First, the data on expenditures required for computation of either Fisher's Ideal index or the Tornqvist index are available only at the quarterly frequency.
Just as it is not possible with existing source data to calculate the textbook version of the Laspeyres index, so it is not possible to calculate the textbook versions of either Fisher's Ideal index, the Tornqvist index, or a geometric-means index.
Used as the true, benchmark cost-of-living index, Fisher's ideal index can assess the degree of substitution bias inherent in the fixed-weight Laspeyres calculation.
The percent difference between the 1994 Fisher's ideal index and the corresponding 1994 Laspeyres index represents the degree of substitution bias:(44)
In both the fixed-base and the chainweight contexts, die Fisher's ideal index
and the Tomqvist index may be constructed.