How serious are these problems? And how much, if at all, should they change what we think about inequality?
Well, the answer seems to be not too serious, except for the recent British numbers. Let's go through them. Giles identifies three basic types of issues. The first are simple transcription errors. He finds, for example, that Piketty accidentally entered Sweden's wealth data from 1908 instead of 1920. But despite this mistake, Giles concludes that "there appear to be few problems with the choices made by Prof. Piketty for Sweden"—which you can see in Giles's chart below, comparing his corrected calculations (red) with Piketty's (blue).
In other words, there are data-entry errors, and they're embarrassing, but they don't change the big picture.
The next concern is methodological. Giles thinks Piketty should average European data by population, not by country. He doesn't like that Piketty draws trends between large gaps in the numbers. Or that Piketty labels data from, say, 2004 as "2000" on some of his charts. And Giles isn't sure why Piketty has put together some of his wealth data—which is sparse, and needs to be adjusted, if not constructed—the way that he has. But these aren't errors. They're questions. Ones that Piketty should answer, but still just questions.
The last problem is the most significant. Giles points out that Piketty seems to have mixed up different sources on British wealth the last few decades, and overestimated their inequality. You can see Piketty's numbers (blue) versus the raw data (red) below. This does need to be explained.
Bu this doesn't seem to be a Reinhart and Rogoff situation. Their Excel errors really did change their conclusions. Piketty's don't. Unless, like Giles, you average inequality by population instead of by country—which is debatable, at best, since Piketty is only concerned about inequality within countries.
Still, it's another reminder that economics is the least exact science. That's why it's critical for researchers to make their data public, so everyone else can double and triple check it. To his credit, Piketty has done just that. Now he should tell us a little more about his methods. (And don't worry, that won't bore us. We were already willing to read 700 pages about the history of inequality.)