
 Start

2463
 Prefix

This suggests that permanent shocks have more complex dynamics than a
random walk, which is the basic assumption of the CO and MBN approaches.
However, it is also found that the estimation of the output gap on the basis of an
estimated VAR is imprecise, which is consistent with results obtained by
 Exact

Staiger, Stock and Watson (1996)
 Suffix

with a different methodology. The spectra of the transitory
components (output gaps) resulting from the empirical applications of the CO, MBN
and LRRO methodologies differ from one another. Indeed, only the LRRO transitory
component has a peak at businesscycle frequencies, i.e., cycles lasting between 6 and
32 quarters.
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4202
 Prefix

S'il
faut en croire ces résultats, la dynamique des chocs permanents serait plus complexe
qu'une marche aléatoire, laquelle est au coeur des méthodes CO et MBN. Les auteurs
constatent cependant que l'écart de production calculé à l'aide d'un vecteur
autorégressif estimé manque de précision, ce qui est conforme aux résultats obtenus
par
 Exact

Staiger, Stock et Watson (1996)
 Suffix

au moyen d'une autre méthode. Les spectres des
composantes transitoires (écarts de production) qui résultent de l'application
empirique des méthodes CO, MBN et LRRO diffèrent les uns des autres.
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 Prefix

As a result, various methods have been
proposed to uncover the permanent and transitory components of output.
One of these methods consists of using mechanical filters such as the
HodrickPrescott (HP) filter or the bandpass filter (BK) proposed by
 Exact

Baxter and King (1995).
 Suffix

However, mechanical filters have been criticized. For example,
Harvey and Jaeger (1993) and Cogley and Nason (1995) show that spurious
cyclicality can be induced by the HP filter when it is used with integrated or nearly
integrated data.
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 Start

7193
 Prefix

One of these methods consists of using mechanical filters such as the
HodrickPrescott (HP) filter or the bandpass filter (BK) proposed by Baxter and King (1995). However, mechanical filters have been criticized. For example,
 Exact

Harvey and Jaeger (1993) and Cogley and Nason (1995)
 Suffix

show that spurious
cyclicality can be induced by the HP filter when it is used with integrated or nearly
integrated data. Guay and StAmant (1996) reach the more general conclusion
that the HP and BK filters perform poorly in identifying the cyclical component of
time series that have a spectrum or pseudospectrum with Granger’s typical
shape, i.e., the shape characteristic o
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7378
 Prefix

For example,
Harvey and Jaeger (1993) and Cogley and Nason (1995) show that spurious
cyclicality can be induced by the HP filter when it is used with integrated or nearly
integrated data.
 Exact

Guay and StAmant (1996)
 Suffix

reach the more general conclusion
that the HP and BK filters perform poorly in identifying the cyclical component of
time series that have a spectrum or pseudospectrum with Granger’s typical
shape, i.e., the shape characteristic of most macroeconomic time series.
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7683
 Prefix

Guay and StAmant (1996) reach the more general conclusion
that the HP and BK filters perform poorly in identifying the cyclical component of
time series that have a spectrum or pseudospectrum with Granger’s typical
shape, i.e., the shape characteristic of most macroeconomic time series.
 Exact

Baxter and King (1995) and
 Suffix

others note that twosided filters such as
the HP and BK filters become illdefined at the beginning and the end of samples.
For this reason, they recommend discarding three years of quarterly data at both
ends of the sample when using the HP filter.
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7961
 Prefix

Baxter and King (1995) and others note that twosided filters such as
the HP and BK filters become illdefined at the beginning and the end of samples.
For this reason, they recommend discarding three years of quarterly data at both
ends of the sample when using the HP filter. Van
 Exact

Norden (1995)
 Suffix

stresses the fact
that this is a very significant limitation for policymakers interested in estimating
1. For a discussion of how the estimation of potential output can affect the formulation of
monetary policy, see Boschen and Mills (1990) or Laxton and Tetlow (1992).
the current level of the output gap.
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8204
 Prefix

Van Norden (1995) stresses the fact
that this is a very significant limitation for policymakers interested in estimating
1. For a discussion of how the estimation of potential output can affect the formulation of
monetary policy, see
 Exact

Boschen and Mills (1990)
 Suffix

or Laxton and Tetlow (1992).
the current level of the output gap.
Another strategy for identifying the permanent and transitory
components of output involves the use of univariate techniques such as the
unobserved components approach suggested by Watson (1986) and the BeveridgeNelson (1981) method.
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8232
 Prefix

Van Norden (1995) stresses the fact
that this is a very significant limitation for policymakers interested in estimating
1. For a discussion of how the estimation of potential output can affect the formulation of
monetary policy, see Boschen and Mills (1990) or
 Exact

Laxton and Tetlow (1992).
 Suffix

the current level of the output gap.
Another strategy for identifying the permanent and transitory
components of output involves the use of univariate techniques such as the
unobserved components approach suggested by Watson (1986) and the BeveridgeNelson (1981) method.
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8491
 Prefix

of how the estimation of potential output can affect the formulation of
monetary policy, see Boschen and Mills (1990) or Laxton and Tetlow (1992). the current level of the output gap.
Another strategy for identifying the permanent and transitory
components of output involves the use of univariate techniques such as the
unobserved components approach suggested by
 Exact

Watson (1986) and
 Suffix

the BeveridgeNelson (1981) method. However, Quah (1992) has shown that “without additional
ad hoc restrictions those [univariate] characterizations are completely
uninformative for the relative importance of the underlying permanent and
transitory components.
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8554
 Prefix

Another strategy for identifying the permanent and transitory
components of output involves the use of univariate techniques such as the
unobserved components approach suggested by Watson (1986) and the BeveridgeNelson (1981) method. However,
 Exact

Quah (1992)
 Suffix

has shown that “without additional
ad hoc restrictions those [univariate] characterizations are completely
uninformative for the relative importance of the underlying permanent and
transitory components.
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 Prefix

One
example is a decomposition method proposed by Cochrane (CO) which is based on
the permanentincome theory and uses consumption to define the permanent
component of output. Multivariate extensions of the BeveridgeNelson
decomposition method (MBN) have also been applied to identify the trend
component of output
 Exact

(Evans and Reichlin 1994).
 Suffix

However, a major restriction in
the univariate context, which is maintained in the multivariate extensions, is that
the permanent component of output behaves like a random walk. This assumption
is difficult to reconcile with the widely held view that the permanent component
of output is, at least in part, driven by technological innovations.
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 Prefix

However, a major restriction in
the univariate context, which is maintained in the multivariate extensions, is that
the permanent component of output behaves like a random walk. This assumption
is difficult to reconcile with the widely held view that the permanent component
of output is, at least in part, driven by technological innovations. As underlined by
 Exact

King et al. (1991),
 Suffix

“productivity shocks set off transitional dynamics, as capital is
accumulated and the economy moves towards a new steadystate.” Lippi and
Reichlin (1994) go even further, arguing that modelling the trend in output as a
random walk is inconsistent with standard views concerning the dynamics of
productivity shocks.
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9924
 Prefix

This assumption
is difficult to reconcile with the widely held view that the permanent component
of output is, at least in part, driven by technological innovations. As underlined by
King et al. (1991), “productivity shocks set off transitional dynamics, as capital is
accumulated and the economy moves towards a new steadystate.”
 Exact

Lippi and Reichlin (1994)
 Suffix

go even further, arguing that modelling the trend in output as a
random walk is inconsistent with standard views concerning the dynamics of
productivity shocks. Adjustment costs on capital and labour, learning and
diffusion processes, habit formation and time to build all imply richer dynamics
than a randomwalk process for technology shocks.
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In this paper, we compare some of the techniques briefly introduced
above with the structural vector autoregression methodology based on longrun
restrictions imposed on output (LRRO) proposed by
 Exact

Blanchard and Quah (1989), Shapiro and Watson (1988), and King et al. (1991)
 Suffix

in theory (Section 2) and in
applications (Section 3). In Section 2, we note that one characteristic of the LRRO
method is that it does not impose restrictions on the shortrun dynamics of the
permanent component of output.
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 Prefix

We find
that the answer is “yes” when the entire output gap series is considered, but “not
really” when one is interested in estimating the output gap at a specific point in
time. In the latter case, the estimation of potential output and the output gap is
indeed imprecise. This is consistent with recent results reported by
 Exact

Staiger, Stock and Watson (1996)
 Suffix

for the estimation of the NAIRU. Another interesting result is
that, of the methods we consider, only the LRRObased one generates an output
gap with a peak at business cycle frequencies as defined by Burns and Mitchell
(1946), i.e., cycles lasting between 6 and 32 quarters.
2 Methodologies used for estimating the trend in output
2.1 The approach based on the LRRO methodology
In this section,
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 Prefix

This is consistent with recent results reported by Staiger, Stock and Watson (1996) for the estimation of the NAIRU. Another interesting result is
that, of the methods we consider, only the LRRObased one generates an output
gap with a peak at business cycle frequencies as defined by
 Exact

Burns and Mitchell (1946),
 Suffix

i.e., cycles lasting between 6 and 32 quarters.
2 Methodologies used for estimating the trend in output
2.1 The approach based on the LRRO methodology
In this section, we briefly present the LRRO decomposition methodology
involving longrun identifying restrictions (LRRO) and explain how it can be used
to estimate potential output.2
Let be a n x 1 stationary vector includ
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 Prefix

vector including a n1vector of I(1)
variables and a n2vector of I(0) variables such that.3 By the
Wold decomposition theorem, can be expressed as the following reduced form:
(1)
Zt
Zt∆X1t′X2t′,()′=
Zt
Ztδt()CL()εt+=
δt()CL() Σi0=
∞
CiL
i
=
where is deterministic, is a matrix of polynomial lags,
is the identity matrix, the vector is the onestepahead forecast errors
2. See
 Exact

Watson (1993)
 Suffix

for a more detailed presentation of the LRRO approach.
3. I(d) denotes a variable that is integrated of order d.
C0In=εt
in given information on lagged values of,, and
with positive definite. We suppose that the determinantal polynomial
has all its roots on or outside the unit circle, which rules out the nonfundamental
representations emphasized by Lippi and Reichlin (1993).
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 Prefix

C0In=εt
in given information on lagged values of,, and
with positive definite. We suppose that the determinantal polynomial
has all its roots on or outside the unit circle, which rules out the nonfundamental
representations emphasized by
 Exact

Lippi and Reichlin (1993).
 Suffix

Equation (1) can be decomposed into a longrun component and a
transitory component:
(2)
ZtZtEεt()0=Eεtεt′()Ω=
ΩCL()
Ztδt()C1()εtC∗L()εt++=
C1() Σi0=
∞
=CiC∗L()CL()C1()–=
C11()
X1tC11()
X1t
where and.
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Equation (1) can be decomposed into a longrun component and a
transitory component:
(2)
ZtZtEεt()0=Eεtεt′()Ω=
ΩCL()
Ztδt()C1()εtC∗L()εt++=
C1() Σi0=
∞
=CiC∗L()CL()C1()–=
C11()
X1tC11()
X1t
where and. This decomposition
corresponds to the multivariate BeveridgeNelson decomposition — see
 Exact

Evans and Reichlin (1994) and King et al. (1991).
 Suffix

We define as the longrun
multiplier of the vector. If the rank of is less than n1, there exists at
least one linear combination of the elements in that is I(0). In other words,
there exists at least one cointegration relationship between these variables — see
Engle and Granger (1987).
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If the rank of is less than n1, there exists at
least one linear combination of the elements in that is I(0). In other words,
there exists at least one cointegration relationship between these variables — see
 Exact

Engle and Granger (1987).
 Suffix

The LRRO approach assumes that has the following structural
representation:
(3)
Zt
Ztδt() ΓL()ηt+=
where is a nvector of structural shocks,, and (a
ηtEηt()0=Eηtηt′()In=
Γ0Γ0′Ω=εtΓ0ηt=
simple normalization).
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From (2) and (3) we have:
(4)
CL() ΓL()Γ0
–1
=
C1()ΩC1()′
C1()ΩC1()′ Γ1()Γ1()′=
Γ0
C1()
C1()
This relation suggests that we can identify matrix with an appropriate
number of restrictions on the longrun covariance matrix of the structural form.
 Exact

Blanchard and Quah (1989) and Shapiro and Watson (1988)
 Suffix

use longrun
restrictions to identify shocks with having full rank. King et al. (1991)
work in a context where the rank of is less than n1 and they use
cointegration restrictions.
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(2) and (3) we have:
(4)
CL() ΓL()Γ0
–1
=
C1()ΩC1()′
C1()ΩC1()′ Γ1()Γ1()′=
Γ0
C1()
C1()
This relation suggests that we can identify matrix with an appropriate
number of restrictions on the longrun covariance matrix of the structural form.
Blanchard and Quah (1989) and Shapiro and Watson (1988) use longrun
restrictions to identify shocks with having full rank.
 Exact

King et al. (1991)
 Suffix

work in a context where the rank of is less than n1 and they use
cointegration restrictions.
Let us assume that the log of output is the first variable in the vector
. It is then equal to:
(5)
Z1t
∆ytμyΓ1
p
()ηLt
p
Γ1
c
()ηLt
c
=++
ηt
p
ηt
c
where is the vector of permanent shocks affecting output and is the vector
containing shocks having only a transitory effect on output.
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Potential output
based on the LRRO method is then:
(6)
∆yt
p
μyΓ1
p
()ηLt
p
=+
Thus, “potential output” corresponds to the permanent component of output. The
part of output due to transitory shocks is defined as the “output gap.” It is
important to note that we do not talk in terms of “demand” or “supply” shocks as
in
 Exact

Blanchard and Quah (1989),
 Suffix

but simply in terms of permanent and transitory
shocks.
2.2 Comparison with other multivariate methods
In this section, we examine the features of two alternatives to the LRRO
approach: the multivariate BeveridgeNelson decomposition (MBN) and
Cochrane’s outputconsumption decomposition (CO).4
The MBN decomposition defines potential output as the level of
out
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With reference to equation (2), where output is the first element of, we write the
following decomposition:
(7)
Zt
∆ytμyC11()εtC1∗L()εt++=
Potential output is defined by the first two terms on the righthand side of (7):
(8)
∆yt
p
=μyC11()εt+
4. See
 Exact

Cogley (1995)
 Suffix

for another comparison of the MBN and CO methodologies.
Potential output is thus simply a random walk with drift.
Cochrane (1994) uses a twovariable VAR including GNP and
consumption to identify the permanent and transitory components of GNP.
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With reference to equation (2), where output is the first element of, we write the
following decomposition:
(7)
Zt
∆ytμyC11()εtC1∗L()εt++=
Potential output is defined by the first two terms on the righthand side of (7):
(8)
∆yt
p
=μyC11()εt+
4. See Cogley (1995) for another comparison of the MBN and CO methodologies.
Potential output is thus simply a random walk with drift.
 Exact

Cochrane (1994)
 Suffix

uses a twovariable VAR including GNP and
consumption to identify the permanent and transitory components of GNP. The
bivariate representation is augmented with lags of the ratio consumption to GNP.
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 Prefix

Indeed, the validity of the
permanentincome hypothesis would imply that the last two terms of the
consumption equation are equal to zero and that. It is not clear to
what the CO decomposition corresponds if consumption is not a random walk.5
 Exact

Cochrane (1994)
 Suffix

notes that the measure of potential output obtained on the basis
of the CO method would be equivalent to the one obtained from the LRRO
approach if the transitory effect of permanent shocks to GNP and consumption
were exactly the same, i.e., if and.
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 Prefix

walk.5
Cochrane (1994) notes that the measure of potential output obtained on the basis
of the CO method would be equivalent to the one obtained from the LRRO
approach if the transitory effect of permanent shocks to GNP and consumption
were exactly the same, i.e., if and. However,
these restrictive conditions are unlikely to occur in practice.
As pointed out by
 Exact

Lippi and Reichlin (1994),
 Suffix

modelling the trend in
output as a random walk is inconsistent with most economists’ interpretation of
productivity growth. Indeed, it is generally believed that technology shocks are
absorbed gradually by the economy.
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 Prefix

Working in a univariate
framework, Lippi and Reichlin must constrain the dynamic of the trend to follow
a particular shape (Sshape dynamic) in order to identify the trend and cyclical
components. Again, a decisive advantage of the LRRO approach is that it lets the
data determine the shape of the diffusion process of permanent shocks.6
5. Stochastic growth models — such as in
 Exact

King et al. (1988)
 Suffix

or King et al. (1991) — imply that
the ratio of the log of GNP to the log of consumption is stationary but that consumption is
not a random walk because the real interest rate is not constant.
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 Prefix

Again, a decisive advantage of the LRRO approach is that it lets the
data determine the shape of the diffusion process of permanent shocks.6
5. Stochastic growth models — such as in King et al. (1988) or
 Exact

King et al. (1991)
 Suffix

— imply that
the ratio of the log of GNP to the log of consumption is stationary but that consumption is
not a random walk because the real interest rate is not constant. In these models, the
transitory component of permanent shocks to consumption is not equal to zero.
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 Prefix

al. (1988) or King et al. (1991) — imply that
the ratio of the log of GNP to the log of consumption is stationary but that consumption is
not a random walk because the real interest rate is not constant. In these models, the
transitory component of permanent shocks to consumption is not equal to zero. The LRRO
decomposition is compatible with the prediction of these models.
6.
 Exact

Kuttner (1994)
 Suffix

proposes a method based on the univariate unobserved stochastic trend
decomposition of Watson (1986) augmented with a Phillipscurve equation. As with the
BeveridgeNelson decomposition, Kuttner’s approach constrains potential output to follow
a randomwalk process.
μΓy
p
()η1t
p
+
Γ
p∗
()L
Γy
p
() Γ1c
p
=()1
Γy
p∗
() ΓLc
p∗
=()LΓy
p
() Γ1c
p
=()1
One implication of def
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 Prefix

In these models, the
transitory component of permanent shocks to consumption is not equal to zero. The LRRO
decomposition is compatible with the prediction of these models.
6. Kuttner (1994) proposes a method based on the univariate unobserved stochastic trend
decomposition of
 Exact

Watson (1986)
 Suffix

augmented with a Phillipscurve equation. As with the
BeveridgeNelson decomposition, Kuttner’s approach constrains potential output to follow
a randomwalk process.
μΓy
p
()η1t
p
+
Γ
p∗
()L
Γy
p
() Γ1c
p
=()1
Γy
p∗
() ΓLc
p∗
=()LΓy
p
() Γ1c
p
=()1
One implication of defining potential output as a random walk with
drift is that when the contemporary effect of a positive permanent sh
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 Prefix

The use of this variable,
which we suppose to be stationary, makes the comparison between the different
methodologies easier. We also consider a case where we add a nominal variable to
the information set as recommended by
 Exact

King et al (1991).
 Suffix

In a vector form, the
structural shocks and the variables used in the VARs can be expressed in the
following way:
∆y
εPεT
yc
ηt
εP
εT
=Zt
∆y
yc–
=
and
or
and
ηt
εP
εT1
εT2
=Zt
∆y
yc–
∆i
=
We use quarterly data on U.
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23881
 Prefix

The autoregressive reducedform VAR of the model is first estimated:
q
ZtΠiZti–et+
=∑
i1=
withqthe number of lags and a vector of estimated residuals with
.
It is crucial that the estimated VARs include a sufficient number of
et
Eetet()Σ=
lags. Indeed, Monte Carlo simulations by
 Exact

DeSerres and Guay (1995)
 Suffix

show that
using a lag structure that is too parsimonious can significantly bias the estimation
of the structural components. These authors also find that informationbased
criteria, such as the Akaike and Schwarz criteria, tend to select an insufficient
number of lags, while Wald or likelihoodratio (LR) tests, using a generaltospecific approach, perform much bett
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26960
 Prefix

2, models in which the permanent
component of output is a random walk imply that the economy is below (above)
potential in the transition period following a permanent positive (negative) shock
to output. To the extent that the transition primarily reflects factors associated
with an adjustment in the supply side of the economy, assuming that potential
7.
 Exact

Blanchard and Quah (1989) and Gali (1992),
 Suffix

among others, report similar results.
output follows a random walk can be misleading. It could, in particular, provide
misleading signals about the extent of inflationary pressures in the economy.
Chart 3 shows the output gaps calculated on the basis of the LRRO
methodology in the bivariate and trivariate cases.
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30271
 Prefix

Nevertheless, the correlation between
the output gaps identified on the basis of the CO and MBN methodologies is rather
small, indicating that consumption may not be a random walk. This is consistent
with results reported in
 Exact

Watson (1993),
 Suffix

showing that the spectrum of the first
difference of consumption has a peak at businesscycle frequencies. In Section 2,
we noted that if consumption followed a randomwalk process, the CO and MBN
methodologies would give identical results.
8.
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CHART 5: Uncertainty surrounding the estimation of the output gap
MBN
Confidence interval
LRRO
Confidence interval
The main message of Chart 5, which would apply to other estimates
of the output gap reviewed in this paper, is that there is a substantial amount of
uncertainty surrounding the estimation of the output gap.
 Exact

Staiger, Stock and Watson (1996),
 Suffix

using a different methodology, reach a similar conclusion
concerning the estimation of the NAIRU. This uncertainty should probably be
taken into account by policymakers who use the output gap to guide their
decisions.
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33230
 Prefix

ones
discussed in this paper is that, unlike mechanical filters, they reflect at least some
of the uncertainty.
3.2 Spectra analysis
Chart 6 shows the estimated spectra of the CO, MBN (trivariate case) and LRRO
(trivariate case) output gaps plus those resulting from the application of two
mechanical filters: the HodrickPrescott filter (HP) and the bandpass filter (BK)
proposed by
 Exact

Baxter and King (1995).
 Suffix

Loosely speaking, the spectrum of a series is
that series expressed as the integral of random periodic components that are
mutually orthogonal. The total area below the spectrum corresponds to the
variance of the series.
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33972
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We use a parametric estimator of the
spectra for which ARMA processes were fitted.9
The spectra resulting from the LRRO, HP, and BK output gaps have
their peak at businesscycle frequencies as defined by
 Exact

Burns and Mitchell (1946),
 Suffix

i.e., frequencies corresponding to cycles lasting between 6 and 32 quarters. Indeed,
the peaks in the spectrum of the HP, BK and LRRO gaps correspond to cycles
lasting around 20 quarters.
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34807
 Prefix

The spectrum of the gap resulting from the twovariable MBN
application (not shown on the graph) has the same shape as the threevariable
9. For an introduction to spectral analysis see
 Exact

Hamilton (1994).
 Suffix

The order of these processes
was determined on the basis of the Akaike criteria.
case, although with a lower peak and a smaller total variance. The latter result is
not surprising, since it is well known that the MBN methodology gives a transitory
component whose importance increases with the number of series used to identify
it.
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35330
 Prefix

The latter result is
not surprising, since it is well known that the MBN methodology gives a transitory
component whose importance increases with the number of series used to identify
it.
CHART 6: Spectra of the output gaps
0.08
0.07
HP filter
0.06
0.05
BK filter
CO
0.04
LRRO (3 variables)
0.03
MBN (3 variables)
0.02
0.01
0
00.050.10.150.20.250.30.35
fraction of pi
 Exact

Cogley and Nason (1995) and Harvey and Jaeger (1993)
 Suffix

show that the
HP filter amplifies businesscycle frequencies when compared with the firstdifference of integrated or highly persistent time series. Guay and StAmant
(1996) extend this result to the BK filter but also note that, when compared with
macroeconomic series in level terms, the HP and BK filters minimize the
importance of businesscycle frequencies.
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 Prefix

CHART 6: Spectra of the output gaps
0.08
0.07
HP filter
0.06
0.05
BK filter
CO
0.04
LRRO (3 variables)
0.03
MBN (3 variables)
0.02
0.01
0
00.050.10.150.20.250.30.35
fraction of pi
Cogley and Nason (1995) and Harvey and Jaeger (1993) show that the
HP filter amplifies businesscycle frequencies when compared with the firstdifference of integrated or highly persistent time series.
 Exact

Guay and StAmant (1996)
 Suffix

extend this result to the BK filter but also note that, when compared with
macroeconomic series in level terms, the HP and BK filters minimize the
importance of businesscycle frequencies.
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36375
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It is difficult to compare the
spectra of MBN output gaps with the others.
4 Conclusions
In this paper, we compared different techniques that are used to measure
potential output. We started with a brief explanation of why we think that
mechanical filters such as the HodrickPrescott filter and the bandpass filter
proposed by
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Baxter and King (1995)
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perform poorly in accomplishing this task.
We then compared the LRRO approach based on longrun restrictions with two
alternative multivariate approaches: the one proposed by Cochrane (1994) and
the multivariate BeveridgeNelson methodology.
 (check this in PDF content)

 Start

36598
 Prefix

We started with a brief explanation of why we think that
mechanical filters such as the HodrickPrescott filter and the bandpass filter
proposed by Baxter and King (1995) perform poorly in accomplishing this task.
We then compared the LRRO approach based on longrun restrictions with two
alternative multivariate approaches: the one proposed by
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Cochrane (1994) and
 Suffix

the multivariate BeveridgeNelson methodology. We argued that one advantage
of the approach based on longrun restrictions is that it allows for estimated
transitional dynamics following permanent shocks.
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37502
 Prefix

with permanent shocks and that the output gap series
estimated on the basis of LRRO approach, Cochrane’s approach, and the
multivariate BeveridgeNelson methodology are different in the time and
frequency domains. We note, in particular, that only the output gap associated
with the LRRO approach has a peak at businesscycle frequencies as defined by
 Exact

Burns and Mitchell (1946),
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i.e., cycles lasting between 6 and 32 quarters. However,
the estimates are imprecise for specific points in time and it appears difficult to
distinguish between these methodologies in that context.
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37789
 Prefix

However,
the estimates are imprecise for specific points in time and it appears difficult to
distinguish between these methodologies in that context. This later result is
consistent with the conclusions of
 Exact

Staiger, Stock and Watson (1996).
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 (check this in PDF content)