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Appendix I. Methodology for Decomposing the Revision to the CAPB
We define the CAPB as a share of GDP of year t as of vintage v, as follows:
where Rv,t represents real revenue and is a function of output,
We then decompose the cross-vintage change in the CAPB ratio to GDP into the contributions of individual sub-components
In a similar way, we also calculate the contribution of other subcomponents and a residual term. The only difference is with respect to the contribution of output revisions since the impact of output on the CAPBto GDP ratio is through two channels: the denominator effect as well as indirectly though the cyclical effect on revenues. Therefore, to calculate the contribution of output, we take into account the endogenous impact on revenues. As such, the contribution of output is calculated as:
Appendix II. The Size and Distribution of Revisions to Output and Potential Output Over Alternative Horizons
Appendix III. Estimating the Cross-Vintage Correlation of Output and Potential Output Growth
In this section, an empirical correlation between short term growth surprises and long term potential growth revisions across a specific horizon is estimated. Given that we are interested in the implications of output gap revisions, arguably, revisions in output and potential output levels would be of more direct relevance. However, any correlation analysis would be biased by data revisions. To minimize the impact of such data revisions, growth rates are used rather than levels.1 Furthermore, instead of using the budget horizon, the following analysis is based on a different horizon, as defined below, in order to better capture other relevant reference points for implementing fiscal policy.
The authors are grateful to Michal Andrle, Helge Berger, James Daniel, Natan Epstein, Estelle Liu, Camelia Minoiu, Rodrigo Valdez, Daria Zakharova and seminar participants at the IMF for helpful comments and suggestions. We would also like to thank Geraldine Mahieu, Cristina Cheptea, and Sarika Chinta for assisting with the collection of the data, charts, and document formatting respectively.
The European Commission produces potential output series based on both the Hodrick-Prescott filter and the Production Function method. We use the latter estimates, which are underpinning the estimates of the cyclically adjusted balances presented in the general government data forecast tables.
The revisions above are focused on the budget horizon since this is most relevant operationally for fiscal policy-making. For completeness, we also examined the size of revisions over longer time horizons and the qualitative results above continue to hold. We find that the output gap was also revised significantly beyond the budget horizon as output and potential output continued to be revised for another two years. The mean absolute error from the budget preparation vintage to the final vintage three years later was 2.6 percent of GDP, compared with the 1.3 percent of GDP revision over the budget horizon as noted above. These revisions reflect not only output surprises but also significant revisions in potential GDP. For a more detailed discussion of revisions to output gap over time beyond the budget horizon and the contributing factors, see Appendix II.
By extending the horizon to three years, we lose the observations in the last two years. Thus, all estimations are based on data from 2003-2010.