New Classical Models and Unobserved Aggregates

The New Classical macroeconomic models seek to explain observed cyclical fluctuations in real activity by agents’ reactions to nominal demand disturbances, about which they have incomplete information. While these models are driven by incomplete information about stochastic shocks, it is invariably assumed that agents have comprehensive information about the structure of the model, the associated probability distributions and the past values of all relevant variables. This paper analyses a simple New Classical model where agents cannot observe any lagged values of the true aggregate of an important variable – the money stock – but can see (lagged values of) an imperfectly measured estimate of this aggregate. Agents filter this noisy signal and all other available information to produce optimal estiimates (i.e., rational expectations) of the current and lagged aggregate money stocks. Analytically tractable expressions are obtained from the stationary solution to the inherent recursive Kalman filtering problem. It is found that, under fairly general conditions, this filtering process induces serially correlated errors into the agents’ expectations of the money stock, even though their expectations are rational. This serial dependence feeds through to generate a persistent response of real activity to demand shocks. Futhermore, it is shown that the correlation of unanticipated movements in the measured money stock with movements in real activity, may not be indicative of the relationship between activity and the true money stock. These results suggest that incomplete information about macroeconomic variables may explain some of the observed business cycle persistence and some of the instances of a lack of a sizeable measured correlation between real output and money supply innovations.