A government that wants to increase welfare by subsidizing either an industry’s sales or process innovations or both has to account for possible changes of production, when firms can foresee the government’s actions. In an optimal control framework welfare can be increased by subsidizing...

On purpose to extract trend and cycle from a time series many competing techniques have been developed. The probably most prevalent is the Hodrick Prescott filter. However this filter suffers from diverse shortcomings, especially the subjective choice of its penalization parameter. To this point...

Penalized splines have become a popular tool to model the trend component in economic time series. The outcome of the spline predominantly depends on the choice of a penalization parameter that controls the smoothness of the trend. This paper derives the penalization of splines by frequency...