What cycles? Data detrending in DSGE models

It is widely-known that different methods of detrending data yield different business cycle features. The choice of the detrending method, however, is usually arbitrarily made. This paper aims at revealing potential pitfalls of different detrending methods for the estimation of a standard medium-scale DSGE model. By comparing nine popular detrending methods, we find that model parameter estimates, variance decompositions, optimal monetary policies, and out-of-sample forecasting performances of the model are all sensitive to how the data are detrended. We also discuss some possible criteria to choose among different methods.