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- Cochrane, J. H. 1994. “Permanent and Transitory Components of GNP and Stock Prices.”

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- Prefix
- 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.

- In-text reference with the coordinate start=19093
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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.

- In-text reference with the coordinate start=36598
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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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- Cogley, T. 1995. “Evaluating Non-Structural Measures of the Business Cycle.” Draft Paper.

Total in-text references: 1- In-text reference with the coordinate start=16144
- Prefix
- 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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- Gali, J. 1992. “How Well Does the IS-LM Model Fit Postwar US Data?”Quarterly Journal of Economics 107: 709-38.

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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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- Hamilton, J. D. 1994.Time Series Analysis. Princeton University Press.

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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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- Kuttner, K. N. 1994. “Estimating Potential Output as a Latent Variable.”Journal of Business and Economic Statistics 12: 361-68.

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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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- Quah, D. 1992. “The Relative Importance of Permanent and Transitory Components: Identification and Some Theoretical Bounds.”Econometrica 60: 107-18.

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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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- Van Norden, S. 1995. “Why Is It So Hard to Measure the Current Output Gap?” Unpublished. Bank of Canada.

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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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- Watson, M. W. 1986. “Univariate Detrending Methods with Stochastic Trends.”Journal of

Total in-text references: 2- In-text reference with the coordinate start=8491
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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.

- In-text reference with the coordinate start=20823
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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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- 51
- Watson, M. W. 1993. “Vector Autoregressions and Cointegration.”Handbook of Econometrics, vol. 4. Bank of Canada Working Papers 1997 97-1Reconsidering Cointegration in International Finance:

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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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- 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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