Estimating DSGE models with zero interest rate policy

This 2017 Journal of Monetary Economics paper by Mariano Kulish, James Morley, and Tim Robinson addresses a practical problem in Bayesian estimation of DSGE models: once the policy rate is pinned at its zero lower bound (ZLB) for an extended period, it loses its usual variation as an observable, and standard Kalman-filter-based estimation methods built around a single, time-invariant rational-expectations solution break down. Rather than assuming the duration of the fixed-rate episode is known or fully pinned down by the model’s other shocks, the authors treat the expected duration of the ZLB regime, d^e_t, as a discrete free parameter, estimated jointly with the structural parameters of an otherwise standard Smets-Wouters (2007)-style DSGE model that is augmented with 2- and 5-year nominal bond yields (following Graeve, Emiris, and Wouters 2009). Because expected duration can change over time as new information arrives, the solution takes the form of a time-varying-coefficient VAR computed by backward recursion from the eventual return to the conventional policy rule, and estimation proceeds via a two-block Metropolis-Hastings sampler (one block for the sequence of expected durations, one for the structural parameters), with an informative prior on expected duration built from Federal Reserve Bank of New York Primary Dealer surveys and Blue Chip Financial Forecasts. Applied to quarterly U.S. data from 1983Q1 to 2014Q2, with a 22-quarter ZLB subsample beginning 2009Q1, the posterior mean of expected duration starts below one year in 2009, rises sharply after the Federal Reserve’s August 2011 calendar-based forward guidance announcement (posterior mass shifting from below two years to above it), peaks around 2012, and falls back during the 2013 “taper tantrum,” with posterior standard deviations considerably tighter than the prior, indicating durations are reasonably well identified by the data. The estimated model implies the ZLB constrained policy with probability close to one in 17 of the 22 ZLB quarters (with non-negligible, 15-20 percent, probability of slack in five quarters, and even then only a few basis points on average), and a counterfactual removing the ZLB constraint (letting the estimated Taylor rule set negative rates) implies cumulative losses over those 22 quarters of 45.3 percent for output, 45.2 percent for consumption, and 97.9 percent for investment, alongside a roughly 1.5-percentage-point-lower 5-year yield and a comparatively modest inflation difference — a pattern the authors read, following Del Negro et al. (2015), as consistent with a risk-premium/net-worth shock driving the bulk of the recession rather than a shock that would also move inflation sharply. A generalized-impulse-response exercise built around the 2013 taper-tantrum event, in which expected duration falls by about five quarters, implies an average cumulative increase in the federal funds rate path of 292 basis points and an immediate roughly 10-basis-point rise in the 5-year yield, together with declines in output, consumption, investment, and hours, but only a relatively small fall in inflation. The authors flag as limitations that their approach assumes a single, common expected duration across all agents at each date (no heterogeneous beliefs) and does not penalize estimated duration paths that would imply the ZLB should have been violated.

James Morley | Macro Paper Warehouse

Estimating DSGE models with zero interest rate policy