Statistics Denmark

Prices and Consumption

Sejroegade 11, 2100 København Ø, Denmark

The harmonised index of consumer prices (HICP) is a consumer price index (CPI) that is calculated according to a harmonised approach. It measures the change over time of the prices of consumer goods and services acquired by households (inflation).

Due to the common methodology, the HICPs of the countries and European aggregates can be directly compared.

European classification of individual consumption according to purpose (ECOICOP)

The HICP covers the final monetary consumption expenditure of the household sector.

The main statistical variables are price indices.

The basic unit of statistical observation are prices for consumer products.

3.6.1. Statistical target population

The target statistical universe is the 'household final monetary consumption expenditure' (HFMCE) on the economic territory of the country by both resident and non-resident households. The household sector to which the definition refers, includes all individuals or groups of individuals irrespective of, in particular, the type of area in which they live, their position in the income distribution and their nationality or residence status. These definitions follow the national accounts concepts in the European System of Accounts.

3.6.2. Coverage error population

No deviations.

3.7.1. Geographical coverage

The HICP refers to the economic territory of a country as referred to in paragraph 2.05 of Annex A to ESA 2010, with the exception that the extraterritorial enclaves situated within the boundaries of a Member State or a country are included and the territorial enclaves situated in the rest of the world are excluded.

3.7.2. Coverage error regions

The target is to cover all parts of Denmark and our samples are designed accordingly.

3.8.1. Start of time series

The HICP series started in January 1997.

3.8.2. Start of time series - national specifics

The Danish HICP is available from 1997 to the present.

See the HICP database

2015=100

The following units are used:

• Index point
• Percentage change on the same period of the previous year (rates);
• Percentage change on the previous period (rates);
• Percentage share of the total (weights).

HICP is a monthly statistics.

Harmonised Indices of Consumer Prices (HICPs) are harmonised inflation figures required under the Treaty on the Functioning of the European Union. Regulation (EU) 2016/792 of the European Parliament and the Council of 11 May 2016 (OJ L 135) sets the legal basis for establishing a harmonised methodology for the compilation of the HICP and the HICP-CT.

This regulation is implemented by Commission Regulation (EU) 2020/1148 of 31 July 2020.

Further documentation, can be found in Eurostat’s website - HICP dedicated section, namely recommendations on specific topics, under the methodology page, and guidelines, under the quality page.

None.

Regulation (EC) No 223/2009 of the European Parliament and of the Council, of 11 March 2009, on the transmission of data subject to statistical confidentiality to the Statistical Office of the European Communities.

'Persondataloven' gives restrictions regarding publication and sharing of data that can be attributed to individual persons. 'Forvaltningsloven' rules that data collected for statistical purposes cannot be shared with other public authorities for other purposes.

This means that the individual price observations collected for the HICP are being treated as confidential whereas weights and item descriptions are not being treated as confidential.

Statistics Denmark will never publish data that can be attributed to an individual person or a single company. Only aggregated data will be published.

In line with the Community legal framework and the European Statistics Code of Practice Eurostat disseminates European statistics on Eurostat's website (see point 10 - 'Accessibility and clarity') respecting professional independence and in an objective, professional and transparent manner in which all users are treated equitably. The detailed arrangements are governed by the Protocol on impartial access to Eurostat data for users.

The HICP is released according to Eurostat’s Release calendar.

The calendar is publically available and published at the end of the year for the full following year.

The Danish HICP is always released simultaneously to the public at 8:00 a.m. on the 10th of the month or the first working day thereafter following the month in which the data were collected.

The Danish HICP is released to all users at the same time. No one outside Statistics Denmark gets access to the data before publication.

The Danish HICP is always released simultaneously to the public at 8:00 a.m. on the 10th of the month or the first working day thereafter following the month in which the data were collected.

Monthly

The Danish HICP and CPI is issued in the written news release 'Nyt fra Danmarks Statistik' at www.dst.dk every month (in Danish only).

The data are also released in the statistical databank www.statistikbanken.dk which is available in Danish and English. Furthermore the overall indices can be found at the dedicated web page: www.dst.dk/priser

The HICP is published with one decimal (both index levels and rates of change).

The data are released simultaneously to all interested parties at 8:00 a.m. on the 10th of the month or the first working day thereafter following the month in which the data were collected, by issuing the news release 'Nyt fra Danmarks Statistik' at www.dst.dk. 

No publications apart from the news release is being produced.

Overall indices and sub-groups down to the 5-digit ECOICOP level are published at www.statistikbanken.dk 

The Danish HICP can be accessed directly at www.statbank.dk/pris117. The Danish HICP-CT can be accessed directly at www.statbank.dk/pris118.

Researchers wishing access to Danish HICP micro data should contact Statistics Denmark to enquire whether it will be possible to get access to the data given the specific circumstances. Micro data will always be made anonymous so that it cannot be attributed to a single individual company.

The Internet web site (https://www.dst.dk/da/Statistik/emner/priser-og-forbrug/forbrugerpriser) disseminates time series for the overall CPI, the net price index and the Danish Harmonised Index of Consumer Prices (HICP). Furthermore different documentation and the weights used in the calculations are also presented here.

The HICP Methodological Manual provides the reference methodology for the production of HICP. (https://ec.europa.eu/eurostat/web/products-manuals-and-guidelines/-/KS-GQ-17-015)

10.6.1. Documentation on methodology - national specifics

The methodology is described in a 'Statistical documentation' which can be found at https://www.dst.dk/da/Statistik/emner/priser-og-forbrug/forbrugerpriser/forbrugerprisindeks and documentation is available on the homepage as well.

See Eurostat's Compliance Monitoring Report of 2021.

Quality reports have so far not been issued. 

The European Statistics Code of Practice is being followed (https://ec.europa.eu/eurostat/web/quality/european-statistics-code-of-practice).

Statistics Denmark has provided information for the evaluation of compliance whenever it was requested by Eurostat. The latest compliance monitoring visit was carried out in 2021. See Eurostat's Compliance Monitoring Report of 2021.

The compilation of the Danish HICP is carried out by a limited number of people working closely together and all being situated at the central office. This group is responsible for all tasks connected to the production of the HICP. Hence rigid quality assurance measures are not deemed necessary.

11.1.1. Quality management - Compliance Monitoring

Compliance Monitoring

11.1.2. Quality assurance - national specifics

The following control procedures are in place in Denmark regarding the production of the HICP:

• Short descriptions of work routines in connection with index calculations and publications exist and are being used in the production.
• Check lists exist for the various tasks in connection with the HICP production, ensuring that tasks are completed in the right order.

A user handbook for the Oracle computer system used for data entry and calculations also exists.

• At least two different people check the quality adjustments carried out.
• Before publication at least two different staff members check the calculated indices.
• Once a month a so-called 'quality meeting' is held where the sample is reviewed and revisions proposed and discussed as well as other subjects in connection with the quality of the HICP. Changes to HICP legislation are also tackled at these meetings.
• A methodological manual describing both the CPI and HICP in detail exists and is publically available on the CPI/HICP website: dst.dk

11.2.1. Compliance monitoring - last report and main results

The last available compliance or follow-up report can be found in the dedicated HICP section ‘Compliance Monitoring’ of Eurostat’s website, under ‘Methodology’.

11.2.2. Quality assessment - national specifics

Formal national quality assessments of the Danish HICP has not been made.

In addition to being a general measure of inflation, the HICP is also used in the areas of:

• wages, social benefit and contract indexation;
• economic forecasting and analysis;
• measuring specific price trends;
• accounting purposes and deflating other series;
• inflation targeting by central banks;
• cross-country economic comparisons.

The euro area (evolving composition) index is used by the European Central Bank (ECB) as the main indicator for monetary policy management. The ECB and the European Commission's Directorate-General for Economic and Financial Affairs (DG ECFIN) use the HICP for assessing price stability and price convergence required for entry into European Monetary Union.

Other users include: National Central Banks, financial institutions, economic analysts, the media and the public at large.

12.1.1. User Needs - national specifics

The users of the HICP are primarily the European Central Bank, the European Commission, the Ministry of Economic and Business Affairs, and the Danish National Central Bank. As HICP has been calculated on a comparable basis in all EU countries, the figures are primarily used where there is a need for comparing development in consumer prices across countries.

User satisfaction surveys are not performed but the general view is that quality of the Danish HICP is satisfactory. Once a year a meeting is held with main Danish users of price statistics and this is the usual response to the HICP.

The ECOICOP indices at 5-digit level for the HICP and HICP-CT being produced can be seen in the weights table available at https://www.dst.dk/da/Statistik/emner/priser-og-forbrug/forbrugerpriser/forbrugerprisindeks

Some 5-digit level indices with a weight below one of a thousand are not being produced.

Overall accuracy
The overall reliability of the HICP is considered to be high.

Sources of inaccuracy

The sample
The HICP is calculated on the basis of a sample of approx. 24 500 prices collected from some 1 500 shops, companies and institutions throughout Denmark. Most prices are by far collected monthly. For goods and services, where the prices typically change less frequently, prices are collected more rarely, for instance quarterly or biannually. For clothing and fresh food etc. prices are collected by price collectors who visit the individual shops. For the biggest supermarket chains for COICOP groups 1 and 2, they are also covered by scanner data. For the remaining groups of goods and services, prices are mainly obtained from digital questionnaires, list prices from supermarkets outside COICOP group 1 and 2 are also used. Finally, Statistics Denmark obtains information on prices on a number of selected goods and services by telephone or via the Internet. The weights are created on the basis of the information about the composition of consumption expenditure according to the national accounts and the Household Budget Survey.

No calculation has been made of the uncertainty connected with sampling in the HICP. The statistical uncertainty inherent in the weights affects the uncertainty in the HICP, but the effect is very limited. The non-response in the sample is estimated to be less than 1 percent.

In addition to the 'general' uncertainty connected with sampling, there are a number of sources of potential bias in the HICP, which can be grouped as follows:

Substitution between goods
Bias due to substitution between goods is a result of the fact that for different reasons (changes in income and in relative prices or preferences), consumers substitute between different goods, although an unchanged composition of consumption is assumed in the calculation of the price index. The HICP is calculated as the weighted arithmetic average of the most detailed price indices (elementary aggregate indices) with their respective budget shares used as weights. At this level of the index calculation no allowances are therefore made for the consumers' substitution between different groups of goods and services (elementary aggregates). However, the elementary aggregate indices are calculated as geometrical indices. Thereby it is assumed that the consumers hold unchanged budget shares. This means that if the price of a commodity rises by x percent, the consumers are assumed to reduce their consumption of the commodity by x percent. For these groups a certain substitution has thus been recognised in the index.

Substitution between shops
This type of bias arises when the consumers for the same commodity change from shops with high prices to shops with lower prices. The HICP is calculated monthly on the basis of price information from the same shops. If, e.g. greater shares of the consumers' expenditure from July until August is accounted for by discount shops with lower prices, this will not in itself have an impact on the index. Only when a shop has been included for at least two months in succession are the prices from there included in the index calculation.

Changes in quality
In calculating a price index it is assumed that the baskets of goods that are compared are identical, also with respect to the quality of the goods. Consequently, in the case of changes in quality the prices should, in principle, be adjusted for this. As the value of the actual changes in quality is not known, it is naturally difficult to calculate estimates for bias, due to lack of quality adjustment.

New commodities
The sample for the HICP is continuously updated, but for practical reasons often with a certain time lag. This means that new products are frequently not included in the compilation of the index x when they are first introduced on the market, and not until prices have been available for two months in succession. Furthermore, at the beginning of a product's lifetime it is often impossible to obtain any information about sales. Finally, a great deal of uncertainty is associated with the task of defining whether it is actually a new product or just improved versions/varieties of already existing products.

Calculation formula
The first step in the index calculation consists of calculating the elementary aggregate index from the prices collected (and any weights for these prices). To the extent that the index calculated on this basis deviates from the 'true' price rise, it is a formula bias. Frequent updates of the weights and the sample can reduce the potential bias as a result of the consumers' substitution between goods and shops and the appearance of new goods.

Statistics Denmark does not produce numerical estimates of HICP sampling errors because they are difficult to quantify due to the complexity of price index structures and due to use of non-probability sampling. For products, probability sampling is not possible due to incomplete knowledge of the full product universe.

Non-sampling errors are in general not quantified.

The full set of HICPs is published each month according to Eurostat’s Release calendar, usually between 15 and 18 days after the end of the reference month.

Each year, the January release is published at the end of February to allow for the annual update of the weights, both of individual product groups and the relative country weights of Members States in the country group aggregates.

The euro area flash estimate is published on the last working day of the reference month or shortly after that.

Since the March 1997, launch of the HICP release, the HICP for the country groups aggregates has always been published on the dates announced in Eurostat’s Release calendar.

HICPs across Member States aim to be comparable. Any differences at all levels of detail should only reflect differences in price changes or expenditure patterns.

To this end, concepts and methods have been harmonised by means of legislation. HICPs that deviate from these concepts and methods are deemed comparable if they result in an index that is estimated to differ systematically by less than or equal to 0.1 percentage points on average over one year against the previous year (Article 4 of Council and Parliament Regulation (EU) 2016/792).

HICP data are fully comparable over time. There have been several improvements in methodology since the HICP was introduced, with the aim of improving reliability and comparability of the HICP. These changes may have introduced breaks in time series. However back calculations under the newer standards were performed when appropriate basic data was available.

Differences between the HICP and national CPI

The national CPI and the HICP are based on exactly the same price observations for the same items collected from the same outlets. Gross prices are used in both cases. There is also no difference between the methods of calculating the national CPI and the HICP. The only difference is the coverage.

All expenditure consumption included in the HICP is also included in the national CPI, but owner-occupied dwellings and insurance in connection with owner-occupied dwellings are not included in the HICP; they are included in the national CPI instead.

The HICPs are internally coherent. Higher level aggregations are derived from detailed indices according to well-defined procedures.

Not available

The HICP series, including back data, is revisable under the terms set in Articles 17-20 of Commission Implementing Regulation (EU) 2020/1148.

17.1.1. Data revision - policy - national specifics

The revision policy is not to revise the Danish HICP once it has been published except in case of big errors in the data or calculations. In general the Danish HICP is not revised.

Data are considered final when published and are not revised except in cases of big errors. The Danish HICP has not been revised during the last 10 years.

18.1.1. Weights

The sources of the weights are the National Accounts at the highest level (figures for approximately 70 consumption groups are available) and the Household Budgetary Survey at the lowest level. There are approximately 450 national weights at the elementary aggregate level. In some cases other sources for the subdivision are used as well e.g. for public transportation.

There are no regional weights.

Below the ECOICOP level outlet weights and in some cases detailed product weights are being used. The outlet weights are based on figures on total turnover from the Danish Business Register. For food outlet weights are used which differ between product groups and these weights are based on market analysis reports. Detailed product weights are to a large degree based on information from the HBS but other sources are also used (e.g. no of issued newspapers, no of pupils in private schools).

Explicit weights for outlets and in detailed products are used below the level of elementary aggregate indices. Hence weighted geometric averages for the elementary aggregate indices are being used. Between 1 and some 20 price observations are collected for every specific product and specific outlet. Explicit weights are applied above this level. See the figure below. Around 1/3 of the product prices calculated below uses explicit outlet weights and around 20 percent of the elementary indices are calculated using explicit product weights. Most of the elementary indices consist of only one product group and in these cases no detailed product weights is naturally used. Where weights otherwise are not available equal weighting is used.

The weights at elementary aggregate level are updated every year, this has been the case since the implementation of former Commission Regulation (EC) No 1114/2010 on HICP weights in 2012. Before that the weights were only updated every third year. The implementation did not result in any changes to compilation and data sources of the weights.

The weights below the elementary level are updated approximately every second year.

The current weights are based on National accounts data for household consumption at the 4-digit ECOICOP level. The weights are further subdivided to the 5 and 6-digit ECOICOP levels using the relative consumption pattern in the HBS. The weights were updated from 2019 to year 2020 using the development from year 2019 to year 2020 in the quarterly national accounts at the level of the 4-digit COICOP. The 4^th quarter of year 2020 in the quarterly national accounts were estimated using the development from the first three quarters of year 2019 to the first three quarters of year 2020 and multiplying this with the value of the 4^th quarter of year 2019. 

The weights are price-updated from the average of 2020 to December 2020 using the development in elementary aggregates at the 6-digit ECOICOP level.

18.1.1.1. Compilation at elementary aggregate level

See 18.1.1

18.1.1.2. Compilation of sub-index weights

See 18.1.1

18.1.1.3. Compilation of sub-index weights

See 18.1.1

18.1.1.4. Weights – plausibility checking

The plausibility of zero weights are checked annually with colleagues from National accounts and the HBS.

18.1.1.5. Price updating

The weights are price-updated from the average of year t-1 to December t-1 using the development in elementary aggregates at the 6-digit COICOP level.

The weights are not price updated from the usual weight reference period (year t-2) to the previous year (year t-1).

18.1.1.6. Compilation of total household final monetary consumption expenditure

The country weight calculation are based on National accounts data from year t-2 updated to year t-1 using developments in the quarterly national accounts from year t-2 to year t-1. However the figures for Income in kind and Pension are from year t-2 (assumed to be the same in year t-1).

The 4th quarter of year t-1 in the quarterly national accounts were estimated using the development from the first three quarters of year t-2 to the first three quarters of year t-1 and multiplying this with the value of the 4th quarter of year t-2.

18.1.2. Prices

The HICP is compiled on the basis of a sample of approximately 25,000 price observations collected from approximately 1,600 shops, companies, and institutions all over the country. The prices are collected by questionnaires or by means of price collectors who visit the individual shops. Prices on food and beverages and household items are to a large extent covered by the use of scanner data from supermarket chains. Prices are also obtained via the Internet. Most prices are by far collected monthly. For goods and services, where the prices typically change less frequently, prices are collected more rarely, for instance quarterly or biannually

18.1.2.1. Data Source - overview  

The annex shows the sources of price data at the level of elementary aggregates.

18.1.2.2. Scanner data - general information

Prices on food and beverages and household items are to a large extent covered by the use of scanner data from the four biggest supermarket chains in Denmark. These four chains have a total market share for food and beverages of approximately 80 per cent.

18.1.2.3. Web scraping - general information

Web scraping is currently not used in the Danish HICP.

18.1.3. Sampling

18.1.3.1. Sampling design: locations for survey

The sample of prices is not geographically stratified but the prices are collected from all parts of Denmark to make sure that the sample is representative. Many prices are collected by means of questionnaires which make it possible to collect prices from everywhere – including the countryside. Prices for some fresh foods, footwear and clothing are mainly collected from outlets located in towns, since these prices are collected by price collectors. Scanner data includes all the individual supermarket outlets.

18.1.3.2. Sampling design: outlets

Prices are collected from approximately 1650 retail outlets every month. The outlet sample can in principle be updated every month. If an outlet leaves the sample it is immediately replaced. Likewise new outlets can be included in the sample any given month.

Whenever an outlet closes a new outlet from the same geographical area is drawn from the Danish Business Register. Furthermore the outlet sample is actively adjusted on an ongoing basis to keep it representative over time. For example shops selling music can be replaced by internet shops from where music is sold in a digital format.

When selecting outlets for the sample it is attempted to cover different types of outlets, that is, specialised stores, supermarkets and discount stores. Furthermore, outlets are chosen in order to get a broad geographical coverage.  

The outlets are selected based on their turnover. Outlets with relatively high turnovers are being covered, whereas outlets with limited turnover in general are not selected for the sample. This sort of sampling is known as cut-off sampling. The Danish Business Register is used for information regarding turnover. In addition to selection based on turnover it is also attempted to select outlets that are price leaders. When selecting outlets for the sample the burden on the respondents is also considered.

18.1.3.3. Sampling design: newly significant goods and services

The representative goods and services in the sample are selected using purposive sampling. The specific brand etc. of an item is then mainly chosen by the outlets in the sample. For instance, Statistics Denmark decides that prices for MP3 players should be sampled. It is then for the outlets in the sample to select which MP3 player to report a price for. The outlets are instructed to choose the most representative MP3 player according to sales, for example. When prices are collected by price collectors, it is the price collector that selects the brand etc.

The item/product specifications used for all the representative goods and services are relatively broad (e.g. MP3 player or refrigerator without freezer). 

Usually replacement product-offers are chosen according to similarity. If however no similar products are available or the similar products are known not to be representative the stores in the sample and the price collectors have been instructed to select the most representative product instead of the old product disregarding any differences between the old and the new product. Necessary quality adjustments are then handled centrally at Statistics Denmark.   

Every month a 'quality meeting' is held with participation of the entire central HICP staff. At these meetings one of the 12 COICOP groups in the sample is scrutinized and potential newly significant goods and services are identified as well as obsolete goods and services are being identified. In this way the full sample is scrutinized over the 12 months in a calendar year. 

At the HICP section at Statistics Denmark each member of the production team has been given responsibility for a subset of the COICOP. This member both handles the questionnaires and is primary with regards to quality corrections. Furthermore he/she monitors the markets that are in this subset of the COICOP. This gives hands on experience that is very important in the production of the HICP.

The knowledge as consumers of the central staff as well as information in the media about changes in the consumer markets are used to identify potential new or obsolete goods and services. Information from the persons from central staff also working as price collectors is also valuable. Different data sources are then used to check whether the potentially significant goods should be included in the HICP or on the other hand some goods excluded from the sample. The data sources are often found by contacting organizations representing different consumer branches. 

Newly significant goods and services can be introduced into the sample every month as long as they belong to the existing elementary aggregates.

Price data is collected every month.

18.3.1. Price collection surveys

The price collection by price collectors is in Denmark focused on the collection of prices on fresh foods, clothes and shoes.

The price collection in Denmark are handled by a private company, selected through EU public procurement every 5th year.

Statistics Denmark is responsible for the training of the price collectors. In addition, Statistics Denmark has to equip the price collectors with a hand held device and continuously ensure the quality of the incoming data.

The private company that collects the prices for Statistics Denmark, are responsible for the collection of prices in all selected urban areas every month based on the guidelines given by Statistics Denmark, as well as ongoing training of new price collectors.

The price collection includes about 10,000 prices each month by the price collectors. In addition, about 15,000 prices are collected through questionnaires sent to stores by sending a link to a digital questionnaire or are found on the internet by the CPI central staff.

Price collection in Denmark is outsourced to a private company to be responsible for the collection in 20 urban areas. There are about 25 collectors covering the urban areas and each price collector works approx. three days a month on this task.

Price collectors receive a half-day introduction to the price collection. At the meeting the price collectors are informed about the consumer price index construction as well as an introduction to the handheld device. They are learning about the change in goods, quality changes and other typical challenges in the price collection. 

A detailed guide for the price collectors is in use. The guide covers both theoretical issues regarding the CPI, training in use of the hand held device and the focus is on the price collection, product replacement, product offers and the other challenges in the job.

Detailed written material is provided to all price collectors, so they can collect the best possible prices.

Prices are collected on the internet from web shops for a number of products and services by the central staff. More and more outlets in Denmark are providing their prices on their web pages as well as having actual web shops. Examples on product groups were prices are being collected from the internet is computers, TV and radio, cultural services and music downloads and clothing. In some cases the prices are used as representative for products purchased by internet (e.g. clothing) and in other cases  the prices also represent prices in physical outlets (e.g. computers). 

18.3.2. Timing of price collection

Prices from most product groups are collected between the 7th and 15th of every month. For fresh foods the prices are collected between the 7th and 18th of every month to make sure that prices for different fresh foods are collected from at least two different working weeks.

For almost all product groups the prices from the same outlet are collected only once during the month. Energy prices are however collected up to three times a month throughout the month from the same outlets.

The standards of the Commission Regulation No 701/2006 on temporal coverage where implemented in May 2007 by using an overlap sample using the new standards as well as the old. The use of the overlap sample ensured that there was no break in the indices. Before the change all prices were collected between the 7^th and the 15^th of the month. 

Controls on the quality of the data
When data are entered into the database they are checked manually for obvious errors. Before calculating the HICP, the consistency of the data is checked automatically. Checks are made to see whether there is a price match between the current and previous month for all observations and to detect decimal errors.
Extremes are detected automatically by the Hidiroglou-Berthelot (HB) model for product groups with more than five price changes. For product groups with less than five price changes, extremes are identified as price changes of more than 10 percent. The extremes are checked manually and included or excluded accordingly.
When the indices have been calculated, they are checked manually for unusual changes.

18.4.1. Data validation - price data

When data are entered into the database they are automatically checked for obvious errors. Extreme price changes are immediately subject to manual controls.

Before calculating the HICP, the consistency of the data is checked automatically. Checks are made to see whether there is a price match between the current and previous month for all observations and to detect decimal errors.

Extremes are detected automatically by the Hidiroglou-Berthelot (HB) model for product groups with more than five price changes. For product groups with less than five price changes, extremes are identified as price changes of more than 10 percent. The extremes are checked manually and included or excluded accordingly. 

When the indices have been calculated, they are checked manually for unusual changes.

18.5.1. Elementary price index formulae

Elementary indices

Elementary indices in the Danish HICP are calculated using the Jevons index.                    

The index formula is a weighted Jevons. The Jevons index has to a large extent been chosen due to the good axiomatic properties of the geometric index.

The weighting is made on two levels: on the COICOP 8-digit level (product prices) and at the store level. The COICOP 8 level weights are to a large extent based on the household budget survey and the COICOP specific store weights are based on information on turnover from the Business Register. 

Store prices are based on an unweighted geometrical average of the actual price observations for the same products collected from the same store or chain of stores.

Product prices are the geometrical weighted average of the different store prices. Explicit weights are applied whenever reliable data is available.

Basis prices are calculated across the product prices of products/services belonging to the same product group. Explicit weights are applied whenever reliable data is available. In some cases the basis prices is calculated across just one product price.

Finally, the monthly elementary indices are calculated as the monthly change in the basis prices and the result is chained to the elementary index series.

Higher level indices

Indices above the elementary index level is calculated using a Laspeyres-type index or theoretically a Lowe index.

In practice the Laspeyres-type index is calculated using weights that correspond to the relative share of total consumer expenditure in the different elementary aggregates.

The resulting indices are finally chained to prior 'links' of the indices where other elementary aggregate weights have been applied.

Price observations are entered into the calculations with two decimal places. For instance a price entered could be 105,85 kr. or 105 Danish kroner and 85 øre.

Weights at the level of the elementary aggregates are entered into the system rounded to million kroner. For instance the weight for rice is 441 million Danish kroner in the HICP in 2013. These weights are recalculated automatically by the compilation system into budget shares using all decimals in the calculations and these budget shares are used for calculating the indices.

Weights below elementary aggregates at the level of stores and products are entered into the compilation system as budget shares rounded to percentages. For instance a store weight could be 34 percent.

All decimals are used in the compilation of the indices and the final indices are rounded to one decimal. Published rates of change are based on the indices rounded to one decimal.

18.5.2. Aggregation of different data sources

See 18.5.1.1.

18.5.3. Chaining, linking and splicing methods

See 18.5.1.1. A splicing technique is not applied.

18.5.4. Quality adjustment – Detailed information

In general implicit quality adjustments are made for most products and services in the sample. When the quality is assessed not to have changed significantly, the entire price difference is taken into the index (direct comparison). Broad product descriptions are applied so small changes in the products and services will not be considered as quality changes in this regard. When the quality change is assessed to be significant, the price change between items leaving and entering the sample is usually imputed by the average price change in the corresponding elementary aggregate (bridged overlap method). The rest of the price difference between the items leaving and entering the sample is implicitly assumed to be due to a quality difference. The assessment in this procedure is done together by at least two persons from the central staff using as far as possible detailed information about the products found for instance on the internet. This method is used for almost all products and services. As the assessment is done on a case-by-case basis it is considered to be an acceptable method.

In some cases overlapping prices are used if the price of the new good is known in the overlapping month.

For IT-equipment the 'monthly matched model and chaining' method is used.

Explicit quality adjustments are only made for rents, internet connections and in case of quantity changes (especially food products). For used cars an hedonic model is implicitly being used, as the price index is based on model-prices from a private company.

The link to show no price change method is never applied.

The incidence of quality changes is not explicitly monitored and no statistics is compiled about quality changes.

18.5.5. Seasonal items

All seasonal products are treated with the method labelled 'counter-seasonal estimation' (Article 2 of Commission Implementing regulation (EU) 2020/1148). This has been the case since 2003 in the Danish HICP. Before 2003 the prices were usually carried forward when out of season.

There are not many seasonal food products in Denmark so seasonal goods in Denmark are mainly clothing and footwear. Package holidays are also treated as seasonal items (summer vacations and skiing holidays) and the same is true for amusement parks.

Not applicable.

None.