👍Discretizing Nonlinear, Non-Gaussian Markov Processes with Exact Conditional Moments

After working on the maximum entropy discretization method in Tanaka & Toda (2013, 2015), in 2014 I wanted to apply the method for discretizing Markov processes. Because I didn’t have sufficient programming skills or knowledge of potential applications, I asked my colleague Johannes Wieland if he knew a good graduate student to work with, and he referred me to Leland. At that time, Leland was working on the estimation of nonlinear state space models using discretization (which later became his job market paper), so our interests matched. Leland played an instrumental role for this project such as suggesting discretizing the conditional distributions, coding, and finding interesting applications. We owe Craig Burnside for suggesting using a closed-form asset pricing model to evaluate solution accuracy, and Jim Hamilton for suggesting avoiding simulations entirely.

We initially submitted this paper to Econometrica. We had two positive and two negataive reports, and one of the negative one complained about the possibility of matching higher order moments, which we pointed out in a footnote but did not implement out of laziness. I regret that maybe if we did it from the beginning, we might have been able to publish this paper at Econometrica. When we sent the paper to QE, we exercised the option to transfer Econometrica reports, and the review process was painless.

I believe the discretization method in this paper is still the best in the literature and has been applied in many papers by other researchers.