Signal extraction and the propagation of business cycles

This paper studies a class of models developed by Townsend (1993) and Sargent (1991). These models feature dynamic signal extraction problems in which firms with heterogeneous information draw inferences from endogenously generated time series about the value of common persistent shock. Because the information firms receive is partially determined by the expectations of other firms, each firm must 'forecast the forecasts of others'. Moreover, since it is common knowledge that everyone is in the same situation, there occurs an infinite regress in expectations, in which each firm attempts to forecast the forecasts that other firms make about its own forecast, and so on. Townsend and Sargent develop methods for solving this infinite regress problem, and discuss the possibility that in these models expectations themselves become a source of business cycle propagation. This paper contributes in two ways to the work of Townsend and Sargent. ; This paper contributes in two ways to the work of Townsend and Sargent. First, it solves analytically the fixed point problem posed by the infinite regress in expectations. Having an analytical solution facilitates empirical work. Second, it assesses empirically the potential role of forecast errors as a business cycle propagation mechanism. I find that forecast errors can indeed make a quantitatively significant contribution to the propagation of business cycles.