Forecast combination, non-linear dynamics, and the macroeconomy

Abstract

This paper introduces the concept of a Forecast Combination Equilibrium to model boundedly rational agents who combine a menu of different forecasts in a way that mimics the behavior of actual forecasters. The equilibrium concept is consistent with rational expectations under certain conditions, while also permitting multiple, distinct, self-fulfilling equilibria, many of which are stable under least-squares learning. The equilibrium concept is applied to a Lucas-type monetary model and to a Fisherian monetary model with a Taylor rule. The existence of multiple equilibria is shown to depend on the aggressiveness of monetary policy in both models. In the latter, a more aggressive response to inflation is required in the Taylor rule than is typically found in this class of model to ensure a unique and learnable equilibrium. Real-time learning simulations with a constant gain illustrate some appealing properties of this approach including time-varying volatility and sharp movements in inflation, similar to actual data, while assuming only i.i.d. random shocks.