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 http://www.dollarsandsense.org/blog), 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.