Ghostbusting which output gap really matters

Authors: Andreas Billmeier

Publish Date: 2009/08/27

Volume: 6, Issue: 4, Pages: 391-419

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Abstract

Reflecting domestic demand pressures the output gap has important implications for economic analysis This paper assesses the usefulness of four commonlyused gap measures for a small set of European countries The main results are that the policy implications can be very different depending on the gap measure and that consequently care should be exercised when employing any such measure Moreover the paper investigates in a simple inflation forecasting framework the common assertion that the output gap could improve the forecasting accuracy For annual observations however these measures rarely provide useful information and there is no single best measure across countriesI thank Mike Artis Anindya Banerjee Robert A Feldman Bob Flood Lusine Lusinyan and Sofia SoromenhoRamos for their comments on earlier versions of this paper as well as Helge Berger seminar participants at the IMF and especially Elena Loukoianova for productive discussions Francisco Nadal De Simone shared some Gauss code This paper should not be reported as representing the views of the IMF The views are those of the author and do not necessarily reflect the views of the IMF or IMF policyThe penalty parameter λ controls the smoothness of the series by setting the ratio of the variance of the cyclical component and the variation in the second difference of the actual series A higher value for λ implies a smoother trend and hence more volatile gaps In the extreme case of λ→∞ the trend is a straight line The standard value in the literature is λ = 100 for annual data which is also assumed as a base case in what follows14In a policyrelated context the traditional HodrickPrescott measure poses a substantial problem the filter as described above is fundamentally a twosided filter that is computation of the underlying trend at time t is based on observations before and after period t Economic policymakers instead will—at the time of decisionmaking—only dispose of an estimate of the output gap that is based on a purely backwardlooking evaluation of potential output To avoid this inconsistency this chapter uses a “realtime” output gap series HPrt that is constructed based on the conventional HP filter This new series consists of “last observations” that is realtime estimates of the underlying trend in the last observation period t given the information set in period tThis approach is subject to two important caveats First an observation for output produced in period t has to be a prediction while the economy is still in period t and will be finally observed only in t+1 for example data on 1999 GDP is only issued at best in the course of 2000 Second data may be revised in later periods We abstract from these important details since the empirical analysis builds on yearly observations implying that by the end of a given year the first three quarters of the yearly figure for output have already been observed and provide a sound footing for an endyear estimate Annual data are also less likely to be affected by substantial data revisions since these revisions usually occur in the periods immediately following the quarterly observation hence mostly before the end of the calendar year In addition revisions due to seasonal factors are limited for annual dataOther prominent drawbacks of the HP filter in the version described above have been well documented in the literature and include the possibility of finding spurious cycles for integrated series the somewhat arbitrary choice of λ as well as the neglect of structural breaks and shifts15 The discussion of the optimal λ is circumvented here by comparing three values Ravn and Uhlig 2002 argue a value of 625 for annual observations based on the assumption that λ = 1600 is the optimal value for quarterly data which is not necessarily true for our sample as we assess a variety of countries We compare the countries in the sample for three λ values including one that is quantitatively similar to the one suggested by Ravn and Uhlig 200216 Section 431 elaborates on the robustness of the results with regard to the choice of λEconomic fluctuations occur at different frequencies displaying for instance seasonal or business cycle duration Starting from the classical assumption contained in Burns and Mitchell 1946 that the duration of business cycles takes between 6 and 32 quarters the approach to extracting those cycles from a stationary time series is relatively straightforward from the frequency domain perspective The original series should be filtered in such a way that fluctuations below or above a certain frequency are eliminatedThis can be achieved with the help of a socalled exact bandpass filter BPF An exact BPF acts in principle as a double filter it eliminates frequencies outside a range here the business cycle frequency For estimation purposes however these filters are usually spelled out in the time domain since integrated series—such as real GDP—could traditionally not be handled by frequency domain approaches due to a leakage problem the frequency responses generated by the discrete Fourier transform of an I1 process are dependent across fundamental frequencies Corbae and Ouliaris 2006 However transformation of the exact bandpass filter back into the time domain results in a moving average process of infinite order For this reason Baxter and King 1999 Christiano and Fitzgerald 2003 and others have provided time domain approximations to the exact band pass filter capable of dealing with integrated series Their method involves a tradeoff between the quality of approximation and the ability to smooth the series at the extreme points of the sample since every additional lag employed in the estimation process improves the filter but translates into one lost observation at either end of the series This in turn substantially diminishes the attractiveness of this class of filters for policyrelated analysis

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