A Mathematical Model of Perceived Price Changes Based on Kullback–Leibler Information and Data Analysis of Price Change Perception

This paper proposes a mathematical model of price change perception in economic environments. The model introduces the Kullback–Leibler (KL) divergence between the expected price and the observed price as an index of attentional salience and integrates Takemura’s (1998, 2021) Mental Ruler Theory with the attention framework based on KL information proposed by Itti and Baldi (2009). We refer to this model as the SKL (Sum of the Kullback–Leibler Divergence) model, which explains the psychological mechanism underlying price judgment processes. Within this framework, the evaluation function for price change judgments is formulated as the integral of attentional salience, where attention is represented by the KL divergence associated with price changes. The proposed model is evaluated using 18 years of quarterly data (2008–2026) from the Bank of Japan’s Opinion Survey on General Public’s Views and Behavior, together with corresponding Consumer Price Index (CPI) data. Its explanatory power is assessed by comparison with conventional linear models, traditional psychophysical function models, and models based solely on KL information. The results indicate that the proposed model provides relatively superior explanatory performance, particularly in capturing periods of substantial changes in perceived inflation.