Isomorphic Dynamic Programs

TL;DR

This paper explores how dynamic programs can be related through isomorphisms, enabling transfer of properties, improved numerical methods, and insights into economic preferences.

Contribution

It introduces conjugacy methods from dynamical systems to analyze relationships between dynamic programs, revealing when optimality properties are preserved and how transformations enhance computations.

Findings

Optimality properties transmit via order isomorphisms.

Isomorphisms between preferences allow result transfer.

Transformations improve numerical accuracy significantly.

Abstract

We study relationships between dynamic programs by applying conjugacy methods from dynamical systems theory. When two dynamic programs are connected by an order isomorphism, we show that optimality properties transmit from one formulation to the other. We apply these results to Epstein--Zin preferences with time preference shocks, obtaining a sharp characterization of when optimality holds. We also show that multiplicative Kreps--Porteus preferences and risk-sensitive preferences are isomorphic, so that well-known results for the latter carry over to the former. Finally, we demonstrate how isomorphic transformations can improve the numerical accuracy of value function approximations, with gains of two orders of magnitude in a multisector real business cycle model.