We propose an approach to solving and analyzing linear rational expectations models with general information frictions. Our approach is built upon policy function iterations in the frequency domain. We develop the theoretical framework of this approach using rational approximation, analytic continuation, and discrete Fourier transform. Conditional expectations, which are difficult to evaluate in the time domain, can be calculated efficiently in the frequency domain. We provide the numerical implementation accompanied by a flexible object-oriented toolbox. We demonstrate the efficiency and accuracy of our method by studying four models in macroeconomics and finance that feature asymmetric information sets, endogenous signals, and higher-order expectations.
This article is concerned with frequency-domain analysis of dynamic linear models under the hypothesis of rational expectations. We develop a unified framework for conveniently solving and estimating these models. Unlike existing strategies, our starting point is to obtain the model solution entirely in the frequency domain. This solution method is applicable to a wide class of models and allows for straightforward construction of the spectral density for performing likelihood-based inference. To cope with potential model uncertainty, we also generalize the well-known spectral decomposition of the Gaussian likelihood function to a composite version implied by several competing models. Taken together, these techniques yield fresh insights into the model's theoretical and empirical implications beyond what conventional time-domain approaches can offer. We illustrate the proposed framework using a prototypical new Keynesian model with fiscal details and two distinct monetary-fiscal policy regimes. The model is simple enough to deliver an analytical solution that makes the policy effects transparent under each regime, yet still able to shed light on the empirical interactions between U.S. monetary and fiscal policies along different frequencies.
This article illustrates a widely applicable frequency-domain methodology to solving multivariate linear rational expectations models. As an example, we solve a prototypical new Keynesian model under the assumption that primary surpluses evolve independently of government liabilities, a regime in which the fiscal theory of the price level is valid. The resulting analytical solution is useful in characterizing the cross-equation restrictions and illustrating the complex interaction between the fiscal theory and price rigidity. We also highlight some useful by-products of such method which are not easily obtainable for more sophisticated models using time-domain methods.
An analytic function method is applied to illustrate Geweke's (2010) three econometric interpretations for a generic rational expectations (RE) model. This delivers an explicit characterization of the model's cross-equation restrictions imposed by the RE hypothesis under each interpretation. It is shown that the degree of identification on the deep parameters is positively related to the strength of the underlying econometric interpretation, and observationally equivalent models may arise once the cross-equation restrictions are interpreted in a minimal sense. This offers important insights into the econometric modeling and evaluation of dynamic economic models.
We generalize the linear rational expectations solution method of Whiteman (1983) to the multivariate case. This facilitates the use of a generic exogenous driving process that must only satisfy covariance stationarity. Multivariate cross-equation restrictions linking the Wold representation of the exogenous process to the endogenous variables of the rational expectations model are obtained. We argue that this approach offers important insights into rational expectations models. We give two examples in the paper—an asset pricing model with incomplete information and a monetary model with observationally equivalent monetary-fiscal policy interactions. We relate our solution methodology to other popular approaches to solving multivariate linear rational expectations models, and provide user-friendly code that executes our approach.