An application of weighting approaches to assess the sensitivity of business survey estimates to “the unit problem”

Abstract

“The unit problem” in business statistics is that there is no consistent, natural unit for a business structure. Administrative processes quite often mandate the creation of particular units, but there is often no easy way to relate them to each other. Since the statistical view of units for sampling purposes is often derived from administrative systems, it can be quite difficult to define what population is being estimated, or to assess how this differs from the target concept.

In this paper we consider a variety of weighting approaches as possible estimation strategies for complex units in a business survey. Standard estimation approaches use units as defined on the business register, including their auxiliary information. In some structural surveys, information is gathered on more than one type of unit, for example on enterprises and local units. Basic classification information is available at both levels, so it is possible to construct an estimator at either level separately, or, using the integrated weighting approach of Lemaître and Dufour (1989), for both levels simultaneously. I will examine what sort of effect this has on estimates and the associated standard errors. Where surveys repeat on the same populations and there is some trading of units back and forth, it is also possible to conceive of the whole as a longitudinal study. There are some real challenges in treating a succession of cross‐sectional samples as a longitudinal approach, but I investigate the possibility that changes in the population resulting from acquisition/disposal of whole ‘units’ (for some suitable definition) can be investigated using generalised weight share methods (Lavallée 2007) to estimate the impact of structural differences.

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ORCID for Paul A. Smith: orcid.org/0000-0001-5337-2746

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