The 29 reference contexts in paper Chantal Dupasquier, Alain Guay, Pierre St-Amant (1997) “A Comparison of Alternative Methodologies for Estimating Potential Output and the Output Gap” / RePEc:bca:bocawp:97-5

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    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 Staiger, Stock and
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    Watson (1996)
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    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 business-cycle frequencies, i.e., cycles lasting between 6 and 32 quarters.
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    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 Staiger, Stock et
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    Watson (1996)
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    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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    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 Hodrick-Prescott (HP) filter or the band-pass filter (BK) proposed by Baxter and
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    King (1995).
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    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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    Guay and St-Amant (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 pseudo-spectrum with Granger’s typical shape, i.e., the shape characteristic of most macroeconomic time series. Baxter and
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    King (1995) and
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    others note that two-sided filters such as the HP and BK filters become ill-defined 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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    Baxter and King (1995) and others note that two-sided filters such as the HP and BK filters become ill-defined 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
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    Norden (1995)
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    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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    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
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    Watson (1986) and
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    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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    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 Beveridge
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    Nelson (1981)
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    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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    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,
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    Quah (1992)
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    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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    In this paper, we compare some of the techniques briefly introduced above with the structural vector autoregression methodology based on long-run restrictions imposed on output (LRRO) proposed by Blanchard and
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    Quah (1989),
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    Shapiro and Watson (1988), and King et al. (1991) 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 short-run dynamics of the permanent component of output.
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    In this paper, we compare some of the techniques briefly introduced above with the structural vector autoregression methodology based on long-run restrictions imposed on output (LRRO) proposed by Blanchard and Quah (1989), Shapiro and
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    Watson (1988), and
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    King et al. (1991) 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 short-run dynamics of the permanent component of output.
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    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 Staiger, Stock and
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    Watson (1996)
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    for the estimation of the NAIRU. Another interesting result is that, of the methods we consider, only the LRRO-based 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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    vector including a n1-vector of I(1) variables and a n2-vector 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 one-step-ahead forecast errors 2. See
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    Watson (1993)
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    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 non-fundamental representations emphasized by Lippi and Reichlin (1993).
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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 long-run covariance matrix of the structural form. Blanchard and
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    Quah (1989) and
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    Shapiro and Watson (1988) use long-run 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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    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 long-run covariance matrix of the structural form. Blanchard and Quah (1989) and Shapiro and
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    Watson (1988)
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    use long-run 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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    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 Blanchard and
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    Quah (1989),
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    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 Beveridge-Nelson decomposition (MBN) and Cochrane’s output-consumption 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 right-hand side of (7): (8) ∆yt p =μyC11()εt+ 4. See
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    Cogley (1995)
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    for another comparison of the MBN and CO methodologies. Potential output is thus simply a random walk with drift. Cochrane (1994) uses a two-variable 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 right-hand 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.
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    Cochrane (1994)
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    uses a two-variable 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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    Indeed, the validity of the permanent-income 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
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    Cochrane (1994)
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    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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    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.
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    Kuttner (1994)
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    proposes a method based on the univariate unobserved stochastic trend decomposition of Watson (1986) augmented with a Phillips-curve equation. As with the Beveridge-Nelson decomposition, Kuttner’s approach constrains potential output to follow a random-walk 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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    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
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    Watson (1986)
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    augmented with a Phillips-curve equation. As with the Beveridge-Nelson decomposition, Kuttner’s approach constrains potential output to follow a random-walk 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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    The autoregressive reduced-form 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 DeSerres and
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    Guay (1995)
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    show that using a lag structure that is too parsimonious can significantly bias the estimation of the structural components. These authors also find that information-based criteria, such as the Akaike and Schwarz criteria, tend to select an insufficient number of lags, while Wald or likelihood-ratio (LR) tests, using a general-tospecific approach, perform much bett
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    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. Blanchard and
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    Quah (1989) and Gali (1992),
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    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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    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
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    Watson (1993),
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    showing that the spectrum of the first difference of consumption has a peak at business-cycle frequencies. In Section 2, we noted that if consumption followed a random-walk 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. Staiger, Stock and
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    Watson (1996),
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    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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    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 Hodrick-Prescott filter (HP) and the band-pass filter (BK) proposed by Baxter and
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    King (1995).
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    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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    The spectrum of the gap resulting from the two-variable MBN application (not shown on the graph) has the same shape as the three-variable 9. For an introduction to spectral analysis see
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    Hamilton (1994).
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    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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    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 Hodrick-Prescott filter and the band-pass filter proposed by Baxter and
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    King (1995)
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    perform poorly in accomplishing this task. We then compared the LRRO approach based on long-run restrictions with two alternative multivariate approaches: the one proposed by Cochrane (1994) and the multivariate Beveridge-Nelson methodology.
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    We started with a brief explanation of why we think that mechanical filters such as the Hodrick-Prescott filter and the band-pass filter proposed by Baxter and King (1995) perform poorly in accomplishing this task. We then compared the LRRO approach based on long-run restrictions with two alternative multivariate approaches: the one proposed by
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    Cochrane (1994) and
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    the multivariate Beveridge-Nelson methodology. We argued that one advantage of the approach based on long-run restrictions is that it allows for estimated transitional dynamics following permanent shocks.
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    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 Staiger, Stock and
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    Watson (1996).
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