Live-Blogging Piketty: An Interlude (Response to Chris Giles)

Should We Count Out Piketty Due to Sum Math Errors?

While I am here in Paris reading Capital in the Twenty-First Century carefully, the book has dominated the headlines again. Having just spent a good deal of time thinking about its numbers (see my Dollars & Sense blog posts at, I thought it would be useful to reflect on the piece published this past weekend in the Financial Times.

There, Chris Giles provides a detailed and lengthy argument against Piketty. He claims there are many instances where Piketty has used the wrong numbers in making his calculations and that many assumptions Piketty makes in doing his research are incorrect.

First, an important point– data transcription and math errors occur all the time in economics. It is a sort of dirty and hidden secret. Typically errors are not discovered and don’t make front page news. One cost of being an economic rock star is that the data Paparazzi hang on to your every number.

But the gotcha reception of finding math mistakes is worth reflecting on. I have been amused by smug claims that Piketty supporters unthinkingly accepted his numbers, and that Giles has proven Piketty to be totally wrong. Even before examining any numbers, it is easy to see that these claims succumb to the same mistake that they accuse Piketty’s supporters of making. I cannot think of any better evidence that Capital in the Twenty-First Century has hit a raw nerve in the socio-economic psyche.

More seriously, some bloggers and even some economists have compared the Giles “discoveries” to the recent Rogoff and Reinhart brouhaha. In this case, a University of Massachusetts graduate student, trying to replicate empirical results as a class assignment, found several errors in the Excel spreadsheet that Rogoff and Reinhart used to claim that when debt-to-GDP figures exceed 90%, economic growth slowed. Once these errors were corrected, the 90% tipping point disappeared. Since there was no tipping point, governments could stimulate the economy, fight unemployment and increase debt levels without worrying about a slowdown in economic growth.

There was another scandal involving Martin Feldstein back in the 1970s. Feldstein published a paper in the Quarterly Journal of Economics (regarded as one of the top half dozen economics journals) in 1974 showing that Social Security reduced the US personal savings rate. Feldstein then used his results to push for privatizing Social Security in order to increase savings in the US. When two research economists at the Social Security Administration obtained Feldstein’s data to do additional analysis, the first thing they tried to do was replicate the study. What they found was a programming error; when corrected this changed the conclusion of Feldstein’s paper—Social Security tended to increase the individual savings rate.

Such mistakes are rarely intentional. Rather, the problem is a human tendency to believe the things that confirm your expectations and the human tendency to make mistakes. When results turn out as expected, economists do not look for errors in their numbers or their calculations. On the other hand, when results turn out contrary to one’s intuitions, the first thing that economists do is seek out the errors in their math and their data. So there is always a bias in empirical work; you tend to confirm your intuitions.

Just because errors are inevitable is no reason to dismiss all empirical results. Be skeptical; but do not dismiss. In other words, the question is not (as Neil Irwin titles his column in the New York Times on May 25th) “Did Thomas Piketty Get His Math Wrong?”. Rather, the important question is how much do the math mistakes matter. Do they affect the main results significantly? Or, worst of all, do they require a totally different story (as in the Rogoff-Reinhart and Feldstein cases)? If Piketty made some errors and this has little impact on his results, it is not a big deal.

To be honest, I have not looked at the actual computations on Piketty’s website since I am still working my way through his book. However, I do have some concerns with the methodology he employs to arrive at some of his figures. These are all spelled out in my previous blogs on Capital. But before addressing the claims of Giles, let me summarize the main argument of Piketty.

Piketty makes the case that inequality tends to rise in developed capitalist economies as a result of three empirical facts. First, a slow annual growth rate (1 percent, maybe close to 2 percent). Second, returns on wealth of around 5 percent per year (as has existed over long stretches of history). And third, the fact that the distribution of wealth is more concentrated than the distribution of income. This being the case, it follows that those with lots of wealth will see (on average) their annual gains (or their income) rise around 5 percent each year, while those without much wealth will see their incomes (on average) grow only 1 percent or so annually (the growth rate of the economy). Income inequality rises as does wealth inequality.

There should be no dispute that wealth is distributed more unequally than income. This has long known to be the case thanks to the Federal Reserve’s Survey of Consumer Finances and the work of Edward Wolff at NYU. Not even Giles questions this.

The key figures are the 5% and 1-2%. The 1-2% annual growth rates come from standard government data sources. Yes, there are problems with these figures. The way we compute GDP is flawed (e.g., we exclude the underground economy). But these flaws are similar from year to year, so the measured growth of GDP is a reasonably good figure. Since our numbers are not perfect, economists sometimes tweak the data to account for changes in the size of the underground economy over the business cycle. But these are minor issues. The GDP data is ok to measure economic growth over time. The more contentious and more salient issue is whether economies can grow faster than 1-2%. Robert Solow, who won a Nobel Prize in Economics for his work on growth theory, claims this is possible in his review of Capital; Giles is silent on the question of economic growth rates.

This brings us to the final figure—the 5% return on wealth. This is the key figure in Capital. If this number actually is closer to 2% percent than 5%, wealth and income grow at the same rate, and we don’t have to fear growing inequality. Unfortunately, Giles does not discuss this number either and so he ignores the entire argument of Piketty.

Instead, what Giles shows, and what he takes as a refutation of Piketty, is that the share of wealth received by the top 10% and top 1% are not growing as fast as Piketty estimates. But, and this is the important point, as long as wealth inequality is increasing, this supports Picketty. Maybe it does not support Piketty as much as Piketty’s own calculations, but it does support him. Unlike the Rogoff-Reinhart and Feldstein cases, there is no refutation of Piketty here. That would require a clear demonstration that wealth shares owned by the very rich have been falling over a long period of time.

It is now time to say a few words about the Giles article itself.

Giles claims that Piketty made lots of math mistakes and bad assumptions in his work, and that this has led to incorrect estimates of wealth shares. Rather than correcting these mistakes, and then recalculating final figures (as happened in the Rogoff-Reinhart and Feldstein cases), Giles is content to point out the errors and then present his own numbers.

Giles notes that Piketty’s estimate of the share of total wealth held by the top 10 percent (77%) in the UK is much higher than the official government estimate (44%). Giles also compares Piketty’s estimates with other estimates of the share of wealth held by the top 10% and the top 1% in the UK. All show high levels of wealth inequality before World War I, then a sharp decline until around 1970 or 1980, and then an increase in the wealth shares of the richest 10% and 1%. Piketty’s data shows a larger increase than all the other sources at the end of the 20th century; but all sources show an increase.

Giles then provides his own estimates, which sort of follow Piketty and the other estimates until 2010. Then, wealth shares for the very wealthy fall according to Giles. Given the sharp drop in stock values in the late 2000s, I am inclined to lean toward Giles’s figures for 2010 rather than the Piketty figures. However, it needs to be remembered that this is only one data point, and it is for a point in time when stock values (an asset held mainly by those at the very top of the wealth distribution) fell sharply. The issue concerns long-term trends, and the 2010 data (or any one year of data for that matter) does not answer this question. In fact, it really does not address this question at all. It is like picking a cold day in winter and using this as proof that global warming is a myth.

But there is a much bigger problem with this whole endeavor.

All the alternative estimates that Giles presents of wealth shares are based on household survey data (including the 44% government estimate of the wealth held by the top 10% in the UK). Economists recognize that survey data underestimate wealth inequality and income inequality because the very wealthy are more likely to lie about their wealth and income than everyone else.

This was why Piketty sought better sources to measure wealth and income distribution (estate tax returns and individual income tax returns). Of course, people lie on tax forms too. Income from wealth hidden in off-shore tax havens will not get reported on tax forms. But tax forms are more reliable sources than what people say when asked about their wealth. So, it is hard not to give the benefit of the doubt to Piketty here. Even if the two sources were equally good (or equally flawed), the truth should lie close to halfway between the government survey estimate of wealth shares and the estimate of Piketty. This would show a clear upward trend during the past several decades, confirming Piketty’s views of capitalism. But even if Giles figures are correct, the best we can say is that maybe wealth inequality has not increased as much as Piketty estimates. As long as wealth inequality has increased in the second half of the twentieth century, this confirms the main argument of Piketty. All the data seems to point in this direction.

Giles identifies a number of other flaws and condemns Piketty for these. He notes some transcription errors, which are inevitable, as noted above. Giles also complains about how Piketty sometimes tweaks numbers from other sources. But this is something all economists do when they know that some numbers are wrong because of problems such as a non-representative sample or because some important information (e.g., the underground economy) is missing from standard measures. Most of these seem to me rather trivial. Errors can always be corrected and tweaks done in different ways.

The important issue, the bottom line, is always whether these changes lead to a different empirical conclusion. This does not seem to be the case for the transcription problems and data tweaking. Presenting numbers based on worse data refute Piketty also does not change the story.

In sum, Giles has offered up a weak critique of Piketty. At best, he shows that wealth inequality is increasing less than Piketty says it is. At his worst, he ignores the argument made in Capital. To repeat, the problem is that Giles does not mention and does not question of the 5% returns on wealth. Piketty’s point is that because wealth is distributed so unequally (a point that virtually no one objects to), high returns to wealth (relative to economic growth) will push up inequality. This is not an empirical matter that may contain lots of mistakes. It is a fundamental property regarding how capitalist economies work. This is the brilliant insight of Capital. Giles has not refuted it. Even worse, he does not even attempt to do so. In many respects, and in retrospect, it is hard to see what all the fuss has been about.

–Steve Pressman

Live-Blogging Piketty: Reading Pt. III

Chris Giles and Ferdinando Giugliano raised some concerns about Thomas Piketty’s data in yesterday’s Financial Times. (See Naked Capitalism’s useful post on the flap.) Our reviewer Steve Pressman sent in his lastest “live-blogging” post with this note:  “Since the numbers in Piketty’s book have become such a hot topic today, I got inspired to finish up the next blog posting. My take, as you will see, is that Piketty’s numbers are too conservative and underestimate the problem of rising income and wealth inequality. Thus, even if the Financial Times is correct about some errors by Piketty, his results will likely hold given the problems I identify.”  –Chris Sturr

Capital in the Twenty-First Century Part III

Part 3 of Capital moves us from the functional to the personal distribution of income. The personal distribution of income concerns how total income gets divided among the nation’s households.

Economists have developed several measures of how equal personal income gets distributed. The most famous and most popular of these is the Gini coefficient, named after Italian statistician Corrado Gini, who created the measure in 1912.

I don’t especially like the Gini coefficient. Some reasons are technical and not worth discussing here. A few are non-technical and warrant brief mention. The value of the Gini coefficient can vary between 0 and 1, with zero being perfect equality (all households get the same income) and 1 (one household gets all the income). This seems very counter-intuitive—my brain tells me that 1 should be perfect equality rather than zero. More important, the meaning of the Gini coefficient is neither obvious nor intuitive. What exactly does a value of .443 (the US figure for 2009) show, how does it compare to a value of .349 (the US figure for 1979), and how much more equal was US income distribution in 1979 compared to more recently?

Like Piketty, I prefer simple measures that are easy to understand. My work on income distribution focuses on the poor and the middle class. The measure that made Piketty famous before Capital was published is the share of total income received by those making the most money. He has measured the fraction of income going to the top 10%, the top 1%, the top .1%, and the top .01% of households.  

For the US, Piketty has estimated income shares of the highest earning households since 1913, the year the US first introduced income taxes. He has made estimates for many other countries, including some developing nations such as Argentina and Uruguay. These figures are all available through the World Top Incomes Database that Piketty developed ( They make for some rather disturbing reading.

Before I summarize the main results, it is worth remembering Piketty’s main thesis. Wealth is distributed more unequally than income and grows faster (the rate of return on capital historically has been 5%) than wages, which grow only as fast as the economy grows (1%, or close to 2% if we are lucky). Consequently, the total income (wages plus returns to wealth) of those with lots of wealth grow faster (5%) than those without wealth (1% or so). Over time, the personal distribution of income becomes more and more unequal, as does the distribution of wealth.

France is where Piketty began. He gained access to income tax data and estimated the share of total income received by those at the top of the distribution. In France, the share of income received by the top 10% dropped from 45% in the early 20th century to 30% after World War II, mainly due to the reduced income from wealth as a result of two world wars. The share of the top 1% fell from 20% to 8% over the same time frame, again mainly due to the decline in income from wealth; wage income remained steady for top income recipients.

Of course Piketty recognizes that the distribution of wage income can change over time and that it can be changed by economic policy. He explains (p. 289) how French President de Gaulle increased the minimum wage in France after French students rioted in 1968. Soon thereafter the minimum wage was indexed to the mean wage and then increased several times. This shifted the distribution of wage income to those making relatively little, increased the wage share and lowered the share of capital income in total national income a bit. However, it had little impact on the share of total income going to the top of the distribution because most of their income comes from returns to wealth and these amounts are so large that they dwarf any small changes due to a rising minimum wage.

The story for most of Europe is similar.

The story for the US is a bit different. Unlike France, in the US the income shares of those at the top look U-shaped. The top 1% received nearly 25% of all income in 1928, right before the Great Crash. Their share of total income fell to around 10% from the 1950s to the end of the 1970s—not much different than the share of the top 1% in France. Starting in the 1980s the share of the top 1% began a steady rise back to 20%.

Today the top 10% of earners in the US (those making more than $108,000 in 2010) receive nearly 50% of total income and the top 1% (those making more than $352,000) around 20% of total income. Over the past several decades, most income gains in the US have gone to the top .1% or so (those making more than $1.5 million); everyone else has struggled to keep from falling behind.

The US story is mainly about rising wage inequality; capital income is less important. Overall, Piketty (p. 300) blames capital income inequality for only one-third of the rise in inequality in the US. In contrast, in Europe, the largest part of the overall inequality increase is due to the rising capital gains of those at the top of the distribution.

I do have some questions and concerns about all this. Because increases in wealth may not be realized (e.g., stocks may not be sold) and reported as income, Piketty may underestimate the actual returns to wealth in the US. Moreover, the US has increasingly made returns to wealth tax free. For example, IRAs and Roth IRA let people move money into accounts where the interest is not taxed. They were designed as a way to aid individuals saving for retirement. I have contributed the maximum every year for several decades. In addition, I have money taken out of my pay, which then doesn’t count as taxable income, for my retirement. If this money is not reported on my income tax returns, it is not included in the figures the Piketty uses to calculate top income shares. I am not in the top 1% of earners, so my “hidden” gains would not impact his results very much; but I am sure that many households in the top 1% have accumulated much more tax-free income than I have managed to accumulate. In fact, many of the very wealthy typically have significant municipal bond holdings, which are free of income taxation for all levels of government.

So, inequality in the US may not only be worse than Piketty reports (more on this later), but the US may look a lot like Europe. Even if his numbers are accurate, the extremely high wage inequality he finds will result in a great deal of wealth being accumulated by the top .1%. As Piketty himself notes, as the children of high wage recipients receive large inheritances, the US will come to look like Europe—with a large rentier class whose income comes mainly from the wealth they inherited.

Whether continuously rising inequality is sustainable is an important issue. Piketty sees popular discontent rising and two possible responses to it—repression and justification

Repression requires that state power (acting on behalf of the very affluent) keep people from revolting.

Justification requires getting people to believe that the wealthy deserve their high incomes. Standard economic theory provides one justification. It sees each person’s income as the result of their marginal productivity. The additional revenue I bring in to my employer is what I get paid. My income, whether high or low, depends on what I do and what I can contribute.

There are many problems with this. One of Piketty’s main complaints is that marginal productivity theory fails to explain the actual distribution of wage income across countries and over time– a point that I wish he emphasized a bit more. Starting with marginal productivity theory, economists explain greater wage inequality as the result of globalization and technological change. Globalization requires many workers to compete with workers in other countries who are willing to work for less; technological change means that the few workers who can use new technologies will see their incomes soar.

The problem here, Piketty points out, is that the consequences of these two phenomena are not the same throughout the world. As we saw above, wage inequality has barely budged in France while it has soared in the US. Yet new technology impacts both countries to the same extend; so too does globalization. These answers don’t seem to be good answers.

There are other problems with the theory. For example, marginal productivity is impossible to determine when individual productivity and individual contributions depend on teamwork. In a few places (pp. 305, 311) Piketty makes it clear that he recognizes this problem; but his instincts are to steer clear of theoretical debates and just focus on the numbers. His main argument against the marginal productivity story is empirical– a large percentage of the very rich do not earn their income. The very unequal personal distribution of income is mainly driven by the even more unequal distribution of wealth. Because wealth has been so concentrated, and because the returns to wealth are so large (especially relative to average income gains), income inequality becomes more and more unequal.

Other factors also contribute to rising inequality. Piketty points out that the 5% annual returns to capital are average returns, averaged over all people and over all the different kinds of wealth that people hold. Sometimes, however, averages do not tell us a lot. When Bill Gates goes into a soup kitchen, the average income in the room is likely to be in the millions of dollars. But this does not describe very well most people there.

Similar things hold regarding the returns on wealth. Those with very little wealth tend to hold most of it in checking accounts (which pay no interest) or savings accounts (which pay almost no interest). The middle class has a large fraction of its wealth in home equity. The annual returns on real estate, historically, have not nearly been as great as the returns on stocks and bonds and other financial assets, which comprise a large portion of the wealth of those with lots of wealth. This means that the middle class will have an even harder time catching up with the wealthy.

Even worse, Piketty thinks the rate of return to wealth possessed by the insanely rich exceeds the rate of return received by the moderately insanely rich and that these returns exceed those of the merely rich. He argues that the richer you are the more patient you can be and the easier it is to hire great investment advisors. If the very best advisors do a lot better than the next tier of investment advisor, and if they are going to charge a fixed fee for their advice, this works out to be a smaller percentage of your gains and a smaller percentage of your total wealth the larger your wealth is. So the rich can afford better advice, and this advice yields them greater returns.

In a brilliant attempt to examine this empirically, Piketty looks at returns to college endowments based on the size of the endowment. Indeed, he finds that Harvard and Yale and Princeton do better than schools with smaller endowments and that the rate of return to college endowments is a function of size. More bad news for income and wealth inequality!

As noted above, I do have a few concerns with story Piketty tells in Part III of Capital.

First, there are questions regarding the functional distribution and income from wealth. My last blog posting noted problems with how income gets categorized. Above I noted that a good deal of capital income is excluded from individual income tax forms. Better measures of capital income and labor income may show that the US actually looks a lot like Europe when it comes to income and wealth distribution.

Second, Piketty’s results are very conservative, something he acknowledges (p. 281f.); however, I wish he had stressed this point more. As noted above, using data from income tax returns misses a large part of individual income from wealth—in particular, gains in the value of assets that do not get reported on individual income tax returns (only the gains from sold assets are reported). To be a little more specific here, reported capital gains on tax returns reflect gains from all the years someone owns an asset.

Consider the following. If I bought 100 shares of Apple stock in March 2009 I would have paid around $100 a share or $10,000. Selling the stock now I would get over $600 a share, or more than $60,000. The difference, around $50,000 would be my capital gain for the year.

However, I did not really make $50,000 this year even though I report it on my income tax as having been received entirely during this year. I effectively made $50,000 over 5 years, or $10,000 per year. But my tax return says that I made the entire amount in 2014 and nothing in the previous 4 years.

The big question is how much this matters for Piketty’s results. If realized capital gains are similar to actual gains, his results may not be perfect, but they will be pretty damn good. On the other hand, if people tend to hold on to their gains and not sell (maybe because they don’t want to have to pay taxes on their capital gains), Piketty’s results underestimate the true problem of growing inequality. The top income recipients receive lots of capital gains, but because their stock holdings are not sold, the wealth income of the top .1% will be much larger than Piketty estimates.

Despite these issues, Part III of Capital is important. It discusses the relevant facts about personal income distribution and explains why inequality is likely to rise in the future. It is all very depressing.

Steve Pressman