Regional Price Index Number: Theory and its Application to the Prefectural Price Index in Japan

We construct the regional price indexes using the retail price survey and the family income and expenditure survey in Japan. We compare various index numbers, giving special attention to recent developments in index number theory. The main findings are as follows: 1) The prefectural price index, including imputed rents, exhibits heterogeneity across prefectures to a great extent for all the index number formulas. The largest difference across prefectures is greater than 20% points. 2) Excluding the imputed rents, we find the tendency for heterogeneity to be small, that is, less than 10% points at the most, which is consistent with the official regional price index number by the Japanese Statistical Bureau. 3) Prefecture level index numbers for foods are generally remarkably similar. 4) For non-food items, selecting the index number formula becomes important. In particular, the Jevons Index and the Constant Elasticity of Substitution (CES) Unified Price Index (CUPI) exhibit significant differences form other index number formulas, such as the Geary-Khamis, Fisher, and Abe-Rao indexes. The estimation results show that the effects of the imputed rents are substantial, whereas the choice of the index number formula is also important, suggesting the decisive role played by the selection of the “appropriate” index number formula in applied research.