Comments on: Single and two-stage cross-sectional and time series benchmarking procedures for small area estimation

Abstract

Pfeffermann, Sikov, and Tiller (hereafter PST) have provided a nice review of the literature on benchmarking in small area estimation, and also presented a new twostage benchmarking procedure for small area time series models. The latter further develops previous work of Pfeffermann and Burck (1990) and Pfeffermann and Tiller (2006). My remarks here will focus on some general points they surface related to the differing rationales for external benchmarking (as is commonly practiced with time series data from repeated business surveys) versus internal benchmarking (as is commonly practiced in small area estimation). PST (Remark 3) note that external benchmarking lowers variances of estimates, “when the benchmark is a known constant... and the benchmark constraint is correct.” In fact, even when the external benchmark data are survey estimates with sampling error, benchmarking may lower variances relative to the variances of predictors that make no use of the benchmark data (this being subject to a condition given byBell et al. (2012) noted by PST in Remark 3). Thus, variance reduction provides one reason for doing external benchmarking. Note, however, that when the benchmark data contain sampling error, maximum variance reduction results from optimal predictors that do not force exact agreement with the “benchmarks”, though they pull the predictions towards them (Hillmer and Trabelsi 1987). One may question whether such optimal prediction should be called “benchmarking”? Doing so may draw useful connections with exact benchmarking, since exact benchmarking results, in the limit, when the variances of the benchmarks go to zero.