The grouped frequency distribution of taxable income in New Zealand for 2000-2001 is given in Appendix Table 3. This distribution is for income from all sources, and covers employed and self employed individuals. A histogram of this distribution is shown in Appendix Figure 1. The second mode at the bottom of the distribution raises a problem when using the standard two-parameter lognormal distribution. The pragmatic solution was adopted of adjusting the frequencies at the bottom of the distribution, as shown by smaller marked blocks for the two lowest income classes. It has in fact been found that New Zealand bimodal distributions can be modelled using a mixture distribution comprising a weighted average of lognormal and exponential distributions; see Bakker and Creedy (1999)
The resulting values were then used to obtain the mean and variance of logarithms reported above. The implied arithmetic mean value (using the properties of the lognormal mentioned above) was found to be close to the arithmetic mean calculated directly from the distribution.
Ad valorem tax-exclusive indirect tax rates are required for the same commodity groups as listed in Appendix Tables 1 and 2. In most cases the appropriate rate is simply the GST rate of 0.125. For rent and overseas travel, the rate is zero. In other cases, particularly where excises are involved, the computation of an effective ad valorem rate is complicated by the use of unit taxes, in combination with GST, and by the need to consolidate a wide variety of goods into a single category. The non-zero rates differing from the standard GST rate are as follows: road vehicles 0.07054; vehicle ownership expenses 0.58642; tobacco products 2.39845; alcohol 0.46819; recreational vehicles 0.0625; financial, insurance and legal services 0.0625; and expenditure not elsewhere included 0.23. For details on the computation of these rates, see Young (2002).