Determinate liquidity traps

•Regime-switching New Keynesian model with recurring Zero Bound (ZB) episodes.•Determinacy imposes trade-off between ZB frequency and expected duration.•Longer ZB episodes are less likely to be determinate.•Fundamental transmission is sensitive to ZB frequency and shock persistence.•“Puzzling” transmission properties do not arise for determinate ZB episodes and aggressive active policy stance.

I study the long run determinacy tradeoff-recurrent episodes of passive monetary policy are (in)determinate if their expected duration is long (brief)-when passive policy is at the zero bound. On-going regime change implies qualitatively different shock transmission from the standard New Keynesian model. For US baseline parameter values, I find temporary fiscal stimulus is effective, while adverse supply shocks can be expansionary if the central bank's active policy stance is weak and/or if the liquidity trap's average duration exceeds 3 quarters.