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Macroeconomic Dynamics, 18, 2014, 959984. Printed in the United States of America. doi:10.1017/S1365100512000703
ATANAS CHRISTEV
Heriot-Watt University andIZA
SERGEY SLOBODYAN
CERGE-EI
If private sector agents update their beliefs with a learning algorithm other than recursive least squares, expectational stability or learnability of rational expectations equilibria (REE) is not guaranteed. Monetary policy under commitment, with a determinate and E-stable REE, may not imply robust learning stability of such equilibria if the RLS speed of convergence is slow. In this paper, we propose a renement of E-stability conditions that allows us to select equilibria more robust to specication of the learning algorithm within the RLS/SG/GSG class. E-stable equilibria characterized by faster speed of convergence under RLS learning are learnable with SG or generalized SG algorithms as well.
Keywords: Adaptive Learning, Expectational Stability, Stochastic Gradient, Speed of
Convergence
1. INTRODUCTION
Adaptive learning and expectational stability (E-stability) arise naturally in self-referential macroeconomic models. The literature on adaptive learning assumes that economic agents act as econometricians who run recursive regressions using historical data to inform their decisions. The asymptotic outcome of adaptive learning algorithms may be consistent with rational expectations. Evans and Honkapohja (2001) provide the methodology and derive the conditions under which recursive learning dynamics converges to rational expectations equilibria (REE). If economic agents use recursive least squares (RLS) learning to update their expectations of the future (or learn adaptively), then only E-stable REE can be the asymptotic outcomes of a realtime learning process. Equilibria, stable under a particular form of adaptive learning, are also called learnable.1 Hence, E-stability is a necessary condition for RLS learnability.
We are grateful to Chrissy Giannitsarou, John Duffy and George Evans for the encouragement to pursue this project. We are also indebted to two anonymous referees and an Associate Editor of the Journal for helpful suggestions on improving the paper. Financial support from the Royal Society of Edinburgh is gratefully acknowledged. All remaining errors are our own. Address correspondence to: Atanas Christev, Department of Economics, Mary Burton Building, Room 1.4, Heriot-Watt University, Riccarton, Edinburgh EH14 4AS, UK; e-mail: [email protected].
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2013 Cambridge University Press 1365-1005/13 959
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LEARNABILITY OF ESTABLE EQUILIBRIA
960 ATANAS CHRISTEV AND SERGEY SLOBODYAN
Evans and Honkapohja (2001) also draw attention to the lack of general results on stability...