Is the Elasticity of Intertemporal Substitution Constant?∗

This paper shows that the CRRA specification of intertemporal preferences (implying a constant elasticity of intertemporal substitution, or EIS), imposes surprising limitations on within period budget allocations. Consequently, the constant EIS assumption can be tested with demand data. In fact, the parameter of the CRRA utility function is pinned down completely by the shape of Engel curves; if preferences are CRRA then the EIS could in principle be estimated without any variation in the interest rate. The fact that a price elasticity can be estimated without variation in the relevant price illustrates just how strong the constant EIS assumption is. The constant EIS assumption is rejected by demand data. We also show analagous results can be obtained for more general HARA preferences.