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6.2.2  Source deductions (PAYE)

As before, the simple abbreviation PAYE is used to denote total source deductions, where approximately 97% of total source deductions are PAYE deductions from salaries, wages and social assistance benefits, and the remainder are from employer contributions to registered superannuation schemes. Here the macroeconomic variable used as a tax-base proxy for the PAYE forecast is compensation of employees (COE).

Figure 4 – Source deductions (PAYE) and compensation of employees (COE)
The top plots show PAYE (solid black) and its forecast (dashed black), scaled COE (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 PAYE (black), COE (red), tax ratio (blue), tax ratio trend (green) and residual error (cyan).
Figure 4: Source deductions (PAYE) and compensation of employees (COE).
Source: The Treasury

The results of applying decompositions (21) and (22) are shown in Figure 4 together with PAYE and its forecast, COE and its forecast, the associated tax-to-COE ratio and its forecast, and the tax ratio trend. Forecasts of PAYE and COE have both underestimated actual outcomes over the last 4 years (5 years for COE). The tax ratio trend provides a good fit to the tax ratios with a generally downward trend in the late 1990s, when some personal tax rates were reduced and income thresholds were increased, and a slight increase more recently, with the introduction of the 39% tax rate.

The boxplots in Figure 4 show that, for decomposition (21), COE forecast errors are significantly biased downwards and it is these that are contributing to the same significant bias of the forecast errors for PAYE. The tax ratio percentage forecast errors, although more often negative than positive, do not appear to be significantly biased and are less volatile than the COE percentage forecast errors. For decomposition (22), the boxplots show few signs of bias, but the percentage forecast errors due to forecasting the tax ratio trend are more volatile than those of the non-systematic error component. The personal tax cuts of 1 July 1996 and 1 July 1998 have also introduced additional volatility in these components over the period 1996 through to 1999. These observations are supported by the summary statistics given in Table 5.

PAYE revenue Yt and its components: compensation of employees Xt, associated tax ratio Rt, tax ratio trend αt and residual et

Table 5 – Summary statistics for PAYE revenue percentage forecast errors
  Yt Xt Rt αt et
Bias -1.67 -1.39 -0.28 -0.24 -0.04
Standard deviation 2.00 2.38 1.33 1.75 1.43
RMSE 2.54 2.66 1.30 1.69 1.36
Lag one autocorrelation 0.50 0.44 -0.01 -0.21 -0.70

Source: The Treasury

The lag one autocorrelations of the various components given in Table 5 are, for the most part, not significantly different from zero. The exception is the residual component which has a significant negative correlation, most likely due to the alternating pattern over the 1996-1999 period that resulted from the personal tax cuts of 1 July 1996 and 1 July 1998.

The components of decomposition (21) were not significantly cross-correlated, but there was a significant negative correlation between the components of decomposition (22) at lag zero with the other lags being non-significant. This contemporaneous correlation is likely to be an artefact of the personal tax cuts of 1 July 1996 and 1 July 1998.

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