Thomas Piketty, depreciation and the elasticity of substitution

When “Capital in the 21st Century” was published in English earlier this year, Thomas Piketty’s book was met with rapt attention and constant conversation. The book was lauded but also faced criticism, particularly from other economists who wanted to fit Piketty’s work into the models they knew well (Equitable Growth’s Marshall Steinbaum replied to many of those criticism here.) Now, a new working paper by the National Bureau of Economic Research shows how one of the more effective critiques of the book might not be as powerful as once thought.

A particularly technical and effective critique of Piketty is from Matt Rognlie, a graduate student in economics at the Massachusetts Institute of Technology. Rognlie points out that for capital returns to be consistently higher than the overall growth of the economy—or “r > g” as framed by Piketty—an economy needs to be able to easily substitute capital such as machinery or robots for labor. In the terminology of economics this is called the elasticity of substitution between capital and labor, which needs to be greater than 1 for r to be consistently higher than g. Rognlie argues that most studies looking at this particular elasticity find that it is below 1, meaning a drop in economic growth would result in a larger drop in the rate of return and then g being larger than r. In turn, this means capital won’t earn an increasing share of income and the dynamics laid out by Piketty won’t arise.

Here are the technical details for Rognlie’s critique. He argues that Piketty doesn’t account for depreciation, or the wearing down of capital and machinery over time. Because firms need to replace this old capital, net investment in capital is lower than gross investment. This in turn means the net elasticity of substitution between capital and labor is necessarily lower than the gross elasticity. Rognlie argues that because Piketty cares about net measures, the elasticity of substitution between net capital and labor needs to be greater than 1. But if Piketty’s story depends upon an assumption of a net elasticity that is higher than 1, then that is far too high given what Rognlie finds in the empirical evidence.

Enter the new paper by economists Loukas Karabarbounis and Brent Neiman, both of the University of Chicago. Karabarbounis and Neiman previously documented the global decline in the share of income going to labor. The pair of scholars find that technology, through declines in the prices of investment goods, is responsible for the decline in the labor share.

Their new paper investigates how depreciation affects the measurement of labor share and the elasticity between capital and labor. Using their data set of labor shares income and a model, Karabarnounis and Neiman show that the gross labor share and the net labor share move in the same direction when the shift is caused by a technological shock—as has been the case, they argue, in recent decades. More importantly for this conversation, they point out that the gross and net elasticities are on the same side of 1 if that shock is technological. In the case of a declining labor share, this means they would both be above 1.

This means Rognlie’s point about these two elasticities being lower than 1 doesn’t hold up if capital is gaining due to a new technology that makes capital cheaper. To be clear, Rognlie is aware that this could happen, but Karabarbounis and Neiman’s data shows that it is happening. And as Karabournis and Neiman find a gross elasticity greater than 1, the net elasticity is greater than 1 as well.

In short, this new paper gives credence to one of the key dynamics in Piketty’s “Capital in the 21st Century”—that the returns on capital can be higher than growth in the economy, or r > g. But this isn’t to say the case is closed. Far from it. The results as detailed by Karabournis and Neiman don’t hold up if the share of labor has declined for reasons other than technological change, such as globalization or institutional changes.

But for the second time in two weeks, a new empirical paper shows that Piketty’s work has strong empirical grounding.

October 20, 2014


Nick Bunker


Economic Inequality

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