Benchmarking a triplet of official estimates

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.