Medium term endogenous fluctuations in three-sector optimal growth models

Following the recent contribution of Beaudry et al. [8], we exploit a three-sector optimal growth model without frictions to provide new insights regarding the emergence of endogenous medium-term fluctuations. Notably, our 3-sector model shows that matching the empirical evidence critically depends on agents' preferences, particularly the consumption of a bundle of (at least) two final goods. Endogenous fluctuations are therefore likely to occur through both relative inter-sector differences in capital intensity and intertemporal consumption allocations based on substitution effects between the two final consumed goods. We thoroughly characterize the economy's dynamics and establish the existence of clear conditions related to (Hopf) bifurcation values, as well as closely examining the theoretical periodicity of the corresponding limit cycles. Using a calibration of the US economy, our model is able to reproduce the observed peak range of spectral density at around 8 to 10 years of the cyclical component of gross domestic product, gross private investment, personal consumption expenditures, and of the corresponding price deflator series. Furthermore, such limit cycles are generated under very plausible technological parameters and estimates of the elasticities of intertemporal substitution.