Interactions in DSGE models: The Boltzmann-Gibbs machine and social networks approach

While DSGE models have been widely used by central banks for policy analysis, they seem to have been ineffective in calibrating the models for anticipating financial crises. To bring DSGE models closer to real situations, some of researchers have revised the traditional DSGE models. One of the modified DSGE models is the adaptive belief system model. In this framework, changes in sentiment can be expounded by a Boltzmann-Gibbs distribution, and in addition to externally caused fluctuations endogenous interactions are also considered. Methodologically, heuristic switching models are mesoscopic. For this reason, the social network structure is not described in the adaptive belief system models, even though the network structure is an important factor of interaction. The interaction behavior should ideally be based on some kind of social network structures. Today, the Boltzmann-Gibbs distribution is widely used in economic modeling. However, the question is whether the Boltzmann-Gibbs distribution can be directly applied, without considering the underlying social network structure more seriously. To this day, it seems that few scholars have discussed the relationship between social networks and the Boltzmann-Gibbs distribution. Therefore, this paper proposes a network based ant model and tries to compare the population dynamics in the Boltzmann-Gibbs model with different network structure models applied to stylized DSGE models. We find that both the Boltzmann-Gibbs model and the network-based ant model could generate herding behavior. However, it is difficult to envisage the population dynamics generated by the Boltzmann-Gibbs model and the network-based ant model having the same distribution, particularly in popular empirical network structures such as small world networks and scale-free networks. In addition, our simulation results further suggest that the population dynamics of the Boltzmann-Gibbs model and the circle network ant model can be considered with the same distribution under specific parameters settings. This finding is consistent with the study of thermodynamics, on which the Boltzmann-Gibbs distribution is based, namely, the local interaction.