Is Time an Illusion? A Bootstrap Likelihood Ratio Test for Shock Transmission Delays in DSGE Models

Several business cycle models exhibit a recursive timing structure, which enforces delayed propagation of exogenous shocks driving short-run dynamics. We propose a bootstrap-based empirical strategy to test for the relevance of timing restrictions and ensuing shock transmission delays in DSGE environments. In the presence of strong identification, we document how likelihood-based tests in bootstrap-resamples can be used to empirically assess short-run restrictions placed by informational structures on a given model's equilibrium representation, thereby enhancing coherence between theory and measurement. We evaluate the size properties of our procedure in short time series by conducting a number of numerical experiments on a popular New Keynesian model of the monetary transmission mechanism. An empirical application to U.S. data from the Great Moderation period allows us to revisit and qualify previous findings in the field by lending support to the conventional (unrestricted) timing protocol, whereby inflation and output gap do respond on impact to monetary policy innovations.