Economic Dynamics Under Heterogeneous Learning: Necessary and Sufficient Conditions for Stability

I provide sufficient conditions and necessary conditions for stability of a structurally heterogeneous economy under heterogeneous learning of agents. These conditions are written in terms of the structural heterogeneity independent of heterogeneity in learning. I have found an easily interpretable unifying condition which is sufficient for convergence of an economy under mixed RLS/SG learning with different degrees of inertia towards a rational expectations equilibrium for a broad class of economic models and a criterion for such a convergence in the univariate case. The conditions are formulated using the concept of a subeconomy and a suitably defined aggregate economy. I demonstrate and provide interpretation of the derived conditions and the criterion on univariate and multivariate examples, including two specifications of the overlapping generations model and the model of simultaneous markets with structural heterogeneity.