Should We Count Out Piketty Due to “Sum” Math Errors?

Steven Pressman, Guest Blogger

Economist Steven Pressman has been “Live-Blogging” on his reading of Thomas Piketty’s Capital in the Twenty-First Century, and related controversies, at the Dollars & Sense blog. This post combines two installments, focused on the attempted refutation of Piketty by the Financial Times Chris Giles, and Piketty’s rejoinder.

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, I thought it would be useful to reflect on the piece published May 23 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 U.S. personal savings rate. Feldstein then used his results to push for privatizing Social Security in order to increase savings in the United States. 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 25) “Did Thomas Piketty Get His Math Wrong?” Rather, the important question is how much 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%, maybe close to 2%). Second, returns on wealth of around 5% 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% each year, while those without much wealth will see their incomes (on average) grow only 1% 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 are 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% (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 show 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) do 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 offhore 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 seem 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 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.

Piketty versus Giles, Part II

The controversy surrounding Capital in the Twenty-First Century just doesn’t want to go away. At the end of May, Piketty released a technical appendix seeking to refute the main points made by Chris Giles concerning the accuracy of Piketty’s estimates of wealth inequality. Giles quickly responded with a statement summarizing the debate and the remaining points of contention.

Perhaps the most important point to make about the first Giles article in the Financial Times is that it shows a great deal of guile and at the same time is beguiling.

From a political or policy perspective, the piece did what it intended to do—cast doubt on the Piketty project. Anyone who doesn’t like the message of Piketty, or his policy proposals, can now cite the Financial Times piece while repeating the mantra that Piketty’s estimates have “unexplained errors.” Those on the far right can claim Piketty lied or just made up numbers so that he can tax the wealthy. Such a backlash has already begun; googling “Piketty errors” or searching for this phrase on Twitter provides many examples of people who are convinced that Piketty lied and that the Financial Times caught him at it. None of these commentators seems to have read Piketty’s response, to which we now turn.

Piketty has produced a lengthy (10 page, single spaced) “Technical Appendix,” which he calls a “Response to FT.” A lot of what is there repeats what appears in an even lengthier data appendix on Piketty’s website to accompany his book. The “Response to FT” does explain and justify Piketty’s decisions regarding data selection and tweaking data, and does respond to the charges made by Giles. It is available here.

In his FT response, Piketty admits that his wealth data are sketchy and somewhat speculative. But he also notes that his estimates are very conservative—the concentration of wealth seems to be growing even faster than he had estimated. Evidence supporting this comes from economists Saez and Zucman, using a dataset and a methodology that is superior to the one used by Piketty.

More to the point, whatever one might think about the quality of wealth data and some technical issues regarding how to best tweak empirical data, there is no denying that income and wealth inequality have risen sharply over the past several decades. We do not have to resort to Piketty to learn this. It is obvious to anyone who has paid attention to what has been going on in the world economy. Data from the U.S. Census Bureau, the Federal Reserve, and tax returns all say the same thing—income and wealth inequality are rising in the United States. Luxembourg Income Study data shows a trend of rising income inequality in most all developed nations.

Finally, in his response to Giles, Piketty does admit that he should have done weighted averages (by country size) rather than simple averages when measuring wealthy concentration in Europe based on data from different countries. However, he notes that using a weighted average yields results that are not very different from the results using an unweighted average—mainly because changes in the distribution of wealth were so similar in most European nations.

Let’s conclude with the May 30 response by Chris Giles. Giles starts by summarizing the three main points where he and Piketty agree.

First, wealth data is far worse than income data. Of this there should be no doubt. Income data come from individual income tax returns. Wealth tax data come from estate returns. Estate tax returns do not get filed every year by everyone, and annual data are subject not only to annual variations in asset prices but also variations in who happens to die in a particular year. So these data is far less accurate as a measure of annual wealth distribution in any one year than income tax returns, which give a reasonable estimate of income distribution in any given year.

Second, both Giles and Piketty agree that for summarizing data from Europe, Piketty should have used weighted averages (weighting country data by population size) rather than using simple averages. This, however, is not a weighty difference. The numbers tell a very similar story about wealth inequality over time whether one uses a simple average or a weighted average.

Third, Giles and Piketty agree that during most of the 20th century wealth inequality declined. This decline took place between World War I and around the 1970s. It was the result of wealth destruction (especially in Europe) due to two wars and high top marginal tax rates imposed to fight the wars.

Giles then move on to several points of disagreement.

First, he complains about Piketty’s failure to explain his data and data tweaks. Piketty actually did respond to this in his May 28 Technical Appendix. He may not have responded in a way or with the detail that Giles wanted, but Piketty did provide a thorough response.

To repeat a point I made before, because I think it is so important, there will ALWAYS be data problems and questions. Pointing them out does not move the argument forward and does not increase our knowledge concerning inequality. The right approach is to tweak the data differently, or correct what you think are errors, and recalculate.

This is the only way we can know the extent to which Piketty’s results depend on his decisions regarding handling the data. This is what UMass-Amherst graduate student Thomas Herndon did with the Reinhart and Rogoff data, and this is why he was able to refute their claim that when debt levels exceed 90% of GDP economic growth stalls.

Instead of taking this approach, when Giles “corrects” Piketty, he just makes estimates (and reports those of others) that come from his own preferred data—survey data. The problem here is that survey data on wealth is worse than estate tax data, mainly because there is no way to check the numbers that people give to whoever calls and asks them about their wealth. The very wealthy are known to understate their wealth when asked. Data from estate tax forms, which Piketty relies on, can be checked against other sources and lying can result in tax penalties. This reduces understatement of true wealth by those at the very top of the wealth distribution.

Having said this, there is something to be said in favor of Giles’s actual wealth distribution estimate for the UK. This is a point I made in my original blog on the lengthy Giles article. We know, from Piketty’s own data, that wealth inequality in the United States and Europe (see p. 349 of his book) declined in the 1930s following the 1929 stock market crash. This is only to be expected since the bottom half of the population has no wealth to speak of and so cannot lose anything following a market crash. The middle class, those between the top 10% of wealth owners and the median wealth owner, have a large chunk of their wealth tied up in home equity. It is only the wealthy who own large amounts and fractions of financial assets.

As a result, I would have expected to see a drop in wealth inequality in 2010. The S&P 500 fell over 25% between its peak in 2007 and 2010. In the UK, the FTSE 100 fell by around 20% over this same time period. Giles does find that wealth inequality fell in 2010; but Piketty found a small increase. This is a significant difference.

It seems unlikely that different data sources would explain this great difference in 2010 results. After all, different data sources were used by Piketty and Giles for all their estimates of wealth inequality; yet, and despite the claims made by Giles, only in 2010 did this make a big difference. For most other years, the patterns were very similar even though the actual numbers differed.

There is another possible explanation for such divergent results, one that totally escaped my attention the first time I read Giles’s piece in the Financial Times. Giles provides estimates for both 2000 and 2010; the decline in wealth inequality takes place between these two years. Between 2000 and 2010 the FTSE declined by around 10%.

In contrast, when Piketty provides data on wealth he lists it as data for a single year—1940, 1960, etc. But Piketty notes that these numbers are abbreviations for entire decades. The year 1940 refers to the average over the entire period from 1940 to 1949, or (to be a bit more precise) for all available data in this time period. The main reason for doing this is that wealth varies a good deal from one year to the next because stock prices are so volatile. Decade averages enable us to see long-term trends.

So Piketty’s figure for 2000 is really a figure for 2000 to 2009. Even more important, if his figure for 2010 includes any years after 2010 (this is not clear from the information I could find immediately), his estimates will show wealth inequality falling by less or maybe even increasing, since his extra years are all years of market recovery following a big plunge at the end of 2008. If Piketty is averaging several years of data and Giles is not, this would help explain the different results they get. Giles is comparing 2000 with something near the bottom of the Great Recession; Piketty is comparing a mediocre decade on average for stocks, with two or three other mediocre years. From this perspective, it is not surprising the Giles finds a decline in wealth inequality and Piketty finds a small increase.

Finally, even if Giles’s estimate is completely right for 2010, and even if Piketty is wrong, data for one year prove nothing. Piketty is concerned with long-term trends. After the sharp rise in stock prices in 2013, I would bet that the top wealth shares in the UK have again moved up.

Overall, I do not see anything in Giles that casts doubt on Piketty’s conclusions about income and wealth inequality. Nor do they cast doubt on his numbers or his tweaking of the data. It is pretty clear that inequality is a problem and, if Piketty is right, they are going to be getting much worse—unless we find the political will to stop it from happening.

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