Statistical methodology has thus far been lagging in providing guidance = for consideration and treatment of business units in the production and use= of business and economic statistics. The Scientific Committee of EESW17 ha= s formed a working group (footnote: Members: Boris Lorenc (chair), Arn= out van Delden, Peter Struijs and Li-Chun Zhang) to prepare a sh= ort statement paper on the subject. Its aim is three-fold: (i) to summarise= the core aspects of the unit error and the associated unit problem, (ii) t= o stimulate the discussions to clarify and improve our understanding of the= system of statistical units, which is needed for the production of Nationa= l Account and various relevant national and international business/economic= statistics, (iii) to provide the background for an integrated approach to = the unit problem in business statistics, including the development of neces= sary statistical methods for the evaluation and treatment of unit error fro= m a total survey error perspective. Comments, thoughts, and suggestions of = EESW17 participants are invited and warmly welcome.

There is a distinction between administrative and statistical business u= nits. Administrative units are created for administrative purposes outside = the statistical system. For instance, legal units (LeU) are a type of admin= istrative units that one expects to find in every country, even though thei= r definition varies over countries. Another example is tax units that exist= in some countries, which are created for taxation and do not coincide with= the legal units. Administrative business units are generally maintained by= external owners and imported to the statistical system more or less freque= ntly. They are also the starting points for creation and maintenance of sta= tistical business units.

Statistical business units are created within the statistical system for= the purpose of producing statistics. Typically, intrinsic relationships be= tween statistical units are inferred and articulated in terms of a classifi= cation, or a model of units. For example, the current Eurostat model of sta= tistical units consists of the unit types enterprise group (EG), enterprise= (ENT), local unit (LoU), kind of activity unit (KAU) and local kind of act= ivity unit (LKAU) (fig.). Or, t= he Institutional Unit, which is closely related to the ENT, may be subdivid= ed into units of homogeneous production (UHP) for the purpose of National A= ccounts, where the UHPs are not the same unit type as the KAUs.

Creation of statistical units is necessary because administrative units = do not exist for statistical purposes nor are they seen as able to fully me= et the needs of the users of statistics. For instance, many economic theori= es are based on the assumption that the business units possess a level of a= utonomy in decision making. In contrast, the administrative unit LeU entail= s legal (or fiscal) accountability, the structure of which does not necessa= rily coincide with that of business decision making.

Ideally speaking the system of statistical units should mirror busi= ness data availability as well as possible so as to improve data collection= . For instance, the EG and ENT are created to capture better than the LeU t= he business management, operation and accounting structure. But in pra= ctice this is not always achieved. Especially, some of the lower-level stat= istical units types may present challenges to businesses' own understanding= of reality. For example, the business may find it difficult to extract the= required data (e.g. sales, purchases, profit) for the LKAU, in which = case the delivered data may refer to some proxy unit (e.g. LeU) instead.

In survey methodology, there is a distinction between the study unit (of= the target population), the sampling unit, the reporting unit (i.e. the en= tity within a business that is actually able to deliver the required data),= etc. The system of statistical units is created having the user needs in m= ind. The two approaches do not fully align with each other, in the sense th= at there does not always exist a many-to-one mapping from one set (of units= ) to the other. Moreover, the administrative units are relevant with respec= t to survey compliance, or the reduction of response burden and survey cost= by the increasing uptake of administrative data.

U= nit Error and Unit Problem

Choice of the business unit type is an important decision in the design = and operation management for a statistical product. By the term =E2=80=9Cun= it error=E2=80=9D we refer to the errors in statistical outputs, which are = caused by the identification, characterisation and delineation of the relev= ant statistical units and the relationships between them. In addition, by t= he term =E2=80=9Cunit problem=E2=80=9D we refer to the challenges and obsta= cles to our understanding of the unit errors and our efforts to deal with t= hem. The unit problem may be related to the practice of business surveys, t= he design of relevant statistical processes, as well as the conceptualisati= on of the system of statistical units.

Unit errors can be appreciated in terms of a discrepancy between =E2=80= =98what one aims to obtain=E2=80=99 and =E2=80=98what one obtains=E2=80=99.= Below are some generic situations where the discrepancy arises.

There is

**observation error**in the data that is avai= lable, such as when a value is missing or misreported. The discrepancy is b= etween the results based on the true data and the erroneous data. For insta= nce, the administrative record shows that an LeU is active in the economic = sector =E2=80=9C12345=E2=80=9D, whereas it is in fact active in the sector = =E2=80=9C21345=E2=80=9D. This can potentially affect the characterisation (= e.g. NACE) and identification (e.g. inclusion in the frame) of the statisti= cal units related to this LeU. (Some other examples of observation err= ors in data are given in Appendix 1.)Van Delden (2017) provides a breakdown of observational = errors in different stages of data processing for statistical purposes. We = would like to mention specifically two types of observation error here.

= =E2=80=A2 Profiling error of large and complex business units (footno= te: Profiling is the activity to delineate the statistical units associated= with large or complex businesses, including relationships) may result= in erroneous statistical units, which tend to have a large impact on the o= utput.

=E2=80=A2 Consolidation (or apportion) error may be unavoid= able when the available data needs to be transformed (or disaggregated), be= cause the required data is missing or simply unavailable. For example, turn= over of the VAT units may need to be transformed to that of ENTs, where the= two units have many-many relationships. Or, the quarterly data may need to= be disaggregated to monthly data. (footnote: Consolidation concerns exclud= ing internal flows from values reported by units that are underlying a = ;targeted composite unit type. Deconsolidation is the opposite situation)**Implementation error**may be the case with respect t= o the relevant regulation or statistical unit model (e.g. Fig. 1). The disc= repancy is between the results from correct and incorrect implementation. F= or instance, the regulation of Business Register (BR) may be misinterpreted= , or it may not cover the extra complications in a given country (e.g. exis= tence of tax units in addition to LeUs), etc.- There may exist inconsistencies and shortcomings in the statistical uni=
t model or relevant regulation, the
**definition error**. The discrepancy is between the results with and without= such inconsistencies. For example, the unit model depicted in Fig. 1 does = not include the means to guarantee that one obtains the same ENTs directly = from the LeUs or indirectly via the EGs. Another example, the definition ac= tually allows an LoU to have activity in different locations (towns). - There is ultimately the discrepancy between the ideally delineated unit=
s under a consistent unit model and the units that the users need or expect=
for their purposes. For instance, Brion et al. (2014) have documented such=
discrepancies between the actual business demography of SMEs in France whi=
ch is based on the LeUs, and the user expectation of business demography ba=
sed on autonomous units like the ENTs. One may refer to this as the
**conceptualisation error. As long as there is a (non-negligible) c= onceptual mismatch, improving the implementation of existing relevant regul= ation cannot overcome the unit error in statistical products. More discussi= ons regarding the conceptualisation difficulties can be found in the Villag= e Bakery Example (Appendix 2).<= /li>**

We believe that unit error should be included and recognised in the TSE = framework, in the same spirit alongside the other types of error, such as s= ampling error, non-response error, measurement error, etc. In other words, = while it is important and helpful to try to reduce the unit errors in indiv= idual data, it is necessary to approach the unit problem from a more integr= ated perspective. As indicated by the above analysis of the various generic= situations that can lead to unit error, a single-minded focus on the opera= tional aspects of the statistical process will have little effect at all re= garding the conceptualisation and definition errors, and only limited and p= otentially biasing effects on the observation error.

The effects of the actual unit errors in the collected data, their treat= ment in data processing and adjustment in statistical estimation need to be= understood and articulated under the TSE framework. In terms of data colle= ction and integration, the unit error is rooted in the representa= tion side of TSE framework (Groves et al, 2004; Zhang, 2012). The different= situations of discrepancy that can cause the unit error are inter-related,= so that it is important to keep such =E2=80=98interactions=E2=80=99 in min= d when dealing with the unit problem. Moreover, the unit error will also af= fect measurement errors and relevance errors on the measurement side of the= TSE framework, whereas the causes of potential errors on the measurement s= ide can as well affect one=E2=80=99s approach to the unit problem.

Regardless of one=E2=80=99s approach to the unit problem, the effects of= the unit error that remains in the data need to be evaluated with respect = to the User Value Criteria below, including the so-called quality dimension= s.

a) Relevance (e.g. output that make sense to users) is ultimately rooted= in the conceptualisation of the system of statistical units.

b) Coherence (e.g. between annual and short term statistics, national to= tals based on different units, etc.) seems mostly related to the various ty= pes of observation error and to the conceptualisation of the system of stat= istical units.

c) Accuracy (e.g. avoiding bias of various causes) is amply discussed un= der the TSE framework.

d) Timeliness does not call for a treatment that is specific to the unit= error.

e) Comparability (e.g. if the unit system or classification changes) can= be a challenge with respect to all types of unit error over time.

f) Accessibility (e.g. with regard to unduly complex system) seems above= all related to the conceptualisation of the system of units.

g) Cost to the statistical system (e.g. profiling) is directly affected = by the operational features, but can ultimately be attributed to the concep= tualisation.

h) Response burden (e.g. using =E2=80=93 or not using =E2=80=93 data tha= t exists in business accounting systems or administrative sources) is again= rooted in the conceptualisation.

Brion et al. (2014). The Geneva wor= kshop. (Will provide ref later. Perhaps they also published somewhere else,= later.)

Delden, A. van (2017). Issues when integrating data sets with different = unit types. CBS Discussion Paper 2017-05. Available from www.cbs.nl.

Groves, R.M., F.J. Fowler jr., M.P. Couper, J.M. Lepkowsk=
i, E. Singer, & R.Tourangeau (2004). *Survey Methodology *=
(New York: Wiley Interscience).

Zhang, L.-C. (2012). Topics of statistical theory for register-based sta=
tistics and data integration. *Statistica Neerlandica* 66, =
;41=E2=80=9363.