Accuracy and reliability

Overall accuracy

The samples for each industry are selected top-down to achieve as high turnover coverage as possible. The largest companies represent themselves and smaller companies represent a group. In practice this means that price developments collected from larger companies carry more weight than price developments collected from smaller companies. It is assumed that the price developments in the samples expresses the price developments in the whole population.

The weights are based on the National Accounts balances for 2019, which is based on multiple in-house primary sources (for example Purchases and Sales by Enterprises, Production and Turnover in Manufacturing Industries, Retail Trade and International Trade). The current weights were implemented along with the publication of the index for the first quarter of 2023. It should be noted that there is a four year delay in the weights used and therefore aggregate measures may not be fully representative of the current state of the Danish economy if large structural shifts have been experienced.

Sampling error

The samples for each industry are selected top-down to achieve as high turnover coverage as possible. The samples are thus not based on the probability of sampling selection corresponding to the importance of each service. To match the turnover balances in the National Accounts, prices are strictly collected from companies within the specific six-digit industries. This means that prices are collected, with no regards to comparability across the given industry, as long as the company is allocated in that specific industry in the Statistical Business Register. This criteria is complied with as far as possible, meaning that the elementary indices reflect the price developments of the companies within the industries, rather than reflecting the price development of a specific type of service. There may in this respect arise sampling errors if a company is misallocated in the Statistical Business Register.

The sample is therefore not a random sample and it is not possible to estimate the overall size of the sampling error.

Non-sampling error

In the second quarter of 2020 Denmark experienced social restrictions due to Covid-19 shutdowns. In subsequent periods societal constraints were lifted and reinstated on a needs basis. Despite these times of shifting restrictions it has been possible to publish the Producer Price Index for Services as per the planned schedule with the exception of 51.1 Passenger Air Transport for the second quarter of 2020. The industry index has been imputed with the index change from the same quarter last year. Non-response from the remaining industries is mainly unchanged compared to the same periods last year. Therefore, it is assessed that the industry indices does not have an increased amount of uncertainty due to COVID-19.

Statistics Denmark applies quality adjustments on a case-by-case basis and uses the best method that the data and provider contact enables. As time passes, the services in the sample gets replaced. Because the new services often have different quality than the services that they replace, there is continuous quality adjustment of the index. When replacing services, new services are not included in the index before their prices are observed in two subsequent periods. A bias can arise in cases where price changes coincide with changes in quality. Methods for dealing with quality changes are described in Eurostat's methodology guide for developing Producer Price Index for Services.

A further general observation is that there may be cases where obsolete commodities stay too long in the sample and that new commodities are introduced too late. The companies are requested both continuously, but also systematically, approximately every two years, about reviewing the commodities that they report prices in relation to whether they are still representative of the company's general sales or imports. If this is not the case they are requested to replace obsolete commodities with new ones.

Errors may also arise if a company reports a price for a wrong item. This is usually due to misunderstandings, for example, in connection with staff changes in the company reporting. In addition, errors can occur in connection with the registration of completed forms at Statistics Denmark. Such potential errors are both assessed via automated and manual means and are not considered to be a source of significant errors.

The price index is calculated as a fixed commodities basket index of the Laspeyres-type. This means that, in the calculation of the index, an unchanged composition of goods through time is assumed. In the real world, companies substitute between products for various reasons (e.g. changed relative prices, preferences or technology). This means that the calculated price development in the price index may lose representativeness over time where undetected commodity changes are taking place. This is attempted to be minimized by sample updates every five years, as well as companies being requested both continuously (quarterly data validation) and systematically, approximately every two years, about reviewing the commodities that they report prices (the fixed commodities basket) in relation to whether they are still representative of the company's general sales or imports.

The quarterly non-response is less than 1 per cent. It is therefore not considered to be a major source of error. If the non-response should take place for essential services, imputation is used where the non-response price development is imputed with the development of the elementary aggregate they belong (class mean imputation). In other cases, prices are considered unchanged (carry forward imputation is utilized).

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

Overall the indices of the Producer Price Index of Services is assessed to be of high quality and representative for the price development for the given services sold by Danish producers. This assessment relies on the data used for the index, which consists of 1700 prices distributed on approximately 60 industry codes. Within each industry, the largest companies are selected based on the company turnover (top-down) to achieve as high turnover coverage as possible for each industry. Together with the weights encompassing the main part of all Danish trade as well as the continuously monitoring of the quality of the sample.

There are large differences between the industries which the Producer Price Index for Services covers. There is great variation in the number of companies from industry to industry. In some industries it is possible to cover a large amount of turnover with a small sample, whereas in others, it is difficult to cover a small amount of turnover even with a large sample. Hence it is not possible to determine a common quality benchmark across all industries, and the quality will vary more for more disaggregate indices.

A comprehensive quality assessment is therefore based on a combination of assessing turnover coverage, the number of companies and prices in the sample and the quality of the collected prices, including the pricing methods used. The quality of the statistic is being continually monitored and improvements are made where it is assessed that the quality can be levered. Conducting quality work therefore includes making replacements within- and increasing the sample with more respondents. Asking existing respondents to report more prices, or use better pricing methods to define and calculate prices.

Furthermore, the quality of this statistic can be assessed by to what extent the statistic is relevant, accurate and reliable, timely and punctual, comparable and accessible to the users. You can read how the index lives up to these goals in the sections with the corresponding headlines.

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 published and are not revised unless an error is observed..