Economic Dynamics under Heterogeneous Adaptive Learning: Aggregate Economy Sufficient Conditions for Stability

Abstract

We provide sufficient conditions for stability of a linear structurally heterogeneous economy under heterogeneous learning of agents, extending the results of Honkapohja and Mitra (2006), Kolyuzhnov (2011), and Bogomolova and Kolyuzhnov (2019). Sufficient conditions for stability under heterogeneous mixed RLS/SG learning for four classes of models: models without lags and with lags of the endogenous variable and with t - or ( t - 1)-dating of expectations, are provided for the cases of the diagonal structure of the shock process behaviour or the heterogeneous RLS learning and are presented in terms of structural heterogeneity and are independent of heterogeneity in learning. The results are based on the negative diagonal dominance approach and are provided, first, in terms of the existence of the weights for aggregation of endogenous vatiables and of expectations across agents, interrelated in a special way, and then in terms of the E -stability of a suitably defined aggregate economy. The fundamental nature of the approach adopted in the paper allows one to apply its results to a vast majority of the existing and prospective linear and linearized economic models (including estimated DSGE models) with adaptive learning of agents.