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A FREQUENCY-DOMAIN APPROACH TO DYNAMIC MACROECONOMIC MODELS

Published online by Cambridge University Press:  10 September 2019

Fei Tan
Fei Tan*
Affiliation:
Saint Louis University Zhejiang University of Finance and Economics
*
Address correspondence to: Fei Tan, Department of Economics, Chaifetz School of Business, Saint Louis University, 3674 Lindell Boulevard, St. Louis, MO 63108-3397, USA. e-mail: tanf@slu.edu. Phone: +1(314)977-2123.
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Abstract

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.

Keywords

Solution MethodBayesian InferenceSpectral DensityMonetary and Fiscal Policy
Type
Articles
Information
Macroeconomic Dynamics , Volume 25 , Issue 6 , September 2021 , pp. 1381 - 1411
Copyright
© Cambridge University Press 2019

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Footnotes

An earlier draft of this paper was circulated under the title “Testing the fiscal theory in the frequency domain.” I thank Majid Al-Sadoon, Yoosoon Chang, Junjie Guo, Eric Leeper, Laura Liu, Joon Park, David Rapach, Apostolos Serletis (the coeditor), Todd Walker, two anonymous referees, and participants of the 2015 Midwest Econometrics Group Meeting at St. Louis Fed for helpful comments. Financial support from the Chaifetz School of Business summer research grant is also gratefully acknowledged.

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