Sparse restricted perceptions equilibrium

We study model selection under bounded rationality and the impact of monetary policy on the equilibrium choices of forecasting models. We use the concept of sparse rationality (recently developed by Gabaix, 2014 and 2020), where paying attention to all possible variables is costly and agents can choose to under-emphasize particular variables, and may even fully exclude some of them. Our main question is whether an initially mis-specified equilibrium (the restricted perceptions equilibrium, or RPE) is compatible with the equilibrium choice of sparse weights describing the allocation of attention to different variables by the agents inhabiting this RPE. In a simple New Keynesian model, we find that the agents adhere to their initial mis-specified AR(1) forecasting model choice when monetary policy is less aggressive or inflation is more persistent. We also identify a region in the parameter space in which the agents find it advantageous to pay attention to no variables at all.