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

6  Analysis

We focus primarily on the one-year-ahead tax revenue forecasts prepared by the Treasury for the annual May or June Budget since it is these forecasts and their associated forecast errors that are subject to the greatest scrutiny. A top-down analysis of the tax revenue forecast errors was undertaken using the decompositions developed in Section 4. The same analysis was also undertaken for the other forecasting horizons with larger errors overall that increase with forecast horizon as expected. However, apart from scale, the results are very similar.

The total tax revenue forecast error was first disaggregated into its component tax types using the decompositions of Section 4.2. In particular, the proportionate error decomposition (10) is given by


where e(Y(t)) is the proportionate forecast error for the total tax revenue and the e(Yj(t)) are the proportionate forecast errors for the individual tax types. The tax share Pj(t) measures the tax revenue for tax type j as a fraction of the total tax revenue Y(t).

Figure 1 – Tax revenues as a percentage of total tax revenue
PAYE (red), GST (green), corporate tax (blue), net other persons tax (cyan) and other taxes (magenta)
Figure 1: Tax revenues as a percentage of total tax revenue. />
Source: The Treasury

Plots of the Pj(t) expressed as percentages are given in Figure 1 where it can be seen that they evolve slowly and smoothly over time as expected. In general, it is evident that the last available value of any tax share Pj(t) should provide an excellent one-year-ahead forecast of Pj(t+1). The averages of the tax shares Pj(t) are given in Table 1 and indicate that PAYE (37%) and GST (26%) are the largest tax revenues with the remaining tax revenues each less than 20% of total tax revenue in the period under examination (June years 1995 through to 2005).

Table 1 – Means and standard deviations of individual tax revenues
% of total tax revenue PAYE GST Corporate Net OP Other
Mean 37.3 26.3 14.5 7.7 14.1
Standard deviation 0.7 1.3 1.5 0.8 1.0

Source: The Treasury

Each individual tax revenue proportionate forecast error e(Yj(t)) was then further decomposed into a component due to forecasting Xj(t), the macroeconomic variable used as a proxy for the associated tax-base, and a component due to forecasting the tax ratio . Using (15), this decomposition is given by


where, as before, the e(.) denote proportionate forecast errors of the components concerned.

Finally, the proportionate forecast error e(Rj(t)) of each individual tax ratio is further decomposed into an error in forecasting the systematic tax ratio trend, and a non-systematic error. This decomposition based on (18) is given by


where e(αj(t)) is the proportionate forecast error for the tax ratio trend αj(t) and nj(t) is the non-systematic random error. The latter provides a measure of the best accuracy that can be achieved using the benchmark models adopted.

Note that the additive nature of the decomposition (20) implies that it is the weighted errors , and,, rather than their unweighted forms, that contribute to the proportionate forecast error for the total tax revenue. Because of their importance, we refer to these as weighted proportionate forecast errors in what follows.

Fitting the benchmark model to the tax ratio data Rj(t) entails estimating the unobserved trends αj(t). Many trend estimates are possible. We have chosen to use the trend estimate proposed by Hodrick and Prescott (1997) for the identification of business cycles, the so-called Hodrick-Prescott filter, which fits a trend to all the available data points. No attempt was made to optimise the smoothing parameter λ of this trend filter and the same value as that given in Hodrick and Prescott (1997) was used (λ =1600). In general, this procedure worked well and gave trend estimates that were smooth and ran through the middle of the data leaving residuals that were, for the most part, well-approximated by uncorrelated random errors with zero mean and common variance (non-systematic white noise).

The Hodrick-Prescott trend filter cannot be used directly for forecasting future values of the unobserved trends αj(t). However, it and other more general filters such as the Kalman filter, can be underpinned by parametric stochastic trend models that can be used to forecast future values of αj(t). See Harvey and Jaeger (1993).

In the following sections, these forecast error decompositions are applied and a limited statistical analysis undertaken. Since the data runs from 1995 to 2005 inclusive, only 11 observations are available for any one series and so the statistical results obtained are at best indicative.

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