1. United Nations Economic Commission for Europe Statistical Division Calculation of the consumer price index - Recommendations of the CPI Manual Joint EFTA/UNECE/SSCU Seminar July 2007 Presentation by Carsten B. Hansen, UNECE

2. UNECE Statistical Division Slide 2July 2007 Overview 1.Overview of the CPI Manual 2.Calculation of the CPI 3.The size and distribution of the sampled prices 4.E-commerce 5.Useful links

3. UNECE Statistical Division Slide 3July 2007 1.Introduction 2.Uses of CPIs 3.Concepts and scope 4.Expenditure weights 5.Sampling 6.Price collection 7.Adjusting for quality changes 8.Item substitution and new products 9.Calculation of the CPI in practice 10.Special cases 11.Errors and bias 12.Organization & management 13.Publication and dissemination 14.The system of price indices 15.Basic index number theory 16.Axiomatic and stochastic approaches 17.The economic approach, I 18.The economic approach, II 19.Price index using an artificial data set 20.Elementary indices 21.Quality changes and hedonics 22.Seasonal products 23.Durables and user costs Overview of the CPI Manual

4. UNECE Statistical Division Slide 4July 2007 Calculation of the CPI The CPI calculated in 2 stages: 1. Elementary aggregate indices Calculated on basis of a sample of prices for individual products – and perhaps individual price weights 2. Higher-level indices Calculated as weighted averages of elementary aggregate indices, using the expenditure shares as weights

5. UNECE Statistical Division Slide 5July 2007 Calculation of the CPI Construction of Elementary aggregates Groups of goods or services that are as similar as possible, and preferably fairly homogeneous. Should consist of products with similar expected price movements; try to minimize the dispersion of price movements

6. UNECE Statistical Division Slide 6July 2007 Calculation of the CPI Calculation of elementary aggregate price indices: The arithmetic mean of the price ratios – Carli index The ratio of arithmetic mean prices – Dutot index

7. UNECE Statistical Division Slide 7July 2007 Calculation of the CPI The geometric mean of the price ratios = the ratio of geometric mean prices – Jevons index How to decide which formula to apply? The economic approach The axiomatic or test approach

8. UNECE Statistical Division Slide 8July 2007 Calculation of the CPI The economic approach: Assume utility maximizing households with perfect information. Derive the cost of living index as the ratio of the minimum expenditures of keeping constant utility: The basket is allowed to vary in response to consumer substitution Usually, quantities are not available in practice The assumptions are often not realistic =>Difficult or impossible to calculated a COLI in practice

9. UNECE Statistical Division Slide 9July 2007 Calculation of the CPI The axiomatic approach: Select a number of tests – or axioms – that that the index should meet. Important tests are: Proportionality: If all prices change x%, the index should also change by x% Commensurability: The index should be invariant compared to the unit in which prices are recorded Time reversal: The index from period 0 to period t should equal the reciprocal of the index from t to 0 Transitivity: The index from 0 to 1 multiplied (chained) by an index from 1 to 2 should equal a direct index from 0 to 2.

10. UNECE Statistical Division Slide 10July 2007 Calculation of the CPI Carli fails last two – time reversal and transitivity Dutot fails commensurability Jevons passes all four =>Jevons recommended as the preferred index in general CarliDutotJevons Proportionalityyes Commensurabilityyesnoyes Time reversalnoyes Transitivitynoyes

11. UNECE Statistical Division Slide 11July 2007 Calculation of the CPI Example 1: Substitution effect in the Jevons index MayJuneJune/May Item A10,0011,001,10 Item B10,009,000,90 Arithm. Mean10,00 1,00 Geomean10,009,950,99 Carli100,00 Dutot100,00 Jevons 99,50 Jevons allows the households to consume more of B and less of A. Carli and Dutot keeps the implicit quantities constant

12. UNECE Statistical Division Slide 12July 2007 Calculation of the CPI Example 2: The Dutot index depends on initial price level MayJuneJune/May Item A10,0011,001,10 Item B20,0018,000,90 Arithm. mean15,0014,500,97 Geomean14,1414,070,99 Carli100,00 Dutot96,67 Jevons 99,50 Jevons and Carli are independent of the price levels Dutot weights the price changes after the initial price level

13. UNECE Statistical Division Slide 13July 2007 Calculation of the CPI Example 3: Upward bias in the chained Carli MayJuneJune/May Item A20,0025,001,25 Item B25,0020,000,80 Arithm. mean22,50 1,00 Geomean22,36 1,00 Carli102,50 Dutot100,00 Jevons 100,00 Carli gives more weight to price increases than to decreases. A chained Carli is upward biased and should not be used. If in July prices return to the prices of May, a chained Carli gives 102,50 * 102,5/100 = 105,06 !

14. UNECE Statistical Division Slide 14July 2007 Calculation of the CPI Chained or direct elementary aggregate indices?  A direct index compares the prices of the current month with those of a fixed reference month  A chained index compares month-to-month price changes and multiplies the monthly indices into long-term price indices Chained and direct index give same results for Dutot and Jevons Carli is not transitive and upward biased. Monthly chained indices appear to have some practical advantages in the treatment of missing prices and imputations

15. UNECE Statistical Division Slide 15July 2007 Calculation of the CPI The Calculation of Higher Level Indices Target indices  Economic index: Fisher, Walsh or Törnqvist  Basket index: Lowe or Laspeyres (?) – or Walsh The situation in practice b 0 t T Weight reference period Price reference period Current period End of index link

16. UNECE Statistical Division Slide 16July 2007 Calculation of the CPI In practice, higher-level indices are calculated as the expenditure share weighted arithmetic average of the elementary price indices: It is up to the statistical office to decide whether to price- update the weights from b to 0, or not Caution with automatic price-updating for items with unusual price development, e.g. pc’s, high-tech.

17. UNECE Statistical Division Slide 17July 2007 The size and distribution of the sampled prices Outlets and products may be selected on the basis of a (stratified) probability sample, cut-off sampling, or other measures. From time to time the sample should be examined and updated to ensure its representativity. Optimize the sample – avoid over-sampling and save resources and reduce the response burden

18. UNECE Statistical Division Slide 18July 2007 Numbers of price observations Population (in mio.) Total no. of observations No. of prices per mio. inhabitants Luxembourg0,46.65615.162 Ireland3,842.37911.056 Finland5,245.8708.853 Denmark5,325.0004.674 Austria8,053.4756.667 Sweden8,929.8993.366 Portugal10,3103.69110.110 Belgium10,391.9808.962 Greece10,933.6873.082 Netherlands16,0115.5227.226 Spain (E)40,5119.1432.943 Italy (I)57,0288.5535.066 United Kingdom (UK)59,0130.9812.220 France (F)60,9171.0882.809 Germany (D)82,3326.6153.971 Ukraine47,3275.0005.814 EU-15378,81.584.5394.184 D, E, F, I, UK299,61.036.3803.459

19. UNECE Statistical Division Slide 19July 2007 The size and distribution of the sampled prices A practical way of assessing the distribution of prices: 1)Calculate the average percentage contribution of each elementary index on the 12-months rate of change of the total CPI for a period of a year or more 2)Compare the average relative importance of the elementary indices with the relative distribution of prices 3)The distribution of price observations should, roughly, correspond to the importance of the elementary indices This is a general measure only – there are exceptions, e.g. for goods and services with very few suppliers.

20. UNECE Statistical Division Slide 20July 2007 E-commerce What is E-commerce? Traditional goods/services purchased from Internet sites - books, CDs, IT-equipment, clothing, Goods or services sold exclusively on internet sites - special models/brands of existing products - Internet-banking - e-newspapers Consumption of Internet provided services - connection to Internet - e-mail - games - Internet TV and telephone services (Skype etc.)

21. UNECE Statistical Division Slide 21July 2007 E-commerce The growing importance of E-commerce and the competition between E-commerce and traditional outlets is likely to lead to different price developments As E-commerce grows, it therefore becomes more important to include it in the CPI Inclusion of E-commerce may influence both the weights of the CPI and the price changes Data sources for the weights The household budget survey IT related medias and journals, research articles, surveys

22. UNECE Statistical Division Slide 22July 2007 E-commerce Steps to be taken: Estimate the importance (weight) of E-commerce Compare the development of E-prices with that of normal prices Decide whether to include or exclude E-commerce If included, select the goods or services to be priced Decide which Internet web pages/E-outlets from where to collect prices In principle the recorded prices should be net of transport and delivery costs (should be recorded under transport services). However, in practice it is not always possible to disentangle delivery costs

23. UNECE Statistical Division Slide 23July 2007 Useful links  Consumer price index Manual. Theory and practice. ILO (2004). Electronic version available on: www.ilo.org/public/english/bureau/stat/guides/cpi/index.htm www.ilo.org/public/english/bureau/stat/guides/cpi/index.htm  The Ottawa Group on Price Statistics. Webpage: www.ottawagroup.org www.ottawagroup.org  The Voorburg Group on Services Statistics. Webpage: http://www4.statcan.ca/english/voorburg/ http://www4.statcan.ca/english/voorburg/  Papers from joint UNECE/ILO meetings on CPI are available on: www.unece.org/stats/archive/docs.date.e.htm www.unece.org/stats/archive/docs.date.e.htm