application of the de-trending filter in an attempt to improve the reliability of the real-
time estimates. But as mentioned above reliability will only be improved if ‘good’
forecasts are produced. Indeed, since the Hodrick-Prescott filter implicitly assumes the
data are generated by an IMA(2,2) model, if future values are forecast using an
alternative model, this then raises concerns about why the Hodrick-Prescott filter is itself
used if an IMA(2,2) model is not believed to be the ‘true’ model. In any case, given that
the European Commission must be uncertain about the accuracy of their measure and also
still expect revisions to their real-time output gap estimates they should, as we consider
below, produce a measure of uncertainty associated with it and in turn the cyclically
adjusted budget deficit. Even if the estimates are not revised, they are not known with
certainty, and hence must have a sampling distribution. As the Hodrick-Prescott filter is a
mechanical device it is possible that the uncertainty of the estimates would have to be
bootstrapped from the data, but it is still possible to estimate uncertainty measures.
Real-time and ‘Final’ Estimates of the Output Gap in the Euro-area
To investigate the unreliability of real-time output gap point estimates for Euro-area
economies the following experiment is undertaken. Full sample or final estimates of the
output gap are derived using data available over the (full) sample-period using data up to
2006q1. Real-time output gap estimates are computed recursively from 1980q1. We use
data from the 1960s to 1980q1 to provide a real time estimate of the output gap for
1980q1.124 Then data up to 1980q2 are used to re-estimate the output gap (that involves
re-estimation of the parameters of the models used to measure the output gap) and obtain
real-time estimates for 1980q2.125 This recursive exercise, designed to mimic real-time
measurement of the output gap, is carried on until data for the period up to 2006q1 are
used to estimate the real-time output gap for 2006q1. These last estimates are the ‘final’
values, where real time and full sample estimates converge.
Throughout we use only the latest vintage of GDP data. What we call the real-time
estimate is strictly the quasi-real estimate of Orphanides and van Norden (2002). If we
considered real-time data we should expect to find an even greater degree of unreliability
associated with the real-time estimates. Nevertheless revisions to published GDP data
were found by Orphanides and van Norden (2002) to be less important than so-called
statistical revisions. Statistical revisions are explained by the arrival of new data helping
macroeconomists, with the advantage of hindsight, better understand the position of the
business cycle, and also perhaps revising what model they use to identify and estimate it.
124
125
We ignore the fact that GDP data are published with, at least, a one-quarter lag.
In the notation of Harvey and Trimbur (2003) we set m=n=2 in each recursive sample, although for
the UK we consider also increasing n to n=3. The models are not subjected to standard goodness-of-
fit tests to help identify potential weaknesses/model mis-specification. Future work should consider
this.
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