Refined Estimation of Service Price Differentials and their Effect on Productivity among Regions in Japan: Treatment of Commerce, and Transforming into Value-added Deflator (Japanese)

In measuring regional productivity differences, it is important to pay due attention to service price differentials among regions. Although we dealt with this task in Tokui and Mizuta (2017), two significant unsolved questions remain. In this paper we tackle these two remaining issues; the first is how to estimate regional price differentials in commerce, and the other is how to derive value-added deflators from gross-product based price indexes. Since the SNA manual defines wholesale and retail output as the total value of the trade margins, we calculate the corresponding price data item by item from regional retail price data multiplied by the margin rate of each item. The Country-Product-Dummy Method of Tao and Timmer (2000) is applied to these data to produce indexes of regional price differentials in commerce. The estimated price indexes still include such costs as heating and lighting, communication, and advertisement expenses. To derive the value-added deflator from these gross-product based price indexes we derive converting formula from the Translog unit cost function. Based on these two refinement-of-service price differentials among regions we newly analyze regional productivity differences in Japan.