Nonparametric Analysis of Multi-Output Production with Joint Inputs

Abstract

We present a novel framework for analyzing cost minimizing production behavior in multi-output settings. Our specific focus is on dealing with joint inputs, i.e. inputs that are simultaneously used for the production of multiple outputs. Here, we distinguish between two possible approaches. The cooperative approach takes a centralized perspective and assumes cost minimization at the aggregate firm level. By contrast, the noncooperative approach adopts a decentralized view and assumes cost minimization at the level of the individual output departments, which implies the possibility of free riding behavior for the joint inputs. Our framework is non-parametric in nature, which means that it allows for analyzing production behavior while avoiding (nonverifiable) prior functional structure for the production technology. We show that it naturally extends the existing nonparametric framework for analyzing single output production. We establish rationalizability conditions for cooperative as well as noncooperative production behavior. In addition, we introduce goodness-of-fit measures for evaluating the degree of violation of these conditions. An empirical application to the English and Welsh drinking water and sewerage sector shows the practical usefulness of our framework. Specifically, we compare the empirical validity of the cooperative and noncooperative models for describing the observed production behavior.

Keywords: cooperative behavior, noncooperative behavior, multi-output production, joint inputs, nonparametric analysis, water sector

JEL Classification: C14, D21, D22, D24