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I would like to thank Mike Artis, Anindya Banerjee, Robert A. Feldman, Bob Flood, Lusine Lusinyan, Paulo Neuhaus, and Sofia Soromenho-Ramos for their comments on an earlier version of this paper as well as Helge Berger, seminar participants at the IMF, and especially Elena Loukoianova for productive discussions.
This sample of countries represents a relatively heterogenous set of small and large European economies, including the European G-7 economies with the exception of Germany due to data problems.
The evaluation period, 1990-2002, was chosen to investigate an economically rather interesting period in Europe: Finland experienced a major crisis after the burst of an asset bubble, and Italy and the United Kingdom exited from the ERM, see above.
For example, I do not analyze the class of factor-based forecasts; see the series of papers by Stock and Watson (1989,1991,1999). Another common decomposition, pioneered by Beveridge and Nelson (1981), is omitted due a lack of sufficient data.
See, e.g., Denis, Mc Morrow, and Roeger (2002). Proietti, Musso and Westermann (2002) evaluate unobserved components models based on the production function approach for the Euro area as a whole.
Svensson (2003) provides an extensive survey. More specifically, the consequences of output gap uncertainty for the Taylor rule are discussed by Smets (1998) for the U.S. and by Eleftheriou (2003) for the Euro area.
The report of the Economic Policy Committee acknowledges the output gap as an essential —but so far only intermediate—input for assessing the progress made by countries towards achieving the goal of medium-term fiscal balance; see European Commission (2001).
The output gap measures differ in the amount of parameters estimated. The issue of parameter instability due to the relatively short estimation period is acknowledged, but not pursued further.
The same holds true for a limited number of other cases, including the one of a large estimation sample size relative to the prediction sample size; see, e.g., Diebold (2001). McCracken (2000) points out that under the same conditions, parameter uncertainty is not necessarily irrelevant for the moments of non-differentiable functions of parametric forecasts and forecast errors such as the mean absolute error.
Output gap in 2002.
For both countries (and across all gap measures), the degree of business cycle integration did not increase substantially after 1990 when compared to pre-1990 (with the exception of the UK-Finnish cycles). While an interesting subject in itself, the issue of business cycle synchronization is beyond the scope of this paper.
This measure differs from the first difference of the gap considered above in that two measures could signal an improvement (Δgap > 0) but not necessarily the same cyclical position (negative vs. positive gap).
Proietti, Musso, and Westermann (2002) find that the first difference of the output gap (but not the level) is a significant predictor of inflation in the Euro area. Selected experiments with differenced output gap measures yielded results close to the ones presented and have, hence, been omitted; see also the rather similar correlations between gaps in levels and differences in Table 1.
As Stock and Watson (1999) point out, this specification assumes that (i) the inflation rate is integrated of order one (I(1)); (ii) xt is I(0); and (iii) both are, hence, not cointegrated. Moreover, the constant intercept implies that the ”natural rate” of the output gap is constant. In this literature, inflation is commonly modeled as an I(1) process. Results not reported here have confirmed this assumption for wage and CPI inflation in the sample countries; for Finland see also the discussion in the Appendix of Billmeier (2004). While the output gap may seem to behave like an integrated process over limited periods of time, it is clearly mean-reverting from a theoretical perspective.
Given that a main ingredient of the output gap based on the production function approach—the natural rate of unemployment—is derived from a similar framework, the evaluation could expected to be biased in favor of this approach. This, however, does not hold true for at least two reasons: (a) the framework described in Appendix I.D is based on wage inflation whereas the evaluation measures performance in forecasting CPI inflation; and (b) the natural rate of unemployment is only one building block of potential output according to the production function approach—with total factor productivity being quantitatively much more important most of the time.
Parameter estimates of equation (8), while not reported to conserve space, are broadly in line with expectations. In particular,
This is true under the assumptions that the relevant price index, e.g., the CPI, contains imported goods and that the exchange rate pass-through is positive.
This effect would be even more noticeable if the forecast took parameter uncertainty into account; see Section IV.A.
For a maximum of one lag, the frequency domain approach is just as good as the univariate forecast.
The production function approach is almost significant for a maximum of one and three lags, indicating some scope for a better performance of a refined estimate of gap based on the production function.
This follows Burns and Mitchell (1946) and Hodrick and Prescott (1997); see Section IV.D for a robustness check regarding the value of λ. Ross and Ubide (2001) discuss alternative approaches to determine the parameter λ endogenously.
Orphanides and van Norden (2002) show that ex-post revisions of output gap estimates for quarterly US GNP data are of the same order of magnitude than the gap itself. The bulk of the revisions, however, is attributed to unreliable end-sample estimates, not revisions of published data.
See, e.g., Harvey and Jaeger (1993), King and Rebelo (1993) and Cogley and Nason (1995) for overviews of the shortcomings. Billmeier (2004) provides an illustration of another problem of the HP filter, the end-sample bias. The discussion of the optimal λ is circumvented here by comparing 3 values. While Ravn and Uhlig (2002) argue a value of 6.25 for annual observations, they base their argument on the assumption that λ = 1600 is the optimal value for quarterly data (which is the common assumption for the United States, but not necessarily true for other countries). Artis, Marcellino and Proietti (2002) argue the superiority of the band-pass version of the HP-filter.
As Corbae and Ouliaris (2002) explain, this is due to a “leakage problem.” The frequency responses generated by the discrete Fourier transform of an I(1) process are dependent across fundamental frequencies.
Blanchard and Quah (1989) also show that small violations of the identification scheme (e.g. lasting effects on output stemming from nominal shocks through a wealth effect) are of minor consequence. The empirical set up has been employed and documented numerous times in the literature; see, e.g., Clarida and Gali (1994) for a more detailed description of the approach in the context of a three-variable model.
Early work on the production function approach includes Artus (1977). Subsequent research has refined the approach in various directions, see, e.g., De Masi (1997) for a recent overview of work done at the IMF. Proietti, Musso and Westermann (2002) use unobserved components models based on a production function to determine potential output in the euro area.
In other words, the full-capacity stock of capital is usually approximated by the actual stock of capital. For a more elaborate approach, using French data on capital operating time, see Everaert and Nadal De Simone (2003).
Of course, the choice of a filter to detrend the unemployment rate and TFP adds an element of discretion.
This approach—known as the “GAP model”—was recently adopted by the European Commission; see Denis, Mc Morrow, and Roeger (2002) and Planas and Rossi (2003). In the Commission’s work, the new methodology substitutes for more “traditional” approaches—such as the Hodrick-Prescott filter—and, at the same time, unifies the Commission’s efforts toward a consistent representation of business cycles in the member countries.