Modeling economies of scope in joint production: Convex regression of input distance function

Modeling of joint production has proved a vexing problem. This paper develops a radial convex nonparametric least squares (CNLS) approach to estimate the input distance function with multiple outputs. We document the correct input distance function transformation and prove that the necessary orthogonality conditions can be satisfied in radial CNLS. A Monte Carlo study is performed to compare the finite sample performance of radial CNLS and other deterministic and stochastic frontier approaches in terms of the input distance function estimation. We apply our novel approach to the Finnish electricity distribution network regulation and empirically confirm that the input isoquants become more curved. In addition, we introduce the weight restriction to radial CNLS to mitigate the potential overfitting and increase the out-of-sample performance in energy regulation.