Behavioral Learning Equilibria
Social Science Research Network
We propose behavioral learning equilibria, where boundedly rational agents learn to use a simple univariate linear forecasting rule with correctly specified unconditional mean and first-order autocorrelation. In the long run, agents learn the best univariate linear forecasting rule, without fully recognizing the more complex structure of the economy. An important feature of behavioral learning equilibria is simplicity and parsimony, which makes coordination of individual expectations on such an
... ctations on such an aggregate outcome more likely. In a first application, an asset pricing model driven by AR(1) dividends, a unique behavioral learning equilibrium exists characterized by high persistence and excess volatility, and it is stable under learning. In a second application, the New Keynesian Phillips curve, multiple equilibria co-exist, learning exhibits path dependence and inflation may switch between low and high persistence regimes. Since the 1970's the Rational Expectations Hypothesis (REH), introduced in Muth (1961) and applied in macroeconomics by Lucas (1972) and others, has become the dominant paradigm in macroeconomics. An Rational Expectations Equilibrium (REE) requires that economic agents' subjective probability distributions coincide with the objective distribution that is determined, in part, by their subjective beliefs. There is a vast literature that studies the drawbacks of REE. Some of these drawbacks include the fact that REE requires an unrealistic degree of computational power and information on the part of agents. Alternatively, the adaptive learning literature (see, e.g., Honkapohja (2001, 2011) and Bullard (2006) for extensive surveys and references) replaces rational expectations with beliefs that come from an econometric forecasting model with parameters updated using observed time series. A large part of this literature involves studying under which conditions learning will converge to the rational expectations equilibrium. When the perceived law of motion (PLM) of agents is correctly specified, convergence of adaptive learning to an REE can occur. However, generally REE is not the only fixed point in self-referential systems and one should not expect learning to always converge to an REE. Whenever agents have misspecified PLMs a reasonable learning process may settle down to some sort of misspecification equilibrium. In the existing literature, different types of misspecification equilibria have been proposed: a Restricted Perceptions Equilibrium (RPE) where the forecasting model is underparameterized (Sargent, 1991; Evans and Honkapohja, 2001); a self-confirming equilibrium where beliefs are only correctly specified on the equilibrium path (Sargent, 1999); and a Stochastic Consistent Expectations Equilibrium (SCEE) (Hommes and Sorger, 1998; Hommes et al., 2013) 1 . A SCEE is a very natural misspecification equilibrium, where agents in the economy do not know the actual law of motion or even recognize all of the explanatory variables, but prefer a parsimonious forecasting model. The economy is too complex to fully understand and therefore, as a first order approximation, agents forecast the state of the economy by simple autoregressive models. In the simplest model applying this idea, agents run an univariate AR(1) regression to generate out-of-sample forecasts of the state of the economy. The idea was first introduced as Consistent Expectations Equilibrium (CEE) in Hommes and Sorger (1998) , following Grandmont's (1998) idea of a self-fulfilling mistake, 1 Branch (2006) provides a stimulating survey discussing the connection between these types of misspecification equilibria.