Estimating DSGE-model-consistent trends for use in forecasting

The workhorse DSGE model used for monetary policy evaluation is designed to capture business cycle fluctuations in an optimization-based format. It is commonplace to log-linearize models and express them with variables in deviation-from-steady-state format. Structural parameters are either calibrated, or estimated using data pre-filtered to extract trends. Such procedures treat past and future trends as fully known by all economic agents or, at least, as independent of cyclical behaviour. With such a setup, in a forecasting environment it seems natural to add forecasts from DSGE models to trend forecasts. While this may be an intuitive starting point, efficiency can be improved in multiple dimensions. Ideally, behaviour of trends and cycles should be jointly modeled. However, for computational reasons it may not be feasible to do so, particularly with medium- or large-scale models. Nevertheless, marginal improvements on the standard framework can still be made. First, pre-filtering of data can be amended to incorporate structural links between the various trends that are implied by the economic theory on which the model is based, improving the efficiency of trend estimates. Second, forecast efficiency can be improved by building a forecast model for model-consistent trends. Third, decomposition of shocks into permanent and transitory components can be endogenized to also be model-consistent. This paper proposes a unified framework for introducing these improvements. Application of the methodology validates the existence of considerable deviations between trends used for detrending data prior to structural parameter estimation and model-consistent estimates of trends, implying the potential for efficiency gains in forecasting. Such deviations also provide information on aspects of the model that are least coherent with the data, possibly indicating model misspecification. Additionally, the framework provides a structure for examining cyclical responses to trend shocks, among other extensions.