In a previous blog post, I discussed the data issues in Piketty’s work. While some of the points made regarding the accuracy of the data might be valid, it appears that there are more fundamental issues we should be focusing on.
Two very good points are made by Matt Rognlie on Marginal Revolution. The first one relates to the elasticity of substitution between labor and capital. Most of the literature works with a gross production function, however Piketty, because of his focus on net income, works with a net production functions. But this leads to corresponding elasticities that are half of those in the gross case. On top of that, Piketty argues, probably in a wrong way, that this elasticity should be higher than one. But how important are these? They are actually essential to the main point made by Piketty, since this elasticity of substitution leads to a relationship between K/Y, capital-output ratio, and the user cost of capital, r+delta. Thus, Piketty needs much higher values for this ealsticity in order to get the magnitude of change in K/Y as he suggests.
A second key point relates to the fundamental point of Piketty’s Capital, namely that as the total capital income rK/Y increases, r-g, the difference between the return on capital and growth, will grow too. And this is related to the so-called second law of capitalism, according to which, in the long run, K/Y=s/g, where s is the savings rate. Here, we can already see how fundamental is the issue of setting the elasticity of substitution high: only if this elasticity is higher than 1, can we have a large increase in rK/Y, holding the rate of savings constant. Furthermore, for small but realistic falls in r, these relations cannot generate an adequate increase in K/Y as predicted by Piketty, unless the elasticity of substitution becomes unrealistically high.
Although a bit more technical, the arguments by Matt Rognlie point to the very key issues in Piketty’s Capital that have been largely ignored. While Piketty has responded in detail to the data issues, it would be interesting to see an equally extensive reply to these issues too.