Piketty Notes and Quotes, 3: A Childish Passion for Mathematics

From the Introduction, one of my favorite passages in the book, and one that really sets the methodological basis for the whole argument:

“I should perhaps add that I experienced the American dream at the age of twenty-two, when I was hired by a university near Boston just after finishing my doctorate.  This experience proved to be decisive in more ways than one.  It was the first time I had set foot in the United States, and it felt good to have my work recognized so quickly.  Here was a country that knew how to attract immigrants when it wanted to!  Yet I also realized quite soon that I wanted to return to France and Europe, which I did when I was twenty-five.  Since then, I have not left Paris, except for a few brief trips.  One important reason for my choice has a direct bearing on this book: I did not find the work of US economists entirely convincing.  To be sure, they were all very intelligent, and I still have many friends from that period of my life.  But something strange happened: I was only too aware of the fact that I knew nothing at all about the world’s economic problems.  My thesis consisted of several relatively abstract mathematical theorems.  Yet the profession liked my work.  I quickly realized that there had been no significant effort to collect historical data on the dynamics of inequality since Kuznets, yet the profession continued to churn out purely theoretical results without even knowing what facts needed to be explained.  And it expected me to do the same.  When I returned to France, I set out to collect the missing data.

To put it bluntly, the discipline of economics has yet to get over its childish passion for mathematics and for purely theoretical and often highly ideological speculation, at the expense of historical research and collaboration with the other social sciences.  Economists are all too often preoccupied with petty mathematical problems of interest only to themselves.  This obsession with mathematics is an easy way of acquiring the appearance of scientificity without having to answer the far more complex questions posed by the world we live in.  There is one great advantage to being an academic economist in France: here, economists are not highly respected in the academic and intellectual world or by political and financial elites.  Here they must set aside their contempt for other disciplines and their absurd claim to greater scientific legitimacy, despite the fact that they know almost nothing about anything.”

 

It is a testimony to the incorrigibility of the economics profession in America that the most substantial critique of Piketty’s work to emerge from that quarter is that “Unless I’m missing something, the formal [mathematical] apparatus in Piketty’s book simply is not capable of generating the results he touts.”  In other words, “Sure he’s demonstrated that something actually happened historically, but he hasn’t proven mathematically that it’s capable of happening!”

11 thoughts on “Piketty Notes and Quotes, 3: A Childish Passion for Mathematics

  1. Alastair J Roberts

    Interesting, given the impression of the standard French thinker: “That’s all very well in practice, but does it work in <i>theory?</i>” Perhaps the pattern is reversed when it comes to economics.

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  2. Joe Carter

    <em>In other words, "Sure he’s demonstrated that something actually happened historically, but he hasn’t proven mathematically that it’s capable of happening!" </em>

    Actually, that gets it exactly backwards. The only reason Piketty can claim that it "happened historically" is because of the statistical data. Without that data, there is no evidence to support his claims.

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    • Brad Littlejohn

      But Joe, the objection, as I understand it, isn’t that the empirical statistical data (of capital/income ratios, etc.) is flawed, but that it can’t be replicated predictively by a mathematical equation that fits accepted norms of neoclassical economics.

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      • Joe Carter

        If it can’t be replicated, then where did the date come from?

        Claims about capital/income ratios, changes in wealth, rates of inequality are all based on . . . mathematics. Someone had to count the numbers and collate the data. What data is Piketty basing his claims on? He is making claims about historical data without actually have that data to base his conclusions on.

        As they note in the critique at Financial Times, "The conclusions of Capital in the 21st century do not appear to be backed by the book’s own sources."

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      • Brad Littlejohn

        Joe, have you actually read the book? I think your objection here is confusing two very different roles for mathematics in the argument. To calculate things like what the historical numbers tell us about what the capital/income ratio was at a certain date is very different from attempting to calculate, based on various assumptions (anchored in data, to be sure) about the depreciation and return on capital, the marginal productivity of labor, etc., what the elasticity of substitution for capital and labor are. The latter involves several levels more of abstraction. If the predictions derived from the latter equations yield results different from actually happened in history, then it suggests that the assumptions going into this math are flawed, and fail to take into account certain empirical realities (i.e., politics). This would be Piketty’s argument.

        As far as the FT critique, did you see Piketty’s response? (http://blogs.ft.com/money-supply/2014/05/23/piketty-response-to-ft-data-concerns/) There is nothing surprising about the fact that in such an absolutely enormous collation of data there are flaws; Piketty himself is eager above all for improvements in the data, and this is precisely why he has made it all publicly available. Obviously he’s not trying to "cook the books," as he explains: "Let me first say that the reason why I put all excel files on line, including all the detailed excel formulas about data constructions and adjustments, is precisely because I want to promote an open and transparent debate about these important and sensitive measurement issues (if there was anything to hide, any “fat finger problem”, why would I put everything on line?)."

        Piketty is inviting all the world’s economists and statisticians to dig into the data and improve it. If, in the end, the result is that his overall narrative and theses are disproven, then his book will still have been an immensely important contribution. As it is, though, I see little evidence that various improvements in the dataset will alter the overall picture, which appears very widely corroborated indeed.

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      • Joe Carter

        I think your objection here is confusing two very different roles for mathematics in the argument.

        Maybe I am, for I certainly confused by your point. Piketty is making claims about historical data when such data does not exist. He neither knows where at a date in the past or has a way to accurately calculate them today. In other words, much of his empirical analysis is being done with the empirical data.

        Am I wrong about that? If Piketty were presenting a math-free theory that wasn’t rooted in actual historical data, I would give it a pass (because it would be easy to ignore such speculation). But Piketty seems to be saying that the numbers he is talking about are based on actual data, and not just something he pulled out of thin air.

        Obviously he’s not trying to "cook the books,"

        I’m certainly willing to give him the benefit of the doubt on that point. As your quote above makes clear ("the discipline of economics has yet to get over its childish passion for mathematics") he probably just didn’t have as much interest in the math stuff as he does for the theory side. It’s much easier for a researcher to make mistakes on the areas that don’t really interest them. I’m not saying his nefarious, just sloppy.

        * If, in the end, the result is that his overall narrative and theses are disproven, then his book will still have been an immensely important contribution.*

        Perhaps so. But it would also undercut the justification for his policy prescriptions, which are the main reason his book is being (over)praised. If wealth inequality is not rising, then is certainly undercuts his primary theory.

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      • Brad Littlejohn

        Again, Joe, have you actually read the book? Or a significant part thereof? I think doing so would help you clarify your criticisms.

        For instance, I’m not sure what you mean when you say "Piketty is making claims about historical data when such data does not exist. He neither knows where at a date in the past or has a way to accurately calculate them today."

        And it’s hard for me to believe that anyone who read the book would say "he probably just didn’t have as much interest in the math stuff as he does for the theory side. It’s much easier for a researcher to make mistakes on the areas that don’t really interest them." He has invested far far more time and effort in raw collection, collation, and clarification of data than he has in theorizing. The presence of some errors in such enormous and complex datasets does not necessarily make him "sloppy."

        In any case, though, as you say you still aren’t clear about what I’m saying about the relationship of math and history in his argument, I will try to clarify further in a later post (probably some time next week).

        But it would also undercut the justification for his policy prescriptions, which are the main reason his book is being (over)praised.To be sure, which is why I certainly think that the kind of drastic international policy prescriptions he suggests, even if feasible, would be premature until the data and theory has been cross-examined and refined further. That said, there are some pieces of data (i.e., about the explosion of income inequality in the US) that are indisputable, and for which it is probably high time to consider policy options.

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      • Joe Carter

        No, I haven’t read the book. But I’m not sure how they would address the criticisms (unless FT is simply making up stuff).

        *He has invested far far more time and effort in raw collection, collation, and clarification of data than he has in theorizing. *

        Then why does he have charts and graphs for historical data that does not exist?

        hat said, there are some pieces of data (i.e., about the explosion of income inequality in the US) that are indisputable, and for which it is probably high time to consider policy options.

        Actually, I think claims about income inequality in the US are highly disputable. I think focusing on income inequality rather than, say, consumption inequality is rather absurd. Until Americans start claiming that it’s a problem that someone makes $50K a year while their neighbor makes $25K and thinks that we should we redistribute such income, it’s hard to take claims about income inequality seriously. No one has every shown that preventing Bill Gates from becoming a billionaire would help poor Americans. Yet doing so would have certainly prevented inequities in income.

        I suspect in 30 years we are going to look back at the debates over income inequality and realize it was an absurd metric to focus on. It’s going to be the equivalent of price controls, an idea that we wonder why any economically astute human would think was rational.

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      • Brad Littlejohn

        "No, I haven’t read the book. But I’m not sure how they would address the criticisms (unless FT is simply making up stuff)."Well, it would help put them in perspective, by showing the role the particular data points in question play in his narrative and argument. Whereas Giles at FT gleefully acts like he’s picked apart Piketty’s whole case, the reality is that he’s nuanced a few numbers in a single chapter, without altering the overall picture.

        "Then why does he have charts and graphs for historical data that does not exist?"I honestly have no idea what you’re referring to; so far as I’ve seen, nobody has made this charge.

        "I think focusing on income inequality rather than, say, consumption inequality is rather absurd."Um, but that’s precisely one of the big problems with income inequality—that it tends to be much greater than consumption inequality, thus lowering overall consumption. I assume you’re familiar with Robert Reich’s work on this?

        "I suspect in 30 years we are going to look back at the debates over income inequality and realize it was an absurd metric to focus on. It’s going to be the equivalent of price controls, an idea that we wonder why any economically astute human would think was rational."Whereas I think that we’re going to look back on these debates in 30 years and wonder how a large sector of the population and intellectuals managed to convince themselves that this was no big deal, much as we now look back on segregation (though of course, as a moral issue, that’s a much more open-and-shut case than this one).But as we’ll have to both wait quite awhile for vindication, apparently, how ’bout I make you a deal? In 30 years, if you’re right, I’ll buy you a bottle of Lagavulin; if I’m right, you buy me a bottle. 😉

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  3. John Horvat

    After his emphatic declaration of war on modern economics, I was surprised by Piketty’s failure to abide by his own rules of engagement. We are immediately introduced to his mathematical formula of r>g from which explains the inevitability of “excessive” inequality in almost classical fashion. There are literally dozens and dozens of supporting charts. The reader is immersed in numbers, figures and data. His presentation does not work in conjunction with the social science but rather makes these disciplines subservient to his inexorable law of economics.

    John HorvatAuthor of Return to Order: From A Frenzied Economy to an Organic Christian Society

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