Commensurability and Characterization of Normalization Conditions for Cost-of-Living Comparisons under Time-Varying CES Preferences

• Provides a solution to the problem of choice of normalization. • Illustrates how the simple and intuitive commensurability axiom can be used to solve the normalization problem. • Provides a justification for the normalization used in Redding and Weinsten (2020) . • Simple numerical illustration to show how additive normalization (used recently in Carluccio et al, 2023 ) fails to satisfy commensurability. We show that the normalization conditions for a CES utility function with time-varying preferences (Redding and Weinstein, 2020) must be of weighted-geometric mean form to ensure commensurability of price indexes, and numerically illustrate failure of additive normalization to satisfy commensurability.