2 PROBLEMS IN APPLYING LJUNG PROJECTION ALGORITHMS TO THE ANALYSIS OF DECENTRALIZED LEARNING

We show that Ljung's projection algorithms, which have recently been used by economists to establish convergence to rational expectations equilibrium, do not seem to apply to learning or forecasting behavior that one would normally call ''decentralized.'' If the algorithm is defined in a way that allows individuals to have differing information, then Ljung's theorem does not apply. And even if a similar theorem could be proved that would allow for differing information, there remains a Lyapunov-like condition that is central to Ljung's projection method and which requires that individual beliefs be narrowly related to the equilibrium and to one another.