Recall that the PCE applies a chained Fisher index
, while the CPI applies a fixed-bundle Laspeyres with weights updated biannually.
In a similar way, the chained index measuring the cohort effect between cohort 1 and k, using the Fisher index
in Equation (17) and for (j, k) [member of] a, is the following:
Similarly, we estimated the national-level Fisher index
Using the equations in the text, both a Laspeyres index L and a Fisher index
F will have values of 1.
The Tornqvist index fails to satisfy some of the desirable axioms that the Fisher index
satisfies, yet the empirical results are essentially identical.
A final Fisher index
was performed for cafeteria and laundry services.
For example, to compute IP growth as an annually weighted Fisher index
for the second half of 1996 requires unit value added for 1996 and 1997.
In effect, the discrepancy between the sum of the industry output volumes and the aggregate output volume that arises in a Fisher index
or chained index framework will translate into a discrepancy between the sum of the productivity change contributions and the aggregate productivity change.
This section examines some ATPI series, based on the Fisher index
formula, for several class-of-service and point-of-origin categories.
This paper uses the Fisher index
to construct market sector and industry productivity series to provide methodological continuity with Diewert and Lawrence (1999), who also used the Fisher index
when constructing productivity series for New Zealand.
Therefore, the Fisher index
, calculated as the geometric mean of the Paasche and the Laspeyres, is used.
In the new formulation, the weights are expressed as unit value added (a price) to facilitate the aggregation of IP as an annually weighted Fisher index
for the recent period.