Analytic Policy Function Iteration

We propose a novel approach of solving and analyzing linear rational expectations models with endogenous information frictions. Our approach is build upon policy function iterations in the frequency domain. We develop the theoretical framework of this approach using rational approximations, analytic continuation, and discrete Fourier transform. We provide the numerical implementations accompanied with a computational toolbox. We demonstrate the efficiency and accuracy of our method by studying four models in macroeconomics and finance that feature ``learning from price'', higher-order expectations, and general equilibrium rational inattention