We propose estimating DSGE models in which the central bank fixes the policy rate for an extended period of time and apply our approach to estimate expected durations of the Federal Reserve’s zero interest rate policy since 2009. We find a large increase in expected duration in 2011 with the move to calendar-based guidance and a decrease in 2013 with the ‘Taper tantrum’. These changes are identified by the influence of expected duration on output, inflation and interest rates at longer maturities. The structural model measures the severity of the zero lower bound constraint and the effects of unconventional policy.