Growth Rates Preservation (GRP) temporal benchmarking: Drawbacks and alternative solutions
Section 6. Conclusions
Two well-known multiplicative benchmarking methods are Denton Proportionate First Differences (PFD) and Growth Rates Preservation (GRP). It is generally agreed that GRP has the strongest theoretical foundation. It better preserves initial growth rates than Denton PFD. However, from a technical point of view, Denton is the easiest method to apply. Because of this, and because Denton PFD is often a good approximation of GRP, Denton PFD is more popularly applied.
In this paper two drawbacks of GRP are demonstrated that, to the best knowledge of the authors, have not been mentioned elsewhere.
The first drawback is that GRP does not satisfy the time reversibility property. According to this property it should not matter for the results whether forward or backward growth rates are preserved. That is, benchmarking an original time series, or a “reversed” time series, should lead to the same benchmarked series. Since direction of time is irrelevant for any benchmarking application, any benchmarking method should preferably satisfy time reversibility. Moreover, a benchmarking method that does not satisfy time reversibility may yield entirely difficult conclusions on the timing of economic events depending on the chosen time direction. For these reasons forward and backward GRP methods should preferably be discouraged.
In this paper two alternative GRP methods are presented that do satisfy time reversibility. The first alternative, a new GRPS method, preserves both forward and backward growth rates. The other alternative, an existing GRPL method, preserves logarithms of the forward growth rates.
A second drawback of all GRP methods in this paper are the singularities in its objective functions. Complications of this are: avoidance of close to zero outcomes, irregular peaks in results and unnecessary negative values in benchmarked results.
These problems actually occurred in an illustrative application on real-life data. Although unnecessary negative values only occasionally occurred, reconciliation adjustments are much more irregular than for Denton PFD. Since smoothness of reconciliation adjustments (BI ratios) is often the main interest of benchmarking, asymmetric GRP methods can be discouraged for many applications.
While the literature considers Denton PFD “a good approximation” of the ideal GRP method, our main conclusion is that Denton PFD is even more appropriate than standard GRP for many applications. Denton is computationally easier to apply, it does not suffer from the problems related to time irreversibility and a singular objective function. Furthermore, the approximation of Denton PFD’s results is even more close for the time-symmetric versions of GRP than for standard GRP.
However, when growth rate preservation is the key point of interest, a time-symmetric version of GRP can also be a good choice, most in particular GRPL. Time symmetric methods preserve growth rates slightly better than Denton PFD, satisfy time reversibility and suffer less severe from the drawbacks of a singular objective function than standard GRP.
Acknowledgements
The authors would like to thank three reviewers and the associate editor for useful comments that greatly contributed to improving the paper.
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