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The uncertainty of government debt projections.

Since 1998, fiscal policy in the UK has been guided by two rules: the golden rule to borrow over the economic cycle only to invest, such that the average annual surplus on the public sector current budget as a share of GDP is greater or equal to zero; and the sustainable investment rule that public sector net debt should not exceed 40 per cent of GDP over the economic cycle.

The Treasury publishes forecasts of its fiscal target variables on a regular basis in its Budget and Pre-Budget Reports. As a further guide to the likely course of fiscal policy it is useful to have an idea of the uncertainty around these forecasts. The Treasury does not publish probability bands around its forecasts of the average surplus on the current budget or of public sector net debt (PSND), although it does publish the mean absolute error of its net borrowing projections one and two years ahead.

The uncertainty associated with evaluating fiscal policy against the golden rule is twofold, in the sense that not only is there uncertainty with respect to the future course of the target variable (the average surplus on the current budget), but there is also uncertainty about the dating of the economic cycle and hence the period over which the target variable should be measured. This latter source of uncertainty is potentially quite large. For example, in an assessment of the uncertainty of output gap estimates for the Euro Area, Mitchell (2003) suggests that the uncertainty of output gap estimates is such that in real time one can never statistically rule out that the economy is at full capacity. The uncertainties that need to be considered in evaluating the sustainable investment rule would seem more straightforward, in that they do not involve an assessment of the economic cycle. The Treasury has repeatedly suggested that to "meet the sustainable investment rule with confidence, net debt will be maintained below 40 per cent of GDP in each and every year of the current economic cycle". (1)

To assist evaluation of the fiscal position vis-a-vis the golden rule, the NIESR has published confidence bands around its quarterly forecast of the current budget surplus in this Review since January 2003. These confidence bands are derived from stochastic simulations using the National Institute Global Econometric Model (NiGEM) as described in NIESR (2003) and Barrell and Hurst (2003). The shocks employed in these stochastic simulations are drawn from past shocks to the structural equations of NiGEM. The benefit of this approach over the use of historical forecast errors to generate confidence intervals is that it takes into account changes in the fiscal and monetary environment, i.e. the error bands generated by this method vary according to the present structure of the economy.

The uncertainty of PSND projections can be evaluated using the same method. Figure 1 shows the root mean square error (RMSE) of projections for PSND as a per cent of GDP implied by the same set of stochastic simulations used to assess the uncertainty of projections for the current budget balance. Assuming that prediction errors are unbiased and normally distributed, the RMSE shown in figure 1 can be used to construct confidence bands around projections of PSND. On this basis figure 2 illustrates confidence bands around the Treasury's forecast, published in last year's Pre-Budget Report, alongside the 40 per cent debt ceiling implied by the sustainable investment rule. The forecast for March 2006 is assumed to be two quarters ahead. Similarly, the forecasts for March 2007 and March 2008 are assumed to be six and ten quarters ahead.


The confidence intervals around the Pre-Budget Report projection suggest that, given current policy plans, the Treasury should expect to tighten fiscal policy in order to meet its sustainable investment rule with a chance of 1 in 10 next fiscal year and a chance of 1 in 5 in 2007-8.

As a robustness check it is instructive to compare estimates of uncertainty obtained by different methods. Table 1 shows the mean absolute error (MAE) and the RMSE of Treasury forecasts of PSND as a per cent of GDP under the current fiscal regime. As shown in the table, these are taken from a very small sample and are therefore not particularly accurate estimates of forecast error properties. Comparing the RMSE of the Treasury's historical forecast error in table 1 with the RMSE obtained by stochastic simulations in figure 1, it appears that in the very near term both methods suggest a similar degree of forecast error for PSND as a per cent of GDP. The RMSE of Pre-Budget Report projections of the debt stock for March of the following year is 1.0 per cent of GDP. The RMSE implied by stochastic simulations for two quarters ahead projections of the debt stock is 1.1 per cent of GDP.

Further out the stochastic simulations show a smaller prediction error than those implied by historical forecast errors, although the small sample size has to be emphasised. (2) The RMSE of Pre-Budget Report projections of the debt stock for March two and three years following publication is 2.7 and 4.1 per cent of GDP compared to the RMSE implied by stochastic simulations of 1.9 and 3.5 per cent of GDP. In other words, based on historical forecasting performance, the Treasury perhaps should be less confident of meeting the sustainable investment rule than figure 2 suggests.


(1) The statement, "The Government's fiscal rules--the golden rule and the sustainable investment rule--are both defined over the cycle", in another Treasury publication (HM Treasury, 2002) suggests an element of ambiguity as to the appropriate method of evaluating the sustainable investment rule.

(2) The forecast error variance for public sector net borrowing is published by the Treasury for a larger historical sample. Exploiting the relationship between net borrowing and net debt, it is possible to derive an estimate of the variance of 'historical' forecast errors for PSND based on the forecast error variance for public sector net borrowing. This method has recently been adopted by the Institute for Fiscal Studies to construct error bands around its Green Budget projections of PSND. At a glance it would appear that the RMSE obtained in this manner is slightly greater than that implied by stochastic simulations for the time frame analysed here.


Barrell, R. and Hurst, I. (2003), 'Benchmarks and targets under the SGP: evaluating safe deficit targets using NiGEM', National Institute Economic Review, 185, pp. 54-63.

HM Treasury (2002), 'Core Debt: An Approach to Monitoring the Sustainable Investment Rule', April.

--(2005), 'Britain meeting the global challenge: enterprise, fairness and responsibility', Pre-Budget Report, December, HMSO.

Mitchell, J. (2003), 'Should we be surprised by the unreliability of real-time output gap estimates? Density estimates for the Euro area', revised in 2005. NIESR Discussion Paper 225.

NIESR (2003), 'Uncertainties in the public sector forecast', National Institute Economic Review, 183, pp. 41-2.

Ian Hurst and Rebecca Riley, Thanks to Ray Barrell, Simon Kirby and Martin Weale for helpful suggestions.
Table 1. Properties of HM Treasury public sector net debt projections
(% of GDP)

Forecast horizon MAE RMSE Sample size
End March
of year
publication BR PBR BR PBR BR PBR

1 1.6 0.8 2.1 1.0 6 7
2 3.3 1.9 3.9 2.7 5 6
3 3.9 3.5 4.3 4.1 4 5

Notes: MAE is the mean absolute error of the forecast; RMSE is the
root mean square error of the forecast; sample includes Pre-Budget
Reports 1998-2004 and Budget Reports 1999-2004.
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Author:Hurst, Ian; Riley, Rebecca
Publication:National Institute Economic Review
Geographic Code:4EUUK
Date:Jan 1, 2006
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