united nations economic commission for europe statistical division calculation of the consumer price...

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


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


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



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



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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• 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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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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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.



• 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



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



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



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 !



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



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



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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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


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


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.


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.)


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


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


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

united nations economic commission for europe statistical division calculation of the consumer price...

Documents

unece slide

cpi manual slide

practice slide

test approach slide

useful links slide

system of price indices

elementary indices

price collection