time estimates. We note that while one might consider an output gap estimator for which
there is no parameter uncertainty (such as the Hodrick-Prescott filter), so that the filtered
and real-time estimates are equivalent, our experience suggests that there remains a
significant difference between the real-time and ‘final’ output gap estimates; e.g. see
Mitchell (2003).
Table 7.2 The Unreliability of Real-time Output Gap Point Estimates
|
mean |
min |
max |
s.d. |
correlation |
RMSE | ||
|
‘final’ |
-0.042 |
-2.353 |
2.117 |
0.958 |
1 |
0 | |
|
Belgium |
filtered |
-0.025 |
-1.526 |
1.029 |
0.555 |
0.51 |
0.827 |
|
realtime |
-0.016 |
-1.265 |
0.975 |
0.492 |
0.391 |
0.89 | |
|
‘final’ |
-0.15 |
-2.516 |
2.496 |
1.44 |
1 |
0 | |
|
France |
filtered |
-0.405 |
-1.541 |
1.165 |
0.691 |
0.773 |
1.038 |
|
realtime |
-0.231 |
-1.768 |
1.161 |
0.555 |
0.59 |
1.203 | |
|
‘final’ |
-0^.0^83 |
’”-2.399"” |
”3.533’” |
’’’Г.423 ” |
1 |
^^^^^0 | |
|
Germany |
filtered |
-0.212 |
-2.187 |
2.432 |
1.033 |
0.644 |
1.103 |
|
realtime |
-0.299 |
-2.402 |
1.852 |
1.064 |
0.485 |
1.317 | |
|
.....final'----. |
'”-0.048 ” |
”-3.732"” |
^^3.659^^^ |
”1.597” |
1 |
^^^^^0 | |
|
Italy |
filtered |
-0.388 |
-2.661 |
1.455 |
1.029 |
0.726 |
1.156 |
|
realtime |
-0.316 |
-2.499 |
1.67 |
1.064 |
0.614 |
1.291 | |
|
‘final’ |
-0.158 |
”-3.275 ” |
”2.877” |
1.491 |
1 |
0 | |
|
Netherlands |
filtered |
-0.124 |
-1.718 |
0.954 |
0.647 |
0.687 |
1.148 |
|
realtime |
-0.079 |
-1.227 |
0.716 |
0.536 |
0.232 |
1.465 | |
|
‘final’ |
0.001 |
-1.139 |
0.842 |
”0.337” |
1 |
0 | |
|
Spain |
filtered |
0.021 |
-0.86 |
0.743 |
0.285 |
0.467 |
0.325 |
|
real time |
0.039 |
-1.005 |
1.228 |
0.371 |
0.385 |
0.396 | |
|
‘final’ |
-0.43 8 |
-4.998 |
4.868 |
”2.461 |
1 |
0 | |
|
UK |
filtered |
0.481 |
-2.181 |
3.136 |
1.207 |
0.84 |
1.835 |
|
real time |
0.317 |
-2.9 |
2.474 |
1.071 |
0.405 |
2.375 | |
Notes: s.d. is the standard deviation of the output gap; correlation vs. ‘final’ is the correlation of the filtered
or real-time output gap estimate against the full-sample estimate; RMSE is the root mean squared error of
the filtered or real-time estimate against the ‘final’ estimate.
Uncertainty Associated with Output Gap Estimates
It is not simply a question of this output gap forecast proving to be right and another
forecast proving to be wrong. Point forecasts are better seen as the central points of
ranges of uncertainty. A forecast of 2% must mean that people should not be surprised if
the output gap turns out to be a little larger than that. Moreover perhaps they should not
be very surprised if it turns out to be much larger or indeed nothing at all. Therefore,
consistent with recent developments in the forecasting literature, it is important to provide
a description of the uncertainty associated with real-time output gap estimates via interval
or density forecasts. Indeed, the ‘optimal’ real-time estimate of the output gap need not
equal the mean or conditional expectation. It can be ‘rational’ to use biased real-time
estimates. Furthermore, measures of uncertainty are useful in their own right if interested
in analysing and communicating, for example, risk and volatility, or the probability of a
downturn. Our concern in this chapter is with producing measures of uncertainty
associated with the cyclically adjusted budget deficit estimate, as measured in real-time.
190