3.3 Illustrative Examples

In order to provide an illustration of the nature of the relationships involved and the sensitivity to variations in the elasticity of taxable income, it is useful to consider the change to the income tax structure in New Zealand, made in the 2010 Budget. Table <ref>dist</ref> provides summary information regarding the distribution of annual personal taxable incomes in the 2008/09 tax year, the most recent year for which data are available.[13] For comparison purposes the tax rates and thresholds shown in the table relate to the structure in 2009/10. The overall arithmetic mean taxable income is $35,507.

Table 2 provides summary information about the pre- and post-2010 Budget tax structures, for the taxable income distribution of Table 1. In the 2010 Budget, all the income thresholds were left unchanged, but the marginal tax rates were reduced, in particular the top marginal rate. Given the relatively low value of the income threshold above which the top rate applies, this tax bracket contributes a higher proportion of total income tax revenue than the other brackets, even though it contains only ten per cent of taxpayers. This compares with the second tax bracket which contains over forty per cent of all taxpayers. The final column of the table reports the revenue elasticity in each tax bracket, evaluated at arithmetic mean income within the bracket. For each tax structure, this elasticity is highest in the third tax bracket because the value of arithmetic mean income in the bracket is relatively closer to the effective income threshold than for the other brackets. For those in the first tax bracket, the average and marginal tax rates are equal and hence the revenue elasticity is unity. The Budget change in the marginal tax rates has little effect on the revenue elasticities.

Figure 3: Elasticity of Total Tax Revenue wrt Tax Rates: Pre-2010 Budget

Figure 4: Elasticity of Total Tax Revenue wrt Tax Rates: Post-2010 Budget

Figures 3 and 4 show the variations in the elasticity, , for each tax bracket, as the elasticity of taxable income increases. As demonstrated above, the value of each falls linearly with the elasticity of taxable income, but the rate of decrease is less in the post-2010 Budget structure. In each case the elasticity, , for the lowest income tax bracket remains approximately constant. Although the elasticity is highest in the third tax bracket, the value of falls slightly faster in the top marginal rate bracket. This is because the value of τ / (1 - τ) is higher for the higher marginal tax rate, along with the fact that the top-rate bracket contributes a higher proportion of aggregate tax revenue. The reduction in the higher marginal tax rates, resulting from the 2010 Budget, implies that the revenue elasticity, , continues to be positive, for higher values of the elasticity of taxable income.

In these diagrams, the ‘total' line is drawn on the assumption that the elasticity of taxable income is the same for all tax brackets. However, this is unrealistic. Some evidence regarding the elasticity for New Zealand taxpayers is reported in Claus et al. (2010). They found that for those in the lower tax brackets, the estimated elasticities were very small, but for the top marginal tax rate the responses were substantial. For top-rate taxpayers, the values were mainly in the range 0.5 to 1.2. These findings have potentially important implications. For the higher marginal tax rates, the diagrams show that if the elasticity is above around 0.6, further increases in the rates could lead to reductions in total income tax revenue.[14] Aggregate revenue is clearly most responsive to changes in the second marginal rate even if, as seems unlikely, the elasticity of taxable income is relatively high.