Statistical processing

Source data

Information from private enterprises are collected directly from the enterprises or via their payroll agencies. For members of the Confederation of Danish Employers (DA), the Danish Employers’ Association for the Financial Sector (FA) and the Danish Pharmaceutical Association, data is reported in bulk from the respective associations.

First and foremost, data reported from public enterprises come from the major public payroll transfer systems (such as SLS – the government’s payroll system and KRL – the local government payroll system) supplemented by a number of private payroll processing services. E.g., payroll information from the Lutheran Church of Denmark is reported via a private payroll system.

Data collected for the annual earnings statistics (the structure of earnings survey) is used for calculation of the payroll weights in the standardised index of average earnings.

Statistics Denmark’s statistical business register (ESR) is used to determine sector, industry and number of persons employed.

The payroll reporting is collected for the middle month of each quarter. Specifically, the payroll reporting must contain the following:

• For the first quarter, the payroll period must include week 7
• For the second quarter, the payroll period must include week 20
• For the third quarter, the payroll period must include week 33
• For the fourth quarter, the payroll period must include week 46

This means that for the first quarter for employees paid monthly, the reporting must be for the month of February, whereas for employees paid every fortnight, the reporting must be for weeks 6 and 7 or weeks 7 and 8 only.

Frequency of data collection

Data is collected on a quarterly basis.

Data collection

For reporting from the private sector, the following applies:

The collected data consists only of sampling from the enterprises’ IT systems for payroll administration of their employees on an individual level. For the main part, this takes place as system-to-system reporting, where e.g. the payroll systems report data for their customers (the private enterprises) directly to Statistics Denmark.

Private enterprises that have proprietary payroll systems make their own reporting to Statistics Denmark. The Danish Employers’ Confederation and the Danish Employers’ Association for the Financial Sector collect data from their own members and report it to Statistics Denmark via a system-to-system solution.

For reporting from the public sector, the following applies:

Statistics Denmark receives the main part of the data material as data extracted from the major public payroll transfer systems via system-to-system solutions. For government employees, Statistics Denmark receives data mainly from the Agency for Public Finance and Management and Silkeborg Data. For local and regional authority employees, data is provided mainly by their payroll data office, KRL. In addition, data is reported from some few private payroll processing services, also via system-to-system solutions.

Data validation

Before the index is calculated, the data basis is subjected to a validation process for the purpose of uncovering and eliminating any erroneous reporting as well as outliers.

Initially, data is cleansed of logical errors and inconsistencies in the reporting. This is done by first putting data through an automatic control, which e.g. ensures that it is possible to calculate hourly earnings correctly.

To ensure that an individual employment relationship does not weigh more than what corresponds to a full-time position, there is a ceiling on how many hours the individual employment relationship is allowed to weigh. The ceiling is equivalent to a full-time position. For fixed salary employees, the number of hours is truncated at 160.3 hours per month, and for employees paid by the hour at 139.1 hours per month.

For the private sector, the initial validation takes place at an aggregate level (enterprise level defined by CVR no.) as well as at an individual level (the individual employment relationship), whereas the initial validation for the other sectors only takes place on an individual level. In the private sector, data is first validated at an aggregate level for so-called key enterprises.

Key enterprises where the average hourly earnings increase or decrease by more than 50 percent compared to previous quarter are excluded. The same applies to changes in the occupational compositions. Key enterprises with a shift in occupational compositions by more than 50 percent compared to previous quarter are excluded. In this way, an adjustment is made for key enterprises with high fluctuations in their reporting, which may potentially affect the index at publication level.

Subsequently, the hourly earnings are validated for the individual employment relationship in all sectors. The validation takes place by grouping the employment relationships by sector, industry (36-grouping), occupation (main groups in DISCO-08) and type of employment.

Outliers in relation to the individual hourly earnings are identified within the grouping using a statistical diagnostic procedure that uses interquartile ranges to identify outliers (the Tukey method). The observations characterised as outliers are eliminated. The purpose of this validation process is to ensure that the published indices are not distorted by a few extreme observations (outliers).

Finally, data is subjected to trouble-shooting based on an upper and a lower threshold value for the hourly earnings. This is done because there may be hourly earnings that are not considered to be outliers (based on the Tukey method), but which are estimated to be unrealistically high/low. Thus, individual observations with hourly earnings of more than DKK 5,000 or less than DKK 50 are removed.

Data compilation

Employment relationships, for which hourly earnings cannot be assessed, are not included in the data base of the index – this also applies to employment relationships with special forms of pay. Thus, the index does not reflect:

• Employees who do not have a regular pay and where time factors are not included in the calculation of earnings (e.g. taxi drivers, waiters paid on a commission basis or newspaper carriers paid according to altering routes and number of papers distributed)
• Employees where other time factors than hours performed are included in the calculation of earnings (e.g. employees paid by the day, lorry drivers involved in the transport of cargo destined for export markets)
• Employees who receive supplementary pay from other authorities or who are not paid by the same rules as other employees of the enterprise due to employment rehabilitation or similar (e.g. trainees and flexiworkers)
• Employees working from home without fixed hours of work, including employees in family care programmes
• Board members and others who are not employees, including resigned employees for whom back pay is managed via the payroll system (e.g. payment of compensation in accordance with non-compete or customer clauses, pay etc. for employees released from duty)
• Employees taxed according to special rules (e.g. employees stationed abroad, seamen in foreign trade and plane cabin crew, or employees with DIS collective bargaining agreements
• Employees under various employment programmes for young people and unemployed persons
• Persons paid in the form of fees or charges
• Sheltered jobs in connection with employment rehabilitation
• Special groups such as conscripts, members of local councils, election officials and the like

Employees who are employed in enterprises in the industry Agriculture, forestry and fishing are not included in the index calculation. For the private sector, employment relationships from enterprises with less than 10 employees are not included.

The standardised index of average earnings is compiled in a hierarchical system where the collected (validated) payroll data is first divided into homogeneous groups, which is the most detailed level for the grouping of employees. Then each employment relationship is allocated an individual weight that takes into account the proportion of the employment relationship to a full-time position.

Further, a sample weight is allocated to employees in the private sector. The sample weight ensures that the sample is raised to the target population by taking into account the design of the sample, voluntary reporting as well as non-response.

Next, base indices are calculated for each homogeneous group as the relationship between the average hourly earnings in the current and previous quarter, where the average hourly earnings are calculated as the weighted arithmetic average of the hourly earnings for all employees in the individual homogeneous groups.

Subsequently, the detailed base indices are weighted together to sub- and total indices using the payroll weights for each homogeneous group – a weight that is kept for four quarters. The payroll weights are based on the underlying data for the structure of earnings survey and ensures that the published sub- and total indices reflect the population. At the same time, this weight ensures that the measured development in earnings is not influenced by changes in the number of employees in the homogeneous groups.

The payroll weights are replaced once a year in connection with the calculation of the third quarter, since it is only at this point that the weight basis from last year’s structure of earnings survey becomes available. Changes in the compositions of the population, i.e. a changed distribution of the total sum of earnings will be reflected in a change in the payroll weights. Thus, a change in the occupational composition within a particular industry will therefore be reflected in the index when the base indices are weighted together with changed payroll weights.

When calculating the complete index series, index 100 is calculated first as the average of the first four quarters. Then the total index series is calculated by linking all sub-indices for the weight year on the end quarter of the previous weight year. In the standardised index of average earnings, the linking is made only on the aggregate index series (sub-indices and total indices).

Adjustment

A separate cost effect is used to adjust for the effect of free-choice systems, which corresponds to the free-choice products’ contribution to the development in earnings. This effect is compiled by Confederation of Danish Employers (DA) at industry level, and is multiplied on the sub-indices in connection with publication of the second quarter.