Expectations Formation, Sticky Prices, and the ZLB

At the zero lower bound (ZLB), expectations about the future path of monetary or fiscal policy are crucial. We model expectations formation under level-$k$ thinking, a form of bounded rationality formalized by García-Schmidt and Woodford (2019) and Farhi and Werning (2019), consistent with experimental evidence. This process does not lead to a number of puzzling features from rational expectations models, such as the reversal puzzle, or implausible large fiscal multipliers. Optimal monetary policy at the ZLB under level-$k$ thinking prescribes keeping the nominal rate lower for longer, but short-run macro-economic stabilization is less powerful compared to rational expectations.