Learning under misspecification: a behavioral explanation of excess volatility in stock prices and persistence in inflation

We propose a simple misspecification equilibrium concept and a behavioral learning process explaining 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. 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 SCEE arise and a low and a high persistence misspecification equilibrium co-exist. Learning exhibits path dependence and inflation may switch between low and high persistence regimes.