Is the elasticity of intertemporal substitution constant?

In all common models of inter-temporal allocation, the assumption of a constant elasticity of intertemporal substitution (EIS) imposes surprising limitations on within-period budget allocations. Consequently, the constant EIS assumption can be tested with demand data. In fact, the EIS is pinned down completely by the shape of Engel curves: if the EIS is constant then the EIS can be estimated without variation in the interest rate. 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.