Behavioral Learning Equilibria

2014

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...

Macroeconomic Dynamics, 2020

Drawing on a considerable empirical literature that reveals persistent and endogenously time-varying heterogeneity in inflation expectations, this paper embeds two inflation forecasting strategiesone based on costly ex ante full rationality or perfect foresight, and the second based on costless ex ante bounded rationality or extrapolative trend-followingin a dynamic macroeconomic model. Drawing also on the significant empirical evidence that inflation forecast errors may have to exceed some threshold before agents abandon their previously selected inflation forecasting strategy, we describe agents as switching between inflation forecasting strategies according to evolutionarily satisficing learning dynamics. We find that convergence to a long-run equilibrium consistent with growth, unemployment and inflation at their natural levels may be achieved even when heterogeneity in inflation expectations (with predominance of the extrapolative trend-following foresight strategy) is an attractor of an evolutionarily satisficing learning dynamic perturbed by mutant agents. Therefore, in keeping with robust empirical evidence, heterogeneity in strategies to form inflation expectations (with prevalence of boundedly rational expectations) can be a stable long-run equilibrium.

SSRN Electronic Journal

We introduce the concept of behavioral learning equilibrium (BLE) into a high dimensional linear framework and apply it to the standard New Keynesian model. For each endogenous variable, boundedly rational agents use a simple, but optimal AR(1) forecasting rule with parameters consistent with the observed sample mean and autocorrelation of past data. The main contributions of our paper are fourfold: (1) we derive existence and stability conditions of BLE in a general linear framework, (2) we provide a general method for Bayesian likelihood estimation of BLE, (3) we estimate the baseline NK model based on U.S. data and show that the relative model fit is better under BLE than REE, (4) we analyze optimal monetary policy under BLE and show that it differs from REE. In particular, we find that the transmission channel of monetary policy is stronger under BLE at the estimated parameter values.

2013

Appendix on the New Keynesian Philips Curve with Infinite Horizon Learning (not for publication) Cars Hommes, Mei Zhu ∗ a CeNDEF, School of Economics, University of Amsterdam Roetersstraat 11, 1018 WB Amsterdam, Netherlands b Institute for Advanced Research, Shanghai University of Finance and Economics, and the Key Laboratory of Mathematical Economics(SUFE), Ministry of Education, Shanghai 200433, China

SSRN Electronic Journal, 2000

Rational expectations assumes perfect, model consistency between beliefs and market realizations. Here we discuss behaviorally rational expectations, characterized by an observable, parsimonious and intuitive form of consistency between beliefs and realizations. We discuss three case-studies. Firstly, a New Keynesian macro model with a representative agent learning an optimal, but misspecified, AR(1) rule to forecast inflation consistent with observed sample mean and first-order autocorrelations. Secondly, an asset pricing model with heterogeneous expectations and agents switching between a mean-reverting fundamental rule and a trend-following rule, based upon their past performance. The third example concerns learning-to-forecast laboratory experiments, where under positive feedback individuals coordinate expectations on non-rational, almost self-fulfilling equilibria with persistent price fluctuations very different from rational equilibria.

2020

Rational expectations assumes perfect, model consistency between beliefs and market realizations. Here we discuss behaviorally rational expectations, characterized by an observable, parsimonious and intuitive form of consistency between beliefs and realizations. We discuss three case-studies. Firstly, a New Keynesian macro model with a representative agent learning an optimal, but misspecified, AR(1) rule to forecast inflation consistent with observed sample mean and first-order autocorrelations. Secondly, an asset pricing model with heterogeneous expectations and agents switching between a mean-reverting fundamental rule and a trend-following rule, based upon their past performance. The third example concerns learning-to-forecast laboratory experiments, where under positive feedback individuals coordinate expectations on non-rational, almost self-fulfilling equilibria with persistent price fluctuations very different from rational equilibria. JEL Classification: D84, D83, E32, C92

Handbook of Monetary Economics, 2010

This chapter investigates the implications of adaptive learning in the private sector's formation of inflation expectations for the conduct of monetary policy. We analyze the determinants of optimal monetary policy in the standard New Keynesian model, when the central bank minimizes an explicit loss function and has full information about the structure of the economy, including the precise mechanism generating private sector's expectations. The focus on optimal policy allows us to investigate how and to what extent a change in the assumption of how agents form their inflation expectations affects the principles of optimal monetary policy. It also provides a benchmark to evaluate simple policy rules. We find that departures from rational expectations increase the potential for instability in the economy, thereby strengthening the importance of managing (anchoring) inflation expectations. We also find that the simple commitment rule under rational expectations is robust when expectations are formed in line with adaptive learning.

Journal of Economic Behavior & Organization, 2015

In the learning-to-forecast laboratory experiments in Hommes et al. (2005), three different types of aggregate asset price behavior have been observed: monotonic convergence to the stable fundamental steady state, dampened price oscillations and permanent price oscillations. We present a simple behavioral 2-type heuristics switching model explaining individual as well as aggregate behavior in the experiment. Based on relative performance, agents switch between a simple trend-following and an anchor and adjustment heuristic that differ in how much weight is given to the long run average price level. The nonlinear switching model exhibits path dependence through coexistence of a locally stable fundamental steady state and a stable (quasi-)periodic orbit, created via a so-called Chenciner bifurcation. Depending on initial states, agents coordinate individual expectations either on a stable fundamental steady state path or on almost self-fulfilling persistent price fluctuations around the fundamental steady state.

Journal of Economic Dynamics and Control, 2008

In this paper we study the properties of an asset pricing model where boundedly rational agents respond to incoming news about economic fundamentals such as future dividends. Our aim is to characterize the resulting fluctuations of the market price around the timevarying underlying fundamental value. The starting point is an asset market in which agents can choose among two different degrees of information regarding future dividends. At the same time agents also try to learn the growth rate of the dividend generating process. Their interaction leads to prices that deviate perpetually from the fundamental value in the short run but stay close to it in the long run. In particular, prices exhibit time-varying nonlinear mean reversion, with parameters determined by the learning process.

European Economic Review, 2014

Earlier research on optimal monetary policy under learning uses optimality conditions derived under rational expectations. In this paper instead, we derive optimal monetary policy when the central bank knows the algorithm followed by agents to form their expectations and makes active use of the learning behavior. There is a well known intratemporal tradeoff between inflation and output gap stabilization. We show there is also an intertemporal tradeoff generated by the central banks possibility to influence future expectations. The optimal interest rate rule reacts more aggressively to out-of-equilibrium inflation expectations than what would be optimal under rational expectations, as the central bank exploits its possibility to "drive" future expectations closer to equilibrium. Moreover, if beliefs are updated according to recursive least squares, the optimal policy is time-varying. * We are grateful to Seppo Honkapohja, Albert Marcet and Ramon Marimon for very helpful comments and suggestions. All the remaining errors are our own.