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Accuracy and reliability

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National Accounts, Economic Statistics.
Christina Just Brandstrup
+45 39 17 36 33

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National Accounts

The ability of the National Accounts to describe the economic reality accurately partly depends on the uncertainty associated with the sources and partly on the model assumptions underlying the calculation of the national accounts. Some parts can be calculated more accurately than others, as there is better access to source data. The first versions for a period's national accounts will be more uncertain than the final version, which comes after three years, as new sources are continuously revised.

Overall accuracy

Some parts of the national accounts can be calculated more accurately than others, because there is better source data in these areas. For example, for the industrial area there is generally quite accurate data, while for Danish-based companies that live from buying and reselling goods abroad, there is less accurate data. Finally, there are also areas where very limited source data exists, including, for example, consumption of owner-occupied housing and undeclared work. In these areas, the figures for the national accounts are almost exclusively based on calculations and estimates, and therefore the accuracy here is expected to be lower.

The first versions of a given period are made before all data for the period is available. The starting point for these versions will be the most recent final annual national accounts. This applies to areas where secure new information is available. Other areas that give an impression of developments - for example, indicators from cyclical statistics - are used for areas where no secure information is available. These preliminary versions will thus be less accurate than later versions. Where the uncertainty may be particularly pronounced is in cases where the actual development turns out to be different from the development of the indicators chosen to project the development. When new data sources are ready, they are incorporated into the new versions and the accuracy improves.

Another condition that affects the precision and reliability of the national accounts is that errors in the many different source statistics of the national accounts can be corrected after the final version of the national accounts has been prepared. At this point, these corrections cannot be included in the national accounts until a main revision is carried out periodically, where long time series of final years can be corrected. This helps to reduce both the reliability and precision of the national accounts. In the long run, however, the precision and reliability of the national accounts are re-established because corrections in the source statistics are included in the main revisions.

Sampling error

Not relevant for these statistics.

Non-sampling error

The National Accounts is a very comprehensive statistic with an elongated production process with many parties involved, undertaking both manual and automatic procedures. During the entire calculation process in the various versions, data consistency checks and checks of various sums and balances are performed on an ongoing basis, which means that many errors are found and corrected well before the figures are published. More rarely, errors are found that turn out to be more extensive or have been found for a number of years. In these cases, the developments in the series are weighted higher than the level in the series and therefore such errors are only corrected in the main revisions, which are made approx. every 5 years. Significant single-fault errors which for various reasons have not been corrected or given rise to increased uncertainty, will be addressed in the related News from Statistics Denmark.

Many of the sources used in the national accounts are not fully comprehensive. Therefore, in many areas enumerations are made to try to achieve full coverage of the economic transactions. For example, companies with few employees are not included in the accounting statistics and there is only limited information on their turnover, input and number of employees. In trying to cover these companies, one must therefore assume that the input structure or production per employee is not significantly different from comparable companies covered by the statistics.

As a result of large differences in statistical coverage, and thus the availability of data, of the various activities of the economy, there is a varying uncertainty in different areas. Particularly in the informal economy, where there is no accounting coverage, as well as the risk of under-reporting in questionnaires, uncertainty will be greater and the risk of coverage errors greater. As with all other parts of the national accounts, this area is calculated according to internationally agreed guidelines and methods of calculation, which try to take account of under-reporting by using enumeration factors. However, the relatively small share of the informal economy of the total economy means that the risk of coverage errors is not decisive for the accuracy of the overall national accounts.

Globalization entails, among other things, that Danish companies are increasingly choosing to organize themselves internationally. Consistent treatment of globalized companies across different statistics presents major challenges. This is particularly problematic for the quarterly and preliminary national accounts, as it requires a very resource-intensive and manual approach to data collection and processing in primary statistics. Therefore, sources that are collected and incorporated into the earliest editions of the national accounts are likely to be inconsistent. The aggregated and very time-consuming calculations of the first editions of the national accounts sometimes mean that these inconsistencies are either not detected or cannot be addressed in both the primary statistics (eg the balance of payments) and the national accounts. In the final version of the national accounts, the problems with the statistical coverage of globalized companies are reduced, but still present. Statistics Denmark is still working to ensure faster, more efficient and consistent processing of globalized companies' reports across statistical areas. As the globalized companies are often very large, some corrections can lead to very large revisions that can directly affect the national accounts' main figures, including GDP.

There are no actual statistics on investment activity in Denmark and currently the most reliable source is the accounting statistics. It is only available after approx. 1.5 years and therefore preliminary estimates of investment activity must be based on, inter alia, the number of employees and turnover in the construction industry. One source of uncertainty is that multi-annual investments must be accounted for in national accounts along the way, while in accounts they are often expensed when the investment is completed. A further source of investment uncertainty is the investment activity of globalized companies in other countries for which there is poor coverage. Work is currently underway in Statistics Denmark to improve statistical coverage of investment activity.

Calculations in constant prices are another source of revisions between the different versions of the national accounts and therefore a source of uncertainty. The reason that larger revisions may occur in fixed prices than in current prices, although the same price indices are available at two calculation times, are composition effect. The first preliminary versions of the national accounts are calculated in a more aggregated level than the final one and therefore a weighted price index is often used, which is typically based on the composition of goods and services in the final final year in, for example, an industry's total production. When calculating the final national accounts, the product dimension is added, which allows for a more detailed and accurate deflation. Thus, if the product mix is different from previous years, it may lead to revisions in fixed prices without necessarily having been revisions in current prices or in the price indices. Consequently, revisions can occur at fixed prices that cannot be traced back to revisions in the source statistics.

The estimate of real growth in output by general government is subject to several types of uncertainty. In the first versions of quarterly national accounts, real growth is calculated according to the input method, which means that the various cost components are deflated with the associated price index, for example input and labor costs. In later versions of both quarterly and annual national accounts, real growth in output by general government is calculated mainly according to the output method via so-called volume indicators. Volume indicators are a way of quantitatively measuring how much is produced in the public sector, for example classes taught in primary schools and hip surgeries in public hospitals. As there is no data for calculating volume indicators in the earliest versions of the national accounts, the transition from the input to the output method may give some variation in the measured real growth in the public sector. In addition, recalculating a quarter or year volume indicator may also give rise to revisions as the data base varies from version to version. In addition, the data methodology and methods of the output method continue to be under development and quality assurance. There are a number of notes regarding measurement of real growth in public consumption, under documentation on the Danish page for Real expenditures by general government.

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:

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 national accounts' publication calendar can be viewed under documentation on the subject page for Annual national accounts.

With approx. 5-10 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.

In connection with the publication of Annual National Accounts in June, a review over revisions and bias i released in the publication series Statistiske Efterretninger - only available in Danish.

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.