Is there a common Eurozone business cycle

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Business cycle uncertainty in real-timeJames
MitchellNational Institute of Economic Social
Research
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The European business cycle

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Real-time measurement of the output gap or the
growth business cycle is important for
policy-makers (e.g. when forecasting inflation or
fiscal balance) Mistakes can be costly For the
US real-time estimates have been found to be
unreliable. See Orphanides and van Norden (2002,
R.E.Stat) Our contribution Measurement and
evaluation of uncertainty associated with
real-time (point) estimates. Application to
Eurozone
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• This paper in two parts
• Consider similar exercise for Eurozone aggregate
  to OvN. Across a range of univariate and
  multivariate measures of the output gap we find
  significant differences between real-time and
  final output gap estimates
• But should we be surprised by this unreliability?
  As forecasters know if within the bounds of what
  was expected real-time point estimates may still
  be useful. Users require not just point estimates
  but an accurate measure of uncertainty associated
  with them

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Alternative estimators of the output
gap Univariate and multivariate
estimators Massmann, Mitchell and Weale survey
univariate estimators See Appendix for
multivariate estimators. Adding economic
information may deliver more accurate real-time
estimates Phillips Curve and Okuns Law suggest
inflation and unemployment contain important
information about output gap Should de-trend
output in multivariate system
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• The following class of multivariate estimators
  are considered
• Unobserved Components bivariate system (output
  inflation) trivariate system ( unemployment)
• Multivariate Hodrick-Prescott filters (bivariate
  case). HP filters be interpreted in state-space
  form. Impose a priori restrictions on variances
  of disturbances to state-vector rather than
  constraining cyclical dynamics to be stationary
  (as with UC models)
• Structural VAR models BQ (no cointegration) and
  KPSW (cointegration)
• Representative univariate estimators (UC-
  Harvey/Trimbur and HP) considered for comparative
  purposes

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Real-time simulation Real-time estimate use data
available at time t. Final estimate uses data
from t1,,t,,T. We ignore data revisions
(revisions to published GDP data). Focus on
statistical revisions hindsight (arrival of new
data) helps us better understand the position of
the cycle, and indeed may cause us to change our
estimator of the cycle Revision final minus
real-time estimate Decompose revision for UC
models by defining quasi-final estimate (filtered
estimate) as opposed to the final estimate (the
smoothed estimate) Difference between quasi-final
and real-time estimates reflects parameter
uncertainty
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Data from 1971q1-2003q1. AWM used to 2000q4.
Updated to 2003q1 using official EUROSTAT data
New Cronos. Real-time estimates computed
recursively from 1981q1 to 2000q1. Simulated
out-of-sample experiment designed to mimic
real-time measurement of the output gap Output
gap (point) estimates evaluated using various
criteria. We focus here on correlation with the
outturn Look at evolution to final estimates
how long does this take?

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Correlation with final estimates note problem
appears to be parameter uncertainty rather than
not knowing future output
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Expansions contractions successfully identified
only after about 3 years
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Part 2 Should we be surprised by this
unreliability of output gap point
estimates? Consider real-time measurement of the
output gap as a forecasting exercise We provide
measures of uncertainty associated with real time
estimates or forecasts Both confidence
intervals and density estimates are
considered Density forecasts of the realisation
of a random variable at some future point in time
provide an estimate of the probability
distribution of the possible future values of
that variable Two approaches to measuring
uncertainty are considered These 2 measures of
uncertainty associated with real-time estimates
are then evaluated in the light of the outturn
(the final estimate)
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• Measuring the uncertainty of real-time estimates
• Exploit state-space representation of output gap
  estimators Gaussianity assumption. Focus on
  filter uncertainty
• 2. Quantify uncertainty due to fact that future
  values of output are unknown but affect real-time
  estimates - 2 sided nature of filters. This is
  achieved by forecasting the future R times
  (bootstrap allowing for parameter uncertainty)
  and at each replication de-trending observed
  output data up to time t and forecasted data from
  (t1) to (th). Dispersion across R at time t
  provides an indication of the uncertainty.
  Forecast using reduced-form ARMA model or VAR
  model 4 periods ahead.
• By-product is that improved (point) estimates
  of the output gap in real-time may be obtained.
  The accuracy of real-time estimates is a function
  of how well future values of the underlying
  series can be forecast can apply less 1-sided
  filter

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Can forecasting help deliver improved real-time
estimates? Focus on the median of the R
forecasts at each point in time Look at
correlation with final estimate again

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Uncertainty associated with Hodrick-Prescott
estimates
Evaluation of interval and density
forecasts
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Uncertainty associated with bivariate HP estimates

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Uncertainty associated with Trivariate UC
estimates

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Wider confidence bands for Gaussian than
bootstrapped bands cover outturn more often
but at expense of more uncertainty Rarely
significantly different from zero policy makers
on this basis could never be sure about the
position of the cycle Given these differences it
is important to ask, which measure of
uncertainty, if any, is best? Use formal
evaluation tests for interval and density
forecasts

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Evaluation of interval and density
forecasts Christoffersen test for interval
forecasts Density forecasts evaluated
statistically whole density Probability
integral transform Diebold, Gunther
Tay Density forecasts are optimal when pits are
i.i.d. uniform. By taking inverse normal CDF
transformation of the pits this can be
re-interpreted as a test for normality Doornik-Ha
nsen normality test Ljung-Box test for serial
dependence in powers of pits
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Both interval and density forecasts, in
general, are rejected There appears to be no
common cause for this Density forecasts are
rejected sometimes on the basis of the
independence test and sometimes due to the
normality test Likewise interval forecasts are
rejected both using the unconditional and
independence test
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Conclusion It has not proved possible to provide
accurate measures of uncertainty associated with
real-time estimates. Not only are real-time point
estimates unreliable but so are measures of
uncertainty associated with them This provides a
challenge to policy-makers in using output gap
estimates in real-time In related work we find
that although real-time output gap estimates
often have little forecasting power over
inflation relative to simple autoregressive
alternatives this does not appear to be due to
the unreliability of output gap estimates but
rather the difficulties of forecasting inflation
per se