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

2  The Treasury's tax forecasting process

Twice each year, the Treasury produces economic and fiscal forecasts. The first forecast each year is usually prepared for the government's annual Budget and published as the Budget Economic and Fiscal Update (BEFU) around May or June. The second forecast is usually released in December, a week or two before Christmas, and published as the Half-Year Economic and Fiscal Update (HYEFU). Prior to 2005, this was known as the December Economic and Fiscal Update (DEFU). In an election year, there may be another forecast published four to six weeks before the general election, called the Pre-Election Economic and Fiscal Update.

The Treasury's economic forecasts are produced by the macroeconomic forecasting team, which devotes four to six weeks to the task at each forecasting round. The macroeconomic forecasters examine recent economic data, the forecasts produced by other New Zealand economic forecasters and discuss the state of the New Zealand economy with many business people around the country. They then run a variety of forecasting models to produce forecasts of many macroeconomic variables, such as GDP and the Consumer Price Index (CPI) of inflation. These forecasts typically cover the current year and the next four years.

The tax forecasts are prepared more-or-less concurrently with the economic forecasts. In the period under examination, a team of three forecasters and a manager prepared forecasts for each of the 20 or so tax types. A tax type is a category of total tax such as PAYE, which is the income tax paid by salary and wage earners, or GST or company tax. Like the economic forecasts, the tax forecasts cover the current year and the following four years. Unlike the economic forecasts, the tax forecasts are for June years. The macroeconomic variables are forecast either quarterly or in March years.

As each part of the economic forecast is prepared, the tax forecasters prepare forecasts of the relevant tax types. For example, as the labour market forecast is prepared, the tax forecasters prepare PAYE forecasts using variables from the labour market forecast. The economic and tax forecasters then examine the labour market and PAYE forecasts together to ensure that they are consistent with each other and with the total economic and tax forecast.

When forecasts have been prepared for each tax type, they are aggregated into a total tax forecast. Three taxes are not forecast by the Treasury. The Ministry of Transport supplies forecasts for Road User Charges (RUC) and motor vehicle licensing fees (MVF), and the Ministry of Economic Development supplies forecasts of Exhaustible Resource Levies (ERL). Collectively, these taxes account for less than 2% of total tax.

The tax forecasts are prepared in terms of both receipts, the tax actually paid to the collecting agency (usually Inland Revenue), and revenue, the tax that is actually due, regardless of whether or not it has been paid. The remainder of this document focuses on tax revenue, although the reasoning is identical for receipts and the results of the analysis for both revenue and receipts are similar.

2.1  Current forecasting methods

In common with many other official agencies around the world, the New Zealand Treasury uses mainly spreadsheet-based tax forecasting models and procedures comprising the following phases.

Phase 1: Determine the nominal tax revenue for the last available year which is the base year.

Phase 2: Adjust the nominal tax revenue for the base year by removing any known anomalies to establish the true underlying tax position for that year.

Phase 3: Apply the forecast growth rates of relevant macroeconomic variable(s) to forecast tax for 1 to 5 years ahead, applying elasticities if required.

Phase 4: Adjust the tax forecasts for anomalies such as tax policy changes, expected shifts in payment dates or taxpayer behaviour, and include any judgemental forecasting adjustments that may be deemed appropriate.

More detailed descriptions of some of the major tax types follow. These serve to illustrate the general nature of the forecasting methods used and how they are implemented.

2.1.1  Source deductions

This is the largest single tax type. It makes up about a third of the total tax collections, around NZ$18 billion out of a total of NZ$51 billion in the year to June 2005. Approximately 97% of source deductions are pay-as-you-earn (PAYE) deductions on wages, salaries and social assistance benefits, with the other 3% being specified superannuation contribution withholding tax (SSCWT).

The forecasting model used during the 1995-2005 period under examination was a quarterly multiplicative model that starts with a history of collections up to the most recently complete quarter. It projects forward by multiplying the collections base by macroeconomic forecasts of wage, salary and employment growth, but also makes adjustments for the progressivity of the individuals' tax scale (higher rates at higher incomes) and payday weightings (most people are paid on a fortnightly cycle). Two components of the source deductions forecast are prepared by other agencies and combined with the Treasury's forecast to produce the final forecast. These components are the Ministry of Education forecasts of PAYE on teachers' salaries, and the Ministry of Social Development forecasts of PAYE on social assistance benefits, which are both small in relation to total source deductions.

More formally, total source deductions SDq for quarter q are given by

where Gq denotes general source deductions excluding PAYE on teachers' salaries Tq and PAYE on social assistance benefits Bq. Forecasts of Gq are obtained by rating up past values by macroeconomic growth rates according to the recursion

where Eq denotes total employment and Wq denotes total, payday-weighted wages and salaries. Note the elasticities of 1 on employment and 1.2 on wages and salaries, with the wage and salary elasticity being estimated by empirical research. Using this recursion and associated forecasts of the macroeconomic growth rates, a forecast for Gq is now calculated for each quarter for the next 20 quarters or so. These quarterly forecasts are then accumulated into annual forecasts. Further ad-hoc adjustments may be made to the annual forecasts, such as adjustments for changes in tax policy or judgemental adjustments.

Throughout the remainder of this report we use the simple abbreviation PAYE to denote total source deductions (PAYE plus SSCWT).

2.1.2  Other persons tax

This is tax paid mainly by individuals and trusts on income that is not withheld, or is under-withheld, at source. Typically, this is tax paid by small-business operators and investors. Terminal tax from wage and salary earners also falls into this category. Net other persons tax, or other persons tax less refunds to all individuals, makes up about 8% of the total tax take.

This tax type is notoriously difficult to forecast. Since it is an amalgam of tax on a variety of sources, it is difficult to find a reliable macroeconomic driver to use for the forecasts. In the past, the Treasury has tried various multiplicative models and a micro-simulation model, but with varying degrees of success.

Currently, the Treasury uses a composite approach with some smaller anomalous components forecast separately using simple straight line extrapolation. The latter include revenue from income summaries (end-of-tax-year reconciliations for salary and wage earners), and rebates for charitable donations and child-minding/housekeeping expenses. With these components removed, the adjusted other persons tax is monthly revenue that has resulted from personal income. This is allocated into past tax years based on sampled data from the Inland Revenue Department (IRD), New Zealand's main tax-gathering agency. Then the monthly data are accumulated to give tax revenue and tax receipts totals for the respective tax years. The resulting annual adjusted other persons tax for tax year t is denoted Ot.

Although various macroeconomic variables have been used over the years to forecast Ot, the one that has been at the heart of all of the models considered is a measure of household entrepreneurial income calculated by Statistics New Zealand. In essence, the Treasury forecasting model assumes that forecasts of Ot follow the recursion

where It denotes entrepreneurial income, and At denotes any judgmental or policy adjustments made. The annual tax-year forecasts of revenue and receipts that result are then spread across budget years using interpolation based on the monthly seasonal patterns observed. Finally, these forecasts are accumulated together with the annual forecasts for income summaries and charitable donation rebates to yield an overall forecast for net other persons tax.

2.1.3  Other tax types

Most of the other tax types use models similar to these. Fringe benefit tax, company tax and GST forecasting models, for example, are based on growth rates of compensation of employees, total operating surplus and nominal domestic consumption respectively. Forecasting models for some of the smaller tax types are even simpler with forecasts of excise duties, for instance, based on trend growth estimates. A different model is adopted for forecasting withholding tax on interest. This uses a regression relationship with compensation of employees, domestic consumption, house prices and interest rates as regressor variables.

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