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Accuracy and reliability

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Prices and Consumption, Economic Statistics
Martin Birger Larsen
+45 3917 3459

mbl@dst.dk

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Consumer Price Index

No calculation has been made of the uncertainty connected with sampling in the consumer price index as the sample is not randomly drawn, but the quality of the consumer price index is accessed to be high.

In addition to the "general" uncertainty connected with sampling, there are a number of sources of potential bias in the consumer price index. One source is the consumers substitution between goods and shops and another source is changes in the sample (se chapter regarding "Non-sampling error").

Overall accuracy

The overall reliability of the consumer price index is estimated to be high based on the views of users.

The accuracy of the total consumer price index is judged by Statistics Denmark to be within plus/minus 0,1 index points.

Sampling error

No calculation has been made of the uncertainty connected with sampling in the consumer price index as the sample is not randomly drawn.

The price indices for April, May, June, July, August, September, October, November, December 2020 and January, February, March, April, May and June 2021 are more uncertain than usual, as the non-response-rate has been significantly higher than normal and some industries have been completely shut down due to Covid-19. Since July 2021 all industries are once again open and included in the price index. Usually, the non-response-rate of price observations is below 0.1 per cent in a month, but in April 2020, the non-response-rate is just under 27 per cent of the prices in the sample. In May 2020 the non-response-rate is just above 11 per cent and in June and July 3.5 per cent. In August 2020 the non-response-rate is just above 2.4 per cent. In September 2020 the non-response-rate is just above 3.8 per cent and in October 1.9 per cent. In November 2020 the non-response-rate is just below 4.2 per cent. In December 2020 the non-response-rate is just below 2.7 per cent. In January 2021 the non-response-rate is around 15 per cent. In February 2021 the non-response-rate is around 15 per cent. In March 2021 the non-response-rate is around 10,9 per cent. In April 2021 the non-response-rate is around 8,9 per cent. In May 2021 the non-response-rate is around 3.0 per cent. In June 2021 the non-response-rate is around 1.7 per cent. This includes a number of industries where the non-response-rate is 100 per cent, as the industries have been completely closed down during the April, May, June, July, August, September, October, November, December 2020 and January, February, March, April, May and/or June 2021 price collection periods. On the topic page is the spreadsheet Manglende prisobservationer i FPI og NPI, which shows the non-response-rate in broken down by elementary aggregate indices. If you take into account the weight of the individual product groups (elementary aggregate indices) in the product basket behind the total price index, then just over 16 per cent of the goods basket behind the price index in April 2020 has been hit by more than 50 per cent non-response-rate in price observations or have been closed down completely, which is why the price trend here has been estimated. This is estimated to have an impact on the uncertainty of the monthly increase in the total price index in April 2020 by up to plus minus 0.2 percentage points. In May 2020 around 9 per cent of the basket has been estimated leading to a uncertainty of the monthly increase in the total price index in May 2020 by up to plus minus 0.15 percentage points. In June 2020 around 2 per cent of the basket has been estimated leading to a uncertainty of the monthly increase in the total price index in June 2020 by up to plus minus 0.05 percentage points. In July 2020 around 1.5 per cent of the basket has been estimated leading to a uncertainty of the monthly increase in the total price index in July 2020 by up to plus minus 0.1 percentage points. In August 2020 around 1.5 per cent of the basket has been estimated leading to a uncertainty of the monthly increase in the total price index in August 2020 by up to plus minus 0.04 percentage points. In September 2020 around 1.5 per cent of the basket has been estimated leading to a uncertainty of the monthly increase in the total price index in September 2020 by up to plus minus 0.03 percentage points. In October 2020 around 1.5 per cent of the basket has been estimated leading to a uncertainty of the monthly increase in the total price index in October 2020 by up to plus minus 0.03 percentage points. In November 2020 around 2 per cent of the basket has been estimated leading to a uncertainty of the monthly increase in the total price index in November 2020 by up to plus minus 0.03 percentage points. In December 2020 around 2 per cent of the basket has been estimated leading to a uncertainty of the monthly increase in the total price index in December 2020 by up to plus minus 0.05 percentage points. In January 2021 around 9 per cent of the basket has been estimated leading to a uncertainty of the monthly increase in the total price index in January 2021 by up to plus minus 0.1 percentage points. In February 2021 around 9 per cent of the basket has been estimated leading to a uncertainty of the monthly increase in the total price index in February 2021 by up to plus minus 0.09 percentage points. In March 2021 around 9 per cent of the basket has been estimated leading to a uncertainty of the monthly increase in the total price index in March 2021 by up to plus minus 0.08 percentage points. In April 2021 around 6,8 per cent of the basket has been estimated leading to a uncertainty of the monthly increase in the total price index in April 2021 by up to plus minus 0.08 percentage points. In May 2021 around 2.2 per cent of the basket has been estimated leading to a uncertainty of the monthly increase in the total price index in May 2021 by up to plus minus 0.06 percentage points. In June 2021 around 1.5 per cent of the basket has been estimated leading to a uncertainty of the monthly increase in the total price index in June 2021 by up to plus minus 0.01 percentage points. Read more on the [Subject page] (https://www.dst.dk/doku/forbrugerprisindeks) (in Danish).

The price indices for March 2020 are marginally more uncertain than usual, as the non-response rate has been 3.2 per cent and therefore slightly larger than normal.

Outlets in the sample is to a large extent selected based on turnover so that firms with a high turnover are being preferred compared to firms with a low turnover (cut-off sampling). Representative goods for the different goods and services are being selected according to expenditure measured by e.g. the Household Budget Survey.

The particular goods in the sample including brand and product weight are being selected by the price collector or data provider.

Non-sampling error

In addition to the "general" uncertainty connected with sampling, there are a number of sources of potential bias in the consumer price index, 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 consumer price index 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 mainly calculated as geometric indices. Thus, it is assumed that the consumers' budget shares remain unchanged. For these groups a certain substitution has thus been recognized in the index.

Substitution between shops: This type of bias arises when consumers for the same commodity change from shops with high prices to shops with lower prices. The consumer price index 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.

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 exact values for bias, due to lack of quality adjustment.

New commodities: The sample for the consumer price index 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 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 expenditure from e.g. the Household Budget Survey. 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.

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 statistical uncertainty is not calculated, but the quality of the consumer price index is accessed to be high based on the views of users.

The level of quality is among other things dependent on the size and composition of the sample, the methods used for quality adjustments in connection with changes in the sample and the data editing of the collected data.

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.