We extend the correspondences between adaptive learning algorithms and the Kalman filter to formulations with time-varying gains. Our correspondences hold exactly, in a computational implementation sense, and we discuss how they relate to previous approximate correspondences found in the literature.

We compare forecasts from different adaptive learning algorithms and calibrations applied to US real-time data on inflation and growth. We find that the Least Squares with constant gains adjusted to match (past) survey forecasts provides the best overall performance both in terms of forecasting...

Previous literature has shown that, in a New Keynesian model, an expectations based policy rule induces E-stability of the fundamental equilibrium, while a fundamentals based one does not. We derive an alternative rule, based only on fundamentals, which can also achieve stability of equilibrium...

In a simple, univariate forward looking model, we show how a class of sunspot equilibria can depend on the relative fraction of agents under heterogeneous expectations. We then investigate if such equilibrium could be brought about by endogenous predictor choice dynamics.