# Wealth Distribution with Random Discount Factors

Published in *Journal of Monetary Economics*, 2019

In 2017, I noticed the NBER working paper by Hubmer, Krusell, and Smith. I was a bit disappointed because although they talked about Pareto distributions (which became fashionable after the 2014 Piketty boom), they didn’t cite any of my papers even though my 2014 JET and 2015 JPE papers were relevant for their model. (In the published version Hubmer et al. (2020), they cite a few of my papers.) It’s true that I don’t belong to the quantitative macro club so folks may not read my papers, but Tony was my advisor at Yale so he can’t say he didn’t know.

So, although it seemed obvious to me, to teach quantitative macroeconomists that heterogeneous discount factors can generate Pareto-tailed wealth distributions (because the saving rate and hence the growth rate of wealth becomes heterogeneous) and how the exponents can be calculated without running any simulations, I decided to write a paper targeted for the applied audience. By this time, Brendan and I had a draft of our Econometrica paper, so I knew how to reverse-engineer a Bewley-Huggett-Aiyagari model with Markov-dependent discount factors to generate Pareto tails with an exact characterization.

I wrote this paper in a week but there was one tricky part. To characterize the optimal consumption rule using dynamic programming, I needed to show the existence of a fixed point of a certain nonlinear operator that is not necessarily a contraction. John Stachurski kindly taught me the trick so I invited him to be a coauthor, but he was busy at the time and declined. During the review process at JME, the handling associate editor, Alisdair McKay, helped me a lot in making the paper attractive to the applied audience. I owe him for suggesting writing Section 4.