Stability under Learning of Equilibria in Financial Markets with Supply Information

In a recent paper Ganguli and Yang [2009] demonstrate, that there can exist multiple equilibria in a financial market model á la Grossman and Stiglitz [1980] if traders possess private information regarding the supply of the risky asset. The additional equilibria differ in some important respects from the usual equilibrium of the Grossman–Stiglitz type which still exists in this model. This note shows that these additional equilibria are always unstable under learning. This is true for both eductive learning following Guesnerie [2002] and adaptive learning via least–squares estimation (cf. Marcet and Sargent [1988] or Evans and Honkapohja [2001]). Regarding the original Grossman–Stiglitz type equilibrium, the stability results are less clear cut, since this equilibrium might be unstable under eductive learning while it is always stable under adaptive learning.