Dissertations

Dissertation Committee:
Sergey Slobodyan (chair)
Petr Zemčík
Andreas Ortmann
Radim Boháček

Abstract:

My dissertation makes a contribution to the field of adaptive learning in macroeconomic models. This contribution is presented in the form of four research papers related to the question of behavior around the point of equilibrium of the models under adaptive learning of agents. These papers constitute different chapters of my thesis.

The first chapter, “Escape Dynamics: A Continuous-Time Approximation” (joint with Anna Bogomolova and Sergey Slobodyan) extends a continuous-time approach to the analysis of escape dynamics in economic models with adaptive learning with constant gain. This approach is based on applying results of the continuous-time version of the large deviations theory to the diffusion approximation of the original discrete-time dynamics under learning. We characterize escape dynamics by analytically deriving the most probable escape point and mean escape time. The continuous-time approach is tested on the Phelps problem of a government controlling inflation while adaptively learning the approximate Phillips curve, studied previously by Sargent [61] and Cho, Williams, and Sargent [17].

The second chapter is presented in the paper “Stochastic Gradient versus Recursive Least Squares Learning” (joint with Anna Bogomolova and Sergey Slobodyan), where we perform an in-depth investigation of the relative merits of two adaptive learning algorithms with constant gain, Recursive Least Squares (RLS) and Stochastic Gradient (SG), using the Phelps model of monetary policy studied in the first paper as a testing ground.

The third chapter, “Economic Dynamics Under Heterogeneous Learning: Necessary and Sufficient Conditions for Stability” takes further the issue of different learning of agents, such as RLS and SG learning, in particular the question of stability of equilibrium under the situation when agents differ in the form of adaptive learning algorithms used, in speed of adaptation of their beliefs about the economy to new information, and in initial perceptions.

The fourth chapter of my dissertation is presented by the paper “Optimal Monetary Policy Rules: The Problem of Stability Under Heterogeneous Learning” (joint with Anna Bogomolova). In this paper we extend the analysis of optimal monetary policy rules in terms of stability of the economy, started by Evans and Honkapohja [31], to the case of heterogeneous learning.

Full Text: “Learning and Macroeconomic Dynamics” by Dmitri Kolyuzhnov