Sufficient Conditions and Necessary Conditions for delta-stability

We provide sufficient conditions and necessary conditions for stability of an economy under structural mixed recursive least squares/stochastic gradient heterogeneous learning of agents with possibly different degrees of inertia. We have found a unifying condition which is sufficient for convergence of an economy under such general type of adaptive learning towards rational expectations equilibrium for a broad class of economic models. We demonstrate and provide interpretation of this condition on an economic example