Rank, Separability, and Conditional Demands

Rank R demand systems that are either conditioned on some good (such as durables) or are separable from that good, are shown to be identical to unconditional demand systems having rank R or R+1. More generally, the rank of a conditional demand system or a separable subsystem is a lower bound on the rank of the corresponding demand system over all goods. This relationship is applied to reinterpret some existing empirical results regarding rank, conditioning goods, and separability. This research was supported in part by the National Science Foundation through grant SES-9905010. I would like to thank Christopher Nicol for a lively debate that led to this paper, and for helpful comments. I’d also like to thank the editors of this journal and anonymous referees for useful comments and suggestions. Any errors are my own. Corresponding Author: Arthur Lewbel, Department of Economics, Boston College, 140 Commonwealth Ave., Chestnut Hill, MA, 02467, USA. (617)-552-3678, [email protected], http://www2.bc.edu/~lewbel/ Extending Gorman (1981), Lewbel (1991) deÞned the general concept of the rank of a demand system, and showed that rank has many important implications for speciÞcation, estimation, aggregation, and welfare calculations. The point