Learnability of Heterogeneous Misspecification Equilibrium

This paper investigates the learnability of the equilibrium under adaptive learning with heterogeneous and misspecified models. Agents have imperfect and mutually different information sets of economic variables, so they form heterogeneous expectations under learning rules that are differently underparameterized. Under heterogeneous learning, the economy converges to a type of restricted perceptions equilibrium, which here is called a Heterogeneous Misspecification Equilibrium (HME). The paper finds that the HME is more learnable than the equilibrium under homogeneous and correctly specified learning rules that corresponds to a rational expectations equilibrium (REE); in other words, the stability conditions of the HME are less stringent than those of the REE. In a basic NK model with a Taylor-type monetary policy rule, for example, the central bank is allowed to choose a wider range of values of policy parameters to ensure the learnability of the HME than that permitted to ensure the learnability of the REE, that is, the Taylor principle. In addition, if the correlation between demand and supply shocks is low, the stability conditions of the HME become further less stringent so that the central bank might not have to address the learnability of the equilibrium.