Cyclical Features of Uzawa-Lucas Endogenous Growth Model

This paper analyzes the cyclical properties of a generalized version of Uzawa-Lucas endogenous growth model. We study the dynamic features of different cyclical components of this model characterized by a variety of decomposition methods. The decomposition methods considered can be classified in two groups. On the one hand, we consider three statistical filters: the Hodrick-Prescott filter, the Baxter-King filter and Gonzalo-Granger decomposition. On the other hand, we use four model-based decomposition methods. The latter decomposition procedures share the property that the cyclical components obtained by these methods preserve the log-linear approximation of the Euler-equation restrictions imposed by the agent’s intertemporal optimization problem. The paper shows that both model dynamics and model performance substantially vary across 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 Uzawa-Lucas model in relation to standard business cycle models under alternative definitions of the business cycle.

Emergence of Cooperation in Heterogeneous Population: A Discrete-Time Replicator Dynamics Analysis

The emergence of cooperation is analyzed in heterogeneous populations where individuals can be classified in two groups according to their phenotypic appearance. Phenotype recognition is assumed for all individuals: individuals are able to identify the type of every other individual, but fail to recognize their own type, and thus behave under partial information conditions. The interactions between individuals are described by 2 × 2 symmetric games where individuals can either cooperate or defect. The evolution of such populations is studied in the framework of evolutionary game by means of the replicator dynamics. Overlapping generations are considered, so the replicator equations are formulated in discrete-time form. The well-posedness conditions of the system are derived. Depending on the parameters of the game, a restriction may exist for the generation length. The stability analysis of the dynamical system is carried out and a detailed description of the behavior of trajectories starting from the interior of the state-space is given. We find that, provided the conditions of well-posedness are verified, the linear stability of monomorphic states in the discrete-time replicator coincides with the one of the continuous case. Specific from the discrete-time case, a relaxed restriction for the generation length is derived, for which larger time-steps can be used without compromising the well-posedness of the replicator system.