united nations economic commission for europe statistical division price statistics seminar on...

United Nations Economic Commission for EuropeStatistical DivisionUnited Nations Economic Commission for EuropeStatistical Division

Price Statistics

Seminar on challenges in economic statistics

Tehran, IranNovember 2008

Presentation by Carsten Boldsen Hansen, UNECE([email protected])

November 2008 UNECE Statistical Division Slide 2

Overview

1. Main types of price indices

2. Construction of price indices

3. Calculation of elementary indices

4. Missing prices, seasonal products and quality changes

5. Basic CPI concepts and measures

6. International recommendations

7. Future challenges for CPI



Consumer price indices

Producer price indices

Export and import price indices

Sectoral 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



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



Export and import price indices (XMPI)XPI measures price change on products produced for export

MPI measures price change on imported products




Sectoral price indices (XMPI)Building and construction price indices

Agriculture, forestry and fishing



2. The construction of price indices

CPIs, PPIs and XMPIs are calculated in two 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 value shares as weights


2. The construction of price indices

The typical aggregation structure

Overall index

Higher-level indices

Elementary Indices

Individual price observations

Value shares(weights)


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 ofelementary indices …


3. Calculation of elementary price indices

Carli index – the arithmetic mean of the price ratios

Dutot index – the ratio of arithmetic mean prices

0:0

1 iC tt i

pP

n p

0 0

0:

0 0

1 1

1 1

i i i it t

Dt

i i

p p p pn nP

p pn n



Jevons index – the geometric mean of the price ratios = the ratio of geometric mean prices

11

0: 10 0

nn iitJ t

t ni i

ppP

p p



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



Example 1: Dutot index depends on the price levelDecember January Index

Product 1 25,53 16,06 62,9

Product 2 69,5 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+100+109,9)/3 * 100 = 90,9

Price changes are weighted according to the price in the reference period:

Price Price weight

Product 1 25,53 0,09

Product 2 69,5 0,23

Product 3 201,67 0,68

Sum 296,7 1,00

Dutot index 62,9*0,09+100*0,23+109,9*0,68 = 103,5



Example 2: Upward bias in the 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!



Example 3: 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



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.



• 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



Chained or direct elementary aggregate indices?

A direct index compares the prices of the current month with those of a fixed reference monthA 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


4. Missing prices, seasonal products and quality change

Missing price observationsWhen in some month(s) it is not possible to collect a price for a product included in the sample

Seasonal productsProducts included in the sample that disappear for a period so that prices cannot be collected in all 12 months of the year

Quality changesChanges in product quality over time should be adjusted for so that the price index shows only pure price changes


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?


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


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.


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.


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



Model 1: Carry forward (a)

0

10

20

30

40

50

60

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Jan

In season price Carry forward price



Model 2: Carry forward (b)

0

10

20

30

40

50

60

J an Feb Mar Apr May J un J ul Aug Sep Oct Nov Dec J an

In season price Carry forward price



Model 3: Impute price (a)

0

10

20

30

40

50

60


In season price Imputation Price increase



Model 4: Impute price (b)

0

10

20

30

40

50

60


In season price Imputation Price increase



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


4. Quality changes

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


4. Quality changes

Example: Quality changes of a PC

May June

Acer Aspire 7720G-6A4G25MIntel Core 2 Duo T57502 Ghz 2 MB L2 Cache17 inch screen1440X900 WXGA56 Kb modem, Lan, W-Lan3,6 KgWindows Vista

Acer Aspire 6920G-604G32 Intel Core 2 Duo T75002,2 Ghz 4 MB L2 Cache16 inch screen1920X1080 WXGA56 Kb modem, Lan, W-Lan3,2 KgWindows Vista

Price 899 euro 899 euro

Estimated value of quality change = 100 euro = 11%

Price index adjusted for quality changes = 100,0 – 11,0 = 89,0


4. Quality changesHICP for computers (09.1.3), 2004 = 100

20

30

40

50

60

70

80

90

100

110

120

2004m01 2005m01 2006m01 2007m01 2008m01

EU Bulgaria Hungary Sweden UK Turkey


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”!


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


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


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


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


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



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 conceptPurchaser prices - the prices that the household actually pay for goods and services, including taxes less subsidies



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


6. International recommendations

The CPI Manual in English/Russian is available from ILO on www.ilo.org/public/english/bureau/stat/guides/cpi/index.htm

Supplementary Handbook: Practical Guide to Compiling Consumer Price Indices. Under production. Draft available on www.unece.org/stats/documents/2008.05.cpi2.htm

Papers from Joint UNECE/ILO meetings on CPI are available on www.unece.org/stats/archive/docs.date.e.htm

Papers from meetings in the Ottawa Group on Price Indices are available from www.ottawagroup.org


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

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