The 15 references with contexts in paper Maral Kichian (1999) “Measuring Potential Output within a State-Space Framework” / RePEc:bca:bocawp:99-9

1
Bai, J. and P. Perron. 1998. “Estimating and Testing Linear Models with Multiple Srtuctural Changes.”Econometrica 66:47-78.
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    This debate has been ongoing for a long time now and has spawned numerous studies on methods of testing for break points when the break time is difficult to pin down. The latest in this category is the extensive work by
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    Bai and Perron (1998).
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    These authors discuss the properties of least squares estimators in a wide class of linear regression models in the presence of multiple structural breaks with unknown break points. These models include cases where the residuals are autocorrelated and heteroskedastic and where there are lagged dependent variables in the regressors.

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    These modifications were motivated partly in response to existing empirical findings on Canadian data, and partly because of the results of diagnostics checking on the basic model. First we focus on the assumed specification for the output equation of the model and apply the
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    Bai and Perron (1998)
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    structural change test with unknown change point. Since we find that we cannot reject a one-time break in the drift of output growth, we estimate versions of the model with a breaking drift. We also estimate a version of the GS model with a modified error structure after detecting the presence of ARCH effects in this equation.

4
Blanchard, O.J. and D.Quah. 1989. “The Dynamic Effects of Aggregate Demand and Supply Disturbances.”American Economic Review 79(4):655-73.
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    The extended multivariate filter (EMVF) used at the Bank of Canada in the quarterly projection model is such a model.1Finally, the authors examine filtering models based on vector autoregressions (VARs). Among these are the structural VAR methods of
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    Blanchard and Quah (1989),
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    the multivariate Beveridge-Nelson decomposition and Cochrane’s (1994) methodology.2 St-Amant and van Norden show that both univariate mechanical filters, as well as their hybrid extensions, may have problems in adequately separating output into trend and meanreverting components.3 These filters perform poorly in extracting business cycle frequencies of 6 to 32 quarters from series such as real GDP

5
Butler, L. 1996. The Bank of Canada’s New Quarterly Projection Model, Part 4. A Semi-
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    both univariate mechanical filters, as well as their hybrid extensions, may have problems in adequately separating output into trend and meanreverting components.3 These filters perform poorly in extracting business cycle frequencies of 6 to 32 quarters from series such as real GDP which have an important permanent component. In addition, they are subject to severe end-of-sample problems. 1.See
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    Butler (1996).
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    2.An example of the application of these methods to U.S. data can be found in Dupasquier, Guay and St-Amant (1999). 3.See also Harvey and Jaeger (1993) and King and Rebelo (1993). As one alternative to the above class of models, St-Amant and van Norden suggest the use of structural VAR (SVAR) methods for measuring trend output.4 These models are favoured because they are not confronted with end-of

8
Cooley, T.F. and M. Dwyer. 1998. “Business Cycle Analysis Without Much Theory. A Look at
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    However, the authors also caution that confidence intervals around the estimated gap are generally wide and that results are sensitive to the variables included in the estimated system. Other reasons for being cautious about the interpretation of the implied dynamics obtained from SVARs are given in
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    Cooley and Dwyer (1998).
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    These authors explain that, since the identification of SVARs is conditional on a set of atheoretical assumptions which cannot be tested, results from the SVAR are quite sensitive to misspecification in these assumptions.

10
Duguay, P. 1994. “Empirical Evidence on the Strength of the Monetary Transmission Mechanism in Canada.”Journal of Monetary Economics 33(1).
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    However, it remains an important question and is left for future research. 15.In fact, if the true process is I(1), but instead an I(2) is assumed, the model may not be well-identified. This adversely affects any inference results from the model. 16.See, for instance,
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    Duguay (1994).
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    17.One such study is by Laxton, Rose and Tetlow (1993). 18.An example is the study by Ricketts and Rose (1995) for Canadian inflation data. See also Fillion and Léonard (1997) for an estimated Phillips curve with various regimes. 4.

15
Dupasquier C., A. Guay, and P. St-Amant. 1999. “A Survey of Alternative Methodologies for
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    adequately separating output into trend and meanreverting components.3 These filters perform poorly in extracting business cycle frequencies of 6 to 32 quarters from series such as real GDP which have an important permanent component. In addition, they are subject to severe end-of-sample problems. 1.See Butler (1996). 2.An example of the application of these methods to U.S. data can be found in
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    Dupasquier, Guay and St-Amant (1999).
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    3.See also Harvey and Jaeger (1993) and King and Rebelo (1993). As one alternative to the above class of models, St-Amant and van Norden suggest the use of structural VAR (SVAR) methods for measuring trend output.4 These models are favoured because they are not confronted with end-of-sample issues.

19
Gerlach, S. and F. Smets. 1997. “Output Gaps and Inflation. Unobservable-components Estimates for the G-7 Countries.” Unpublished Paper, Bank for International Settlements, Basle.
Total in-text references: 6
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    Given that the estimated output gap is used as an indicator to measure the extent of inflationary pressures in the economy, we evaluate the use of such models for the implementation of monetary policy. Our starting point is the
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    Gerlach and Smets (1997)
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    unobserved-components model, which they applied to the G7 countries. After subjecting this model to various diagnostic tests, we modify certain assumptions in it to reflect specific aspects of the Canadian economy.

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    indicateur de l’intensité des pressions inflationnistes au sein de l’économie, l’auteure de l’étude cherche à évaluer si le recours aux modèles espace d’états pour estimer la production potentielle et, partant, l’écart de production peut être d’une quelconque utilité dans la mise en oeuvre de la politique monétaire. Le point de départ de son analyse est le modèle à composantes non observées que
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    Gerlach et Smets (1997)
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    appliquent aux pays du Groupe des Sept. Après avoir soumis le modèle à plusieurs tests de diagnostic, l’auteure modifie certaines des hypothèses initiales pour tenir compte d’aspects précis de l’économie canadienne.

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    fact that we can also directly obtain out-of-sample forecasts on the observable variables in the model, which provide an easy way of assessing the goodness of fit of the adopted specification and of ensuring that our estimates are useful in the formulation of policy. The state-space framework was first used to estimate trend output on U.S. data by Kuttner (1994). It was subsequently extended by
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    Gerlach and Smets (1997) and
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    applied to the G7 countries. For our part, we examine the implications of using different versions and extensions of the Gerlach and Smets (1997) model (hereafter GS) for Canada. In all cases, the output gap is defined as the component of output which is consistent with change in the rate of inflation, all other things being equal.

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    The state-space framework was first used to estimate trend output on U.S. data by Kuttner (1994). It was subsequently extended by Gerlach and Smets (1997) and applied to the G7 countries. For our part, we examine the implications of using different versions and extensions of the
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    Gerlach and Smets (1997)
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    model (hereafter GS) for Canada. In all cases, the output gap is defined as the component of output which is consistent with change in the rate of inflation, all other things being equal. The organization of the paper is as follows.

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    Notice that this is a very general state-space framework so that when no ARCH errors are present in the system, the above filter reduces to the well-known Kalman filter. 3.The Gerlach and Smets model We now move to the presentation of the
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    Gerlach and Smets (1997)
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    model which is a special case of the general model presented above. As mentioned, it is a modification of the Kuttner (1994) model which was originally applied to the United States and where potential output and the slope of the Phillips curve were simultaneously estimated in an unobserved components framework.

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    This model has a good overall fit, plausible parameter estimates, and the best forecast performance. 5.Conclusion In this paper, we assess the implications of using state-space models for measuring potential output (and the output gap) in Canada. The models examined are different versions or extensions of the unobserved-components model of
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    Gerlach and Smets (1997).
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    These modifications were motivated partly in response to existing empirical findings on Canadian data, and partly because of the results of diagnostics checking on the basic model. First we focus on the assumed specification for the output equation of the model and apply the Bai and Perron (1998) structural change test with unknown change point.

25
Hamilton, J. 1986. “A Standard Error for the Estimated State Vector of a State-Space Model”. ournal of Econometrics 33:387-97.
Total in-text references: 1
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    Studies employing these types of models frequently encounter difficulties in finding suitable data for their long-run values. 7.This is the mean square error associated with the estimated state vector and is obtained as a by-product of applying the Kalman filter. It is also known as the filter uncertainty of the model. However, as pointed out by
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    Hamilton (1986),
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    two types of uncertainties are associated with these models: filter uncertainty and parameter uncertainty. If one adopts the Bayesian perspective that the true value of the state vector is random, then our knowledge of it, based on observable variables, is reflected in a probability distribution.

27
King, R.G. and S. Rebelo. 1993. “Low Frequency Filtering and Real Business Cycles.”Journal of
Total in-text references: 1
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    In addition, they are subject to severe end-of-sample problems. 1.See Butler (1996). 2.An example of the application of these methods to U.S. data can be found in Dupasquier, Guay and St-Amant (1999). 3.See also Harvey and Jaeger (1993) and
    Exact
    King and Rebelo (1993).
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    As one alternative to the above class of models, St-Amant and van Norden suggest the use of structural VAR (SVAR) methods for measuring trend output.4 These models are favoured because they are not confronted with end-of-sample issues.

29
Kuttner, K.N. 1994. “Estimating Potential Output as a Latent Variable.”Journal of Business and Economic statistics 12(3):361-68.
Total in-text references: 2
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    uncertainty, must be added to the above. fact that we can also directly obtain out-of-sample forecasts on the observable variables in the model, which provide an easy way of assessing the goodness of fit of the adopted specification and of ensuring that our estimates are useful in the formulation of policy. The state-space framework was first used to estimate trend output on U.S. data by
    Exact
    Kuttner (1994).
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    It was subsequently extended by Gerlach and Smets (1997) and applied to the G7 countries. For our part, we examine the implications of using different versions and extensions of the Gerlach and Smets (1997) model (hereafter GS) for Canada.

  2. In-text reference with the coordinate start=18993
    Prefix
    Notice that this is a very general state-space framework so that when no ARCH errors are present in the system, the above filter reduces to the well-known Kalman filter. 3.The Gerlach and Smets model We now move to the presentation of the Gerlach and Smets (1997) model which is a special case of the general model presented above. As mentioned, it is a modification of the
    Exact
    Kuttner (1994)
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    model which was originally applied to the United States and where potential output and the slope of the Phillips curve were simultaneously estimated in an unobserved components framework. The log of quarterly real output,, is assumed to be the sum of log real potential output, , and a log cyclical component,.

31
Laxton, D., D. Rose, and R. Tetlow. 1993. “Problems in Identifying Non-Linear Phillips Curves:
Total in-text references: 1
  1. In-text reference with the coordinate start=27765
    Prefix
    However, it remains an important question and is left for future research. 15.In fact, if the true process is I(1), but instead an I(2) is assumed, the model may not be well-identified. This adversely affects any inference results from the model. 16.See, for instance, Duguay (1994). 17.One such study is by
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    Laxton, Rose and Tetlow (1993).
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    18.An example is the study by Ricketts and Rose (1995) for Canadian inflation data. See also Fillion and Léonard (1997) for an estimated Phillips curve with various regimes. 4.Extensions and model applicability to Canada 4.1Fine tuning In Table 1 parameters significant at the 10-per-cent level are in bold.

35
Phillips, P.C.B. 1989. “Partially Identified Econometric Models.”Econometric Theory, 5:181-240.
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    the equations in the statespace system on the other, we can still analyze a well-defined macroeconomic system and interpret the parameters and residuals in a straightforward fashion.6(ii) The capacity of the model to provide us directly with confidence intervals around the measured gap or potential.7 (iii) The 4.Another is the TOFU method proposed in van Norden (1995). 5.For more details, see
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    Phillips (1989).
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    6.Ideally, it would be desirable to make use of a fully specified structural and stochastic model. Unfortunately, this also is problematic as it necessitates, among other things, making assumptions on the equilibrium level of the various components used in the production function, as well as its aggregated form.

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Ricketts, N. and D. Rose. 1995. “Inflation, Learning and Monetary Policy Regimes in the G-7 Economies.” Working Paper 95-6. Bank of Canada, Ottawa.
Total in-text references: 2
  1. In-text reference with the coordinate start=27826
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    However, it remains an important question and is left for future research. 15.In fact, if the true process is I(1), but instead an I(2) is assumed, the model may not be well-identified. This adversely affects any inference results from the model. 16.See, for instance, Duguay (1994). 17.One such study is by Laxton, Rose and Tetlow (1993). 18.An example is the study by
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    Ricketts and Rose (1995)
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    for Canadian inflation data. See also Fillion and Léonard (1997) for an estimated Phillips curve with various regimes. 4.Extensions and model applicability to Canada 4.1Fine tuning In Table 1 parameters significant at the 10-per-cent level are in bold.

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    the purpose of the output gap measure is consistency with short term inflation forecasting, and taking into account the relative complexity of our framework, we will not be addressing this issue in the present study. Of more importance is the observed autocorrelation in the inflation equation residuals in all of the models. These effects could be due to misspecified expectations. For instance,
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    Ricketts and Rose (1995),
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    using a Markov-switching model, found three distinct regimes for Canadian inflation between 1961 and 1993. In their model both means and variances change with the state of the economy. If agents know which inflation regime they are in when they make their forecasts, inflation expectations will be different in each state.

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Stuber, G. 1986. The Slowdown in Productivity Growth in the 1975-83 Period: A s Survey of Possible Explanations. Technical Report No. 43. Ottawa:Bank of Canada. van Norden, S. 1995. “Why Is It So Hard to Measure the Current Output Gap?” Mimeograph. Bank of Canada.
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    This supposes that the observed 20.Since these models are non-nested, we do not use likelihood ratio tests to assess the overall goodness of fit. Instead, we rely on indirect criteria to select the best specification. 21.For more detail, see
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    Stuber (1986).
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    slowdown took place very gradually. Yet, an explanation based on a one or two-time break in the drift term is equally likely. Opinions diverge as to the right explanation, but, at this stage, both appear equally valid.

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Watson, M.W. 1986. “Univariate Detrending Methods with Stochastic Trends.”Journal of
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    These variables are included to capture the effects of temporary relative price shocks on inflation. Finally, the error terms are assumed to be mean zero and normally distributed. They enter the 11.This is the assumption made by
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    Watson (1986).
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    It has since been used in a standard fashion in various macroeconomic models. inflation equation as a moving average process to capture any remaining inertia in supply shock variables. This also allows the model to be identified.