My work covers dynamic optimization with a focus on showing existence and uniqueness of equilibria under nonstandard discounting conditions.
My job market paper extends classical dynamic programming theory to the case of state dependent discounting, a specification widely adopted in macroeconomics and finance. The other two papers study negative discounting and its applications in production chain models.
Dynamic Programming with State-Dependent Discounting with John Stachurski
Job Market Paper
Journal of Economic Theory, forthcoming
This paper extends the core results of discrete time infinite horizon dynamic programming to the case of state-dependent discounting. We obtain a condition on the discount factor process under which all of the standard optimality results can be recovered. We also show that the condition cannot be significantly weakened. Our framework is general enough to handle complications such as recursive preferences and unbounded rewards. Economic and financial applications are discussed.
Coase Meets Bellman: Dynamic Programming for Production Networks with Tomoo Kikuchi, Kazuo Nishimura, and John Stachurski
Updated: Dec 04, 2020
R&R at Journal of Economic Theory
We show that, for a range of models related to production networks, competitive equilibria can be recovered as solutions to dynamic programs. Although these programs fail to be contractive, we show that they are fully tractable when matched with the right tools of analysis. These tools add analytical power and open new avenues for computation. As an illustration, we cover applications related to Coase’s theory of the firm, including equilibria in linear production chains with transaction costs and other kinds of frictions, as well as equilibria in production networks with multiple partners. We show how the same techniques also extend to other equilibrium and decision problems, such as the distribution of management layers within firms and the spatial distribution of cities.
Equilibrium in Production Chains with Multiple Upstream Partners with Meng Yu
Journal of Mathematical Economics 83 (2019): 1-10
In this paper, we extend and improve the production chain model introduced by Kikuchi et al. (2018). Utilizing the theory of monotone concave operators, we prove the existence, uniqueness, and global stability of equilibrium price, hence improving their results on production networks with multiple upstream partners. We propose an algorithm for computing the equilibrium price function that is more than ten times faster than successive evaluations of the operator. The model is then generalized to a stochastic setting that offers richer implications for the distribution of firms in a production network.
The Substitution and Pervasiveness Effects of ICT on China’s Economic Growth (in Chinese) with Yuezhou Cai
经济研究 / Economic Research Journal 12 (2015): 100-114