Implementing Linking Methods and Parallel Computations

Transcription

1 Public Disclosure Authorized Public Disclosure Authorized Public Disclosure Authorized International Comparison Program 2011 Implementing Linking Methods and Parallel Computations Sergey Sergeev, Consultant losure Authorized 2/23/2017 Sergey Sergeev: Implementing Linking Methods and Parallel Computations 1

2 ICP 2011 Organization Regional principle: Asia (& Oceania) => ADB (+ ABS) Африка => AfDB Western Asia => ESCWA LAC (& Caribean) => ECLA ECP => Eurostat / OECD / CIS-STAT EU / OECD CIS Singleton countries (Georgia, Iran) Double participants (Egypt, Russia, Sudan) 2/23/2017 Sergey Sergeev: Implementing Linking Methods and Parallel Computations 2

3 Linking the regions general (1) Regional results should be linked into a global consistent set Combination of regional data sets and computation of Global results are the responsibilities of ICP GO However ICP computational procedures should be transparent ICP global results should be reproducible => Starting with the same input data, each researcher should be able to reproduce the official ICP 2011 results 2/23/2017 Sergey Sergeev: Implementing Linking Methods and Parallel Computations 3

4 Linking the regions general (2) Therefore the GO ICP decided that all computational procedures using in the global ICP 2011 should be documented in detail parallel calculations (beside the official calculations making by the GO ICP) should be carried out by several players independently This needs that : - Linking procedures should be described in detail - Some framework of the parallel calculations should be established => the main aim of this presentation 2/23/2017 Sergey Sergeev: Implementing Linking Methods and Parallel Computations 4

5 Linking as a multilateral exercise Some earlier ICP Phases - Linking via selected pairs of countries However it is desirable that each region compared directly with each other, to obtain true multilateral transitive PPPs Reg.1 Reg.6 Reg.2 Reg.5 Reg.3 Reg.4 2/23/2017 Sergey Sergeev: Implementing Linking Methods and Parallel Computations 5

6 Two approaches Ring Comparison (ICP 2005) => A common set of products (Ring List) for a sample of countries from each region ICP 2005: 6 for Africa, 4 for Asia, 4 for OECD, 2 ECLAC and 2 ESCWA Ring comparison on the basis of a small sample of countries does not guarantee the robust results which depend heavily on the choice of countries in the Ring => => ICP Global Core List A common set of products is included in all regional products lists. All countries should attempt to price these overlapped products. PPPs calculated on the basis of these price data are linking factors between regions. Regional representativity of price data and robustness of the results should be substantially increased. 2/23/2017 Sergey Sergeev: Implementing Linking Methods and Parallel Computations 6

7 Input data for Linking Prices for products from the Global Core ICP List (it is not necessary that all countries from all Regions price all items from the Global list; it is sufficient if each region has reasonable no. of price quotations) - Consumer products (601 product ) - Equipment goods (~ products) - Construction input baskets - List of occupations in GG (~50 occupations based on ISCO 88) - Rents (actual and imputed) (dwelling strata for price approach; data for Quantity approach) 2/23/2017 Sergey Sergeev: Implementing Linking Methods and Parallel Computations 7

8 Linking the regions and fixity (1) Constraint - Fixity of all regional results All intra-regional ratios (PPP, PLI, Volume indices) established in regional comparisons remain fixed in the global comparison If the methodological differences in the Regions are relatively small then there should not be big differences between the regional and global results. => One example from the ADB 2005 comparison => 8 South ADB countries 6 South-East ADB countries EKS GDP VIpc (IGD = 100) EKS GDP VIpc (MYS = 100) ADB23 ADB8 BGD BHU IND IRN MDV NPL PAK LKA ADB23 ADB6 FJI IDN MYS PHL CHN THA /23/2017 Sergey Sergeev: Implementing Linking Methods and Parallel Computations 8

9 Linking and fixity (2) However this is not so in the Global ICP: Significant differences between Regional and Global lists Different Regions use different methodologies for: Gon-market services: Productivity Adjustment for CoE (some Regions Yes; some other Go) - Education (some Regions Output approach; some other Input costs approach) - Rents (some Regions Price approach; some other Quantity approach; 3 rd regions reference Volume index) Different level of details for the regional GDP classification Different computational methods in the Regions If Fixity of Regional results is requested then it is impossible to obtain in the Global comparison full inter-regional comparability but it is necessary to attempt to reduce maximally their impact 2/23/2017 Sergey Sergeev: Implementing Linking Methods and Parallel Computations 9

10 Input data for Fixity Combination of regional data sets (in a standard classification) and linking factors Regional BH-PPPs Regional aggregated PPPs Regional aggregated Volume indices (Volume shares) BH NA data in national currencies 2/23/2017 Sergey Sergeev: Implementing Linking Methods and Parallel Computations 10

11 Linking factors Two possible computational approaches Regional approach (RA) [ICP 2005 approach] Calculation of between-regional PPPs Country s data for Linking are combined in the Regional input data sets. The calculations are done for the Regions as some Super-Countries. - Straightforward approach with explicit use of fixity of regional PPPs - Less flexible if the regional methodologies are substantial different (e.g. Productivity Adjustment in Non-market services Yes / No) Country Approach with Redistribution / Reindexation (CAR) All countries participate individually in the Global calculation. Regional results (Volumes or PPPs) from the Global comparison are redistributed / reindexed in accordance with the inter-regional ratios (Volume shares or PPPs) - Fixity of regional results is obtained by an indirect (two-stage) approach - Probably, the differences in the regional methodologies will have some lower impact on the (in)comparability of the Global results with fixity 2/23/2017 Sergey Sergeev: Implementing Linking Methods and Parallel Computations 11

12 Linking BH-PPPs (1) TAG ICP decided that at the BH level the between-regional PPPs should be calculated: (a) Country s prices submitted for the Global list are divided by the country regional BH-PPPs, to convert these into common Regional numeraire. (b) Between-regional BH PPPs "Regional numeraire / World numeraire" are calculated on the basis of price set from (a) by the weighted CP(R)D method Straightforward approach with explicit fixity of regional PPPs: PPP Country / World Gumeraire = PPP Country / Regional Gumeraire * PPP Regional Gum. / World Gum. [Reg. Comp.] [Global Comp.] 2/23/2017 Sergey Sergeev: Implementing Linking Methods and Parallel Computations 12

13 Linking BH-PPPs (2) The between-regional approach but What should be input data for the calculations? Two possible versions: (a) To use individual country s prices (submitted for the Global list and divided by the country regional BH-PPPs) - TAG ICP preference (b) To use Regional average (GM) prices (submitted for the Global list and divided by the country regional BH-PPPs) as regional sets for the calculation of between-regional BH PPPs "Regional numeraire / World numeraire 2/23/2017 Sergey Sergeev: Implementing Linking Methods and Parallel Computations 13

14 Which method to use for BH-PPP? Use of individual country s prices (pro & contra) Advantages: - Whole inter-country price variation is taken into account - Easier to treat importantce / representativity of products Disadvantages: - The Regions are treated non-symmetrically (Regions with higher no. of countries have higher impact on the CPD coefficients world prices) Use of average (GM) regional prices (pro & contra) Advantages: - Straightforward principle One Region One set of data - Symmetrical treatment of Regions Disadvantages: - A part of inter-country price variation is lost - Regional importantce / representativity of products should be defined It is desirable to compute for the analytical purposes both versions 2/23/2017 Sergey Sergeev: Implementing Linking Methods and Parallel Computations 14

15 Calculation of between-regional BH-PPP Official method => weighted CPD (2:1; 3:1; 4) Stochastic approach: weighted least squares (WLS) or as a specific kind of the GK method in geometric (log) terms R 6( r) q π i = { [ P / PPPr] ijr } 1/ r Σ q ijr ; r= 1 j= 1 M 6( r) ijr PPP r = ( [ Pijr/ πi] i= 1 j= 1 i = 1, 2,..., M q ijr ) 1/ i Σq ijr; r = 1, 2,..., N -1 (PPP R = 1) Non-official methods: EKS, EKS*, EKS-S, CPRD 2/23/2017 Sergey Sergeev: Implementing Linking Methods and Parallel Computations 15

16 BH-PPP => Practical steps (1) An fictitious example from the ICP Manual, Chapter 14 3 Regions (Region I countries A, B, C, D; Region II countries E, F, G; Region III countries H, I, J) X 10 products Original price data and within-regional PPPs Region I Region II Region III Product A B C D E F G H I J 1 2* * 20* 600* 6* * 12* 900* * * * * * * * * 6 210* * 12* * 140* * 8 120* 12* * 16 50* * * 10 40* 260* 70* 200* Withinregion PPPs /23/2017 Sergey Sergeev: Implementing Linking Methods and Parallel Computations 16

17 BH-PPP => Practical steps (2) An fictitious example from the ICP Manual, Chapter 14 Prices Deflated by Within-Region PPPs Region I Region II Region III Product A B C D E F G H I J 1 2* * 20* 20* 6* * 2.4* 30* * 9 3* 33.33* * * * * * * * * 10.77* * 2.4* * * * * 10 40* * 12.5* 2/23/2017 Sergey Sergeev: Implementing Linking Methods and Parallel Computations 17

18 BH-PPP => Practical steps (3) An fictitious example from the ICP Manual, Chapter 14 Within-regional, between-regional and global BH-PPPs Country Region Withinregion PPPs Between-regional PPPs (weighted CPD; 3:1) Linked / global set of PPPs A I (1) 1 (2) 1 (3) = (1) x (2) 1 B I C I D I E II F II G II H III I III J III /23/2017 Sergey Sergeev: Implementing Linking Methods and Parallel Computations 18

19 BH-PPP => Practical steps (4) An fictitious example from the ICP Manual, Chapter 14 Between-Regional PPP (Reg I = 1) by different methods CPD unweighted 1:1) CPD (weighted 2:1) CPD (weighted 3:1) CPD (weighted 10:1) CPRD (unweighted) EKS (without*) EKS (with*) Individual prices of the countries Average (GM) regional prices Reg I Reg II Reg III C. Non-R Reg I Reg II Reg III C. Non-R (4 Cou.) (3 Cou.) (3 Cou.) --- (4 Cou.) (3 Cou.) (3 Cou.) /23/2017 Sergey Sergeev: Implementing Linking Methods and Parallel Computations 19

20 2/23/2017 Sergey Sergeev: Implementing Linking Methods and Parallel Computations 20 Linking at the aggregated levels - EKS It was decided by the TAG that the EKS method should be used for the Global aggregation: F-PPP GEKS-F [ ] = K k K j k j k F j q q p p P P 1 1/ ),,, ( j j j j P q p Q ( ) ( ) ( ) [ ] 2 1/ 2 1/,,,,,,,,, = j k j j k k k j j k j k P j k j k L j k j k F q p q p q p q p q q p p P q q p p P q q p p P

21 EKS Global aggregation (1) Two possible approaches: Regional approach (RA) [ICP 2005 approach] Calculation of between-regional aggregated PPPs => Between-regional BH-PPPs and and country s NA data are combined in the Regional input data sets. The calculations are done for the Regions as some Super-Countries. Country Approach with Redistribution / Reindexation (CAR) All countries participate individually in the Global calculation. Regional Totals (Volumes or PPPs) from the Global comparison are redistributed / reindexed in accordance with the Regional ratios (Volume shares = CAR-Volume or PPPs = CAR-PPP) 2/23/2017 Sergey Sergeev: Implementing Linking Methods and Parallel Computations 21

22 EKS Global aggregation (2) ICP 2005 Regional approach (RA) - Regions as Super-Countries Input data: - between-regional BH-PPPs "Regional numeraire / ICP numeraire - GDP breakdowns: Regional NA Totals in regional numeraires (by PPP) EKS aggregation for 5 sets of Regional data Fixity of regional aggregated PPPs as the following: PPP Country / World = PPP Country / Region * PPP Region / World [Regional Comp.] [Inter-regional Comp.] Drawbacks of ICP 2005 RA: - Non-invariancy relatively Regional numeraires - Large countries in a region have higher impact on Reginal NA-Totals (plutocratic country s weights) 2/23/2017 Sergey Sergeev: Implementing Linking Methods and Parallel Computations 22

23 EKS Global aggregation (3) Modified ICP 2005 RA: - to use average (GM) regional numeraires instead country s regional numeraires in input data (this guarantee the invariance) - to use of average democratic regional expenditure shares instead plutocratic regional expenditure weights (this guarantee the symmetrical treatment of all countries within the Regions). The average (democratic) regional BH-shares are simple arithmetic means from national shares (percentages) of the countries belonging to this Region (all countries - large and small - will contribute equally in this case). These modifications keep the main features of the original RA ICP 2005 approach and allow to carry out all calculations in the spirit of the EKS approach consistently at all levels 2/23/2017 Sergey Sergeev: Implementing Linking Methods and Parallel Computations 23

24 Between-Regional Aggregated PPPs (3) An imaginary example: Regional expenditure shares & inter-regional BH-PPPs Region A Region B Region C BH PPP Av.Sh. PPP Av.Sh. PPP Av.Sh Total-GDP xxx 100 xxx 100 xxx 100 Matrix of PPPs by EKS-method (... currency units of row-country per 1 currency unit of column-country) Reg.A Reg.B Reg.C Reg.A Reg.B Reg.C /23/2017 Sergey Sergeev: Implementing Linking Methods and Parallel Computations 24

25 Which method to use for aggregated PPPs? Regional approach (RA) Advantages: - Consitent with the approach used for BHs - Straightforward principle One Region One set of data - Symmetrical treatment of Regions Disadvantages: - Less flexible if the regional methodologies are substantial different (e.g. Productivity Adjustment in Non-market services Yes / No) Country Approach with Redistribution / Reindexation (CAR) Advantages: -Probably, the differences in the regional methodologies will have some lower impact on the (in)comparability of the World results with fixity Disadvantages: -The results by fixity of regional PPPs and volume shares are not equal (The main aim of the ICP is GDP Volume comparison, this has priority) - Many binary F-indices for the countries from different regions will be not reliable. Should be excluded these F-indices from the EKS calculations? 2/23/2017 Sergey Sergeev: Implementing Linking Methods and Parallel Computations 25

26 Country Approach with Redistribution / Reindexation (CAR) TAG ICP decided to use the CAR approach All countries participate individually in the Global calculation Input data: - Country s BH-PPPs Country / ICP numeraire - Country s NA GDP data in a common breakdown Regional Results (Volumes or PPPs) from the Global comparison are redistributed / reindexated in accordance with the Regional ratios: CAR-Volume: Volume Country in the World = = Volume share Country in the Region * Volume Region in the World [Reg. Comp.] [Global Comp.] CAR-PPP: PPP Country / World = = PPP Country / Region * PPP Region / World [Reg. Comp.] [Global Comp.] 2/23/2017 Sergey Sergeev: Implementing Linking Methods and Parallel Computations 26

27 Principal schema of CAR-Volume Fixity of within-regional Volume Shares / VI: Regional Volumes from the Global comparison are redistributed between the countries in accordance with the Regional Volume Shares Region A Region B Region C Countries => A1 A2 Total B1 B2 B3 Total C1 C2 C3 C4 Total Volume in Global ICP Share in Regional ICP Volume (%) Fixed Volume in Global ICP /23/2017 Sergey Sergeev: Implementing Linking Methods and Parallel Computations 27

28 Principal schema of CAR-PPP Fixity of within-regional PPPs: PPPs from the Global comparison are reindexed in accordance with the intra-regional ratios Region A Region B Region C Countries => A1 A2 GM B1 B2 B3 GM C1 C2 C3 C4 GM PPP in Global ICP (C.A1=1) PPP in Regional ICP Fixed PPP in Global ICP Rescaled PPP (C.A1 =1) /23/2017 Sergey Sergeev: Implementing Linking Methods and Parallel Computations 28

29 Aggregated EKS PPP => Practical steps (1) Fictitious example from the former Ch.13 of the ICP Manual 3 Regions (A 4 cou.; B 3 cou.; C 2 cou.); 6 BHs (4 for Consumption and for Investment) Input data / Set 1: BH expenditures in national currencies Region A Region B Region C BH Countries Countries Countries = C = I Total = GDP /23/2017 Sergey Sergeev: Implementing Linking Methods and Parallel Computations 29

30 Aggregated EKS PPP => Practical steps (2) Fictitious example from the former Ch.13 of the ICP Manual 3 Regions (A 4 cou.; B 3 cou.; C 2 cou.); 6 BHs (4 for Consumption and for Investment) Input data / Set 2: Within-regional and between-regional BH-PPP BH Region A Inter- regional PPP of B on A denominate d in currencies of B.1 & A.1 Region B Inter- regional PPP of C on A denominate d in currencies of C.1 & A.1 Region C 1 2 Intra-regional PPPs Intra-reg. PPPs Intra-reg Regional basic heading PPPs linked using the inter-regional PPPs /23/2017 Sergey Sergeev: Implementing Linking Methods and Parallel Computations 30

31 Aggregated EKS PPP => Practical steps (3) Global calculations of PPPs at the GDP level INITIAL MATRIX of DIRECT BINARY FISHER's PPPs (without crucial values for L/P-ratio) (1st line: PPP =... currency units of row-country per 1 currency unit of column-country, 2nd line: L/P ratio) A1 A2 A3 A4 B1 B2 B3 C1 C2 A A A A B B B C C NUMBER of the MISSING VALUES in the Fisher's-matrix = 0 2/23/2017 Sergey Sergeev: Implementing Linking Methods and Parallel Computations 31

32 Aggregated EKS PPP => Practical steps (3) Global calculations of PPPs at the GDP level Matrix of PPPs by EKS-method (... currency units of row-country per 1 currency unit of column-country) A1 A2 A3 A4 B1 B2 B3 C1 C2 A A A A B B B C C All specific cases (like the treatment of the cases where there is no expenditure data for an aggregate or negative expenditure values) and all reference PPPs should be agreed in advance 2/23/2017 Sergey Sergeev: Implementing Linking Methods and Parallel Computations 32

33 Aggregated EKS PPP => Practical steps (4) Results are not equal but the difference is usually small CAR-Volume vs. CAR-PPP (example from former Chapter 13 of the ICP Handbook) CAR-Volume CAR-PPP Volume World Share Volume World Share Reg.A Reg.B Reg.C World CAR-Volume CAR-PPP Volume World Share Volume World Share A A A A B B B C C World TAG decision => CAR-Volume However both versions should be calculated for the analysis 2/23/2017 Sergey Sergeev: Implementing Linking Methods and Parallel Computations 33

34 Aggregated PPP => Practical steps (5) TAG decision => EKS (CAR-Volume) However the calculations by other methods are desirable for the analysis 2/23/2017 Sergey Sergeev: Implementing Linking Methods and Parallel Computations 34

35 Aggregated PPP => Practical steps (6) Coefficients of similarity of country s price structures (GDP): ADB ICP 2005 comparison 2/23/2017 Sergey Sergeev: Implementing Linking Methods and Parallel Computations 35

36 Linking (semi) Singleton Regions: possible options (Semi) singleton Regions: the CIS and the Pacific islands CIS Region EB ICP meeting, Feb 2010: The CIS region will be linked to the OECD through Russia as a bridge country. This decision means: - There will be only one set of results for Russia - the OECD results - CIS countries will be linked to OECD-Eurostat and the World through Russia (CIS comparison) as a bridge country at the BH as well as at the aggregated levels - CIS data for Global list will not go in the global calculations It is not very good that the CIS countries are linked to the World via one country (RUS) only. It would be better to have an expanded region OECD-Eurostat-CIS but it is doubtful that the OECD and Eurostat agree with the version where the Linking factor to the World for the OECD-Eurostat region depends on CIS data Pacific islands Pacific Islands price very limited list of products. Therefore they will not participate in the global computations and will be linked to the World at high aggregated level through some ADB countries and AUS (and GZ?) as the bridges. 2/23/2017 Sergey Sergeev: Implementing Linking Methods and Parallel Computations 36

37 Linking Singleton Country Georgia: possible options Singleton Country: Georgia Georgia is no longer a member of the CIS. It was agreed that Georgia is carried out a bilateral comparison with Armenia. Armenia is a member of the CIS, which is an ICP Region => the bilateral comparison GEO-ARM will allow to link Georgia to the 2011 Global comparison. Basis: CIS 2011 lists and CIS methodology In accordance with this approach, Georgian data will not be included in the global computations. Georgia will be linked to the World through Armenian results as a bridge country at the BH as well as at the aggregated levels. 2/23/2017 Sergey Sergeev: Implementing Linking Methods and Parallel Computations 37

38 Linking Singleton Country Iran: possible options (1) Singleton Country: Iran Iran is not the ADB member. A special arrangement - Turkey has accepted to be involved in a bilateral comparison with Iran aimed at linking Iran to the global result through Turkey, a participant in the Eurostat OECD PPP Program. Linking Iran to the ICP is different for different fields: For the HH: bilateral comparison IR TR based on a common IR-TR list of items (available Bulgarian price data will be used also during the validation) => Iran will be linked for HH to the World through TR as a bridge country at the BH as well as at the aggregated levels For Housing, Government Compensation, Machinery and Equipment, Construction, Health, and Education, Iran would follow the standard ICP methodology and pricing schedule 2/23/2017 Sergey Sergeev: Implementing Linking Methods and Parallel Computations 38

39 Singleton Country: Iran Linking Singleton Country Iran: possible options (2) Linking Iran to the ICP for Housing, Government Compensation, Machinery and Equipment, Construction, Health, and Education at the BH Level It is possible to link Iran to the World (without Iran) using the same procedure as for the between-regional PPPs Iran can be considered as a mini-region. This can be a kind of two-stage CPD procedure: - Calculation of between-regional PPPs and the global BH-PPPs for 5 Regions - Prices of all countries in the World for the Core List items are recalculated into the World numeraire. These country s price in the World numeraire are combined with Iranian prices in NC -Weighted CPD for two regions (World with country s prices and Iran) World numeraire is 1 and Iranian PPP relatively Word numeraire will be obtained from the CPD. All former World PPPs are not changed due to this procedure (fixity is kept). 2/23/2017 Sergey Sergeev: Implementing Linking Methods and Parallel Computations 39

40 Singleton Country: Iran Linking Singleton Country Iran: possible options (3) Linking Iran to the ICP for Housing, Government Compensation, Machinery and Equipment, Construction, Health, and Education at the aggregated Levels If there is an intention to keep the aggregated results of the bilateral comparison Iran Turkey for HH unchanged in the World comparison then the same procedure as for Georgia should be used. However Iran can be treated in the World aggregation in the same way as all other countries: -Iran has for the aggregation the same set of input data as all other countries: BH-PPPs (to a World numeraire) and BH expenditure in the standard ICP Classification. -The unrestricted GEKS is applied for all involved countries (incl. Iran). This allows to obtain Iranian Volumes (real expenditure) for the analytical categories, aggregates and GDP in the World numeraire. -Regional Volume Totals are redistributed within the Regions in accordance with the country s Regionl shares (CAR -Volume approach) -Iranian Volume is kept as it was obtained from the unrestricted GEKS 2/23/2017 Sergey Sergeev: Implementing Linking Methods and Parallel Computations 40

41 Linking Countries with double participation: possible options (1) Double participants: -Russia participates in the OECD comparison as well as in the CIS comparison. - Egypt and Sudan participate in the African comparison as well as in the Western Asia comparison. How these countries with double participation should be treated within the Global comparison? There is no actual problem with Russia. It was officially agreed that Russia will be included for the Global comparison in the EU-OECD Region. The CIS countries will have the link to the Global comparison via RF only. The situation with Egypt and Sudan need a special treatment because both Regions (Africa and Western Asia) want to include these countries in the Regional results. It is impossible to keep fixity for these countries in both Regional comparisons. Therefore some averages from both regional results should be used. 2/23/2017 Sergey Sergeev: Implementing Linking Methods and Parallel Computations 41

42 Linking Countries with double participation: possible options (2) Egypt and Sudan: BH level Option 1 The calculation of between-regional BH-PPPs with individual country s data: => Two sets of price data for Egypt and Sudan from each Region should be included in the computations of the between regional BH-PPPs by the weighted CPD: one set of prices should be recalculated in the African numeraire on the basis of the BH-PPPs from the African comparison and another set of prices in the ESCWA numeraire on the basis of the BH-PPPs from the Western Asia comparison. Respective two global will be calculated for Egypt and Sudanas the following (Egypt as an example): PPP1 Egypt / World = PPP Egypt / Africa * PPP Africa / World [Regional Comparison] [Global Comparison] PPP2 Egypt / World = PPP Egypt / ESCWA * PPP ESCWA / World [Regional Comparison] [Global Comparison] GM from PPP1 and PPP2 should be considered as global BH-PPP for Egypt: PPP Egypt / World = (PPP1 Egypt / World * PPP2 Egypt / World ) 1/2 2/23/2017 Sergey Sergeev: Implementing Linking Methods and Parallel Computations 42

43 Linking Countries with double participation: possible options (3) Egypt and Sudan: BH level Option 2 If one does not want to use double sets of prices from Egypt and Sudan in the global comparison => the unrestricted weighted CPD with individual original country s price datashould be used. The CAR-PPP can be applied to this set. Both regional average PPPs -PPP Africa / World and PPP Western Asia / World - are calculated as the GM with the inclusion of Egypt and Sudan. Respective two global PPPs with the Regional fixity in both Regions can be calculated for Egypt and Sudan during the CAR-PPP procedure as the following: PPP1 Egypt / World = PPP Egypt / Africa * PPP Africa / World [Regional Comparison] [Global Comparison] PPP2 Egypt / World = PPP Egypt / ESCWA * PPP ESCWA / World [Regional Comparison] [Global Comparison] GM from PPP1 and PPP2 should be considered as global BH-PPP for Egypt: PPP Egypt / World = (PPP1 Egypt / World * PPP2 Egypt / World ) 1/2 2/23/2017 Sergey Sergeev: Implementing Linking Methods and Parallel Computations 43

44 Linking Countries with double participation: possible options (4) Egypt and Sudan: Aggregated levels It is assumes that Egypt and Sudan have the same GA data in both Regions Option 1: CAR-Volumes: - the unrestricted GEKS method produces the country s PPPs, the GA aggregates in national currencies are recalculated by the PPPs into Volumes - Regional Volumes for both Regions Africa and Western Asia are calculated with the inclusion of Egypt and Sudan - Respectively two Volumes for Egypt and Sudan with the fixity in both Regions Volume1 Egypt = Volume Africa x Volume Sh. Egypt / Africa [Global Comparison] [Regional Comparison] Volume2 Egypt = Volume Western A. x Volume Sh. Egypt / Western A. [Global Comparison] [Regional Comparison AM from Volume1 and Volume2 should be considered as Volume in the Global comparison for Egypt and Sudan (global PPP indirectly as Exp_Ind / V_Ind) : Volume Egypt = (Volume1 Egypt + Volume2 Egypt ) / 2 2/23/2017 Sergey Sergeev: Implementing Linking Methods and Parallel Computations 44

45 Linking Countries with double participation: possible options (5) Egypt and Sudan: Aggregated levels It is assumes that Egypt and Sudan have the same GA data in both Regions Option 2: CAR-PPP: - the unrestricted GEKS method produces the country s PPPs - Both regional average PPPs Africa / World and Western Asia / World are calculated as the GM with the inclusion of Egypt and Sudan. - Respectively two PPPs for Egypt and Sudan with the fixity in both Regions PPP1 Egypt / World = PPP Egypt / Africa * PPP Africa / World [Regional Comparison] [Global Comparison] PPP2 Egypt / World = PPP Egypt / ESCWA * PPP ESCWA / World [Regional Comparison] [Global Comparison] GM from PPP1 and PPP2 should be considered as PPP in the Global comparison for Egypt and Sudan: PPP Egypt / World = (PPP1 Egypt / World * PPP2 Egypt / World )1/2 2/23/2017 Sergey Sergeev: Implementing Linking Methods and Parallel Computations 45

46 Thank you for your attention! 2/23/2017 Sergey Sergeev: Implementing Linking Methods and Parallel Computations 46