This paper develops a dynamic stochastic general equilibrium model where firms are imperfectly informed. We estimate the model through likelihood-based methods and find that it can explain the highly persistent real effects of monetary disturbances that are documented by a benchmark VAR. The model of imperfect information nests a model of rational inattention where firms optimally choose the variances of signal noise, subject to an information-processing constraint. We present an econometric procedure to evaluate the predictions of this rational inattention model. Implementing this procedure delivers insights on how to improve the fit of rational inattention models.