united nations economic commission for europe statistical division calculation of the consumer price...
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United Nations Economic Commission for EuropeStatistical DivisionUnited Nations Economic Commission for EuropeStatistical 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
July 2007 UNECE Statistical Division Slide 2
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 3
1. Introduction2. Uses of CPIs3. Concepts and scope4. Expenditure weights5. Sampling6. Price collection7. Adjusting for quality changes8. Item substitution and new
products9. Calculation of the CPI in
practice10. Special cases11. Errors and bias12. Organization & management
13. Publication and dissemination14. The system of price indices15. Basic index number theory16. Axiomatic and stochastic
approaches17. The economic approach, I18. The economic approach, II19. Price index using an artificial
data set20. Elementary indices21. Quality changes and hedonics22. Seasonal products23. Durables and user costs
Overview of the CPI Manual
July 2007 UNECE Statistical Division Slide 4
Calculation of the CPI
The CPI calculated in 2 stages:
1. Elementary aggregate indicesCalculated on basis of a sample of prices for individual products – and perhaps individual price weights
2. Higher-level indicesCalculated as weighted averages of elementary aggregate indices, using the expenditure shares as weights
July 2007 UNECE Statistical Division Slide 5
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
July 2007 UNECE Statistical Division Slide 6
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
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July 2007 UNECE Statistical Division Slide 7
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
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July 2007 UNECE Statistical Division Slide 8
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
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July 2007 UNECE Statistical Division Slide 9
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 10
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
Carli Dutot Jevons
Proportionality yes yes yes
Commensurability yes no yes
Time reversal no yes yes
Transitivity no yes yes
July 2007 UNECE Statistical Division Slide 11
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 12
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 13
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 14
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 15
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
July 2007 UNECE Statistical Division Slide 16
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.
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July 2007 UNECE Statistical Division Slide 17
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 18
Numbers of price observations
Population
(in mio.)Total no. of
observationsNo. 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 19
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 goodsand services with very few suppliers.
July 2007 UNECE Statistical Division Slide 20
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 21
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 22
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 23
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