### XMPI Manual Chp. 9

```United Nations Economic Commission for Europe
Statistical Division
Producer Price Indices Recommendations of international manuals
Joint EFTA/UNECE/SSCU Seminar
July 2007
Presentation by Carsten B. Hansen, UNECE
Overview
1.
2.
3.
4.
5.
The family of PPIs
The international manuals
Calculation of the PPI
Basic measures
July 2007
UNECE Statistical Division
Slide 2
The family of PPIs
Producer price indices
Output PPIs
July 2007
Input PPIs
PPI – Production for the
domestic market
PPI – Input from the
domestic market
PPI – Production for
export
PPI – Input from imports
PPI – Total production
PPI – Total input
UNECE Statistical Division
Slide 3
The international manuals


Producer Price Index Manual. Theory and Practice
(2004). Electronic version available on
www.imf.org/external/np/sta/tegppi/index.htm
Export and Import Price index Manual – planned to be
published late 2007/early 2008. Draft chapters available on
www.imf.org/external/np/sta/tegeipi/index.htm
July 2007
UNECE Statistical Division
Slide 4
Overview of the PPI Manual
1.
2.
3.
4.
5.
6.
7.
8.
Introduction
Background and uses of PPIs
Coverage and classifications
Weights and their sources
Sampling
Price collection
Treatment of quality change
Item substitution and new
products
9. PPI calculation in practice
10. Treatment of specific products
11. Errors and bias in the PPI
12. Organization & management
July 2007
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
Publication and dissemination
The system of price statistics
Basic index number theory
Axiomatic and stochastic
approaches
The economic approach
Aggregation issues
Price index using an artificial
data set
Elementary indices
Quality change and hedonics
Seasonal products
UNECE Statistical Division
Slide 5
Calculation of elementary indices
Elementary price indices can be calculated as
Unweighted averages:
•
The arithmetic mean of the price ratios – Carli index
•
The ratio of arithmetic mean prices – Dutot index
•
July 2007
The geometric mean of the price ratios = the ratio of
geometric mean prices – Jevons index
UNECE Statistical Division
Slide 6
Calculation of elementary indices
Weighted averages:
•
Laspeyres price index
La
P0:t
•

p q 

 w 

p q 
i
t
i
0
i
0
i
0
i
0
i
pt 
i 
p0 
Geometric Laspeyres price index
GLa
0:t
P


 p ti 
 i 
 p0 
w
i

p 
w
i
p 
w
i
i
t
i
0
Caution: Explicit weights in Dutot indices may conflict with the
implicit weighting by the price level in this type of an index
July 2007
UNECE Statistical Division
Slide 7
Calculation of elementary indices
How to decide which formula to apply?
•
The axiomatic or test approach - focuses on the
statistical properties of the index
•
The economic approach - focuses on the economic
interpretation of the index
July 2007
UNECE Statistical Division
Slide 8
Calculation of elementary indices
The economic approach to output PPIs
Assuming revenue maximizing producers it shows the ratio of
Revenues, R, with fixed input and technology, v: R(pt,v)/R(p0,v)
•
•
•
Producers keep fixed relative quantities => Carli or Dutot
appropriate
Producers keep fixed revenue shares (not very likely!) =>
Jevons to be preferred
Laspeyres and Paasche provides the lower and upper bounds to
the economic/theoretical output PPI, under normal conditions
July 2007
UNECE Statistical Division
Slide 9
Calculation of elementary indices
The economic approach to input PPIs
Assuming cost minimizing producers, it shows the ratio of costs
(C) with fixed output and technology, y: C(pt,y)/C(p0,y)
•
•
•

Producers (purchasers) keep fixed relative input quantities =>
Carli or Dutot appropriate – not always the case in practice
Producers (purchasers) keep fixed input value shares =>
Jevons to be preferred
Paasche and Laspeyres provides the lower and upper bounds to
the economic/theoretical input PPI, under normal conditions
However, the assumptions are often not fulfilled in reality =>
what formula to use
July 2007
UNECE Statistical Division
Slide 10
Calculation of elementary indices
Conclusions:
•
•
•
•
•
•
•
Jevons has better statistical properties
Don’t give too much weight on the economic approach
for elementary indices
Jevons or Carli may be used for most elementary indices
Dutot should only be used for elementary aggregates that
consists of strictly homogenous products
A chained Carli should not be used because of build-in
upward bias
If weights are available, Laspeyres or Geometric
Laspeyres indices may be calculated.
Be careful to apply weights in Dutot indices
July 2007
UNECE Statistical Division
Slide 11
Basic measures
The prices:
• Output PPI: The prices received by the producer, i.e. basic
•
•
•
prices (SNA) excluding taxes plus subsidies
Input PPIs: The price actually paid by the purchaser, including
taxes net of subsidies, i.e. purchasers‘ prices
Transfer prices
Becomes more common as (international) trade is growing and
posses serious measurement problems
Often they do not reflect real market prices. In such cases:
• Use estimated or imputed prices, or
• Exclude the transfer prices from the index
July 2007
UNECE Statistical Division
Slide 12
Basic measures
The coverage of production and establishments:
• The statistical unit for the PPI is usually the output generating
•


entity, the establishment, as outlined in the SNA
However, globalization, outsourcing and the emergence of
virtual corporations etc. makes the identification of the
statistical unit still more difficult in practice
Be as close as possible to the principle target of the PPI
Coordinate with National Accounts (NA):
- NA may provide the weighting data
- A main use of PPIs is deflation of NA data
Thus, a consistent approach should be aimed at
July 2007
UNECE Statistical Division
Slide 13
•
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
•
Empirical studies indicate that 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”!
July 2007
UNECE Statistical Division
Slide 14
a) 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
b) “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
c)
July 2007
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
UNECE Statistical Division
Slide 15
d) 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
e)
July 2007
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
recorded price
UNECE Statistical Division
Slide 16
f)
cost of producing the old and new item, and the ratio of costs be
g) Experts judgement: Persons with detailed product knowledge value
the difference between the new and old product, and appropriate
h) Hedonic adjustments by use of hedonic regression. Resource and
data demanding
July 2007
UNECE Statistical Division
Slide 17
A, B and C Methods for QA
The Handbook on price and volume measures in national accounts
(Eurostat 2001) divides the quality adjustment methods into three
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
 The Handbook provides useful guidance and numerous practical
examples. It is available from Eurostat’s webpage
 The Voorburg Group on Services Statistics also provides useful
information. Webpage: http://www4.statcan.ca/english/voorburg/
July 2007
UNECE Statistical Division
Slide 18
Unique products
Unique products pose a special problem for quality
•
•
•
•
major equipment projects, special machineries, ships and
aircrafts
IT, management and other types of business services
Telecommunication; tailored equipment and service
agreements
Transport services
=> It is not possible to “compare like with like” and the value of
possible quality changes is difficult to estimate
July 2007
UNECE Statistical Division
Slide 19
Unique products – Model pricing
Model Pricing:
•
Construct a model by combining a set of components that can be
priced over time. The model should be as representative as possible. It
does not have to be a project actually produced or sold on the market.
•
The following criteria applies:
•
The model needs regular update to ensure that it continues to be
representative
•
The model should be defined in terms of outputs, not inputs
•
The prices used should be the actual charged prices, taking account of
profit margins and discounts offered to costumers
July 2007
UNECE Statistical Division
Slide 20
Unique products – Specification prices
Specification Prices:
•
Break down a real product into its key elements. In the successive
periods individual projects are examined and the prices of the matched
set of elements are compared. No ideal, representative model has to be
constructed or updated
•
The following criteria applies:
•
The key elements may become less relevant over time and will need to
be updated regularly
The key elements should be specified in terms of outputs rather than
inputs
•
July 2007
UNECE Statistical Division
Slide 21
International prices
The use of international price indices is an acceptable (B)
method if they can be considered representative of the
price development in the country. Examples:
- Energy and raw material prices
- Computers
•
For example, US compiled hedonic based indices for
computers and peripherals available on Internet may be
used as a data source, adjusting for exchange rate changes
if needed
July 2007
UNECE Statistical Division
Slide 22
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