Design effects of sampling frames in establishments surveys

When stand-alone sampling frames that list all establishments and their measures of size are available, establishment surveys typically use the Hansen-Hurwitz (HH) PPS (probability proportional to size) estimator to estimate the volume of transactions that establishments have with populations. This paper proposes the network sampling (NS) version of the HH estimator as a potential competitor of the PPS estimator. The NS estimator depends on the population survey-generated establishment frame that lists households and their selection probabilities in a population sample survey, and the number of transactions, if any, of each household with each establishment. A statistical model is developed in this paper to compare the efficiencies of the HH and NS estimators in single-stage and two-stage establishment sample surveys assuming the stand-alone sampling frame and the population survey-generated frame are flawless in coverage and size measures.