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- Butler, L. 1996.A Semi-Structural Method to Estimate Potential Output: Combining Economic Theory with a Time-Series Filter. Technical Report No. 77. Ottawa: Bank of Canada.

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- Unfortunately, within this W1λβi framework there is no formal way to choose values for these parameters in an optimal fashion.4 Although the Phillips curve parameters can be estimated a priori, the choice of the weighting coefficient and the smoothing prior is more ad hoc. We use values for the weighting coefficients consistent with those used in the Bank’s extended multivariate filter (see
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- equals 1600, the weighting coefficients and are set to one, and is set to 64 for the last 16 quarters of estimation and zero elsewhere.5 is estimated simply as the mean growth rate of real output in the period of estimation.

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- The procedure continues until the change in the output-gap estimate from one step to the next falls below a pre-specified convergence criterion. λ W1W2W3 gss λ1600= 4 4 πtαiπti–βigti–εt+ +∑ =∑ i0= i1= πtgt βi 4.Alternatively, this problem could be mapped into an unobserved-components model, in which the parameters are estimated by maximum likelihood. 5.See
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- for a discussion of the choice of these weights. Using estimates of the nonaccelerating-inflation rate of unemployment (NAIRU) and the trend rate of capacity utilization, in addition to a Phillips curve, as conditioning information, de Brouwer (1998) sets the weights on each piece of conditioning information to be inversely proportional to the variance of the respective gap.

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- Using estimates of the nonaccelerating-inflation rate of unemployment (NAIRU) and the trend rate of capacity utilization, in addition to a Phillips curve, as conditioning information, de Brouwer (1998) sets the weights on each piece of conditioning information to be inversely proportional to the variance of the respective gap.
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- however, finds that such an approach does not produce estimates substantially different from those produced using a scheme of equal weights on each piece of conditioning information. 3.3The Blanchard-Quah SVAR The Blanchard-Quah (1989) SVAR methodology uses limited long-run restrictions to separate the temporary and permanent components of output.

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- Canova, F. 1994. “Detrending and Turning Points.”European Economic Review 38: 614–23. ———. 1998. “Detrending and Business Cycle Facts.”Journal of Monetary Economics 41: 475– 512.

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- This paper evaluates some of the competing methodologies based on their ability to accurately measure the output gap in a model economy. Because the output gap is unobservable, competing methodologies for estimating it are difficult to assess, and evaluation techniques have varied.
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- Canova (1994),
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- for example, uses the NBER definition of business cycle turning points as a metric for evaluating a battery of detrending methods. He finds that the Hodrick-Prescott (HP) (1997) filter does a good job, relative to other measures, of identifying turning points in U.

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- Ehlgen, J. 1998. “Distortionary Effects of the Optimal Hodrick-Prescott Filter.”Economics Letters 61: 345–49.

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- This is particularly important if we are to attempt to rank the various estimation methodologies, as the assumptions underlying certain estimators may bias our results for or against that technique. For example, identification of the SVAR requires an assumption about the type of non-stationarity in output data. On the other hand, it has been shown (King and Rebello 1993;
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- that one condition under which the HP filter is optimal, in a mean-squared-error sense, is the smoothing parameter,, being equal to the ratio of the variances of innovations in the cyclical and trend components in the DGP.

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- Kuttner, K.N. 1994. “Estimating Potential Output as a Latent Variable.”Journal of Business and

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- . 2.This is equivalent to the form;, where. 3.The estimated (1981 to 2001) historical standard deviation and AR(1) for first-differenced log GDP are 0.79 and 0.53, respectively. ∆yt∗μδ∆y∗t1–εt++= yt∗εt y∗tαy∗t1–νt++=νtδνt1–εt+=αμδ i =∑ δ yt∗αβtρy∗t1–εt+++= Another popular method of estimating the output gap is the unobserved-component method, which includes the state-space model of, for example,
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- Unfortunately, owing to the typical instability of the maximum-likelihood estimates of the state-space model’s parameters, we were unable to incorporate it into this study. In preliminary attempts to incorporate the model, the parameter estimates, in particular either the variance of potential output or output-gap shocks, tended towards zero in most samples.

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- Murchison, S. 2001. “NAOMI: A New Quarterly Forecasting Model Part II: A Guide to Canadian

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- Also, importantly, the core of NAOMI is consistent with the central paradigm of models used in forecasting and projection at the Bank; monetary conditions affect the output gap via an IS curve, which in turn affects inflation via a Phillips curve. Potential output is defined in NAOMI as the level of output consistent with non-accelerating inflation. 1.
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- provides a detailed description of NAOMI’s properties. Some changes to NAOMI were necessary for this study. First, an equation for potential output was added to its specification. In most of the experiments conducted in this paper, the growth rate of potential output is determined by an AR(1) process: ,(1) where is potential output and is an identically, independently distributed (i.i.d.) shock.2

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- In this sample, the three estimates follow the actual gap reasonably closely: the RMSEs for the MVF1, SVAR, and combined approach are 1.66, and 1.46, and 1.49, respectively, lower than the standard deviation of the actual output gap of 2.58. The correlations between the actual and estimated gap are 0.78, 0.86, and 0.83. 12.See
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- for a discussion of supply shocks in NAOMI. 13.For Case 6, it is necessary to lower the coefficient on potential output growth to match the historical autocorrelation of output growth. Also, the ratio of demand-to-supply innovations of 0.6 is the lowest ratio possible, given the correlation between the output gap and potential in this case. 14.

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