An analytical approach to new Keynesian models under the fiscal theory

•I present a frequency-domain method for solving linear rational expectations models.•I derive an analytical solution to new Keynesian models under the fiscal theory.•The solution makes clear the cross-equation restrictions and policy transmission mechanisms.•The method yields useful by-products which are not easily obtainable using time-domain methods.

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.