Asset Prices in a Time Series Model with Perpetually Disparately Informed, Competitive Traders

This paper develops a dynamic asset pricing model with persistent heterogeneous beliefs. The model features competitive traders who receive idiosyncratic signals about an underlying fundamentals process. We adapt Futia’s (1981) frequency domain methods to derive conditions on the fundamentals that guarantee noninvertibility of the mapping between observed market data and the underlying shocks to agents’ information sets. When these conditions are satisfied, agents must ‘forecast the forecasts of others’. The paper provides an explicit analytical characterization of the resulting higher-order belief dynamics. These additional dynamics can explain apparent violations of variance bounds and rejections of cross-equation restrictions.