Transcript Document
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ICP PPP Methods
Regional Course on Price Statistics and ICP Jakarta, Indonesia 5-9 June 2006 TIMOTHY LO
Statistician, International Comparison Program Asian Development Bank
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Outline of Presentation
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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
• • 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:
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 PPP jk should equal the corresponding direct parity PPP jk
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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 • The geometric mean of the price relatives for representative products of the first country
Paasche Type PPP
• The geometric mean of the price relatives for the products representative of second country
EKS Method
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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:
P iA The price of same product “i” in country A P iB The price of same product “i” in country B n A n B The number of products representative in country A 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:
L AB and P AB are given equal weight in calculating F AB
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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 are not transitive, hence, the EKS procedure is applied.
• Fisher satisfies the country reversal test: i.e., if the data for the two countries are interchanged, the resulting index equals the reciprocal of the original index.
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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 F price relatives between A and C and price relatives between B and C.
AB can be calculated by the direct
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: 21
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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.
CPD Method
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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 basic heading.
to obtain multilateral transitive set of PPPs for the basic heading to be close to the binary intransitive PPPs initially calculated for the • 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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