Gresham's Law of Model Averaging

An agent operating in a self-referential environment thinks the parameters of his model might be time-varying. In response, he estimates two models, one with time-varying parameters, and another with constant parameters. Forecasts are then based on a Bayesian Model Averaging strategy, which mixes forecasts from the two models. In reality, structural parameters are constant, but the (unknown) true model features expectational feedback, which the agent's reduced form models neglect. This feedback allows the agent's fears of parameter instability to be self-confirming. Within the context of a standard linear present value asset pricing model, we use the tools of large deviations theory to show that the agent's self-confirming beliefs about parameter instability exhibit Markov-switching dynamics between periods of tranquility and periods of instability. However, as feedback increases, the duration of the unstable state increases, and instability becomes the norm. Even though the constant parameter model would converge to the (constant parameter) Rational Expectations Equilibrium if considered in isolation, the mere presence of an unstable alternative drives it out of consideration.