Bayesian Estimation of DSGE Models: Lessons from Second-order Approximations

This paper investigates a general procedure to estimate second-order approximations to a DSGE model and compares the performance with the widely used estimation technique for a log-linearized economy on a version of new Keynesian monetary model. It is done in the context of posterior distributions, welfare cost, and impulse response analysis. Our findings include the followings. First, we find that all the results of An and Schorfheide (2007) are confirmed with U.S. data. With the nonlinear estimation we can identify parameters that are neglected previously; the marginal data density evaluation shows that data support the nonlinear estimation procedure; and parameter estimates that are related to nondeterministic steady states are quite different from the linear estimates. Second, the estimated welfare differentials are more aggressive for the second-order approximations, that is, the posterior welfare differentials from the linear estimation may underestimate the welfare cost resulted from changes in the monetary policy. Third, the second-order approximation unveils quite different dynamics which are neglected in a log-linearized economy. JEL Classification: C11, C32, C51, C52, E52