Heterogeneous agent models in economics: A study of heterogenous productivity of sectors

Macroeconomic modeling is undergoing a change from the ground up. Previously models based on fully rational representative agents were constructed to give macroeconomics solid microeconomic foundations. However the representative agent models have been shown to be inconsistent with empirical evidence and a new method of approach has emerged, one based on heterogeneity of agents. Recently heterogenous models have been used to simulate expected outcomes but due to their complexity little analytic work has been done. In this paper a basic model of the macro economy, with heterogeneous sectors differentiated by productivity, and driven by a jump Markov process, is investigated and steady state solutions for a sector´s output variance are discovered. We adjust the model to include a gain term, to represent a sector´s reaction to its error signal, excess demand, and then linearize the transition rates and apply the fluctuation dissipation theorem to solve the model.