Environmental and Ecological Statistics

, Volume 25, Issue 4, pp 523–547 | Cite as

Benchmarking a triplet of official estimates

  • Andreea L. ErciulescuEmail author
  • Nathan B. Cruze
  • Balgobin Nandram


The publication of official statistics at different levels of aggregation requires a benchmarking step. Difficulties arise when a benchmarking method needs to be applied to a triplet of related estimates, at multiple stages of aggregation. For ratios of totals, external benchmarking constraints for the triplet (numerator, denominator, ratio) are that the weighted sum of denominator/numerator/ratio estimates equals to a constant. The benchmarking weight, applied to the ratio estimates, is a function of the denominator estimates. For example, the United States Department of Agriculture’s National Agricultural Statistics Service’s county-level, end-of-season acreage, production and yield estimates need to aggregate to the corresponding agricultural statistics district-level estimates, which also need to aggregate to the corresponding prepublished state-level values. Moreover, the definition of yield, as the ratio of production to harvested acreage, needs to hold at the county level, the agricultural statistics district level and the state level. We discuss different methods of applying benchmarking constraints to a triplet (numerator, denominator, ratio), at multiple stages of aggregation, where the denominator and the ratio are modeled and the numerator is derived. County-level and agricultural statistics district-level, end-of-season acreage, production and yield estimates are constructed and compared using the different methods. Results are illustrated for 2014 corn and soybean in Indiana, Iowa and Illinois.


Auxiliary information Corn and soybean estimates End-of season yield Hierarchical Bayes Ratio 



The findings and conclusions in this preliminary publication have not been formally disseminated by the U.S. Department of Agriculture and should not be construed to represent any agency determination or policy. This research was supported in part by the intramural research program of the U.S. Department of Agriculture, National Agriculture Statistics Service. Dr. Nandram’s work was supported by a Grant from the Simons Foundation (#353953, Balgobin Nandram). The authors thank the reviewers for their comments and suggestions. The authors are grateful to Wendy Barboza, Valbona Bejleri, Dave Johnson and Linda Young from the National Agricultural Statistics Service.


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Copyright information

© This is a U.S. Government work and not under copyright protection in the US; foreign copyright protection may apply  2018

Authors and Affiliations

  • Andreea L. Erciulescu
    • 1
    Email author
  • Nathan B. Cruze
    • 2
  • Balgobin Nandram
    • 3
  1. 1.National Institute of Statistical SciencesWashingtonUSA
  2. 2.USDA National Agricultural Statistics ServiceWashingtonUSA
  3. 3.Department of Mathematical SciencesWorcester Polytechnic Institute and USDA National Agricultural Statistics ServiceWorcesterUSA

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