Over at Equitable Growth: Matt Rognlie has a first-rate exposition of his critique of Piketty:
Matt Rognlie: A note on Piketty and diminishing returns to capital: "Capital in the Twenty-First Century predicts...
...a rise in capital’s share of income and the gap r - g between capital returns and growth.... Neither outcome is likely given realistically diminishing returns to capital accumulation. Instead--all else equal--more capital will erode the economywide return on capital.... Piketty (2014)’s inference of a high elasticity from time series is unsound, assuming a constant real price of capital despite the dominant role of rising prices in pushing up the capital/income ratio. Recent trends in both capital wealth and income are driven almost entirely by housing, with underlying mechanisms quite different from those emphasized in Capital.... READ MOAR
In Piketty (2014)’s framework, slower growth will produce a rise in the ratio of capital to income. This, in turn, will bring about an expansion in capital’s share of income.... This will aggravate inequality in the wealth distribution. In short, a key message of Capital in the Twenty-First Century is that capital’s role in the economy will grow in the twenty-first century.... As Piketty (2014) readily acknowledges, diminishing returns may be problematic for this thesis. If the return on capital falls quickly enough when more capital is accumulated, capital’s share of income will fall rather than rise--so that even as the balance sheets of capital owners expand, their claim on aggregate output will shrink.... Most evidence suggests diminishing returns powerful enough that further capital accumulation will cause a decline in net capital income, rather than an expansion.... These conclusions are not definite--there are many obstacles to empirical certainty here--but they do counsel skepticism about Piketty (2014)’s central outlook...
Matt is 100% correct--if all other things are equal, "all other things equal" meaning that the rate of profit is the marginal product of capital from some reasonable neoclassical aggregate production function. As I wrote in my The Honest Broker: Mr. Piketty and the “Neoclassicists”: A Suggested Interpretation, Piketty needs the λ elasticity of the rate of profit with respect to the capital-output ratio to be significantly less than one, and conceptualizing "capital" as a factor of production whose return is determined by its marginal product in a standard neoclassical production function will not get you there.
To quote myself:
The neoclassical assumption that, roughly, that λ=1, damps dynamics in inequality.... Breaking the neoclassical presumption that λ=1 is even more important when we look at the wealthholder share of income S: If λ=1, then S = ρ. Full stop. All of the n (population growth) and g (per capita output growth) and ω (accumulation wedge) terms drop out. And nothing other than shifts in the raw wealth share of income can drive shifts in inequality. Thus there is an even stronger urgent need to break with the default vanilla neoclassical presumptions for Piketty’s argument to go through.... Should it happen to be that λ>1, things are even worse for Piketty. That is the scenario in which accumulation leads to the euthanasia of the rentier. As wealth accumulates–as n + g + ω falls–the wealthholder share of income falls as well. Piketty needs 1>λ for his arguments to be relevant, and 1>λ by a substantial margin for his arguments to be interesting. To further increase the size of the rock that Piketty-as-Sisyphus must roll uphill... focus on the level of real wages.... The things that Piketty says raise inequality–low n, g, and ω–are also the very things that raise real wages. The coming of the plutocrats and a very high societal wealth-to-annual-income ratio is then an unmitigated boon to the working class. If we are to get any form of immiserization argument out of Piketty, we need to break λ=1 and push it far lower.
How to break the neoclassical presumption that λ=1?
Piketty does not seem to see this as a significant difficulty. He is, after all, working primarily off of the history of France–and in large part off of the history of the late Belle Époque French Third Republic. His reference case is thus a universal (male) suffrage democracy with a strong egalitarian, anti-aristocratic, and anti-clerical ethos. Third Republic France had gone through the demographic transition: n was low. Third Republic France did not yet have the industrial research lab: g was relatively low too. Peace and good order and the absence of a culture of either extraordinary conspicuous consumption or philanthropic liturgies among the rising bourgeoisie kept ω low. And the memory of the suppression of the Paris Commune meant that the police could be relied on to keep ρ high on the shop floor.
Piketty thus assumes almost as a matter of course that the wealthier are the wealthy, the more they successfully manage the politics of the political system, even one that is in constitutional-legal terms radically egalitarian and democratic, in order to enhance the bargaining power of wealthholders. The way Piketty sees it, neoclassical economists claim that theory tells them that increasing capital-output ratios must exert strong downward pressure on the rate of profit, but experience tells us that it does not. The neoclassical assumption that λ=1 was adopted to make sense of a world in which the wealthholder share of income did not move. But that is not the world we live in....
Moreover, there is another way to break the neoclassical presumption that λ=1. Humans used to have five ways of creating economic value: through backs, through fingers, through routine control, through smiles, and through creative insight:
- Strong backs–usually those bathed in the steroid testosterone–could do the heavy lifting.
- Nimble fingers could do the fine manipulating.
- Cybernetic control loops could keep the lifting and manipulating on their proper tracks.
- Smiles–in fact, an entire universe of human social interactions–could keep us as a group all pulling in roughly the same direction, playing positive-sum rather than negative-sum economic games, and could also provide the personal services from which we derive so much of our human well-being.
- Genuine creative insight could think up new ways of doing things and new things to do that would be useful: luxurious or convenient, and over the course of time could transform conveniences into necessities, luxuries into conveniences, and invent yet new dimensions of luxury.
The coal, steam, and metal technologies of the First Industrial Revolution devalued the strong backs. The second and third generations of the assembly lines of the Second Industrial Revolution devalued the nimble fingers. But that was okay because every machine and every process still needed a cybernetic controller. And no alternative cybernetic controller could fit in a shoebox and run on 50 W of power. Human brains remain a unique resource, one strongly complementary with capital. With labor a complement to capital the rate of profit could not but fall with an increasing wealth-to-annual-income ratio to the extent that increasing wealth took the form of increasing numbers and sophistication of machines and processes. But now rapidly-exploding information and communications technologies are severely reducing the need for human brains as blue-collar or white-collar cybernetic controllers of machines, processes, and accounting and distribution systems. Rather than just substituting for backs and fingers and leaving brains as complements to capital, now increasing capital substitutes for brains as well. What will be left are smiles–services that are inherently and necessarily personal, “face time”–and genuine creative insight. That is the world we are moving into. And is that world still a world in which labor and capital are complements?
Big questions, all. Unresolved questions, all.
But if this neoclassical presumption that λ=1 is true, Piketty’s argument largely falls apart. And if this neoclassical presumption that λ=1 is not broken in the minds of economists, Piketty’s intellectual influence will be small.
In the framework in which Matt using, the fall in the wealth-to-annual-net-income ratio from 700% in the late Belle Époque Era to 300% in the post-World War II Social Democratic Era ought to hav greatly increased the salience of capital and its ownership in income. As best as I can quickly calculate on the back of my envelope https://www.icloud.com/iw/#numbers/BAJSVe-N4G7pC76gi-SBAzaePdiPnRQH8ICF/20140613_Piketty-Rognlie_Scratch.numbers, if we calibrate the Belle Époque to Rognlie's model, the model sees income from capital back then as roughly 18% of net total income--less than half of its actual value--and sees a sharp rise in the capital share of net income to 25% in the post-WWII Social Democratic Era. That did not happen. Something else is going on that Matt is not modeling.