Is there a Cycle in Real Business Cycle Models?

This paper takes a fresh look on the well known real business cycle model of Kydlard and Prescott [1988], using spectral methods for linear filters. Theoretical spectra of the model are calculated in order to investigate the cycles generated by the combined effect of stochastic disturbances and propagation mechanisms. It is found that all model variables have the same type of cycles as AR(1) processes, except that a three-quarter cycle is introduced by the three-quarter-time-to-build technology. Furthermore, all swings of longer duration than three quarters are very correlated between the variables in the model, as shown by theoretical coherences. Using these results, theoretical correlations can easily be computed, which provides an alternative to the usual simulation exercise. Finally, these results are compared with estimates of empirical spectra and coherences of some important macro aggregates in the United States. In general the model fares pretty well in this comparison, even if the variance of the data than in the model and that the estimated coherences seems lower than predicted by theory. Finally, there is no evidence of any three-quarter cycle in the data