Maintaining and Testing Separability in Demand Systems

We derive a general elasticity representation of the necessary and sufficient conditions for direct weak separability of the utility function. Parametric restrictions required to implement the separability conditions are presented for three common demand systems: the Almost Ideal, Translog, and Rotterdam. Our empirical application uses the Rotterdam model to test a few separable structures within a complete U.S. demand system emphasizing food commodities. Results, based on size-corrected likelihood ratio tests, provide support for commonly used separability assumptions about food and meat demand.