Dynamic Sparse Adaptive Learning

This paper studies convergence properties, including local and global strong E-stability, of the rational expectations equilibrium (REE) under non-smooth learning dynamics, and the role of monetary policy in agents' expectation formation. In a New Keynesian model, we consider two types of informational constraints that operate jointly - Sparse Rationality under Adaptive Learning. We study the dynamics of the learning algorithm for the positive costs of attention, initialized from the equilibrium with mis-specified beliefs. We find that, for any initial beliefs, the agents' forecasting rule converges either to the Minimum State Variable (MSV) REE, or, for large attention costs, to a rule with anchored inflation expectations. With stricter monetary policy the convergence is faster. A mis-specified forecasting rule that uses a variable not present in the MSV REE does not survive this learning algorithm. We apply the theory of non-smooth differential equations to study the dynamics of our learning algorithm.