The role of detrending methods in a model of real business cycles

Abstract

This paper examines three detrending methods in a real business cycle (RBC) model: the Hodrick-Prescott (HP) filter, the Beveridge-Nelson (BN) filter, and the Linear-in-Time (LIT) filter. The HP filter is posited in between the other two, in the sense that the trend from the HP filter is rather smooth with some variation, whereas the trend from the LIT filter is perfectly smooth and the trend from the BN filter includes a unit-root component. The HP filter fails to work as a band-pass filter if the pre-filtered series is integrated, and the failure deepens as the degree of integration becomes higher. However, the filter-oriented sensitivity of the stylized facts are symmetric between the actual data and the simulated data, implying that the sensitivity itself does not invalidate an RBC model's performance in replicating the actual economy.