Evaluating misspecification in DSGE models using tests for overidentifying restrictions

In this paper I discuss the estimation of the process governing the structural shocks (or wedges) to a DSGE model, arguing that a well-specified model would satisfy certain sets of moment conditions. Based on tests for overidentifying restrictions, I compare three specifications of the Taylor rule within a simple New Keynesian model. I find that a rule which allows for the Fed to respond to four lags of inflation shows less evidence of misspecification than one where the Fed responds only to contemporaneous inflation. Raising the coe cient on the output gap to 1 instead of 0.5 gives more ambiguous results.