decided that it was simpler not to impose a rigid distinction between wealth and capital.” (p. 47) 

Let me rephrase the ” R is greater than G” formula that piqued Gave’s derision.  Picketty uses small ‘r’ and small ‘g’ so I will adhere to that: the annual income r derived from capital, as a percentage of that capital stock, will be more than the annual percentage change in real, or inflation adjusted, income/output g.  As Piketty writes: “the inequality implies that wealth accumulated in the past grows more rapidly than output and wages.”

An example:  In the teeny tiny kingdom of Miniscule, the total nonhuman capital stock at the beginning of this year is $100.  It  generated output/income of $10, or 10%. That is r, the return on capital.  This income from capital was part of Miniscule’s total output/income of $30, an increase of $2 over last year’s income/output of $28. To keep the math simple, let’s pretend there was no inflation or depreciation in that year.  The growth in total income/output is about 7%, or $2 / $28.  That is g, the growth rate of output/income.  To recap,  r = 10%, g = 7%.  “r can be significantly higher for long periods of time than the rate of growth of income and output, g.” (p. 571) Is this true?  That’s what Piketty claims to show.

Like Galbraith, I question Piketty’s inclusion of many different forms of wealth which are difficult to measure.  Piketty acknowledges the difficulties in the appendix to a paper he co-authored with Gabriel Zucman in December 2013, “Capital Is Back” and is included as one of the data sources for his book.  Piketty’s thorough explanation of the shortcomings of capital measurements led me to scratch my head and wonder why he decided to include them.

Piketty has no control over accounting conventions adopted by international bodies, yet I’m sure he and his team will be taken to task for the computation of the data that is the responsibility of the various nations included in the study.  A big shout out to Piketty and his collaborators for making the data available.

Back to our tiny kingdom of Miniscule. What if we missed some capital in our tally?  If the capital stock were closer to $120, not $100, then ‘r’, the return on capital would be 8%, not $10% and approximately the same rate of growth as the economy as a whole.

How accurate are the public, or government, capital computations?  In the U.S., the Comptroller General is responsible for auditing the financial statements of the country as part of the Federal Budget.  For ten years, from 1998 – 2008, Comptroller General David Walker refused to certify the financial statements,  listing a number of accounting problems: inadequate  monetary controls, poorly supported adjustments, outdated computer systems, unsupported cash disbursements, an inability to track internal or external fraud and a poorly documented inventory system.  These flawed financial statements are the basis for the capital computations in Piketty’s book.  In the appendix to Capital Is Back, Piketty explains the methodologies used by different nations.   Implicit in these standards is that public capital is understated in the national accounts.  This undervaluation decreases the capital/income ratio while increasing the r, or rate of return, of the capital stock.  Piketty notes the deviations in the various computations of land capital.  In the U.S. only the value of agricultural land is measured (Appendix p. 15).  A vast store of capital in 770 million acres of range land (Source) , more than half of which is private, is thus uncounted, further inflating the r, or return on capital.  70% of the land surface in the U.S. is devoted to livestock grazing (Source). A fundamental weakness in cross country valuations is the assumption that developed countries are more or less similar in most respects.  Key differences in the composition of economies are  factored out of the models.

Human Capital

Piketty separates capital into two categories: human and non-human, including only that non-human capital that can be traded on a market.  This exclusion of human capital may be an appropriate methodology in an analysis of an agrarian economy but is not so when applied to the developed economies of today which rely much more heavily on the human capital amassed through education. This point has been raised by economists Robert Solow and Robert Gordon and Piketty acknowledges this on page 586, note 35.

What are the implications of including educational capital?

Today a person may spend $40,000 to $150,000 to get a college education and expects an inflation adjusted return on that investment  that is greater than the 4% one could get investing in long term Treasury bills.  Developed economies depend greatly on the capital investment that they make in educating most of the young people in a society.  An educated mind is both a capital investment and a leaseable, if not outright tradeable, commodity.  While an employer can not buy an employee’s brain the way one can buy a machine, an employer does lease the knowledge, the output from that brain, by paying a compensation premium to that employee.  Income data from the Census Bureau, the IRS and the Bureau of Labor Statistics enables us to quantify the implied store of value of a college education.  If Piketty’s expansive definition of capital were to include educational capital, what would the resulting capital/income ratio look like?

The Bureau of Labor Statistics estimates an annual return of approximately $24,000 in 2013 for a bachelor’s degree. In 2011, the Census Bureau estimated the number of people in the U.S. with college degrees at 63 million, or 40% of the workforce.  If we guesstimate an average cost of $50K per degree, that is over $3 trillion of capital investment not counted, almost 20% of the $17 trillion in GDP (BEA News Release)  If we were to use the international standard (System of National Accounts) method of computing the present value of a college degree using an average 4.5% return (p. 572), then the capital value of a college degree over a working period of 35 years is over $400,000 per degree and the total is $26 trillion in uncounted capital, 150% of the nation’s GDP.   That inclusion would add $26 trillion to the $65 trillion capital base of the U.S. (p. 151)

If educational capital were included,  the capital/income ratio in the U.S. in 2010 would rise to 620%, far above the 450% calculated by Piketty’s team.  The higher this ratio, the greater the inequality in income and wealth.  By excluding educational capital, Piketty has understated his thesis.  Like Galbraith, I would exclude land and natural resources that are impossible to value.  Unlike Piketty and Galbraith, I would include educational capital, since it is a productive capital.

If we use the BLS figures and guesstimate that 63 million people with college degrees earn an additional $24K per year, then the share of income attributable to capital would increase by $1.5 trillion, from $4 trillion to $5.5 trillion.  As a share of national income, the income from capital would increase to 38% from 28% (p. 222)  The return on capital, r, would stay about the same at a bit over 6%, and more than twice the growth rate of national income in the U.S.


Piketty does not mention the liquidity of a national economy but implies it.  As the capital of a nation becomes more concentrated in a rather small group of families, individuals, and endowments, the trading of capital takes place within a small pool.  The onset of the 2008 financial crisis revealed that a small coterie of investment firms, sovereign funds and mega-banks traded financial instruments among each other.  Contagion in one class of asset – mortgage backed securities – poisoned the financial pool.  Like a gene pool, diversity is the key to survival.

As capital’s share of national income becomes greater, the buyers of capital as a percent of the population shrinks.  Fewer buyers = lack of liquidity.  A nation does have an abiding interest to reduce threats to the stability of its financial system.  The mobility of capital in the global world of finance may be hiding an underlying lack of liquidity.


To offset the increasing accumulation and concentration of wealth, Piketty recommends (p. 517) a progressive wealth tax, ranging from .1% to .5% for most Americans, those with assets of less than 1 million euros, $1.36 million dollars at today’s exchange rate.  Piketty is not done yet.  He notes that the progressive income tax taxes only the income from inherited wealth.  In some countries in Europe, that capital income is exempt from the income tax (p. 496).  Piketty advocates a return to the confiscatory income tax rates of the early half of the 20th century (p. 512 – 513), citing an optimal top tax rate at above 80%.  Bill Gates and Warren Buffett have both pledged to give away most of the billions they have amassed.  Why bother, guys?  If Piketty’s solutions were implemented, the politicians bickering on C-Span every night will take care of that for you guys.  In the U.S. the Constitution would have to be amended if the Federal Government were to enact a wealth tax because the 16th Amendment allows only a tax on incomes.  However, that does not prevent the States from enacting such a tax.

Will a wealth tax solve the problem of growing inequality?  In principle, in a mathematical utopia – the kind of world that economists assume in their models – governments would take corrective action by taxing wealth, thereby offsetting the growing accumulation  and concentration of capital and its increasing share of national income.  Unfortunately, we don’t live in that world.  In the real world, politicians – real people that you and I know – would say “Hey, this is a great excuse to grab more money from the private sector to solve problems!  Solving problems wins votes!  Votes get me re-elected!”  Politicians love problems, and solving them.  That’s why they create so many of them with their policies.

If people think income tax reporting and accounting is a nightmare, wait until they see the wealth tax forms.  Since the rich would pay a progressively higher tax, they would be highly motivated to develop ways of sheltering assets.  The hiding of wealth will become a national pastime.  Gold miners and dealers are shouting “Huzzah!”  Accountants and lawyers will cook up complicated investment vehicles that offer rapid depreciation of assets to reduce the amount of notional wealth one has to report.  Insurance companies will lobby for the purchase of annuities that are then excluded from one’s wealth.  The lobbyists are singing in the streets.  Strike up the band and join the tax parade!

In short, I heartily endorse this proposal just as soon as I sell my house, convert any assets to gold and find a private island in the Caribbean where I can bury my assets in the sand. I do heartily recommend this book, though. The book contains far more that caught my interest than I can touch on – public and private debt and capital, a survey of income taxes in developed countries, to name a few. The author has taken great pains to lay out historical trends in the data, acknowledging and anticipating many objections.  But, like the old country doctor, Dr. Piketty has but one solution. Got a problem?  Add another tax and call me in the morning. I also salute the translator, Arthur Goldhammer, for the flow and grammatical construction of his  English translation.

Next week I’ll look at another disturbing and related topic – education.  A recent analysis suggests that the financial advantage of a college education may be eroding.

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