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On the Normalization Condition for Cost of Living Comparisons under Time-Varying Preferences

Author

Listed:
  • ABE, Naohito
  • Rao, D.S. Prasada
Abstract
There is growing interest in measuring inflation in the presence of time-varying preferences. To make price comparisons under changing preferences, a number of studies are imposing normalization conditions on preference parameters, assuming cardinal utility functions. The resulting price indexes depend on the choice of normalization condition imposed, necessitating a careful specification of this condition. Carluccio et al. (2023) adopt a normalization where the arithmetic mean of the time-varying taste parameters remains constant, whereas Hottman et al. (2016) and Redding and Weinstein (2020) maintain a constant geometric mean. In this paper we invoke the commensurability axiom which requires the price index to be independent of units of measurement. We prove that a necessary and sufficient condition on the normalization condition that ensures commensuarability is the geometric mean-based normalization. Consequently, adopting an arithmetic meanbased normalization condition results in index values that depend on arbitrarily chosen measurement units, such as gallons or 100 milliliters.

Suggested Citation

  • ABE, Naohito & Rao, D.S. Prasada, 2024. "On the Normalization Condition for Cost of Living Comparisons under Time-Varying Preferences," RCESR Discussion Paper Series DP24-1, Research Center for Economic and Social Risks, Institute of Economic Research, Hitotsubashi University.
    • Handle: RePEc:hit:rcesrs:dp24-1
    Note: 15 January, 2024
    as

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    File URL: https://hermes-ir.lib.hit-u.ac.jp/hermes/ir/re/82266/dp24-1_rcesr.pdf
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    References listed on IDEAS

    as
    1. Rahel Braun & Sarah M. Lein, 2021. "Sources of Bias in Inflation Rates and Implications for Inflation Dynamics," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 53(6), pages 1553-1572, September.
    2. Colin J. Hottman & Stephen J. Redding & David E. Weinstein, 2016. "Quantifying the Sources of Firm Heterogeneity," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 131(3), pages 1291-1364.
    3. Stephen J Redding & David E Weinstein, 2020. "Measuring Aggregate Price Indices with Taste Shocks: Theory and Evidence for CES Preferences," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 135(1), pages 503-560.
    4. Carluccio, Juan & Gautier, Erwan & Guilloux-Nefussi, Sophie, 2023. "Dissecting the impact of imports from low-wage countries on inflation," European Economic Review, Elsevier, vol. 160(C).
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Cost of Living; Price Index; Preference Heterogeneity; Characterization;
    All these keywords.

    JEL classification:

    • E31 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Price Level; Inflation; Deflation
    • C43 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Index Numbers and Aggregation

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