Dynamic Sparse Restricted Perceptions Equilibria

This paper studies convergence properties, including local and global strong E-stability, of the rational expectations equilibrium under non-smooth learning dynamics. In a simple New Keynesian model, we consider two types of informational constraints operating jointly - adaptive learning and sparse rationality. For different initial beliefs, we study if the convergence to the minimum state variable rational expectations equilibrium (MSV REE) occurs over time for positive costs of attention. We find that for any initial beliefs the agents’ forecasting rule converges either to the MSV REE equilibrium, or, for large attention costs, to a rule that disregards all variables but the constant. Stricter monetary policy slightly favors the constant only rule. Mis-specified forecasting rule that uses variable not present in the MSV REE does not survive this learning algorithm. Theory of non-smooth differential equations is applied to study the dynamics of our learning algorithm.