Bad maths in Piketty's capitalism critique?

French economist Thomas Piketty at King's College in London on 30 April, 2014. Image copyright Getty Images
Image caption French economist Thomas Piketty says he was ambushed by Financial Times reporters

On Friday the Financial Times published what, even in the stodgy world of global economics, has to be considered a bombshell.

According to an investigation by Chris Giles and Ferdinando Giugliano, French economist Thomas Piketty made a number of errors in his surprise best-selling book, Capital in the Twenty-First Century.

After looking at Piketty's research, Giles says the French economist "appears to have got his sums wrong" - errors that he alleges "skew his findings":

The central theme of Prof Piketty's work is that wealth inequalities are heading back up to levels last seen before the First World War. The investigation undercuts this claim, indicating there is little evidence in Prof Piketty's original sources to bear out the thesis that an increasing share of total wealth is held by the richest few.

Giles details what he identifies as "transcription errors from original sources" and "incorrect formulas". He also alleges that Mr Piketty engaged in cherry-picking some data and filling in missing information to fit his conclusions.

This results, Giles writes, in numbers that indicate trends that cannot be supported. For instance, he says, Mr Piketty's European figures, when corrected, "do not show any tendency toward rising wealth inequality after 1970".

In a response to the allegations, which the Financial Times publishes alongside its original story, Mr Piketty notes that he has made all his data public in order to "promote an open and transparent debate about these important and sensitive measurement issues".

He says that because the data on wealth are from a variety of sources, he had to make a number of adjustments to make them comparable from country to country.

"I have no doubt that my historical data series can be improved and will be improved in the future," he writes. "But I would be very surprised if any of the substantive conclusion about the long-run evolution of wealth distributions was much affected by these improvements."

On Saturday, as the Financial Times's piece became more widely circulated, Mr Piketty sharpened his reply. He told Newsweek's Leah McGrath Goodman that he was ambushed by Giles, and not provided all the information they were going to publish or given sufficient time to respond.

"What's really dishonest is that the small corrections that they make to my series (and with which I disagree) do not make any difference to the overall evolution and to the overall analysis proposed in the book ... and they try to pretend the opposite," he said.

The Financial Times's investigation has sparked a quick reaction from the same cast of commentators and analysts who had debated Mr Piketty's book when it first burst on the US scene in April.

Reuters's Richard Beales says that Mr Piketty's mistakes show a "haphazard" employment of Microsoft Excel spreadsheets, which would "embarrass the greenest investment-banking analyst".

Data collection is never flawless, writes FiveThirtyEight's Nate Silver. Although it's easy to assume numbers in a chart are "pure and clean", he writes, they're either entered or programmed by humans who are capable of making mistakes.

"If researchers kept scrubbing data until it were perfect, they'd never have time for analysis," he says.

Despite some apparent errors, writes the Economist's Ryan Avent, Mr Piketty's conclusions appear to be sound:

First, the book rests on much more than wealth-inequality figures. Second, the differences in the wealth-inequality figures are, with the exception of Britain, too minor to alter the picture. And third, as Mr Piketty notes in his response, Chapter 10 is not the only analysis of wealth inequality out there, and forthcoming work by other economists (some conclusions of which can be seen here) suggests that Mr Piketty's figures actually understate the true extent of growth in the concentration of wealth.

"The Financial Times blew the data issues it identified out of proportion," writes the Manhattan Institute's Scott Winship, who notes that he is no fan Mr Piketty's work. "Giles discovered a couple of clear errors and a number of adjustments that look questionable but have barely any impact on Piketty's charts."

The National Review's Patrick Brennan, on the other hand, says that Giles's analysis unearths "real problems".

"Piketty set out to do something much more audacious than prove that income inequality is rising in the United States and in most wealthy countries - that's relatively easy to prove, even if the increase has been substantially overstated," Brennan writes.

In order to reach the policy prescriptions Mr Piketty advocates, however - such as a global wealth tax - "he needs wealth inequality not just to appear high or to be rising, but to be returning to 19th-Century levels as a matter of economic inevitability".

Given the evidence unearthed by Giles, he contends, Mr Piketty "hasn't yet justified his dramatic conclusions".

On Wednesday Giles blogged a response to the reaction to his article. He says his piece was not a "premeditated attack" or part of a "political agenda".

He adds that he's concerned by those who defend errors in Mr Piketty's work.

"Academic economists have got themselves into a bad spot if undocumented data, errors and tweaks are considered by some acceptable research practise," he writes. He also expresses surprise that economist have been "more forgiving" than the Financial Times over liberties Mr Piketty takes with constructed data.

He then explains why his findings matter:

If someone is claiming to have found a fundamental contradiction of capitalism, predicts the result is a rising share of wealth inequality and uses apparent recent rises in recent wealth inequality as evidence that his theory is correct, those data lie at the core of the book's argument.

Without the rising wealth inequality data across all advanced economies, I would submit that Prof Piketty has a theory without all the necessary evidence.

Mr Piketty, his critics and his defenders rely on a great deal of dense information, charts and economic theories in their debate over his conclusions. It's quite easy for the layperson to be overwhelmed and throw up his or her arms in confusion.

The reality, however, is that the subject of the discussion - whether there is an increasing wealth gap that is creating permanent imbalances in modern society - is a topic of great concern. And the policy remedies, if any are necessary, are the people's responsibility to enact.

Or at least, in a democracy, they should be.