On the band spectral estimation of business cycle models

In this paper, I evaluate the properties and performance of band spectral estimators applied to business cycle models. Band spectral methods are widely used to study frequency-dependentrelationships among time series. In business cycle research, the Whittle likelihood approximation enables researchers to estimate models using only the frequencies those models are best suited to represent, such as the business cycle frequencies. Using the medium-scale model of Angeletos et al. (2018) as a data-generating process, I conduct a Monte Carlo study to assess the finite-sample properties of the band spectral maximum likelihood estimator (MLE) and compare its performance with that of the full-spectrum and exact time-domain MLEs. The results show that the band spectral estimator exhibits considerable biases and efficiency losses for most estimated parameters. Moreover, both the full-information and band spectral Whittle estimators perform poorly in contrast to the time domain estimator, which successfully recovers all model parameters. I demonstrate how these findings can be understood through the theoretical properties of the underlying model, and describe simple tools and diagnostics that can be used to detect potential problems in band spectral estimation for a wide class of macroeconomic models.