Slutsky meets Marschak-The First-Order Identification of Multi-product Production

Abstract

Marschak (1953) suggested that applied research should begin by determining the minimal set of assumptions and data needed to make a prediction of interest. Standard identification analyses correspond poorly to this search, as they have either stringent data (local average treatment effects/IV and non-parametric) or structure (parametric) requirements. Yet, in this spirit, much empirical (Chetty, 2009) and some theoretical work has asked which effects of policy interventions may be forecast from the local observable levels and derivatives of the structure. I formalize this inquiry as the first- order identification problem and illustrate it with the case of multi-product production. Under perfect competition or monopoly, but not standard oligopoly, Slutsky conditions for firm optimization provide strategies for identifying, for example, the effects of price controls. They also test for consistency of conjectural variations.