The second deviation from the benchmark case consists in considering the impact of model uncertainty, while going back to the assumption of common information across all agents. Model uncertainty was first introduced into exchange rate models in the late 1980s in order to explain the persistent expectational errors of market participants about future exchange rates and to explain the high exchange rate volatility. In the second half of the 1970s and 1980s, the dollar consistently depreciated more than investors expected, while in the early 1980s it appreciated more than investors expected. Contributions by Lewis (1989) and Kaminsky (1993) showed that such persistent expectational errors can, in fact, be perfectly rational when there is uncertainty about model parameters. Lewis (1989) considers the standard monetary model, but assumes the existence of a one-time change in the constant term of the money demand equation. By observing the data, agents gradually learn about the new value of the constant term. Kaminsky (1993) assumes that money growth is equal to a drift term plus a random innovation. The drift term can switch between two values based on a Markov process. In both cases, agents learn about the unknown parameters through Bayesian updating.
To illustrate the mechanism for such consistent expectational errors, assume that the fundamental ft in our simple monetary model follows the process
Investors do not know δ. They form Bayesian expectations ...