Structural VARs based estimates of the output gap and their use when forecasting in the Euro Area

1. Structural VARs based estimates of the output gap and their use when forecasting in the Euro Area James Mitchell & Martin Weale

2. Forecasting and the output gap • When output growth is forecastable there is a temporary component, i.e. there is a “cycle” or “output gap”, which in due course reverts to its unconditional mean (of zero) • The output gap is larger the greater the degree of long-run forecastability; only when output growth is unforecastable does output follow a random walk implying there is no output gap

3. Multivariate models • It is well known that multivariate models can, but need not, deliver better forecasts of output growth than univariate models • What variables we use to measure the output gap, along with output, is therefore of central importance in determining the properties of the output gap • We compare and contrast output gap estimates generated using an important class of multivariate decomposition method, namely structural vector autoregressive (SVAR) models

4. SVAR models • A VAR model offers a general dynamic representation of a vector of time-series • This can be considered as the “reduced form” of a “structural” VAR model where the errors now have an economic interpretation • Restrictions are imposed on the structural parameters so they can be identified from the reduced form. • Different SVAR models do this in different ways. A popular choice is to impose restrictions on the long-run effects of shocks – to distinguish permanent and transitory shocks

5. SVARs and the output gap • The output gap in a SVAR is defined as the cumulative sum of “temporary” or “demand” shocks which have no long run effect on output • Basic approach is Blanchard-Quah. Extensions to accommodate cointegration (KPSW) • Cointegration provides information on the number of temporary and permanent shocks. But raises additional identification problems

6. Perceived advantages of SVAR • Potential output does not follow a random walk (or integrated random walk) as in Beveridge-Nelson and “traditional” Unobserved Components models • Identification restrictions are imposed so that potential output has both a random walk component and an additional stationary component • VARs are one, not two, sided filters which may deliver more reliable “real-time” cyclical estimates • Economic motivation is “explicit” • VARs can be estimated by OLS

7. Relationship with other multivariate decomposition methods • But a VAR can always be written in state-space form and SVAR decompositions work off the multivariate BN decomposition • Also a correlated UC model coincides with a BN decomposition • A multivariate correlated UC model has an underlying VARMA representation • In these senses the multivariate decomposition methods are all related

8. Empirical comparison(using Euro-area data from the ECB’s AWM 1970q1-2006q4)

9. Inference is sensitive to measurement

10. Stability of real-time estimates • As well as disagreement about the cyclical position of the economy, output gap estimates are uncertain because estimates are needed in “real time” • Policy makers have to decide, without the benefit of hindsight, whether a given change to output in the current period is temporary or permanent, that is whether it is a cyclical or trend movement • To assess the stability of cyclical estimates in the Euro Area we consider the ECB’s AWM database where Euro Area data are the weighted sum of national data • Data are available from 1970q1-2006q4, and the period from 1990 is then used for out-of-sample recursive analysis • SVAR estimates are known to be sensitive to the chosen lag order in the VAR • As a benchmark we consider a (univariate) Hodrick-Prescott filter

12. But are these output gap estimates useful? • Large revisions to output gap estimates could be an indication of quality, rather than a sign of weakness • A coherent approach is to rank alternative estimators with reference to the ultimate use of the output gap • We might prefer output gap estimators which deliver improved forecasts of inflation • Or, since the output gap, however estimated, is an estimate of the transitory part of output that will die out, we might compare alternative output gap estimates according to their ability to forecast future growth

13. Correlation of SVAR output gaps with output growth at different leads

14. Which output gap estimates are useful? Forecast combination

15. Conclusion • We have considered the use of structural VAR based output gap estimates in business cycle analysis • What variables we use to measure the output gap, along with output, and what restrictions we impose on them, is of central importance in determining both the properties of the output gap and its use when forecasting inflation and/or future output growth • SVAR output gaps do help when forecasting these variables • But combining individual output gap estimates improves predictive power, since it provides a means of integrating out uncertainty about the best single output gap estimator