This paper shows that a power utility specification of preferences over total expenditure (ie. CRRA preferences) implies that intratemporal demands are in the PIGL/PIGLOG class. This class generates (at most) rank two demand systems and we can test the validity of power utility on cross-section data. Further, if we maintain the assumption of power utility, and within period preferences are not homothetic, then the intertemporal preference parameter is identified by the curvature of Engel curves. Under the power utility assumption, neither Euler equation estimation nor structural consumption function estimation is necessary to identify the power parameter. In our empirical work, we use demand data to estimate the power utility parameter and to test the assumption of the power utility representation. We find estimates of the power parameter larger than obtained from Euler equation estimation, but we reject the power specification of within period utility.
elasticity of intertemporal substitution demand systems