On the Extrapolation with the Denton Proportional Benchmarking Method

IMF Working Papers, June 1, 2012

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Canonical URL: On the Extrapolation with the Denton Proportional Benchmarking Method

Statistical offices use benchmarking methods to compile quarterly national accounts (QNA) by:
- Distributing annual, more reliable series of national accounts using quarterly indicator series (i).
- Extrapolating the most recent quarters not yet covered by annual benchmarks.
The Proportional First Differences (PFD) benchmarking method (Denton, 1971) is widely used for distribution but can perform poorly in extrapolation when movements in the indicator series do not match movements in target annual benchmarks.
The IMF’s Quarterly National Accounts Manual: Concepts, Data Sources, and Compilation (2001) recommended an enhanced formula for extrapolation to address these shortcomings.
The paper discusses the rationale for the enhanced technique, proposes a matrix formulation, and presents applications showing improved extrapolations for recent quarters.

Key methodological elements:
- Analysis of the Proportional First Differences (PFD) benchmarking method in both distribution and extrapolation contexts.
- Presentation of an enhanced extrapolation formula recommended by the IMF QNA Manual (2001).
- Proposal of a matrix formulation of the enhanced extrapolation technique.
Contributions:
- Rationale behind the enhanced extrapolation technique is discussed.
- Matrix formulation is provided to formalize the enhanced approach.
- Applications to artificial and real-life benchmarking examples demonstrate improvements in extrapolations for the most recent quarters.

Findings:
- PFD works well for distribution but "may suffer" in extrapolation when indicator movements and benchmark movements are inconsistent.
- The enhanced formula recommended by the IMF Manual (2001) can improve extrapolation outcomes.
- Matrix formulation facilitates implementation and clarity of the enhanced method.
Implications for statistical offices:
- Consider adopting the enhanced extrapolation formula when using indicator-based extrapolation for QNA.
- Use the matrix formulation to implement the enhanced technique in statistical software and workflows.
Use cases demonstrated:
- Artificial benchmarking examples.
- Real-life benchmarking examples.

Source: IMF Working Paper "On the Extrapolation with the Denton Proportional Benchmarking Method", Marco Marini and Tommaso Di Fonzo, June 1, 2012.