Larry Summers on Piketty: Low Bar for Nobel Prizes These Days

Larry Summers on Piketty: Low Bar for Nobel Prizes These Days
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When he’s not botching basic historical facts about tax rates and minimum wages–in ways that conveniently serve his 800 larry summers2political narrative–Thomas Piketty, author of the celebrated Capital in the 21st Century, is botching the basic theory of capital and interest. Here at Mises Canada I’ve already pointed out a fundamental theoretical problem with Piketty’s whole structure. But in Larry Summers’ recent book review, he confirms another enormous problem with Piketty’s whole approach. Here’s Summers:

Economists universally believe in the law of diminishing returns. As capital accumulates, the incremental return on an additional unit of capital declines. The crucial question goes to what is technically referred to as the elasticity of substitution. With 1 percent more capital and the same amount of everything else, does the return to a unit of capital relative to a unit of labor decline by more or less than 1 percent? If, as Piketty assumes, it declines by less than 1 percent, the share of income going to capital rises. If, on the other hand, it declines by more than 1 percent, the share of capital falls.

Economists have tried forever to estimate elasticities of substitution with many types of data, but there are many statistical problems. Piketty argues that the economic literature supports his assumption that returns diminish slowly (in technical parlance, that the elasticity of substitution is greater than 1), and so capital’s share rises with capital accumulation. But I think he misreads the literature by conflating gross and net returns to capital. It is plausible that as the capital stock grows, the increment of output produced declines slowly, but there can be no question that depreciation increases proportionally. And it is the return net of depreciation that is relevant for capital accumulation. I know of no study suggesting that measuring output in net terms, the elasticity of substitution is greater than 1, and I know of quite a few suggesting the contrary.

This is an absolutely devastating observation; it topples Piketty’s whole argument. Incidentally, I first saw a PhD student at MIT raise this point (in the comments of a Tyler Cowen blog post). Brad DeLong didn’t object to the student’s point, and now Larry Summers too is explicitly confirming it. So let me walk people through what’s going on here, to show why it is so critical. (Note that for the rest of this post, I am going to take the standard neoclassical approach to capital and interest at face value; Piketty is wrong even in the narrow confines of his own chosen paradigm.)

With his now famous claim that “r > g” for the indefinite future, Piketty is saying that the real return to capital will remain higher than the growth rate in total output. Therefore, Piketty argues, the size of the “capital stock” measured in terms of “years’ worth of output” will continue to rise in the coming decades. In other words, “capital/income” will increase.

Now if the size of the capital stock rises, what can we say about the share of income going to the capitalists each year, compared to the laborers? Well there are two forces. On the one hand, the larger the capital stock, the more units of capital the owners possess, earning returns out there in the market. So that would tend to make the total earnings of the capitalists go up. On the other hand, the larger the capital stock, the lower we’d expect “r” which is the real return on capital. (This is because of diminishing returns; it’s just as we’d expect wages to fall if the labor stock grows.) So that would tend to make the total earnings of the capitalists go down. The actual outcome depends on which of these two forces is stronger: As the number of units of capital goes up by x%, does the individual earnings per unit fall by more or less than x%? (In the special case of a “Cobb-Douglas production function,” the two forces always exactly balance each other, meaning that capital always earns the same percentage of output each period, with labor getting the rest.)

Piketty wants to scare his readers into believing that the percentage of income each period going to the capitalists will increase over time, meaning that “the workers” will earn a lower portion of total output in, say, 2100 than they do right now. So he needs to argue that the parameters on his assumed production function are such that an increase in the capital stock of x% will lower the return to capital “r” by less than x%. In the jargon of economists, Piketty needs to argue that empirically, the “elasticity of substitution” is greater than 1.

Piketty does indeed try to show this, by pointing to some of the high-end estimates in the literature putting the elasticity at 1.25. Yet as Rognlie the MIT grad student points out, this is confusing gross with net returns. If you are a capitalist who owns a bunch of machines, your *net* income each year is equal to

==> your gross rental income from your machines

==> minus the drop in the market value of your machines, either due to a change in prices or physical depreciation.

So as Rognlie and now Larry Summers confirm, there are no empirical estimates of an elasticity in substitution being so much above 1 that the share of *net* income (after accounting for physical depreciation) going to capitalists would be expected to indefinitely increase over the coming decades, as the capital stock accumulates.

Furthermore, beyond this problem with Piketty’s reading of the literature, Summers points out in his book review that Piketty’s thesis doesn’t work at all when looking at the richest people in America from 1982 – 2012, as Bryan Caplan highlights.

Now you might think that since Summers himself blew up the entire foundation of Piketty’s argument, he (Summers) might chide his fellow progressive economists in their over-the-top praise for the book. Nope… Summers says the book “richly deserves all the attention it is receiving.”

How to explain this apparent imbalance between the coherence of the book’s case, and the praise it is receiving? No need for us to cynically speculate; we can let Larry Summers himself explain what’s going on here:

Piketty, in collaboration with others, has spent more than a decade mining huge quantities of data spanning centuries and many countries to document, absolutely conclusively, that the share of income and wealth going to those at the very top—the top 1 percent, .1 percent, and .01 percent of the population—has risen sharply over the last generation, marking a return to a pattern that prevailed before World War I. There can now be no doubt that the phenomenon of inequality is not dominantly about the inadequacy of the skills of lagging workers. Even in terms of income ratios, the gaps that have opened up between, say, the top .1 percent and the remainder of the top 10 percent are far larger than those that have opened up between the top 10 percent and average income earners. Even if none of Piketty’s theories stands up, the establishment of this fact has transformed political discourse and is a Nobel Prize-worthy contribution.

And there you have it. “Even if none of Piketty’s theories stands up”–and Summers has already shown us that they are prima facie wrong–Piketty should get a Nobel Prize because he’s documented how much richer the super rich have gotten over the last generation.

  • MinorLiberator

    Another great article countering Piketty. My only addition to my reply to OfT above is that, at best, even if somewhat true, this work is an analysis of crony capitalism, not the free market.

    • Harold

      Criticism: You make these claims by ignoring solid Keynesian evidence (the real mainstream amongst most academics, including Summers, except a minority from Uchicago, Harvard, and Wharton). According to you, the supply and demand curve should look like a cross rather than an x. You seem to forget that absolutely nothing in the universe is perfect, especially human functions. You assume elasticity under the tenets of classical mechanics which have marked fundamental issues, one of which is perfect elasticity. I hate to devolve into this theory mongering, but I'll play ball, as there are severe problems with this analysis. Market structures are important, and you seem have ignored that in the present market of capital/labor is a monopoly on capital, driving wages lower ALONG with investment because of an increase in rents. This monopoly is evident in the history of the 20th Century on which Piketty spends 3/4 of his book, and with other evidence such as the Recession and winner-take-all-markets. This cannot be ignored, especially as it proves that labor and capital aren't 1-1, but that much of what we count as NET return is more than what you claim. The valuation of monopolist capital always go up because of marked-up rents, the benefit of being a monopolist. It is gross rental plus (not minus) an increase (rather than decrease) of market valuation, simply driven by a concentration of wealth, outpacing depreciation, especially since depreciation is more subliminal today. This allows the measure of productive capital to appear larger than life when it is just profits that migrate straight back to this capital oligarchy- fluff. You also have no data, just an MIT grad and Summers, which is cute, but I could grab two people (much more actually) of similar merit who disagree. Your lack of data is fatal, a lame effort to avoid placing yourself into a corner. You and I can argue all day about theories, but when it is made evident in numbers, figures that mean something, that count heads, it is entirely obvious that the share of labor to capital has decreased over the past 30 years, bringing it to the condition of most of the thousands of years preceding 1930. Piketty spends so much time on this fact that I doubt that someone making your argument could possibly have read his book. This is why he predicts a high concentration of wealth in 2100, based off sound theory AND historical data. Your mild attempt to dismiss wealth inequality with a justification of social mobility is based off of the laughable conclusion of Larry Summers (hold on guys! There are more Mark Zuckerburg on this list! Phew, I'm glad there's someone else to monopolize the capital market!). As someone who cherishes in both economics, knowledge, and the truth, I would very much appreciate it if you could use your forum for something other than manipulation.

      • Hobbes

        If anything, the 20th century has shown a preponderance of governments busting up monopolies so I fail to see how you can jump from competitive markets where the elasticity of substitution is less than one, to one where it is more than one because the reality needed for that to be true simply doesn't exist.

        Nice try though.

  • Bryce McBride

    One wonders if the periodic wars that civilization endures are simply a means of instituting debt holidays/writeoffs. As we have had no major wars in the developed world since WWII, those with wealth have been able to accumulate without interruption, and since 2000 have been able to do so at a much faster rate thanks to rapidly rising liquidity which has pushed up all asset values. What bugs me about the hoopla surrounding Piketty is that it totally ignores other effects such as the strangely concurrent introduction of pure fiat money with rapidly rising incomes for the financially well-connected….

  • Onlooker from Troy

    This Piketty effort is so clearly a case of having a political ideology and then looking for supportive data (distorting it and hiding that in arcane academic B.S.). He's taken advantage of the Fed's irresponsible monetary policy that has blown a huge bubble that has inflated capital values through the roof, and he then builds a (crappy) case for the extrapolation of that trend into infinity.

    Sounds a lot like the case for catastrophic anthropogenic global warming, eh?

  • Paul Henderson

    All evidence to the contrary let's assume Piketty's theories stand up to your scrutiny (they don't). Even if that were the case (it's not), he's still not teaching the correct lesson. If he was right about capital then the message should be for people to go out and start pooling up as much capital as they could, making themselves wealthier and in turn making society more productive. He could have gone that route, but he chose the tired old redistribution populist route instead.

    • David R. Henderson

      Good point, Paul Henderson

  • lintondf

    "Theories? We don't need no stinking theories!"

Profile photo of Robert P. Murphy

Robert P. Murphy is the Senior Economist at the Institute for Energy Research, and a Senior Fellow with the Fraser Institute. He holds a PhD in economics from New York University. Murphy is the author of Choice: Cooperation, Enterprise, and Human Action (Independent Institute, 2015) as well as numerous other books and hundreds of articles.

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