DSGE model-based forecasting of non-modelled variables

Abstract

This paper develops and illustrates a simple method to generate a DSGE modelbased forecast for variables that do not explicitly appear in the model (non-core variables). We use auxiliary regressions that resemble measurement equations in a dynamic factor model to link the non-core variables to the state variables of the DSGE model.Predictions for the non-core variables are obtained by applying their measurement equations to DSGE model-generated forecasts of the state variables. Using a mediumscale New Keynesian DSGE model, we apply our approach to generate and evaluate recursive forecasts for PCE inflation, core PCE inflation, the unemployment rate, and housing starts along with predictions for the seven variables that have been used to estimate the DSGE model.

Structural Dynamic Factor Analysis Using Prior Information From Macroeconomic Theory

“…By relaxing restrictions implied by the DSGE model, it is possible to move toward a nonstructural factor model. A more recent contribution, related to Boivin and Giannoni (2006), is Schorfheide, Sill, and Kryshko (2010). These authors used a DSGE model to estimate unobserved states of the economy in a first step and then embed these estimates in the information set to forecast a large set of economic time series.…”

“…A disadvantage is that only a limited set of variables-the "core" variables in the DSGE model-can be informative about the unobserved state of the economy. A further difference is that Schorfheide, Sill, and Kryshko (2010) focused on improving forecasts. In contrast, both our approach and that of Boivin and Giannoni (2006) explicitly aim at providing a full-information structural analysis of many economic data series.…”

Evaluating DSGE model forecasts of comovements

“…We use RMSEs and ratios of conditional and unconditional RMSEs as in Schorfheide et al (2010) to form a predictive check. Letŷ i,t+h|j,t andŷ i,t+h|t denote the means of the conditional (given y j,t+h ) and marginal predictive distribution of y i,t+h .…”

“…RMSEs for DSGE model forecasts of US aggregate time series are reported, for instance, in Del Negro et al (2007), Smets and Wouters (2007), Edge et al (2009), Schorfheide et al (2010, Wolters (2010), EG, andSchorfheide (2012). The studies differ with respect to the forecast period as well as the treatment of data revisions.…”

“…While PITs based on predictive densities that are conditioned on future realizations of a subset of variables arise naturally in a multivariate density forecast evaluation setting (see Diebold et al (1999)), they have not yet been applied to assess a DSGE model's ability to forecast comovements. Ratios of RMSEs of unconditional forecasts versus forecasts that are conditioned on the future realization of a subset of variables have first been reported in Schorfheide et al (2010), but that paper does not provide a formal benchmark, such as percentiles of predictive distributions, against which the ratios could be evaluated. Finally, none of the existing papers have set up the forecast evaluation formally as a predictive check in a Bayesian framework.…”