New Keynesian models with sticky prices make stark predictions about how the economy responds to shocks under different monetary policy regimes when short‐term interest rates are constrained by an effective lower bound. We use the Swiss case as a laboratory to find evidence in favour of these predictions. We propose a Bayesian VAR to estimate impulse responses to risk shocks for short periods with a binding effective lower bound and with a publicly announced minimum exchange rate. In line with predictions from theory, we find that with a binding effective lower bound, the responses of the exchange rate, prices, and output become more persistent. However, the minimum exchange rate attenuates this adverse impact.