Restricted Hodrick–Prescott filtering in a state-space framework

The current paper extends previous results on Hodrick–Prescott (HP) filtering and shows that it is possible to implement the judgement-augmented, or restricted, HP filter within the state-space framework. The implementation entails augmenting the vector of measurements and altering one of the system matrices of the state-space model for the HP filter. Restrictions can thereby be incorporated in the HP filter, making, e.g., estimation more accessible. An application to US GDP gap estimation illustrates how the restricted filter could be usefully applied in an empirical macroeconomic setting.