To Log or not to Log? : Proportionality in Time-Dummy Hedonic Price Indexes

Time-dummy hedonic models are widely applied in the construction of quality­adjusted price indexes for goods and services whose characteristics evolve over time. The specification of these models, particularly the transformation applied to the price variable, plays a decisive role in determining measured price change. This paper evaluates transformation choice within the framework of the proportionality axiom in index-number theory, which requires that if all prices in the comparison period are scaled by a positive constant, the index must be scaled by the same con­stant. It is demonstrated that, for time-dummy hedonic regressions with observed characteristics, the logarithmic transformation of prices—combined with the con­ventional exponential mapping of time effects-is the only specification that satisfies proportionality for all admissible datasets. Alternative transformations, including the Box-Cox family, do not generally meet this requirement when characteristics are present, except under highly restrictive, data-specific conditions. This paper provides clear implications for statistical agencies and applied researchers. The theoretical results are illustrated using both simulated datasets and scanner data from Japan, reinforcing the need for aligning hedonic price index construction with axiomatic principles.