Estimating DSGE models with Zero Interest Rate Policy

We propose an approach to estimating structural models in which the central bank holds the policy rate fixed for an extended period of the estimation sample. Embedding this policy in a version of the Smets and Wouters (2007) model that incorporates information from the yield curve to help with identification at the zero lower bound, we jointly estimate the structural parameters for the period of 1983-2014 and the expected duration of the zero interest rate policy in each quarter since 2009. This allows us to assess the effects of the zero lower bound, in particular, how private agents' beliefs about its duration influence output, inflation and interest rates at longer maturities. We find considerable variation in the expected duration over time, with a large increase in 2011 when the Federal Reserve moved to calendar-based forward guidance and a similar decrease in 2013 with the so-called `Taper tantrum'. We also measure the severity of the zero lower bound as a constraint and quantify the associated output losses. Conditional forecasts from the model suggest that a longer expected duration corresponds to higher output growth in the near term, with offsetting lower growth at the time of expected liftoff. Impulse response analysis confirms that an exogenous change in the expected duration has significant effects on the real economy.