ICP PPP Methods

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• ICP PPP Methods
• Regional Course on Price Statistics and ICP
• Male, Maldives
• 25-29 September 2005
• TIMOTHY LOStatistician, International Comparison
  ProgramAsian Development Bank

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Outline of Presentation

• Introduction
• Stages in Calculation Process
• Data Requirements for PPP Calculation and
  Aggregation above the level of BH
• Properties of Price and Volume Indices Used in
  the PPP Calculation
• EKS Method PPP
• CPD Method PPP

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Introduction

• 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.

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Introduction

• Data Requirements for PPP Calculation and
  Aggregation above the level of BH
• Complete set of basic heading expenditures in
  national currencies
• 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
• Computing average annual national average prices
• Aggregating prices to basic heading level
  parities
• 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 Dij (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 Dij 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 pj and pk 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