Report

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 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 July 2007 UNECE Statistical Division Slide 2 Overview of the CPI Manual 1. 2. 3. 4. 5. 6. 7. 8. Introduction Uses of CPIs Concepts and scope Expenditure weights Sampling Price collection Adjusting for quality changes Item substitution and new products 9. Calculation of the CPI in practice 10. Special cases 11. Errors and bias 12. Organization & management July 2007 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. Publication and dissemination The system of price indices Basic index number theory Axiomatic and stochastic approaches The economic approach, I The economic approach, II Price index using an artificial data set Elementary indices Quality changes and hedonics Seasonal products Durables and user costs UNECE Statistical Division Slide 3 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 July 2007 UNECE Statistical Division Slide 4 Calculation of the CPI Construction of Elementary aggregates • Groups of goods or services that are as similar • July 2007 as possible, and preferably fairly homogeneous. Should consist of products with similar expected price movements; try to minimize the dispersion of price movements UNECE Statistical Division Slide 5 Calculation of the CPI Calculation of elementary aggregate price indices: • The arithmetic mean of the price ratios – Carli index 1 pti P i n p0 C 0:t • The ratio of arithmetic mean prices – Dutot index 1 i i i i p t p p p t 0 0 D n P0:t i 1 p i 0 p0 n July 2007 UNECE Statistical Division Slide 6 Calculation of the CPI • The geometric mean of the price ratios = the ratio of geometric mean prices – Jevons index 1n p P p J 0:t i t i 0 p p i t i 0 1n 1n How to decide which formula to apply? • • July 2007 The economic approach The axiomatic or test approach UNECE Statistical Division Slide 7 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: COLI 0:t • • • => C pti ,U C p0i ,U 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 July 2007 UNECE Statistical Division Slide 8 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. July 2007 UNECE Statistical Division Slide 9 Calculation of the CPI Carli Dutot Jevons Proportionality yes yes yes Commensurability yes no yes Time reversal no yes yes Transitivity no yes yes • • • => July 2007 Carli fails last two – time reversal and transitivity Dutot fails commensurability Jevons passes all four Jevons recommended as the preferred index in general UNECE Statistical Division Slide 10 Calculation of the CPI Example 1: Substitution effect in the Jevons index May June June/May Item A 10,00 11,00 1,10 Item B 10,00 9,00 0,90 Arithm. Mean 10,00 10,00 1,00 Geomean 10,00 9,95 0,99 Carli 100,00 Dutot 100,00 Jevons 99,50 Jevons allows the households to consume more of B and less of A. Carli and Dutot keeps the implicit quantities constant July 2007 UNECE Statistical Division Slide 11 Calculation of the CPI Example 2: The Dutot index depends on initial price level May June June/May Item A 10,00 11,00 1,10 Item B 20,00 18,00 0,90 Arithm. mean 15,00 14,50 0,97 Geomean 14,14 14,07 0,99 Carli 100,00 Dutot 96,67 Jevons 99,50 Jevons and Carli are independent of the price levels Dutot weights the price changes after the initial price level July 2007 UNECE Statistical Division Slide 12 Calculation of the CPI Example 3: Upward bias in the chained Carli May June June/May Item A 20,00 25,00 1,25 Item B 25,00 20,00 0,80 Arithm. mean 22,50 22,50 1,00 Geomean 22,36 22,36 1,00 Carli 102,50 Dutot 100,00 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 ! July 2007 UNECE Statistical Division Slide 13 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 July 2007 UNECE Statistical Division Slide 14 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 Weight reference period b July 2007 Price reference period 0 Current period t UNECE Statistical Division End of index link T Slide 15 Calculation of the CPI In practice, higher-level indices are calculated as the expenditure share weighted arithmetic average of the elementary price indices: I 0:t wib I i0:t • • It is up to the statistical office to decide whether to priceupdate 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. July 2007 UNECE Statistical Division Slide 16 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 July 2007 UNECE Statistical Division Slide 17 Numbers of price observations Population (in mio.) Total no. of observations No. of prices per mio. inhabitants Luxembourg 0,4 6.656 15.162 Ireland 3,8 42.379 11.056 Finland 5,2 45.870 8.853 Denmark 5,3 25.000 4.674 Austria 8,0 53.475 6.667 Sweden 8,9 29.899 3.366 Portugal 10,3 103.691 10.110 Belgium 10,3 91.980 8.962 Greece 10,9 33.687 3.082 Netherlands 16,0 115.522 7.226 Spain (E) 40,5 119.143 2.943 Italy (I) 57,0 288.553 5.066 United Kingdom (UK) 59,0 130.981 2.220 France (F) 60,9 171.088 2.809 Germany (D) 82,3 326.615 3.971 Ukraine 47,3 275.000 5.814 EU-15 378,8 1.584.539 4.184 D, E, F, I, UK 299,6 1.036.380 3.459 July 2007 UNECE Statistical Division Slide 18 The size and distribution of the sampled prices A practical way of assessing the distribution of prices: 1) 2) 3) 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 Compare the average relative importance of the elementary indices with the relative distribution of prices 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. July 2007 UNECE Statistical Division Slide 19 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.) July 2007 UNECE Statistical Division Slide 20 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 July 2007 UNECE Statistical Division Slide 21 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 July 2007 UNECE Statistical Division Slide 22 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 The Ottawa Group on Price Statistics. Webpage: www.ottawagroup.org The Voorburg Group on Services Statistics. Webpage: 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 July 2007 UNECE Statistical Division Slide 23