This article proposes a unified framework for solving and estimating linear rational expectations models with a variety of frequency-domain techniques, some established, some new. The solution methodology is applicable to a wide class of models and leads to straightforward construction of the spectral density for performing likelihood-based inference. 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 conventional time-domain approaches can offer. We illustrate the proposed framework using a prototypical new Keynesian model with fiscal details and two determinate 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 US monetary and fiscal policies along different frequencies.
