Forecasting the Forecasts of Others in the Frequency Domain

This paper studies a class of models developed by R. M. Townsend (1983, J. Polit. Econ.91, 546–588) and T. J. Sargent (1991, J. Econom. Dynam. Control15, 245–273). These models feature dynamic signal extraction problems and an infinite regress in expectations. This paper uses frequency domain methods to compute an analytical solution to the fixed point problem posed by the infinite regress in expectations. The advantage of a frequency domain approach vis-à-vis a time domain approach derives from the fact that these models produce equilibria with non-fundamental moving average representations, in which market observations do not reveal the underlying shocks to agents' information sets. As a result, decision rules contain moving average components that are more easily handled in the frequency domain than in the time domain.