For discussion of the “superlative index,” see Diewert (1976) and Sakuramoto (1999). 4  In Japan, the year-on-year rate of increase in the core CPI was higher than that in the private consumption deflator and the GDP deflator in the 1990s, though there had been little difference between these three indices in the preceding period.
There seems to have been a large difference between the three indices since the mid-1990s when deflation measured by  BIS Review 2/2004  3  of this cannot be regarded as the bias in the Paasche price index because CPI, which is a Laspeyres price index, has an upward bias. The Fisher price index is less biased than other price indices.