Cyclical features of the Uzawa–Lucas endogenous growth model

Abstract

This paper analyzes the cyclical properties of a generalized version of the Uzawa–Lucas model. We study the dynamic features of different cyclical components of this model characterized by a variety of decomposition methods. These methods can be classified in two groups. On the one hand, we consider three statistical filters: Hodrick–Prescott, Baxter–King and Gonzalo–Granger. On the other hand, we use four model-based decomposition methods. The latter methods share the property that the cyclical components obtained preserve the log-linear approximation of the Euler-equation restrictions imposed by the agent's intertemporal optimization problem. The paper shows that both the model dynamics and the model performance vary substantially across the decomposition methods. A parallel exercise is carried out with a standard real business cycle model. The results should help researchers to better understand the performance of the Uzawa–Lucas model in relation to standard business cycle models under alternative definitions of the business cycle.