7.2
Estimating the Output Gap and Its Uncertainty
Model Uncertainty
The output gap, the difference between actual and potential output, has an importance in
the popular debate which can tend to run ahead of the problems in measuring it; the
output gap is not observable. The choice of what measure, or estimator, of the output gap
to use is more than a dry academic issue. As the analysis of Canova (1998) showed, for
example, inference can be sensitive to measurement. In this chapter we largely abstract
from issues concerning model uncertainty and consider just one leading output gap
estimator - the Harvey-Trimbur cycle. This is sufficient to make our point that use of the
output gap in real-time can be problematic since it is often measured imprecisely. The
Harvey-Trimbur cycle is a model-based estimator based on unobserved components
(UC). It is a generalisation of the class of Butterworth filters that have the attractive
property of allowing smooth cycles to be extracted from economic time series - indeed
ideal band pass filters emerge as a limiting case; see Harvey and Trimbur (2003).
Statistical and Parameter Uncertainty: Estimation in Real-time
An additional source of uncertainty associated with output gap estimates derives from the
fact that policy makers do not have the luxury of being able to wait before deciding
whether the economy is currently lying above or below its trend level. They have to
decide, without the benefit of hindsight, whether a given change to output in the current
period is temporary or permanent, that is whether it is a cyclical or trend movement. As
discussed by Mitchell (2003) their problem can be interpreted as a forecasting one, since
these real-time output gap estimates are forecasts, in the sense that they are expectations
of the output gap conditional on incomplete information. Only with the arrival of
additional information, such as revised historical data and data not available at the time,
do the output gap estimates eventually settle down at their ‘final’ values.123 These real-
time or end-of-sample output gap (point) estimates have been found to be unreliable, in
the sense that there is a large and significant revision or forecasting error; see Orphanides
and van Norden’s (2002) application to the US economy and Mitchell’s (2003) to the
Euro-area.
Since in the absence of data revisions, revisions to real-time output gap estimates are
explained by forecasting errors, it is important when de-trending in real-time to produce
good forecasts of the (log) level of the underlying series. Application of an UC model can
be seen implicitly to forecast future values optimally. This follows from the fact that for a
correctly specified model, application of the one-sided Kalman filter is equivalent to
application of the two-sided filter (smoother) to the underlying series extended infinitely
into the future with optimal forecasts. These optimal, minimum mean square error,
forecasts are derived via the Kalman filter, exploiting the state-space representation for a
given output gap estimator. There is therefore no need for forecast extensions.
We note that when computing the cyclically adjusted budget deficit the European
Commission in fact rely on a production function approach to measuring the output gap;
see Denis et al. (2006). But since TFP is de-trended with a Hodrick-Prescott filter there
remains an end-of-sample problem. Future values of TFP are therefore forecast prior to
Values are never truly final because data revisions and the arrival of new data are a continuous
process.
186