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7.

Uncertainty Bounds for Cyclically Adjusted Budget Balances

Ray Barrell, Ian Hurst and James Mitchell

7.1 Introduction

This chapter addresses issues concerning the uncertainty surrounding estimates of the
output gap and, in turn, the cyclically adjusted budget deficit. Uncertainty about the size
of the output gap is likely to be reflected in uncertainty about the size of the cyclical
adjustment to be applied to the budget deficit. Our main objective in this chapter is to
evaluate the uncertainty associated with a commonly used estimate of the output gap and
to demonstrate how this should be reflected in uncertainty about the cyclically adjusted
budget deficit. The degree of uncertainty associated with the estimate of the output gap
for a period in the past, when computed now, is noticeably less than that associated with
the estimate of the current (or real-time) gap. Since typically policy-makers are concerned
about the current gap, we focus on evaluation of real time estimates and their uncertainty.
Uncertainty about the cyclically adjusted budget deficit is further compounded by
uncertainty over the link between the output gap and the budget deficit. If the gap were to
be caused by tax rich elements of demand, such as consumption, then the impact of a
given gap on the deficit would be larger than when the gap is caused by changes in a tax
poor component of demand, such as exports. We therefore undertake a further analysis of
the sources of shocks and study their impact on the uncertainty surrounding the budget
deficit.

In the second section of the chapter we discuss methods of estimating the output gap and
the associated uncertainty. We focus on the Harvey-Trimbur (2003) estimator, which
approximates a parametric version of the ideal band pass filter discussed in Baxter and
King (1999). We utilise this estimator in part because it allows an analytical derivation of
its standard deviation, which we present in this section. We then present and evaluate real
time estimates of the output gap and the associated uncertainty for the UK, Germany,
France, Italy, Spain, the Netherlands and Belgium. In the third section we calculate the
cyclically adjusted budget deficits from the real time output gap data and present
uncertainty bands around these estimates. The fourth section looks at the sensitivity of
our results, by applying different coefficients from a model-based analysis of multipliers
to the output gap in the calculation of the cyclically adjusted deficit. The final section
draws conclusions about the difficulties associated with producing reliable estimates of
the cyclically adjusted budget deficit.

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