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Accuracy and reliability

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Labour and Income, Social Statistics.
Jesper Moltrup-Nielsen
+45 3917 3423

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Implicit index of average earnings

For the public sector the statistics are based on data for virtually all employees. For the private sector, there are two factors that can affect accuracy, namely uncertainty in the sample statistics and that there may be problems with the completeness of the reported data from the company.

This index is an where the sum of wages and hours worked is counted in each group (etc. activity sector). Thus, changes in personnel in a given industry will have an impact on the measured wage development.

The figures do not undergo revision; the published figures are usually final.

Overall accuracy

The sample for enterprises and organisations has been drawn in a way that ensures that a high share of the employees in the target population is in fact included in the total sample of enterprises and organisations with at least 10 persons in employment. For example, the statistics include all enterprises with more than 100 persons in employment. This means that the accuracy in industries with a high share of large enterprises is estimated to be close to the true value. For industries with a high share of small enterprises, the uncertainty is higher. However, there is no way of knowing in which direction this uncertainty affects the accuracy. For private enterprises, the completeness of the submitted data is also a source of uncertainty, which can typically be attributed to set-up errors in the enterprises payroll systems, which ultimately generate data for the earnings indices. It may be that e.g. a decomposition is missing in the individual salary components of payroll data, which may affect a calculated development of earnings, and that these flaws cannot necessarily be detected during the diagnostic process. Under-reporting of the extent of irregular payments, for example, may result in an overestimation of the measured development of earnings, since these should actually be included in the applied earnings concept. In general, however, the diagnostic process ensures that the total measured development of earnings and the development of earnings for the largest industry groups show robust results. For the sector general government, which includes the government as well as local and regional authorities, the accuracy is extremely high, since these are complete extracts from the public payroll transfer systems, where errors are extremely rare. The indices for public employees are consequently based on data for more or less everyone in the target population.

In the 2nd quarter of 2020 more enterprises than usual have been removed in the economic industries Culture and leisure activities and Hotels and Restaurants. This is done as many enterprises in these industries have submitted data for a much less number of employees paid by the hour due to the Covid-19 situation. If these enterprises were not removed, the wage development would be overestimated in these industries, as the share of employees paid by the month would rise substantially. These employees generally have a higher wage per hour and this would therefore result in a higher increase in wages for both these industries. None of the two industries are large enough to have an impact on the precision for the total concerning the whole sector of private industries.

Sampling error

For the sector enterprises and organisations, data is collected on the basis of a sample. However, the sample uncertainty has not been calculated at this point, but will be affected by the ratio of smaller enterprises, since all large enterprises (with 100 or more persons in employment) are included in the sample, however, and the quality of their reporting is normally good, the uncertainty mainly applies to small and medium-sized enterprises. In this way, industries with a large share of small enterprises will be more exposed to this uncertainty.

The sector general government is not based on a sample, but contains information for more or less everyone in the total population. As a result, these statistics are not associated with any sampling error.

Non-sampling error

For the sector enterprises and organisations: For private enterprises, under-reporting may occur of certain partial components for the employees’ total earnings. This may be e.g. irregular payments, e.g. bonuses and subsequent adjustments, which are not reported correctly in the data from the enterprises’ payroll systems and in this way, unintentionally influence the calculated development of earnings. It is the assumption that the under-reporting is not intentional, but rather an error caused by an incorrect set-up of the enterprises’ payroll systems, which can be quite difficult to identify with the enterprises themselves. At the same time, it is not necessarily possible to detect data errors in the diagnostic process in connection with the production of statistics, since it is not in the cards that payments of this nature will take place in the relevant pay period. For the sector general government: Minor uncertainty may be associated with the delimitation of the individual earnings and hour concepts in the reporting of data. In connection with the transition of local authorities/institutions to new payroll systems, a number of transitional issues have occurred in the form of errors in the reporting. We discuss these issues with the providers of the reporting public payroll transfer systems on a current basis. A certain level of uncertainty is associated with placing public employees in the correct industry and sector, which is obtained in principle by linking the payroll reporting with Statistics Denmark’s Statistical Business Register (ESR). This is partly due to quality issues with the reported production unit numbers in the payroll reporting, partly the fact that a number of employees with local and regional authorities are classified in terms of industry as local and regional government staff despite the fact that these groups of staff are not in fact working in administrative functions. Statistics Denmark is continuously trying to remedy these uncertainties to the extent possible by using the directly available system administrative information in the payroll reporting in the form of e.g. user numbers, work function codes etc. For all sectors, some uncertainty is associated with the information about the employee’s work function code. This information can be difficult to verify, as it concerns detailed information about the tasks of the individual employee. However, the variable has several levels of detail, and as the standardised index of average earnings only uses the 3-digit level (there are 6 digits altogether), the uncertainty is reduced. It is not possible to indicate a figure for the total uncertainty.

Quality management

Statistics Denmark follows the recommendations on organisation and management of quality given in the Code of Practice for European Statistics (CoP) and the implementation guidelines given in the Quality Assurance Framework of the European Statistical System (QAF). A Working Group on Quality and a central quality assurance function have been established to continuously carry through control of products and processes.

Quality assurance

Statistics Denmark follows the principles in the Code of Practice for European Statistics (CoP) and uses the Quality Assurance Framework of the European Statistical System (QAF) for the implementation of the principles. This involves continuous decentralized and central control of products and processes based on documentation following international standards. The central quality assurance function reports to the Working Group on Quality. Reports include suggestions for improvement that are assessed, decided and subsequently implemented.

Quality assessment

The combined accuracy and reliability is influenced by two factors in particular. First, a sample survey is applied for the sector enterprises and organisations, and consequently, some uncertainty is associated with the earnings index. Second, the completeness of the enterprises’ reported data is also a source of uncertainty, which can typically be attributed to set-up errors in the enterprises’ payroll systems, which ultimately generate data for the earnings indices. Both of these factors may affect the accuracy and reliability of the statistics. Nevertheless, complete troubleshooting of data is performed on a quarterly basis, which ultimately ensures the reliability of the published figures.

Data revision - policy

Statistics Denmark revises published figures in accordance with the Revision Policy for Statistics Denmark. The common procedures and principles of the Revision Policy are for some statistics supplemented by a specific revision practice.

Data revision practice

Only final figures are disseminated. Revisions of the seasonal adjusted figures might occur, as longer time series might change the parameters that are used for the seasonal adjustment. This also relates to figures dating back in time. It is therefore recommended, that in the case of contract regulation and similar only figures that are not seasonally adjusted are used, as these are generally not up for revision.