Accuracy and reliability

Overall accuracy

Some parts of the national accounts can be measured more precisely than others, because better source data are available in those areas. For example, data for the manufacturing industry are generally quite accurate, whereas data for Danish-based companies that live from buying and reselling goods abroad are less precise. Finally, there are also areas where only very limited source data exist, such as the imputed rent of owner-occupied housing and undeclared work. In these cases, the figures in the national accounts rely almost entirely on calculations and estimates, and therefore the precision must be expected to be lower.

The first estimates for a given period are produced before all data for that period are available. The starting point for compilation will be the structure and developments from the most recently finalized national accounts. Where reliable new information exists, it is used. Where such information is not yet available, other sources are applied that provide an impression of developments – for example, indicators from business cycle statistics. These preliminary estimates are therefore less precise than later releases.

Uncertainty is particularly relevant in cases where actual developments turn out to differ from the developments shown by the indicators chosen for extrapolation. As new data sources become available, they are incorporated into the new versions, improving precision. Another factor affecting the accuracy and reliability of the national accounts is that errors in many of the underlying source statistics may be corrected after the final version of the national accounts has already been compiled. At that point, such corrections cannot be incorporated until a comprehensive benchmark revision is undertaken – a process that allows long time series of final years and quarters to be revised. This reduces both the reliability and precision of the accounts in the meantime. In the long run, however, the accuracy and reliability of the national accounts are restored, as corrections to the source statistics are incorporated during the benchmark revisions.

Sampling error

Not relevant for these statistics.

Non-sampling error

The national accounts are a very extensive statistic with a lengthy production process involving many parties and both manual and automated procedures. Throughout the compilation process for the different versions, continuous data consistency checks and checks of various totals and balances are performed, meaning that many errors are found and corrected well before the figures are published. More rarely, errors are discovered that turn out to be more extensive or span several years. In such cases, developments in the series are given more weight than the level of the series, and these errors are only corrected during benchmark revisions, which are carried out roughly every five years. Significant individual errors that, for various reasons, are not corrected or that give rise to increased uncertainty are mentioned in the accompanying News from Statistics Denmark (in Danish).

Many of the sources used in the national accounts are not fully comprehensive. Therefore, in many areas, adjustments are made to try to achieve full coverage of economic transactions. For example, companies with few employees are not included in the accounting statistics, and there is only limited information about their turnover, production consumption, and number of employees. To cover these companies, assumptions must be made that their input structure or production per employee does not differ significantly from comparable companies covered by the statistics.

As a consequence of large differences in the statistical coverage – and thus the data availability – of different economic activities, different areas are measured with varying levels of uncertainty. Particularly in the informal economy, where there is by nature no accounting coverage and a risk of underreporting in surveys, the uncertainty and risk of coverage errors are greater. As with all other parts of the national accounts, this area is compiled according to internationally agreed guidelines and methods, which try to account for underreporting by using adjustment factors. However, since the informal economy makes up a relatively small share of the total economy, the risk of coverage errors is not decisive for the overall precision of the national accounts.

Globalization means that Danish companies increasingly organize themselves internationally. This creates major challenges for ensuring consistent treatment of globalized enterprises across statistics. This is particularly problematic for the quarterly national accounts, as it requires a very resource-intensive and manual approach to data collection and processing in the primary statistics. It is therefore likely that sources included in the earliest versions of the accounts are inconsistent. The aggregated and time-pressured calculations of the first editions sometimes mean that these inconsistencies are either not discovered or cannot be corrected in time in both the primary statistics (e.g., balance of payments) and the national accounts. In the final version of the national accounts, problems with globalized companies are reduced, though still present. Ongoing work at Statistics Denmark aims to ensure faster, more efficient, and consistent handling of reports from globalized companies across statistical areas. Since globalized companies are often very large, even a single correction can result in very large revisions that directly affect the main figures of the national accounts, including GDP.

There is no dedicated statistic on investment activity in Denmark, and currently the most reliable source is the accounting statistics. These are only available after about 1.5 years, so preliminary estimates of investment activity must be based on, among other things, the number of employees and turnover in the construction sector. One source of uncertainty is that multi-year investments must, according to the rules of the national accounts, be recorded as they are made, whereas in company accounts they are often expensed at the time of completion. Another source of uncertainty for investment activity is the investment of globalized companies abroad, for which coverage is poor. Statistics Denmark is currently working to improve statistical coverage of investment activity.

Constant-price calculations are another source of revisions between different versions of the national accounts, and thus of uncertainty. The reason why larger revisions can occur in constant prices than in current prices, even though the same price indices are available at two calculation points, is composition effects. The quarterly and preliminary accounts are compiled in a more aggregated form than the final accounts, and therefore a composite price index is often used, typically based on the most recent final year’s composition of goods and services in, for example, a sector’s total production. When the final accounts are calculated, the product dimension is added, allowing a more detailed and accurate deflation. If the product composition differs from previous years, this can lead to revisions in constant prices without any revisions having been made to current prices or price indices. Thus, revisions in constant prices may arise that cannot be directly traced back to revisions in the source statistics.

The measurement of real growth in public production is associated with several types of uncertainty. In the first releases of the quarterly national accounts, real growth is measured using the input method, meaning that the various cost components are deflated with corresponding price indices, such as intermediate consumption and labour costs. In later releases, real growth in public production is mainly measured using the output method via so-called quantity indicators. Quantity indicators measure how much the public sector produces, such as teaching hours in primary schools or hip operations in public hospitals. Since there are no data for quantity indicators in the earliest versions of the accounts, the shift from the input to the output method may result in variations in measured real growth in the public sector. Furthermore, recalculations of a quarter or year’s quantity indicators can also lead to revisions, as the data basis varies from version to version. In addition, the data basis and methods of the output method are still under development and quality assurance. Several documentation notes on the measurement of real growth in public consumption are available under the documentation section of Expenditure on Public Consumption.

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 ESA 2010 regulation requires that Eurostat assess the quality of data reported under the ESA transmission program. This is done on the basis of the countries' quality reports which are not published independently by Eurostat. The report is prepared annually. Read the quality assessment of Denmark's national accounts in Quality Report, Denmark 2020 - National Accounts.

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

Regular revisions of national accounts for previously published years and quarters are performed according to a fixed rhythm. The quarterly national accounts’ flash release is published 50 days after the reference quarter and re-estimated 90 days after the reference quarter.

With 5 year intervals, main revisions are carried out, where long time series of final national financial years are updated. This improves the accuracy and reliability of the national accounts because all changes and corrections in the source statistics, as well as calculation errors, are taken into account. In addition, manual revisions of all national accounts series are made when new international manuals are adopted. The most recent manual revision of the Danish national accounts was carried out in 2014, while the recent benchmark revision was carried out in 2024.

In connection with the first calculation of the quarterly national accounts, a note is published, which shows the average revision and bias over a 12 quarters period. Read more, only Danish, here Revisioner af det kvartalvise nationalregnskab.