Behavioral Learning Equilibria

Abstract

We propose behavioral learning equilibria as a plausible explanation of coordination of individual expectations and aggregate phenomena such as excess volatility in stock prices and high persistence in inflation. Boundedly rational agents use a simple univariate linear forecasting rule and in equilibrium correctly forecast the unconditional sample mean and first-order sample autocorrelation. In the long run, agents thus learn the best univariate linear forecasting rule, without fully recognizing the structure of the economy. The simplicity of our behavioral learning equilibria makes coordination of individual expectations on such an aggregate outcome more likely. In a first application, an asset pricing model with AR(1) dividends, a unique stochastic consistent expectations equilibrium (SCEE) exists characterized by high persistence and excess volatility, and it is globally stable under learning. In a second application, the New Keynesian Phillips curve, multiple equilibria co-exist and learning exhibits path dependence and inflation may switch between low and high persistence regimes.

A reply to Rosser and Kirman

“…This leads to an equilibrium concept different from RE, with a representative agent using a simple one-dimensional linear heuristic in a higher dimensional linear world that correctly forecasts the first two moments of the distribution. Hommes and Zhu (2014) show that these equilibria typically exhibit much more persistence and excess volatility than RE, consistent with empirical data. Similar to this research strategy, one could allow for heterogeneity, e.g., as in the Brock-Hommes framework, with a class of simple (linear) strategies with endogenous (nonlinear) switching based upon relative performance.…”

“…A promising general strategy to tackle the ``wilderness of bounded rationality'' may be to consider models with simple (linear) heuristics. For example, in a recent paper Hommes and Zhu (2014) follow this route and propose behavioural learning equilibria, where a homogeneous representative agent uses the best univariate linear forecasting rule in a higher dimensional linear world. The simple one-dimensional forecasting rule is mis-specified, but the best rule within this simple class is obtained by pinning down the two parameters by observable quantities: the sample average and the first-order sample autocorrelation of the rule must coincide with empirical observations.…”

House Prices, Expectations, and Time-Varying Fundamentals

“…Examples along these lines include Barsky and Delong (1993), Timmerman (1996), Barberis, Shleifer, and Vishney (1998), Lansing (2006Lansing ( , 2010, Adam, Marcet, and Nicolini (2008), Branch andEvans (2010), Fuster, et al (2012), and Hommes and Zhu (2014), among others.…”

Behaviorally Rational Expectations and Almost Self-Fulfilling Equilibria

“…The first is in macroeconomics, a New Keynesian Philips curve (NKPC) with a representative agent learning the simplest, but misspecified, univariate AR(1) rule to forecast future inflation in an economy that is too complex to fully understand (Hommes and Zhu, 2013). The parameters of the AR(1) rule are pinned down by simple and intuitive consistency requirements: the mean and the first-order autocorrelation of the AR(1) forecasting rule coincide with the realizations.…”