Interactions in the New Keynesian DSGE Models: The Boltzmann–Gibbs Machine and Social Networks Approach

The Boltzmann–Gibbs distribution is currently widely used in economic modeling. One of the applications is integrated with the DSGE (Dynamic Stochastic General Equilibrium) model. However, a question that arises concerns whether the Boltzmann–Gibbs distribution can be directly applied, without considering the underlying social network structure more seriously, even though the social network structure is an important factor of social interaction. Therefore, this paper proposes two kinds of agent-based DSGE models. The first one belongs to mesoscopic modeling in formulating the social interaction with the Boltzmann–Gibbs machine, and the other one belongs to microscopic modeling in that it is augmented by the network-based ant machine. By comparing the population dynamics generated by those different agent-based DSGE models, we find that the Boltzmann–Gibbs machine offers a good approximation of herding behavior. However, it is difficult to envisage the population dynamics produced by the Boltzmann–Gibbs machine and by the network-based ant machine as having the same distribution, particularly in popular empirical network structures such as small world networks and scale-free networks. Thus, the social interaction behavior may not be replaced by the Boltzmann–Gibbs distribution. Special Issue New Approaches in Quantitative Modeling of Financial Markets JEL C63, D85, E12, E32, E3