Model-based estimation of the gross value added in the enterprise groups statistics (VAB-STAGRE)

The Enterprise groups statistics (STAGRE) provide information on the activities and influence of group-controlled companies in Switzerland. These statistics enable us to examine the influence of enterprise groups, in particularly foreign multinationals, within the Swiss production system. 

To further develop the STAGRE statistics, the FSO is exploring ways to leverage the existing information without requiring additional surveys. Modelling is the preferred approach to gradually expand the range of data available, which should in turn offer new dimensions of analysis, especially with regard to globalisation. In the context of the group-enterprise population in the STAGRE, this project focuses on the key variables of gross output (GO), intermediate consumption (IC) and gross value added (GVA). These three variables are fundamental to calculating the economic influence of groups within Switzerland's gross domestic product (GDP). 

The results obtained through this project should ensure compliance with international standards and offer the possibility of conducting analyses according to different dimensions, such as the type of group, its size, country of origin, or economic activities.

The target variables for the project (GO, CI, GVA) are collected through the value-added statistical survey (WS). As the value-added statistical survey is a sample survey, the data are not available exhaustively for all the units covered by the STAGRE. To address this, it is necessary to use estimation techniques, in this case small area estimation (SAE). 

This allows for the development of models exploiting the relationship between the information surveyed in the WS and data from public registers, specifically VAT data and Old-Age and Survivors' Insurance (social security) data. Both of these sources are exhaustive and have the advantage of providing useful additional variables (turnover and income from employment) for the application of SAE techniques. 

The STAGRE population comprises around 50 000 legal units. However, because of the WS-based modelling, the VAB-STAGRE project estimates only cover the overlap between the STAGRE population and the WS sample population and thus exclude enterprises with fewer than 3 jobs in addition to certain NOGA combinations and legal forms. For some of these units that are present in the WS survey sample, the values are directly obtained from the survey data. The SAE_WS techniques are used to predict the WS values, which are then imputed to units not covered by the survey. The individual values obtained through this process are then aggregated to estimate totals for different STAGRE research areas with the aim of achieving a high degree of comparability between these estimates and the results of the WS survey. 

However, this approach presents some challenges, particularly in terms of the explanatory power of the additional variables used in the models. While the correlation can be quite high, especially between the auxiliary variable 'VAT turnover' and the 'WS turnover', the correlation between 'VAT turnover' and variables like 'WS GVA' is weaker. To address this, the project proposes and evaluates various solutions, including calculating different model variants and comparing the accuracy of their predictions (e.g. using the coefficient of determination R2 and root mean squared error RMSE).

A breakdown of the groups' GVA according to their country of origin, i.e. the country in which the head office of the controlling unit is located, shows that non-European groups have been the main contributors to this dynamic. During the 2014 to 2023 period, the average annual growth rate for European countries was 2.8%, while for non-European countries it was 8.4%. The largest increases were recorded for companies based in Japan or China. In relative terms, however, American multinationals remain by far the leaders in the creation of value added, since they alone produce 44.5% of the GVA of all foreign-controlled groups.

The values at the enterprise level are partly imputed from relationship models between administrative data sources and the survey data. As the results developed in this context are still experimental in nature, they should be mentioned with appropriate caveats in any publications referring to the STAGRE GVA estimates. The FSO's efforts to evaluate and improve the quality of the predictions and resulting estimates are still ongoing (e.g. to take into account extrapolation weights in model estimates, studies of the bias of the estimates and estimation of their variance, e.g. using the bootstrap). 
 

By publishing the three STAGRE variables (gross output, intermediate consumption, and gross value added) on the experimental statistics microsite, we will be able to explore the potential of small area estimation (SAE) techniques. Once the results of this modelling approach have reached the required degree of maturity, in accordance with the FSO's quality criteria, the goal in the short to medium term is to standardise the results within day-to-day production of STAGRE. Where appropriate, an extension of the SAE techniques to other variables, such as the remuneration of the 'capital' factor, could also be considered in the future. 
 

Contact: stagre@bfs.admin.ch 
Telephone: +41 58 463 62 66 

The information presented here in the form of experimental statistics is intended to provide insights into our ongoing reflections and development. It is also an opportunity for us to verify the quality of the results and flag any problems. In this context, questions and comments on the VAB-STAGRE are most welcome.