1. Price Statistics Seminar on challenges in economic statistics
Tehran, Iran November 2008
Presentation by Carsten Boldsen Hansen, UNECE

2. Overview Main types of price indices Construction of price indices
Calculation of elementary indices
Missing prices, seasonal products and quality changes
Basic CPI concepts and measures
International recommendations
Future challenges for CPI
November 2008

3. 1. Main types of price indices
Consumer price indices
Producer price indices
Export and import price indices
Sectoral price indices
November 2008

4. 1. Main types of price indices
Consumer price indices (CPI)
Measure of average price change on goods and services acquired by the households for consumption
Used for different purposes:
Measure of general inflation
Compensation – i.e. indexation of wages, pensions, income transfers
Indexation of contracts
Deflation of other economic statistics
Attracts broad interest from many user groups
November 2008

5. 1. Main types of price indices
Producer price indices (PPI)
Output PPIs measure the price change on products (goods and services) sold by the production sector
Input PPIs measure the price change on products acquired as intermediate input by the production sector
Used for different purposes:
Measure of inflation in the production sector
Indexation of contracts
Deflation of other economic statistics
November 2008

6. 1. Main types of price indices
Export and import price indices (XMPI)
XPI measures price change on products produced for export
MPI measures price change on imported products
Used for different purposes:
Measure of inflation in the production sector
Indexation of contracts
Deflation of other economic statistics
November 2008

7. 1. Main types of price indices
Sectoral price indices (XMPI)
Building and construction price indices
Agriculture, forestry and fishing
Used for different purposes:
Measure of inflation in the production sector
Indexation of contracts
Deflation of other economic statistics
November 2008

8. 2. The construction of price indices
CPIs, PPIs and XMPIs are calculated in two 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 value shares as weights
November 2008

9. 2. The construction of price indices
The typical aggregation structure
November 2008

10. 3. Calculation of elementary indices
Elementary indices should consist of:
Products – goods or services – that are as similar as possible, i.e. homogeneous
Products with similar price movements; minimize the expected dispersion of price movements
There are 3 main formulas for calculation of
elementary indices …
November 2008

11. 3. Calculation of elementary price indices
Carli index – the arithmetic mean of the price ratios
Dutot index – the ratio of arithmetic mean prices
November 2008

12. 3. Calculation of elementary price indices
Jevons index – the geometric mean of the price ratios
= the ratio of geometric mean prices
November 2008

13. 3. Calculation of elementary price indices
Exercise 1: Calculation of elementary index
a) Calculate the Carli, Dutot and Jevons indices!
b) Explain and give an interpretation of the results.
c) What are the main advantages/disadvantages of the 3 indices?
d) Which index formula is used for your CPI and PPI?
Dec.
Jan.
% change
prices
A – Local calls 7 9
28,6
B – National calls 20 10
-50,0
C – International calls 28 12
-57,1
November 2008

14. 3. Calculation of elementary price indices
Example 1: Dutot index depends on the price level
December
January
Index
Product 1
25,53
16,06
62,9
Product 2
69,5
100,0
Product 3
201,67
221,67
109,9
Av. Price
98,9
102,4
Dutot index
102,4/98,9 * 100 =
103,5
Carli index
(62, ,9)/3 * 100 =
90,9
Price changes are weighted according to the price in the reference period:
Price
Price weight
0,09
0,23
0,68
Sum
296,7
1,00
62,9*0,09+100*0,23+109,9*0,68 =
November 2008

15. 3. Calculation of elementary price indices
Example 2: Upward bias in the Carli
May
June
June/May
Item A
20,00
25,00
1,25
Item B
0,80
Arithm. mean
22,50
1,00
Geomean
22,36
Carli
102,50
Dutot
100,00
Jevons
Carli gives more weight to price increases than to decreases!
A chained Carli is upward biased and should not be used!
November 2008

16. 3. Calculation of elementary price indices
Example 3: Substitution effect in the Jevons index
May
June
June/May
Item A
10,00
11,00
1,10
Item B
9,00
0,90
Arithm. Mean
1,00
Geomean
9,95
0,99
Carli
100,00
Dutot
Jevons
99,50
Jevons allows the households to consume more of B and less of A.
Carli and Dutot keeps the implicit quantities constant
November 2008

17. 3. Calculation of elementary price indices
How to decide which index formula to use?
Select a number of tests – or axioms – that the index should meet. More 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.
November 2008

18. 3. Calculation of elementary price indices
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
Commensurability no
Time reversal
Transitivity
November 2008

19. 3. Calculation of elementary price indices
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. A Chained Carli is upward biased – should not be used!
Monthly chained indices appear to have some practical advantages in the treatment of missing prices and imputations
November 2008

20. 4. Missing prices, seasonal products and quality change
Missing price observations
When in some month(s) it is not possible to collect a price for a product included in the sample
Seasonal products
Products included in the sample that disappear for a period so that prices cannot be collected in all 12 months of the year
Quality changes
Changes in product quality over time should be adjusted for so that the price index shows only pure price changes
November 2008

21. 4. Missing prices Exercise 2:
Missing prices, seasonal products and quality changes are regular problems in price index compilation
Use of inappropriate methods may lead to serious bias in the price index
a) What are the main problems associated with missing prices, seasonal products and quality changes?
b) What can your price statistics division do to deal with these problems?
November 2008

22. 4. Missing prices Temporarily missing observations:
Omit the item for which the price is missing so that a matched sample is maintained, even though the sample is depleted.
Carry forward the last observed price.
Impute the missing price by the average price change of the prices that are available in the elementary aggregate.
Impute the missing price by the price change of a comparable item.
Carry forward biases CPI towards zero change. Use only if it
can be justified, and only for a very limited period of time
November 2008

23. 4. Missing prices Permanently missing observations:
Where products disappear permanently, a replacement product has to be sampled and included in the index.
The replacement product should, ideally, accounts for a significant proportion of sales, is likely to continue to be sold for some time, and be representative of the market the old product covered.
November 2008

24. 4. Missing prices Permanently missing observations:
Replacements without overlapping prices:
Impute price in previous period to ensure the inclusion of the replacement product does not affect the index
Replacements with overlapping prices:
Involves implicit adjustment for quality difference: the relative prices of the new and old product are assumed to reflect their relative qualities.
For perfect or nearly perfect markets this may be a valid assumption, but for other markets it may not hold.
November 2008

25. 4. Seasonal products Two main approaches: The fixed weight approach
The variable weights approach
The fixed weight approach is most common in use –
in line with a fixed annual basket approach to the CPI
it is necessary to estimate a price in of-season periods
November 2008

26. 4. Seasonal products
Model 1: Carry forward (a)
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27. 4. Seasonal products
Model 2: Carry forward (b)
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28. 4. Seasonal products
Model 3: Impute price (a)
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29. 4. Seasonal products
Model 4: Impute price (b)
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30. 4. Seasonal products Conclusions:
While prices are carried forward, the monthly changes of the CPI will be biased towards zero
imputation avoids, or at least reduces, the bias of the monthly changes of the CPI
the 12 months rate of changes will be (largely) unaffected in all the four models
in the long-term, the CPI will show the correct development in all four models
November 2008

31. What is the problem with quality changes?
The CPI/PPI aims to measure the average price change of a fixed basket of products
Changes in the baskets other than price changes should not influence the index
Collected prices need be adjusted for the value of quality changes to ensure the price index is showing only real price changes
November 2008

32. 4. Quality changes May June Acer Aspire 7720G-6A4G25M
Example: Quality changes of a PC
May
June
Acer Aspire 7720G-6A4G25M
Intel Core 2 Duo T5750
2 Ghz
2 MB L2 Cache
17 inch screen
1440X900 WXGA
56 Kb modem, Lan, W-Lan
3,6 Kg
Windows Vista
Acer Aspire 6920G-604G32
Intel Core 2 Duo T7500
2,2 Ghz
4 MB L2 Cache
16 inch screen
1920X1080 WXGA
3,2 Kg
Price
899 euro
Estimated value of quality change = 100 euro = 11%
Price index adjusted for quality changes = 100,0 – 11,0 = 89,0
November 2008

33. 4. Quality changes HICP for computers (09.1.3), 2004 = 100
November 2008

34. 4. Quality changes
The pace of innovation is high, leading to continual changes in the quality of products
There is not much consistency among countries in the methods they use to deal with quality change
The choice of method can lead to very different results
The way in which a product is replaced by another always imply some assumption about the relative qualities of the 2 products
– You cannot “do nothing”!
November 2008

35. 4. Quality changes
Direct comparison: The price of the new product is compared directly with the price of the old one. Assumption: the 2 are of similar quality and the whole price change is included in the index
“Link to show no change”: The price of the new item is linked into the index. The price change is assumed to equal the quality change and thus not included in the index calculation
Overlapping prices: With overlapping prices the new item can be linked into the index. This assumes that the price difference reflects the value of any quality difference between the two items
November 2008

36. 4. Quality changes
Matched models only. Only those products for which a price is recorded in both the current and the reference period are included in the calculation of the elementary index. This corresponds to imputation, where the price development of the new product is estimated by the average price development of those product for which matched prices have been recorded
Option prices: If the difference between A and C is the inclusion of an extra option, e.g. a CD-ROM drive in a computer, the extra option can be separately priced and appropriate adjustment made in the recorded price
November 2008

37. 4. Quality changes
Production costs: Producers can be asked about the difference in cost of producing the old and new item, and the ratio of costs be applied for adjusting the prices
Experts judgement: Persons with detailed product knowledge value the difference between the new and old product, and appropriate adjustment are made in the recorded prices
Hedonic adjustments by use of hedonic regression. Resource and data demanding
November 2008

38. 4. Quality changes
The Handbook on price and volume measures in national accounts
(Eurostat 2001) divides QA methods into 3 groups:
A methods: most appropriate methods
B methods: those methods, which can be used in case an A method cannot be applied
C methods: those methods, which shall not be used
Follows a case-by-case approach
The Handbook provides useful guidance and numerous practical examples. It is available from Eurostat’s webpage
November 2008

39. 4. Quality changes Some recommendations:
Agree on which methods to use on a case-by-case basis
A mix of simple, implicit methods usually gives good results – the practice in most countries
Produce guidelines to staff/price collectors
Do not apply “link to show no change” as default
Be transparent - document methods
November 2008

40. 5. Basic CPI concepts and measures
The main purpose(s) of the CPI
A measure of inflation or cost of living – or both?
Geographical and population coverage
The national concept: covers the consumption expenditure of resident households, whether made in the country or abroad
The domestic concept: covers the consumption expenditure inside the country, whether made by resident or foreign households
- weighting data may need be adjusted/supplemented!
The price concept
Purchaser prices - the prices that the household actually pay for goods and services, including taxes less subsidies
November 2008

41. 5. Basic CPI concepts and measures
Practical differences in targeting an inflation index or a COLI
Inflation index
COLI
Population coverage
Domestic concept
National concept
Types of acquisition used
Purchases in monetary transactions
May also include own-account production and social transfers in kind
Owner-occupied housing
Net acquisition approach
Rental equivalent or user cost approach
Prices
Actual observed market prices
May also use imputed prices
November 2008

42. 6. International recommendations
The CPI Manual in English/Russian is available from ILO on
Supplementary Handbook: Practical Guide to Compiling Consumer Price Indices. Under production. Draft available on
Papers from Joint UNECE/ILO meetings on CPI are available on
Papers from meetings in the Ottawa Group on Price Indices are available from
November 2008

43. 7. Future Challenges Price collection methods
Treatment of difficult products: e.g. housing, computers, cars, services, telecommunication, health care
Optimization of the sample
Automatic Statistical data editing
Dissemination
November 2008