Predictable Forecast Errors in Full-Information Rational Expectations Models with Regime Shifts

This paper shows that in the presence of Markov regime shifts, Full Information Rational Expectations (FIRE) models lead to predictable, regime-dependent forecast errors. More generally, regime shifts imply that ex-post forecast error regressions display waves of over-and under-reaction to current information over rolling sample windows. Using survey-based forecast data of macroeconomic aggregates, we confirm the existence of such waves. We then estimate a medium-scale DSGE model with regime shifts in the aggressiveness of monetary policy on U.S. data to assess the quantitative importance of the proposed mechanism. Despite the assumption of FIRE, simulated data conditional on the estimated sequence of regime realizations generates ex-post forecast error predictability consistent with reduced-form regressions from the existing literature and large waves of over- and under-reaction across subsamples. Hence, predictabiliy of ex-post forecast errors is neither a sufficient condition to reject FIRE nor by itself a good metric to test alternative theories of expectations formation.