Economic Dynamics under Heterogeneous Adaptive Learning: General Criteria and Sufficient Conditions for Stability

Abstract 
The article extends the results of Honkapohja and Mitra (2006) and Kolyuzhnov (2011) and provides criteria and sufficient conditions for stability in a structurally heterogeneous economy under heterogeneous adaptive learning of agents. The criteria for stability under heterogeneous mixed RLS/SG learning for four classes of models – without lags and with lags of the endogenous variable and with t or t – 1 – dating of expectations – and sufficient conditions for stability for the cases of the diagonal structure of the shock process behavior or the heterogeneous RLS learning are presented in terms of the corresponding Jacobian matrices. In addition, the study presents a very useful criterion for the stability for all types of models under mixed RLS/SG learning with equal degrees of inertia for each type of learning algorithm in terms of stability of a suitably defined average economy with two agents. The derived criteria and sufficient conditions for stability are based on the results of the theory of stochastic approximation and are presented  in terms of mixture of structural and learning heterogeneity, which are essential to get sufficient and necessary conditions for stability irrespective of heterogeneity in learning presented in terms of E-stability of suitably defined aggregate economies, the “same sign” conditions and the E-stability of a suitably defined average economy and its subeconomies. The fundamental nature of the approach adopted in the paper makes it possible to apply the results to  a vast majority of the existing and prospective linear and linearized economic models (including estimated DSGE models) with adaptive learning of agents. 

Keywords 
adaptive learning, stability of equilibrium, heterogeneous agents 

Funding  
This paper was prepared within project XI.170.1.1. “Innovative and Ecological Aspects of the Structural Transformation of the Russian Economy amid a New Geopolitical Reality”, 2019 RAS SB IEIE research plan, no. АААА-А17-117022250127-8.

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