The Variance-Frequency Decomposition as an Instrument for VAR Identification: an Application to Technology Shocks

Abstract: This paper proposes a new framework to study identification in structural VAR models. The framework is based on the variance-frequency decomposition and focuses on the contribution of the identified shock to the variance of model variables in a given frequency range. We use the hours-productivity debate as a connecting thread in our discussion since the identification problem has attracted a lot of attention in this literature. To start, we employ the framework to study the business cycle properties of a set of different identification schemes for technology shocks. Grounded on the simulation results, we propose a new model-based procedure which delivers a precise estimate of the response of hours. Finally, we put all the schemes to work with real data, obtaining substantial evidence in favor of plausible RBC parametrizations, especially from identification restrictions that perform better in simulations. This analysis also reveals that the schemes that recover a very strong response of hours (higher than the implied by typical RBC parameterizations) tend to overstate the contribution of the technology shock to the fluctuations of hours worked at business cycle frequencies. Keywords: Business cycle, frequency domain, hours worked, productivity, vector autoregressions. Classification: C1, E3