Forecast evaluation of DSGE models: Linear and nonlinear likelihood

We apply a Bayesian approach to estimate a small‐scale New Keynesian Dynamic Stochastic General Equilibrium (DSGE) model, solved by linear and nonlinear solution techniques. In particular, the likelihood function for the linearized and nonlinearized models is approximated via the linear and two types of nonlinear filters, respectively. We evaluate the performance of the linearized/nonlinearized model in terms of the log marginal data density and out‐of‐sample forecasting exercise over the transition periods of “Great Inflation” to “Great Moderation” (GI‐GM) and “Great Moderation” to “Great Recession” (GM‐GR). Several results are found as follows. First, it is not clear whether the nonlinearized DSGE model has a better fit than a linearized one to the full sample, and the result is also applied over the transition period of GI‐GM when we compute the time‐varying marginal data density. Second, under the point forecast evaluation, we do not find any statistical evidence that the forecasting performance of DSGE models, either the linearized or nonlinearized one, is better than the VAR models on predicting GDP growth rate, inflation, and interest rates over two transition periods. Moreover, the forecast errors for three data series calculated from either the individual model or the case of “Aggregation across models” in “ Normal” period are significantly lower than those in “ Crisis” period. Third, under the density forecast evaluation across DSGE models, we do not find any significant difference on the sum of log predictive likelihood across models at all forecast horizons for three individual data series. In particular, the above results are also applied to two transition periods and real‐time data sets.