Policy Predictions If the Model Does Not Fit

Abstract

Abstract: This paper uses a novel method for conducting policy analysis with potentially misspecified DSGE models (Del Negro and Schorfheide 2004) and applies it to a simple New Keynesian DSGE model. We illustrate the sensitivity of the results to assumptions on the policy invariance of model misspecifications. JEL CLASSIFICATION: C32, E5 KEY WORDS: Bayesian Analysis, DSGE Models, Misspecification Policy Analysis. 1 Introduction Despite recent successes in improving the empirical performance of dynamic stochastic general equilibrium (DSGE) models, e.g., Smets and Wouters (2003), even large-scale DSGE models su[R]er to some extent from misspecification (see Del Negro, Schorfheide, Smets, and Wouters 2004). In this paper misspecification means that the DSGE model potentially imposes invalid cross-coe[+ or -]cient restrictions on the moving-average representation of the macroeconomic time series that it aims to explain. As a consequence, one typically observes that the forecasting performance of DSGE models is worse than that of vector autoregressions (VARs) estimated with well-calibrated shrinkage methods. On the other hand, DSGE models have the advantage that one can explicitly assess the e[R]ect of policy regime changes on expectation formation and decision rules of private agents. Thus, policy analysis with DSGE models is robust to the Lucas critique and potentially more reliable than conclusions drawn from VARs. This trade-o[R] poses a challenge to policymakers who want to use DSGE models in practice. Del Negro and Schorfheide (2004a) proposed a framework that combines VARs and DSGE models, extending earlier work by Ingram and Whiteman (1994). In this framework DSGE model restrictions are neither completely ignored as in the unrestricted estimation of VARs, nor are they dogmatically imposed as in the direct estimation of DSGE models. Instead the VAR estimates are tilted toward the restrictions implied by the DSGE model, where the degree of tilting is determined by a Bayesian data-driven procedure that trades o[R] model fit against complexity. Del Negro and Schorfheide (2004a) show that priors arising from the same model used in this paper improve both the in-sample and out-of-sample fit of a VAR. In ongoing research (Del Negro and Schorfheide, 2004b) we build upon our earlier work and further develop procedures that are suitable to study the e[R]ects of rare regime shifts with potentially misspecified DSGE models. These procedures can be viewed as a Bayesian alternative to the robust control and minimax approaches that recently have been proposed to cope with model misspecification, e.g., Hansen and Sargent (2000) and Onatsky and Stock (2002). One advantage of Bayesian procedures is that the policymaker can learn from existing data about the extent of the DSGE model's misspecification, and consequently adjust her policies. The present paper applies these procedures to a simple New Keynesian DSGE model. We illustrate that conclusions about the e[R]ects of changing the response to inflation are sensitive to assumptions about the policy invariance of observed discrepancies between model and reality. Section 2 briefly describes the DSGE model. In Section 3 we outline our framework, Section 4 discusses our findings, and Section 5 concludes. 2 The DSGE Model Starting point is a DSGE model in log-linearized form. The model used here is a standard New Keynesian DSGE model, e.g., Woodford (2003), which we now briefly describe (see Del Negro and Schorfheide (2004a) for details). The log-linearized equilibrium conditions consist of three equations in nominal interest rates [[??].sub.t], output [[??].sub.t], and inflation [[??].sub.t] ([sup.~] denotes percentage deviations from the steady state and [DELTA] is the temporal difference operator): Monetary Policy Rule: [[??].sub.t] = [rho]R [[??].sub.t-1] + (1-[rho]R) [[psi].sub.1] [[??]. …