A “quantized” approach to rational inattention

In this paper, I propose a model of rational inattention where the choice variable is a deterministic function of the exogenous variables, and still only a finite amount of information is being used. This holds provided the choice variable is discrete rather than continuous; that is, the mapping from the realization of the exogenous variables to the endogenous ones is piece-wise constant. Thus, limited information is now a source of lumpiness in behavior, rather than a source of noise. The approach is applied to a simple static model of price-setting where individual price setters face aggregate monetary shocks and idiosyncratic productivity shocks. The effect of aggregate money shocks on output and prices is studied. It is shown that as the variance of idiosyncratic shocks become large, the aggregate log price level converges to a linear function of the aggregate money shock, with a coefficient which is strictly between 0 and 1. Consequently, unanticipated aggregate money shocks have real effects on output, in contrast to the sticky price model of Caplin and Spulber (1987). But these effects are smaller than in standard rational inattention models or in the Lucas (1972) misperception model.