provided by Research Papers in Economics
Learning and Endogenous Business Cycles in a Standard
Growth Model 1
Laurent Cellarier2
Department of Economics, University of Guelph, Guelph, Ontario, Canada, N1G 2W1
November 2004
Cyclical or chaotic competitive equilibria that do not exist under perfect foresight are shown to occur in a
decentralized growth model under constant gain adaptive learning. This paper considers an economy populated by
boundedly rational households making one-period ahead constant gain adaptive input price forecasts, and using
simple expectation rules to predict long-run physical capital holdings and consumption. Under these hypotheses,
lifetime decisions are derived as time unfolds, and analytical solutions to the representative household’s problem
exist for a standard class of preferences. Under various characteristics of the model’s functional forms, competitive
equilibrium trajectories under learning may exhibit opposite local stability properties depending whether the
underlying information set accommodates all contemporary data. Calibrated to the U.S. economy, the model
with boundedly rational households may exhibit endogenous business cycles around the permanent regime which
is a saddle point under perfect foresight.
Journal of Economic Literature Classification Numbers: C61, D83, D84, D91, E13, E32.
Keywords: bounded rationality, constant gain adaptive learning, endogenous business cycles.
1 Introduction
Decentralized Neoclassical growth models rely on the assumptions that all economic agents have complete
as well as perfect knowledge of their lifetime environment, and are endowed with unlimited computing
skills. As results, solutions to the households’ intertemporal planning problems in these models are
always carried out and derived once and for all at the beginning of their lifetime. If the planning
horizon faced be these agents is long or infinite, then computing their lifetime decisions and analyzing the
resulting competitive equilibrium trajectories of the economy are extremely complex tasks. In standard
growth models, analytical solutions to the households’ planning problems cannot be derived for general
specifications of preferences, and log-linearizing the optimality conditions around a permanent regime
as in King, Plosser, and Rebelo (1988), has become a frequently used technique to approximate the
competitive equilibrium trajectories.
The equilibrium dynamics of a perfectly competitive economy does not only depend on individuals’
preferences, technologic and demographic factors, but also relies on how forward-looking agents form
their expectations. Since any decisions made by firms and households are based on price and quantity
forecasts, characteristics of their expectation functions and information sets have a significant influence
on the actual path of the economy. In practice, economic agents derive their forecasts on the basis of their
knowledge about the functioning of the economy, and observations of the available data on prices and
quantities. Since knowledge is both incomplete and imperfect at the individual level, expectations are in
reality not always fulfilled and are frequently revised as new information becomes available. As results,
lifetime plans are not always carried out and derived all at once, but instead are set and revised period after
period as time unfolds. This observation is also consistent with the fact that agents’ limited computing
abilities naturally prevent them from solving highly complex problems when making intertemporal plans.
This paper presents a decentralized production economy populated by identical and infinitely lived
boundedly rational households. At any given time period, each of them derives both current and future
1 I thank Richard H. Day for stimulating discussions and helpful comments on the preliminary version of this paper.
2 Tel.: +1-519-824-4120 Ext. 52180, Fax: +1-519-763-8497
E-mail address: lcellari@ uoguelph.ca