## Monday, June 9, 2014

### Piketty's Empirics Are as Bad as His Theory

In my earlier Piketty post, I wrote, "If much of its "reasoning" is little more than neo-Marxist drivel, much of its underlying measurement is nevertheless marvelous." The next day, recognizing the general possibility of a Reinhart-Rogoff error, but with no suspicion that that anything was actually remiss, I added "(assuming of course that it's trustworthy)."

Perhaps I really should read some newspapers. Thanks to Boragan Aruoba for noting this, and for educating me. Turns out that the Financial Times -- clearly a centrist publication with no ax to grind -- got hold of Piketty's data (underlying source data, constructed series, etc.) and published a scathing May 23 indictment.

The chart above -- just one example -- is from The Economist, reporting on the FT piece. Somehow Piketty managed to fit the dark blue curves to the light blue dots of source data. Huh? Sure looks like he conveniently ignored a boatload of recent data that happen to work against him. Put differently, his fits appear much more revealing of his sharp prior view than of data-based information. Evidently he forgot to talk about that in his book.

In my view, Reinhart-Rogoff was a one-off and innocent (if unfortunate) mistake, whereas the FT analysis clearly suggests that Piketty's "mistakes," in contrast, are systematic and egregious.

1. Piketty responded to the FT post a few days after:

http://www.nytimes.com/2014/05/30/upshot/thomas-piketty-responds-to-criticism-of-his-data.html

2. Piketty responded in detail to the argument you found. http://piketty.pse.ens.fr/files/capital21c/en/Piketty2014TechnicalAppendixResponsetoFT.pdf
Helps to check before you rant ..

1. This comment has been removed by the author.

2. I pretty much stand by the rant(s).

3. Wow. No acknowledgement at all that the key FT criticism (about the UK) involved splicing together two data series that misled readers? Your credibility is at stake here -- do you really want to stand by what you wrote???

4. You "pretty much" stand by what you wrote? Which part of what you wrote are you conceding was wrong??? Seems to me that the key criticism of Piketty was incorrect. Do you concede that? If not, what is your argument about why it's okay to splice data series together and mislead on key points?

1. Thanks Mark. See response to Brad DeLong below.

5. I am with Mark Thoma here--the FT blew it very badly on this one. Piketty really ain't as stupid as the FT claimed...

6. I'm very surprised to read that. I'm an econ PhD student and I've read the book and the paper (capital is back) here's what I found:

- very good documentation and transparency of sources and data transformations (better than what I'm used to in economics)
- the book provided a lot of interesting information and figures that I did not know well (from not having read much of the inequality literature). Examples are: data for wealth and income inequality, tax rates, importance of inheritance.
- I have serious problems with Piketty's theory. I just don't buy "fundamental laws" in economics

In conclusion, I loved the data the book provided but I disagree with some of the interpretations and theories put forth.

Most importantly, Piketty is very careful when he presents data to make clear the uncertainty surrounding his and other's estimates. Also, he even presents data that doesn't support his theory. Check out this figure for example:
http://piketty.pse.ens.fr/files/capital21c/en/pdf/F10.1.pdf
If he really was that terribly un-scientific, why would he include that?

"neo-Marxist drivel" is very far away from what the book actually is. He's actually very critical of Marx (e.g. he criticizes his lack of data).

I don't know whether you've read the book, but it doesn't sound like it. My recommendation: read it, you might be surprised.

7. Neo-Marxist drivel? Marx's and Piketty's models are completely different. Marx worked from the labor theory of value. Piketty's model is actually just a redefined version of the neo-classical Harrod warranted growth model...with one big difference. In the Harrod growth model savings ("s") is a fraction of gross income such that in equilibrium investment equals savings from income:

I = sY, where I = investment, s equals the savings rate, and Y equals income.

In the standard Harrod warranted growth model:

g = s / [(K/Y) - s]

where (K/Y) is the capital/output ratio and g is the warranted growth rate.

Piketty reworks the algebra so that the capital/output ratio is on the left side of the equation and the growth rate is exogenous and goes on the right hand side:

(K/Y) = s[(1/g) + 1]

Piketty then drops the "+1" part at the end in order to keep things simpler for the reader, so we get (K/Y) = s/g

As a practical matter dropping the "+1" does not make an material difference to Piketty's results and it makes the "second law" much easier to remember across 577 pages.

The piece that seems to be causing confusion among many academic economists bathed in the tradition of neo-classical growth models is the way he defines "s." In Piketty's model "s" is no longer a constant fraction of gross income. That's mainly because NIPA tables hadn't been invented in the 18th and 19th centuries. Piketty's novel solution is to define "s" as the ratio of the NET change in the stock of wealth (both productive and unproductive wealth) to NET income. Note that Piketty does not use total investment, but only the net change in the wealth stock across time. For example, if last year's wealth was $1000 and this year's wealth stock is$1050, then the change to net wealth is $1050 -$1000 = $50. If net income happened to be$400, then "s" would be $50 /$400 = 12.5%. Notice that the savings rate should really be thought of as the rate at which net wealth accumulates relative to net income. So all of the criticisms about how Piketty ignores depreciation are off the mark. Now suppose that the exogenously given growth rate is 5%. Then under PIketty's model the economy will tend to a K/Y ratio of 12.5% / 5% = 250%. If growth drops to 2%, then K/Y will go to 12.5% / 2% = 625%.

From this it is clear that Piketty's second law is actually just a way of expressing the limit of K/Y given historical rates of net wealth accumulation relative to net income along with the exogenously determined growth rate. This is hardly a neo-Marxist approach. The basic algebra is entirely within the framework of Harrod, Domar and Solow-Swann. What is novel about Piketty's approach is the way he used the data he had available to redefine the variables in those old neo-classical formulations. Instead of a warranted growth rate, what we end up with is a warranted capital/output rate.

8. I really think that the graph from the Economist needs to be pulled from this post: it gives a grossly misleading picture of what the argument is over...