Endogenous vs Exogenously Driven Fluctuations in Vintage Capital Models

In this paper, we present a simple vintage capital growth model in which both exogenous and endogenous fluctuations sources are present. Indeed, it can be seen as a particular case of Caballero and Hammour (1996)'s creative destruction model, with advantage that analytical characterization of the short run and asymptotic dynamics is partially allowed. In particular, we show that job creation follows a delayed-differential equation with periodic coefficients. The delay is equal to the optimal age of capital goods, and can be taken as a measure of the periodicity of the endogenous replacement echoes inherent to vintage models. The period of the coefficients is equal to the period of an exogenous profitability cycle. We mathematically show that job creation is asymptotically periodic, with the same period as the profitability cycle. Furthermore using an explicit numerical method, we find that replacement echoes generally dominate the short run dynamics. Finally, we find that the combination of the two fluctuations sources favors the appearance of asymmetries in job creation and job destruction patterns.