Initial beliefs and the global stability of least squares learning

This article provides an operational framework of global stability analysis when Ljung's (1977) ordinary differential equation (ODE) approach is applied to the recursive stochastic system. We first establish the notion of stable set under which sufficient conditions for the equivalence between them can be translated to restrictions on initial beliefs in agents' forecasts. The maximum ODE-stable set is simply the largest range of initial beliefs. We then demonstrate how to implement this operational framework for the analysis of stability beyond the local sense in some well-known models in the learning literature.