The estimation of the power curve provides an application for methods to estimate production functions consistent with the regular ultra passum law.
It is well known based on fluid dynamics and kinetic energy that the power generated by a wind turbine follows power curve that appears to be S-shaped. In production economics we also believe the production function has a similar S-shaped when the regular ultra-passim law proposed by Ranger Frisch is satisfied. In this research project executed with Hoon Hwangbo and Yu Ding, we are developing a method to estimate a production function that satisfies the regular ultra passum law, is homothetic, has a single output, and allows for noise in the model. Our goal is to improve estimation in small samples through imposing the shape constraints and to develop methods competitive with kernel regression based methods that are currently widely used in the power curve estimation literature.
Working Paper available at SSRN.