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6.2.5  Net other persons tax

This is tax on personal income that is not taxed at source. It includes income tax from self-employed people, trusts, clubs, societies and Maori authorities, together with tax on investments that are not already taxed at source. Again, a variety of forecasting models has been used at various times, drawing on a range of macroeconomic variables. The one variable that has been used in all cases is entrepreneurial income and this was used in the benchmark model and the associated forecast error decompositions.

Figure 7 – Net other persons tax and entrepreneurial income
The top plots show net other persons tax (solid black) and its forecast (dashed black), scaled entrepreneurial income (solid red) and its forecast (dashed red), the associated tax ratio (solid blue) and its forecast (dashed blue), and the tax ratio trend (solid green). The remaining time series plots and boxplots show the percentage forecast errors due to forecasting net other persons tax (black), entrepreneurial income (red), tax ratio (blue), tax ratio trend (green) and residual error (cyan).
Net other persons tax and entrepreneurial income.
Source: The Treasury

The results of the decompositions (21) and (22) are shown in Figure 7 together with net other persons tax and its forecast, entrepreneurial income and its forecast, the associated tax ratio and its forecast, and the tax ratio trend. Forecasts of net other persons tax have tended to overestimate their actual outcomes whereas forecasts of entrepreneurial income have tended to underestimate actual outcomes. The tax ratio trend provides a reasonable fit to the tax ratios, including the period of tax rate reductions in the late 1990s. However, the tax ratio forecasts almost all overestimate actual outcomes.

Highly significant biases are the dominant feature of the boxplots in Figure 7. For decomposition (21), the forecast errors for entrepreneurial income are significantly biased downwards, and those for the tax ratio are significantly biased upwards. These cancel and lead to forecast errors for net other persons tax that are not significantly biased, but do have increased volatility. Note also that the volatility of the tax ratio percentage forecast errors is greater than the volatility of the percentage forecast errors for entrepreneurial income. For decomposition (22), the boxplots show that the significant bias of the tax ratio percentage forecast errors comes from forecasting the tax ratio trend, as expected. These observations are supported by the summary statistics given in Table 8.

Table 8 – Summary statistics for net other persons tax revenue percentage forecast errors

Net other persons tax revenue Yt and its components: entrepreneurial income Xt, associated tax ratio Rt, tax ratio trend αt and residual et

  Yt Xt Rt αt et
Bias 2.79 -4.13 6.93 6.97 -0.04
Standard deviation 5.80 3.92 5.62 4.32 4.59
RMSE 6.20 5.57 8.76 8.09 4.38
Lag one autocorrelation -0.19 -0.24 -0.55 0.16 -0.37

Source: The Treasury

The lag one autocorrelations given in Table 8 are not significantly different from zero with the marginal exception of the tax ratio percentage forecast errors which showed negative autocorrelation due to the cycling between errors above and below the bias level. If real, it is unclear what this effect might be caused by. The components of each decomposition (21) and (22) also showed little evidence of any significant cross-correlation.

6.2.6  Other taxes

The previous tax types account for more than 80% of the total tax take. The remainder is made up of resident withholding tax (RWT), excise taxes, customs duty and a few smaller taxes, some of which are not forecast by the Treasury. Most of these taxes do not necessarily depend on any particular component of GDP. For example, most of RWT is dependent on interest rates, and excise taxes are dependent on long-run growth trends. While a large part of customs duty is tariffs on imported goods, and therefore has some relationship with nominal goods imports, about half of customs duty is excise duty on imported petrol, which is a volume-based duty that can be very volatile as it is dependent on the arrival of bulk fuel shipments. Nevertheless, the aggregate of these other taxes has been analysed using the benchmark model with nominal GDP as the macroeconomic driver or tax-base proxy. Since the components of other taxes have, at best, a loose association with GDP, the resulting decompositions may be of limited use.

Figure 8 – Other tax revenue and nominal GDP
The top plots show other taxes (solid black) and its forecast (dashed black), scaled GDP (solid red) and its forecast (dashed red), the associated tax ratio (solid blue) and its forecast (dashed blue), and the tax ratio trend (solid green). The remaining time series plots and boxplots show the percentage forecast errors due to forecasting other taxes (black), GDP (red), tax ratio (blue), tax ratio trend (green) and residual error (cyan).
Figure 8: Other tax revenue and nominal GDP.
Source: The Treasury

The decompositions (21) and (22) are shown in Figure 8 together with other taxes and its forecast, GDP and its forecast, the associated tax ratio and its forecast, and the tax ratio trend. Forecasts of other taxes and GDP have both underestimated their actual outcomes over the entire 1995-2005 period except for 1998-1999 when the reverse was true. The tax ratio trend provides a reasonable fit to the tax ratios, despite the sharp decrease in the late 1990s.

For decomposition (21), the boxplots in Figure 8 show that the forecast errors for GDP are significantly biased downwards and it is these that are contributing to the same significant bias of the forecast errors for other taxes. The tax ratio percentage forecast errors are not biased, but are more volatile than the percentage forecast errors for GDP. For decomposition (22), the boxplots show no signs of bias and the percentage forecast errors due to forecasting the tax ratio trend are slightly more volatile than those of the non-systematic error component. These observations are supported by the summary statistics given in Table 9.

Table 9 – Summary statistics for other tax revenue percentage forecast errors

Other tax revenue Yt and its components: GDP Xt, associated tax ratio Rt, tax ratio trend αt and residual et

  Yt Xt Rt αt et
Bias -2.14 -1.58 -0.56 -0.52 -0.04
Standard deviation 4.65 1.97 3.70 2.92 2.28
RMSE 4.93 2.46 3.57 2.83 2.17
Lag one autocorrelation 0.24 0.12 0.14 0.23 -0.30

Source: The Treasury

The lag one autocorrelations in Table 9 are not significantly different from zero, and the components of each decomposition (21) and (22) showed no evidence of significant cross-correlation.

6.3  Other forecast horizons

Similar analyses were undertaken for other forecasting horizons. Apart from the size of the forecast errors which, as expected, increase in magnitude with increasing forecast horizon, the results obtained were very similar to the one-year-ahead analyses given in the previous sections. An example of these results is given in the Appendix where the equivalents of Figures 2-9 are given for the case of a two-year-ahead forecast horizon.

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