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ICP PPP Methods
Regional Course on Price Statistics and ICP
Male, Maldives
25-29 September 2005
TIMOTHY LO
Statistician, International Comparison Program
Asian Development Bank
1
Outline of Presentation
I.
Introduction
II. Stages in Calculation Process
III. Data Requirements for PPP Calculation and
Aggregation above the level of BH
IV. Properties of Price and Volume Indices Used in the
PPP Calculation
V.
EKS Method PPP
VI. CPD Method PPP
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Introduction
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•
Basic heading is the lowest level of final
expenditures on GDP for which weights will
be applied under the 155 basic heading
structures
•
A higher level aggregate is an expenditure
class, group or category obtained by
combining two or more basic headings.
Introduction
Data Requirements for PPP Calculation and
Aggregation above the level of BH:
1. Complete set of basic heading expenditures
in national currencies
2. Basic heading PPPs, with country 1 acting as
the reference country and its currency as the
numeraire
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Stages in the Aggregation Process
Three Stages in the Aggregation Process
1. Computing average annual national average
prices
2. Aggregating prices to basic heading level
parities
3. Aggregating basic heading parities to GDP and
other sub-aggregates
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Properties of Price and Volume Indices
Used in PPP Calculation
Base country invariant
Commensurability
Transitivity
Characteristicity
Additivity
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Properties of Price and Volume Indices
Used in the PPP Calculation
Base country invariant
– all participating countries are symmetrical so the
results are not different from the chosen base
country
Commensurability
– all produce results that are invariant to changes in
the units of measurement for prices and quantities
Transitivity
– requires that every indirect parity I PPPjk should
equal the corresponding direct parity PPPjk
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Properties of Price and Volume Indices
Used in PPP Calculation
Characteristicity
– requires the transitive multilateral comparisons
between members of a group of countries to retain
the essential features of the intransitive binary
comparisons that existed between them before
transitivity
Additivity
– values of the expenditure aggregates of participating
countries are equal to the sum of the values of their
components when both aggregates and components
are valued at national prices
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EKS Method
Background:
• named after Elteto, Koves, Szulc
• used by Lazlo Drechsler in the "Weighting of the index
numbers in multilateral comparisons”
• used in the 1960s for comparisons between the
centrally planned economies of eastern Europe
• Formula was proposed 40 years earlier by Gini in "On
the circular test of index numbers", international review
of statistics, Vol. 9, No. 2., 1931
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Salient Features of the EKS Method
• EKS is a multilateral index: comparison between
two countries will be affected by a third country.
• It is transitive: not affected by change of base.
• It is based on binaries so it is most
characteristic of the two countries being
compared. Gives equal weight to all countries.
Least affected by a third country.
• May discard prices even if they are available
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EKS Method
Laspeyres Type PPP
• For each pair of countries two binary PPPs are
calculated
• This is the geometric mean of the price relatives for
representative products of the first country
Paasche Type PPP
• The second geometric mean of the price relatives for
the products representative of second country
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EKS Method
Fisher Type PPP
• The geometric mean of these two PPP is taken to derive
a single binary PPP between two countries
• The result will be a matrix of Fisher PPP calculated
directly between each pair of countries.
• To fill in the gaps in the matrix by taking the geometric
mean of all available Indirect Fisher type PPP bridging
the pair of countries for which direct PPPs are missing
fills the gaps in the matrix
• The matrix is made transitive by applying the EKS
procedure
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EKS Method
• Replacing the Fisher Type PPP between each pair of
countries by the geometric mean of itself squared and
all the corresponding indirect Fisher Type PPP between
pair.
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EKS Method
Given:
Two countries: A and B
Where:
PiA The price of same product “i” in country A
PiB The price of same product “i” in country B
nA The number of products representative in country A
nB The number of products representative in country B
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EKS Method
Laspeyres Type PPP:
• Laspeyres between country A & B
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EKS Method
Paasche Type PPP:
• Paasche between country A & B
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EKS Method
Fisher type PPP:
LAB and PAB are given equal weight in calculating FAB
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EKS Method
Important Notes:
• There are no explicit weights in the calculations of Fisher
Type PPP
• Weights depend on the number of representative products
in the two countries and the size of overlap between them
• The Fisher type PPPs above is not transitive, hence, the
EKS procedure is applied.
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EKS Method
Indirect Fisher:
Given: Countries A, B and C
• The EKS method calculates the indirect PPP between two
countries through a third country
• The indirect fisher for FAB can be calculated by the direct
price relatives between A and C and price relatives
between B and C.
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EKS Method
• EKS PPP is the geometric mean of the direct PPP and all
the indirect PPPs between a pair of countries.
• Direct PPP must have twice the weight of each indirect PPP.
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EKS Method
General form of EKS:
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Salient Features of the CPD Method
• It is multilateral.
• Estimates PPPs by statistical inference rather than a
price index
• It is transitive, not affected by change of base country
• It works on all observations, does not discard any
available price
• Used mostly on basic heading PPP
• May be subject to large residual errors
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CPD Method
The PPPs is log of price observations against a set of
dummy variables define with respect to the product
prices and the participating countries.
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CPD Method
Where:
• Dij and D*ij (i = 1, 2, …, m; j = 1, 2, …, n) are,
respectively, dummy variables for the m products in the
basic heading and the n countries involved in the
comparison.
• Dij and D*ij are equal to 1 when product i is priced in
country j, otherwise they equal 0.
• Once this regression equation is estimated, the PPP for
currency of country k with country j as base can be
obtained by the exponential of the difference in the
estimates of πj and πk taken from the regression
equation
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EKS vs. CPD
EKS METHOD:
• calculates PPPs as an index number
• maximizes characteristicity to obtain multilateral
transitive set of PPPs for the basic heading to be close to
the binary intransitive PPPs initially calculated for the
basic heading.
• Fisher type PPPs are intransitive to begin with but
transitivity can be achieved after applying the EKS
procedure.
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EKS vs. CPD
CPD METHOD:
• Calculates PPPs on the basis of statistical inference
• A multilateral approach which aims to compute transitive
PPPs for the basic heading maximizing the use of data
collected for the basic heading
• Assumes that the pattern of relative prices within a basic
heading is same in all countries whether or not the
product is representative, which conflicts the assumption
of the EKS method.
• Includes representativity as a dummy variable.
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EKS vs. CPD
CPD METHOD:
• CPD method produces transitive PPPs to begin with
unlike EKS.
• Some statisticians consider this method to be more
transparent.
• CPD does not require direct matches because missing
prices can be estimated using regression coefficients of
the respective dummy variables based on prices
collected of the basic heading.
• Sampling errors can be estimated for the PPPs
computed using CPD.
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Conclusion
What is the best method to use for PPP
calculation?
• There is no absolute correct method for PPP.
• CPD and EKS methods give same results at basic
heading PPPs on the condition that all products have
been priced and representivity is not taken into account.
• Experiments with actual data suggest that the
differences in results are not usually significant.
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Thank you
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