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Page 1: Did Thomas Piketty Get His Math Wrong

5/25/2014 Did Thomas Piketty Get His Math Wrong? - NYTimes.com

http://www.nytimes.com/2014/05/24/upshot/did-piketty-get-his-math-wrong.html?smid=tw-share 1/5

http://nyti.ms/TD1JNb

Edited by David Leonhardt

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The UpshotTRUTH IN NUMBERS | NYT NOW

Did Thomas Piketty Get His Math Wrong?

MAY 23, 2014

Neil Irwin

@Neil_Irwin

One of the most common approaches for people writing about Thomas

Piketty’s blockbuster book “Capital in the 21st Century,” about global

inequality, has been to critique his theories and predictions while

effusively praising his data collection. Mr. Piketty, after all, did yeoman’s

work compiling data from tax and other records to try to determine a

history of wealth inequality around the world.

But now The Financial Times is throwing doubt on the data at the

Page 2: Did Thomas Piketty Get His Math Wrong

5/25/2014 Did Thomas Piketty Get His Math Wrong? - NYTimes.com

http://www.nytimes.com/2014/05/24/upshot/did-piketty-get-his-math-wrong.html?smid=tw-share 2/5

core of Mr. Piketty’s work, in a blockbuster report that will open a new

debate on how reliable the book’s excavation of historical patterns of

income and wealth truly are. At issue: Is the most influential economics

book of the year built on bad math?

“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,” writes

Chris Giles, the economics editor of The Financial Times. “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.”

Here is a detailed walk-through of the problems Mr. Giles alleges, and

Mr. Piketty’s detailed response. We have contacted Mr. Piketty, a French

economist, and his publisher, Harvard University Press, for further

comment. May 24 update: In an e-mail to me Saturday morning, Mr.

Piketty wrote: “Of course I welcome open debate and new series. This is

why I put everything online.”

The Financial Times draws comparisons with the spreadsheet and

other errors discovered last year that undermined work by Carmen

Reinhart and Kenneth Rogoff on the relationship between government

debt and growth. But what problems did The Financial Times discover

and how much do they potentially undermine Mr. Piketty’s book?

Some of the issues identified by Mr. Giles appear to be clear-cut

errors, and others are more in the realm of judgment calls in analyzing

data that may not be fully explained by Mr. Piketty but are not necessarily

wrong. Here are some of the specific potential problems that The Financial

Times identifies and how they may come to bear on how we think about

wealth, inequality and Mr. Piketty’s exploration of it.

Simple data errors. In the Reinhart-Rogoff case, a simple math

error in an Excel spreadsheet had a relatively small impact on their final

result, but it generated an outsize share of the attention to a broader

critique of their data.

Mr. Giles identifies a couple of places where Mr. Piketty’s

Page 3: Did Thomas Piketty Get His Math Wrong

5/25/2014 Did Thomas Piketty Get His Math Wrong? - NYTimes.com

http://www.nytimes.com/2014/05/24/upshot/did-piketty-get-his-math-wrong.html?smid=tw-share 3/5

spreadsheets include what appear to be incorrect numbers, pulling a

number for share of wealth held by the top 1 percent in Sweden from 1908

instead of the 1920 level that was intended. These errors may be

embarrassing — and easy to understand — but can also be inevitable when

pulling thousands of data points together as part of a large study. It is not

clear that they have a major impact on Mr. Piketty’s conclusion, though it

would be unsurprising, based on the Reinhart-Rogoff experience, if they

get significant attention.

Arbitrary or unexplained changes. Mr. Giles examined many

of the formulas in Mr. Piketty’s spreadsheets and found unexplained

modifications to some of the data points, for example adding two

percentage points to the share of wealth held by the top 1 percent in the

United States in 1970, and calculating the share of British wealth held by

the top 10 percent in 1870 by adding seemingly arbitrary numbers to the

share held by the top 1 percent.

Questionable methods to arrive at conclusions. Mr. Giles

notes that Mr. Piketty arrives at estimates of European wealth inequality

by averaging results for three countries where he has data, Britain, France,

and Sweden, arguing that this is a poor way to weight because of Sweden’s

much smaller population.

More significantly, Mr. Giles argues that Mr. Piketty constructed data

where there is no cited source. For example, in data for the top 10 percent

wealth share in the United States before 1950, “none of the sources Prof.

Piketty uses contain these numbers, hence he assumes the top 10 percent

wealth share is his estimate for the top 1 percent share plus 36 percentage

points,” he wrote. “However, there is no explanation for this number, nor

why it should stay constant over time.”

Mr. Giles also argues that Mr. Piketty combines different data sources

arbitrarily, using surveys of households in the United States versus estate

tax data for Britain, for example.

But does it matter? Mr. Giles attempts to reconstruct estimates of

wealth inequality, correcting for what he describes as Mr. Piketty’s errors.

Page 4: Did Thomas Piketty Get His Math Wrong

5/25/2014 Did Thomas Piketty Get His Math Wrong? - NYTimes.com

http://www.nytimes.com/2014/05/24/upshot/did-piketty-get-his-math-wrong.html?smid=tw-share 4/5

He finds significantly less evidence of a rising disparity.

Speaking of Britain, for example, Mr. Giles writes, “There seems to be

little consistent evidence of any upward trend in wealth inequality of the

top 1 percent.” He further writes that if one incorporates the different

British data into numbers for Europe as a whole, and weights by

population instead of weighting Britain, France and Sweden equally,

“there is no sign that wealth inequality in Europe is rising again.”

That is a damning conclusion, and if it holds up to scrutiny, would

significantly undermine the case Mr. Piketty mounts. But Mr. Giles himself

writes that “while this post is clear about what is wrong with Piketty’s

charts, it is much less certain about the truth.”

Mr. Piketty, in his response to The Financial Times and in his e-mail

on to me, said that research using other methodologies has affirmed his

broad findings, citing work by Emmanuel Saez and Gabriel Zucman

published since his book was written.

“As I make clear in the book, in the online appendix, and in the many

technical papers I have written on this topic, one needs to make a number

of adjustments to the raw data sources so as to make them more

homogeneous over time and across countries,” he told the F.T. He added,

“I have tried in the context of this book to make the most justified choices

and arbitrages about data sources and adjustments. I have no doubt that

my historical data series can be improved and will be improved in the

future (this is why I put everything online).”

He did not specifically address the accusations of data-entry errors or

give detailed responses to some of Mr. Giles’s criticisms about questionable

assumptions that underlie Mr. Piketty’s broader work.

But in his e-mail to me, he wrote with an almost jovial tone: “Every

wealth ranking in the world shows that the top is rising faster than average

wealth,” adding, “If the FT comes with a wealth ranking showing a

different conclusion, they should publish it!”

It is always a difficult challenge trying to examine economic history

given spotty data from the past and variations in how different countries

Page 5: Did Thomas Piketty Get His Math Wrong

5/25/2014 Did Thomas Piketty Get His Math Wrong? - NYTimes.com

http://www.nytimes.com/2014/05/24/upshot/did-piketty-get-his-math-wrong.html?smid=tw-share 5/5

collect and define data. The new Financial Times report will surely be

examined by specialists and start an important debate over what we really

know about wealth inequality — and whether the best-selling economics

book of the year gets its figures right.

The Upshot provides news, analysis and graphics about politics, policy and everyday life. Follow uson Facebook and Twitter.

A version of this article appears in print on May 24, 2014, on page B1 of the New York edition withthe headline: Economist’s Inequality Study Faces Questions.

© 2014 The New York Times Company