Uncertainty, rationality and complexity in a multi-sectoral dynamic model: The dynamic stochastic generalized aggregation approach

The paper presents a macroeconomic model articulated in a job market and in a goods market with several heterogeneous and interacting agents (namely firms and workers). The agents heuristically adapt their expectations by interpreting the market signals and give rise to macroeconomic regularities. The contributions of the papers are twofold. First, it proposes an innovative application of existing analytical tools to represent complex systems through a dynamic stochastic generalized aggregation (DSG-A) method. The macroeconomic variables are defined as weighted means of the micro-behavioral rules available for agents, where the weights are given by the densities of agents associated to the different strategies. The evolution of the agents' densities is modeled through the master equation, interpreted in a frequentist way. In this context, we are able to microfound opinion dynamics dynamics and to explicitly link the macro-dynamics to the agents' choices. The second and most relevant contribution is in that this approach can be linked to intertemporal optimal control and to the standard hypothesis of economic rational behavior. From this perspective, the zero-intelligence and the perfect rationality represent two extreme cases that can be included in a disequilibrium closed economic system. In particular, due to interaction, if agents are fully rational, we obtain a system with two equilibria: a rational equilibria, which represents the optimal outcome, and an uncertainty equilibria, in which agents' welfare is lower as the propensity to save increases due to precautionary savings. We explore the systems behavior via computer simulations. The paper represents a significant extension of the statistical mechanic approach to macroeconomics and a contribution for bridging this approach to standard DSGE models.