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An Analysis of Tax Revenue Forecast Errors - WP 07/02

7  Conclusions

This report presents an analysis of the New Zealand Treasury's tax revenue forecast errors, both in aggregate and disaggregated by individual tax type. The primary objective was to better determine the major sources of tax revenue forecast error and to identify any potential for methodological improvements. Using a simple structural model as a benchmark, the individual tax revenue forecast errors were first disaggregated into a component due to forecasting the associated macroeconomic driver used as tax-base proxy, and a component due to forecasting the tax ratio. The tax ratio is further disaggregated into a component error due to forecasting the tax ratio trend and non-systematic random error. The latter provides a measure of the best accuracy that can be achieved using the benchmark models adopted.

In terms of their contribution to total tax revenue, PAYE (37%) and GST (26%) are the largest followed by corporate tax (15%), net other persons tax (8%) and other taxes (14%). These tax shares or weights were used to scale the percentage forecast errors of each disaggregated tax revenue component to determine the contribution of that component to the total percentage forecast error. The weighted percentage forecast errors for the various tax revenues indicated that all the individual tax revenue forecasts, with the exception of corporate tax and net other persons tax, were significantly underestimating actual outcomes. As a consequence, the total tax revenue was also significantly underestimated.

After checking for bias, the volatility (standard deviation) of the individual forecast errors is a measure of the precision of the forecasting methods used. Large volatilities indicate poor precision and highlight the need for better forecasting models and methods. Here, corporate tax stood out as the tax revenue that was least precisely forecast since its weighted percentage forecast errors had a standard deviation that was almost three times the average of the others. Overall forecasting performance is measured by the root mean squared error (RMSE), or square root of the sum of the variance and squared bias. This showed that corporate tax was clearly the least precisely forecast, followed by PAYE, then GST and other taxes, with net other persons tax having the smallest RMSE.

The primary forecast error decomposition (21) splits the percentage forecast error for each tax type into a component due to forecasting the macroeconomic variable used as a tax-base proxy, and a component due to forecasting the tax ratio. In terms of bias, all the macroeconomic variables used for tax-base proxies significantly underestimated their actual outcomes resulting in percentage forecast errors with significant downward biases. However the corresponding tax ratio percentage forecast errors all showed no significant bias with the exception of net other persons tax, for which the percentage forecast errors had a significant compensating upward bias. This shows that the main source of tax revenue underforecasting is almost certainly the underforecasting of the macroeconomic variables used as tax-base proxies, rather than the tax ratios.

Conversely, the macroeconomic variables yielded percentage forecast errors that were generally clustered relatively closely about their mean, or bias, and were less volatile than those for the tax ratios. This suggests that the tax ratio forecasts, while unbiased, are less precisely determined than the macroeconomic forecasts.

The contributions to the total tax revenue percentage forecast error of the various tax-share weighted components of the primary decomposition (21) are shown in Figure 9. These summarise and provide further graphical support for the comments made above.

Figure 9 – Tax-share weighted percentage forecast errors
Tax-share weighted percentage forecast errors due to forecasting the associated macroeconomic driver (top plots) and tax ratio (bottom plots) for total tax revenue (black), PAYE (red), GST (green), corporate tax (blue), net other persons tax (cyan) and other taxes (magenta). Time series plots are given on the left and boxplots on the right.
Figure 9: Tax-share weighted percentage forecast errors.
Source: The Treasury

The secondary forecast error decomposition (22) splits the percentage forecast error for each tax ratio into a component due to forecasting the tax ratio trend, and non-systematic random error. This was done using the benchmark model which provided a good fit to the tax ratios considered and, as a result, yielded reasonable decompositions with components that were, in general, not significantly correlated. With the exception of net other persons tax, all tax types yielded percentage forecast errors for the disaggregated components that showed no significant bias. However, the volatility of the error component due to forecasting the tax ratio trend was almost always greater than that of the non-systematic error component (more than twice in the case of GST and corporate tax) indicating that better tax ratio forecasts are needed and could be achieved, even with the simple benchmark model used here.

Some of the percentage forecast error time series show persistence which suggests that they might be serially correlated. However this was not borne out by the Durbin-Watson test which failed to show significant lag one autocorrelations in most cases, even with nominal autocorrelations as large as 0.5. This is partly due to the small sample size of 11 observations and partly because, in this case, even one anomalous pattern of errors in the time series can destroy any patterns seen in the rest of the time series. In cases where there was significant lag one autocorrelation, it could often be explained in other ways. In particular, if random walk predictors are used when there is a trend cycle present in the data (consider the tax ratio time series for total tax revenue and corporate tax for example) then there will be systematic under-forecasting in times of increasing trends and over-forecasting in times of decreasing trends. Adoption of conservative predictors such as these, if sustained over a reasonable period, can lead to eliminate many of these effects

The simple benchmark models adopted are, at best, approximations to the methods the Treasury currently uses or has used in the past. However, judging from the analysis, they appear to have some merit as competing models, if only because of their simplicity. In particular, the benchmark model with a suitable structural parametric model for the trend of the tax ratios could be used for forecasting the tax ratios. Other time series models without macroeconomic drivers could also be used. Simple forecasts such as these would help calibrate the current Treasury forecasts and could be combined appropriately to achieve a better forecast overall. A systematic evaluation of the forecasting accuracy of a selection of the more formal models suggested in Section 3 using historical data would help resolve some of these issues.

Finally, there is the issue of how to best adjust the forecasts of the macroeconomic data from Statistics New Zealand so that they represent forecasts of fully revised data rather than unrevised data. This is an important general issue that extends beyond just tax forecasting and deserves a separate study and analysis.

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