4.1.1 Sensitivity analysis to alternative index number formulae
Section 2 argued there were good justifications on both economic and axiomatic grounds for using the Fisher index to calculate productivity series. However, to give an idea of the sensitivity of New Zealand productivity series to alternative index number formulae, this section presents multifactor productivity series using alternative index number formulae. Alternative multifactor productivity series are also shown in Figure 3. Average growth rates for the alternative productivity series for the period 1988 to 2002 and the sub-periods 1988 to 1993 and 1993 to 2002 are presented in Table 2.[8]
| March Year | Chained Fisher | Chained Törnqvist | Chained Laspeyres | Chained Paasche | Unchained Laspeyres | Unchained Paasche |
|---|---|---|---|---|---|---|
| 1988 to 1993 | 0.09% | 0.09% | 0.13% | 0.05% | 0.12% | 0.06% |
| 1993 to 2002 | 1.32% | 1.32% | 1.30% | 1.34% | 1.50% | 1.12% |
| 1988 to 2002 | 0.88% | 0.88% | 0.88% | 0.88% | 1.00% | 0.74% |
Figure 3 shows that the chained Fisher and Törnqvist indices are almost identical. This is consistent with other studies, which have found little difference between Fisher and Törnqvist indices, and illustrates that these two indexes are approximations for each other. In addition, the chained Laspeyres and Paasche multifactor productivity series are also very similar to the Fisher and Törnqvist multifactor productivity series. Overall, New Zealand market sector multifactor productivity series appear to be relatively insensitive to the choice of index number formulae when productivity series are chained.
Chaining appears to be quite important when measuring market sector productivity in New Zealand. Figure 3 shows a marked increase in the index number spread when comparing unchained Laspeyres and unchained Paasche multifactor productivity series. The unchained Paasche series is similar to the chained Paasche series up to 1993, but diverges thereafter. The unchained Laspeyres series is similar to the Fisher and Törnqvist series, but appears to diverge from 1999. The range of estimates for average multifactor productivity for the period 1988 to 2002 is 0.74% per annum, using the unchained Paasche series, to 1.00% per annum using the unchained Laspeyres series. For the sub-period 1993 to 2002, the range for average multifactor productivity growth is 1.12% per annum, using the unchained Paasche series, to 1.50% per annum, measured using the unchained Laspeyres series.
Notes
- [8]Productivity series used in Figure 3 and underlying the average growth rates reported in Table 2 are available in Appendix 2.
