Incomplete Market Dynamics and Cross-Sectional Distributions

Published in Journal of Economic Theory, 2014

In 2011, I was struggling to find a topic for my dissertation. After three years of foray into unorthodox topics, it was clear I had to work on a more mainstream topic. But I had no interest in game theory or quantitative macro, and people (of course not John) told me it would be a career suicide to do general equilibrium. So I decided to work on power laws. The mechanism I used in my third year paper predicted identical Pareto exponents for the upper and lower tails, which was counterfactual, so I needed a different mechanism. I learned reading Kotz et al. (2001) The Laplace Distribution and Generalizations that the geometric sum of IID random variables is approximately asymmetric Laplace, which is the logarithm of the double Pareto distribution, which in turn fits the data well. Thus I came up with the idea of introducing idiosyncratic investment and mortality risk in a homothetic optimal savings problem so that log wealth becomes the cumulative sum of random variables and the number of terms becomes geometric. (Nowadays this mechanism is well known because many people started working on wealth inequality after the Piketty boom took off in 2014, but in 2011 it was not well known.) Furthermore, in Theorem 15 I proved a more general limit theorem that relaxes the IID or distributional assumptions, which I think is important because it shows the robustness of the mechanism.

I submitted this paper to JET in 2012, hoping that I would get an R&R before my job market. The R&R came after. I had two good reports and another that trashed my paper, falsely claiming that “the double power law finding of the current paper is not novel”. Luckily, the editor did not send back my revised paper to the negative referee so I was able to publish it without too much trouble.

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