ICP PPP Methods Regional Course on Price Statistics and ICP Male, Maldives 25-29 September 2005

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

2. 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

3. 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.

4. 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

5. 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

6. Properties of Price and Volume Indices Used in PPP Calculation Base country invariant Commensurability Transitivity Characteristicity Additivity

7. 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

8. 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

9. 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

10. 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

11. 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

12. 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

13. 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.

14. 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

15. EKS Method Laspeyres Type PPP: • Laspeyres between country A & B  

16. EKS Method Paasche Type PPP: • Paasche between country A & B

17. EKS Method Fisher type PPP: LAB and PAB are given equal weight in calculating FAB

18. 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.

19. 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.

20. 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.

21. EKS Method General form of EKS:

22. 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

23. 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.

24. 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

25. 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.

26. 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.

27. 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.

28. 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.

29. Thank you