DSGE Models, Detrending, and the Method of Moments

One important question in the DSGE literature is whether we should detrend data when estimating the parameters of a DSGE model using the moment method. It has been common in the literature to detrend data in the same way the model is detrended. Doing so works relatively well with linear models, in part because in such cases the information that disappears from the data is usually related to the parameters that also disappear from the detrended model. Unfortunately, in heavy non-linear DSGE models, parameters rarely disappear from detrended models, but information does disappear from the detrended data. Using a simple real business cycle model, we show that both the moment method estimators of parameters and the estimated responses of endogenous variables to a technological shock can be seriously inaccurate when detrended data are used in the estimation process. Using a dynamic stochastic general equilibrium model and U.S. data, we show that detrending the data before estimating the parameters may result in a seriously misleading response of endogenous variables to monetary shocks. We suggest building the moment conditions using raw data, irrespective of the trend observed in the data