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

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 firstorder 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. This manuscript is preliminary. Please do not cite it without the author’s permissions, but please do send along any suggestions for improvement. ∗I acknowledge the generous support of the Milton Fund, which funded excellent research assistance by Stephanie Lo, and the helpful comments of Jon Baker, Severin Borenstein Gary Chamberlain, Raj Chetty, Jerry Hausman, Ali Hortaçsu, Guido Imbens and David I. Levine. I am particularly grateful to Jim Heckman, a conversation with whom largely inspired the research that led to this paper. All errors and misunderstandings are, of course, my own. †Society of Fellows, Harvard University, 78 Mount Auburn Street, Cambridge, MA 02138: [email protected].