Linking and Calculation of Global Results

Transcription

1 Chapter 26 Lnkng and Calculaton of Global Results Ths chapter descrbes the steps and procedures used to calculate global purchasng power partes (PPPs) n the 2011 round of the Internatonal Comparson Program (ICP). The steps and procedures were recommended by the ICP's Techncal Advsory Group (TAG). To calculate the global PPPs, the ICP regons and the Eurostat Organsaton for Economc Co-operaton and Development (OECD) PPP Programme provded for the economes n ther regons the followng nputs: Global core lst (GCL) tem prces n natonal currency Wthn-regon PPPs at the basc headng (BH), aggregate, and analytcal category levels (hereafter referred to as regonal PPPs) followng the ICP Classfcaton Natonal accounts expendtures at the basc headng level n natonal currency The 2011 annual average exchange rates to the U.S. dollar and populaton data. The frst two sectons that follow descrbe the lnkng steps for the standard lnkng approach. The next secton deals wth the nonstandard lnkng approaches and specal partcpaton cases. The standard ICP regons n ICP 2011 were Afrca, Asa and the Pacfc, Latn Amerca, and Western Asa, as well as the Eurostat-OECD regon. Specal partcpaton cases were the two sngleton economes, the Islamc Republc of Iran and Georga; the Commonwealth of Independent States (CIS); the Carbbean; Cuba; the Pacfc Islands; and the dual-partcpaton economes: the Russan Federaton, the Arab Republc of Egypt, and Sudan. Lnkng at the Basc Headng Level Regonal BH PPPs were calculated usng ether the Éltetö-Köves-Szulc* (EKS*) method (Eurostat- OECD and CIS regons) or the weghted country product dummy (CPD-W) 1 method (other ICP regons except Asa and the Pacfc, whch used the unweghted country product dummy [CPD] method). Interregonal lnkng factors were calculated usng the CPD-W method. In ths method, explct weghts of 3:1 were used to weght the mportant tems and the less mportant ones. Calculaton of the BH PPPs n the global comparson nvolves four steps: Step A1. Calculate the regonal BH PPPs based on both the regonal and GCL tems, usng ether the EKS* method or the CPD-W method. 2 BH PPPs must follow the ICP BH classfcaton. When a regon s not followng the ICP BH classfcaton, 3 calculate the BH PPPs accordng to ths classfcaton by aggregatng the BH PPPs usng the respectve natonal accounts expendtures. Step A2. Convert all GCL tem prces n natonal currency for the economes n a regon nto a 455

2 common regonal numérare usng the economy's regonal BH PPPs from step A1. Step A3. Usng the CPD-W method, process the converted GCL tem prces for all regons resultng from step A2 to generate the nterregonal lnkng factors for the basc headngs. These nterregonal lnkng factors are nterregonal BH PPPs, expressed n the regonal numérares to the world numérare. Step A4. To calculate the global economy's PPPs to the world numérare and ensure fxty of an economy's regonal BH PPPs n the global comparson, multply each economy's regonal BH PPP from step A1 by the nterregonal lnkng factor resultng from step A3. The PPPs derved from ths step are the global BH PPPs wth regonal fxty. Lnkng at the Aggregate Level The Gn-Éltetö-Köves-Szulc (GEKS) 4 aggregaton method, wth further redstrbuton of regonal s n accordance wth an economy's regonal shares (known as the country aggregaton wth redstrbuton procedure, CAR-), was used to obtan real expendtures (hereafter referred to as s) and ndrect aggregated PPPs wth regonal fxty. All economes n the standard ICP regons partcpated smultaneously and equally n the global aggregaton usng the GEKS method. The steps for lnkng at the aggregate levels are the followng: Step B1. Calculate the regonal PPPs by applyng the GEKS 5 aggregaton to the regonal BH PPPs from step A1 and the BH natonal accounts data derved n accordance wth the regonal fxty schema. 6 Economy regonal s are derved as nomnal values n natonal currency dvded by the regonal aggregated PPPs. 7 Step B2. Obtan an economy's shares n the regonal results for each level of aggregaton up to the gross domestc product (GDP) usng data from step B1. These data for aggregated headngs and ICP analytcal categores were suppled by the regons. Step B3. Calculate an economy's aggregated PPPs n the global comparson by applyng the unrestrcted GEKS aggregaton to the global BH PPPs derved from step A4 and the natonal accounts BH expendtures n natonal currency for each level of aggregaton up to GDP. The startng pont s a matrx of 150- plus global BH PPPs for 140-plus economes from the standard ICP regons and another matrx of the same sze contanng BH natonal accounts expendtures n natonal currency. Economy s n the global unrestrcted comparson n a global numérare are derved as nomnal values n natonal currency dvded by the aggregated PPPs from the unrestrcted global comparson. Step B4. Obtan the regonal totals n the global comparson by summng up the total s for ndvdual economes for each regon derved from step B3 for each level of aggregaton up to GDP. Step B5. Dstrbute the regonal totals from step B4 among the economes n the regons accordng to the economy shares n the regonal results derved from step B2 n order to uphold regonal fxty for each level of aggregaton up to GDP. Step B6. Calculate the aggregated global PPPs' natonal currency/world numérare ndrectly by dvdng economes' nomnal expendtures by the s derved from step B5 for each level of aggregaton up to GDP. Specal Cases In ICP 2011, n two categores of specal lnkng cases the lnkng approach dffered from the one just descrbed. The frst category covered nonstandard survey methodologes; the second covered nonstandard regonal or economy partcpaton. Nonstandard Lnkng Approaches Housng All economes partcpatng n ICP 2011 were asked to collect annual average rents for a global lst of dwellng types and dwellng stock data: number of dwellngs, usable surface area n 456 Operatonal Gudelnes and Procedures for Measurng the Real Sze of the World Economy

3 square meters, and nformaton on three qualty ndcators avalablty of electrcty, water supply, and n-house tolet. Natonal accounts expendture data on actual and mputed rentals were collected by means of expendture questonnares. However, not all economes were able to report rents and dwellng stock data, and some economes were only able to provde rents for a lmted subset of dwellng types or lmted dwellng stock data. Each regonal coordnatng agency then decded on the best way to use the collected data for ts regon: The Afrca, Latn Amerca, Carbbean, and Western Asa regons calculated ther regonal PPPs on the bass of the rents collected for the global lst of dwellng types, relyng on the same CPD method used for the rest of household consumpton but wthout the mportance ndcators. The Asa and the Pacfc regon, after n-depth analyss of the avalable data, resorted to usng a reference approach and the respectve ndrect PPPs. Ths mples that the relatve s of housng servces between economes were equal to the relatve s of household expendture, excludng rents. The Eurostat-OECD regon used a mx of rents and dwellng stock data. Generally, for economes that have a well-developed rental market that s, those economes that use the stratfcaton method for rents n natonal accounts PPPs were determned on the bass of the rental data, whereas for other economes dwellng stock data were used to obtan estmates of PPPs ndrectly that s, for those economes that were usng the cost approach for rents n natonal accounts. Indrect PPPs are based on the relatonshp prce quantty expendture. An ndrect PPP can be derved by dvdng the expendture on rents from an economy's natonal accounts by the real expendture on rents estmated usng dwellng stock data adjusted for qualty. Ths s known as the quantty approach of estmatng real expendtures drectly and the PPPs ndrectly. The quantty approach was used n the CIS regon, whch was then lnked to other regons usng Russa, a member of the OECD comparson, as the brdge economy. The rental data used to lnk the Afrca, Latn Amerca, and Western Asa regons were the same as those that entered the calculaton of ther regonal PPPs. The lnkng factors for these three regons were calculated by means of the same CPD method used for the lnk of the rest of household expendtures. The Asa and the Pacfc and the Eurostat- OECD regons were lnked to each other and to the rest of the world by the quantty approach through use of the dwellng stock data. The plausblty of each economy's estmate of number of dwellngs was evaluated by calculatng the rato of the number of dwellngs to the total populaton. Economes wth very hgh or very low ratos were not ncluded n the lnkng process. For each economy wth a plausble estmate of number of dwellngs, the data on housng qualty were revewed. Three qualty ndcators were avalable: share of dwellngs wth electrcty, share of dwellngs wth nsde water, and share of dwellngs wth a prvate tolet. Only economes for whch a plausble estmate for all three ndcators was avalable or could be conscously mputed were ncluded n the lnkng process. Government Compensaton Adjustments for productvty dfferences were taken nto account n some regonal comparsons as well as n the global lnkng. Adjustments were made to the PPPs and respectvely to the real expendture estmates for government n the Afrca, Asa and the Pacfc, Latn Amerca, and Carbbean regons. No productvty adjustments were appled to the Eurostat-OECD, CIS, and Western Asa regons because dfferences n labor productvty wthn each of those regons were consdered not very hgh. However, productvty adjustments were made to all regons when the nterregonal lnkng factors were estmated to mantan consstency n the global comparson. For educaton, the Eurostat-OECD regon appled an output approach n whch s are based on numbers of students and average student scores from the Programme for Internatonal Student Assessment (PISA). Wthn-regon PPPs were lnked to the rest of the world usng fve Latn Amercan economes Brazl, Colomba, Panama, Peru, Lnkng and Calculaton of Global Results 457

4 and Uruguay that had data for both the nput approach used by ICP regons and the Eurostat-OECD output approach. The specfc lnkng steps were as follows: Global educaton basc headng PPPs 8 for the standard ICP regons, excludng Eurostat- OECD, were obtaned by multplyng regonal PPPs by the productvty-adjusted lnkng factors. The global basc headng PPPs for the standard ICP regons, excludng Eurostat-OECD, were aggregated usng the GEKS method to obtan the total educaton PPPs. The total educaton lnkng factor for the Eurostat-OECD regon was calculated va fve Latn Amercan economes for whch the output approach was feasble as the rato of the geometrc mean of PPPs from the output approach to the geometrc mean of PPPs from the nput approach. The result was the total educaton lnkng factor for each regon. For global aggregaton coverng all fve standard regons, the sx basc headngs under the ndvdual government consumpton expendture for educaton were collapsed nto one. The result was one basc headng under household consumpton expendture and one headng under ndvdual government consumpton expendture. 9 The global aggregaton resulted n lnked global PPPs, mantanng regonal fxty for all regons. For health, the Eurostat-OECD comparson appled an output approach for government health provders (hosptals) to ts regonal comparson, whch was based on quas-prces for a set of hosptal servces. Basc headng weghts from the health accounts were used for the health PPP aggregaton. For lnkng, Eurostat- OECD provded nput data for government health provders based on the former nput cost approach. Input data for the other health basc headngs were dentcal to those produced by the standard ICP method. 10 However, when fxty of regonal results was appled n the country aggregaton wth redstrbuton (CAR) procedure, the fxty preserved was that of the aggregate analytcal categores resultng from the current health approach used by the Eurostat-OECD comparson. Constructon and Cvl Engneerng The standard ICP 2011 approach for estmatng constructon and cvl engneerng PPPs covered four separate but consecutve steps: Input prces collected for materals, labor, and hre of equpment were allocated to the three constructon category basc headngs (resdental buldngs, nonresdental buldngs, and cvl engneerng works) usng product relevancy nformaton. PPPs for the nput groups (materals, labor, and equpment), or subheadngs under the three basc headngs, were calculated usng the CPD, resultng n nne sets of subheadng PPPs. The subheadng PPPs were aggregated usng resource mxes as weghts, resultng n three sets of basc headng PPPs. PPPs for the three basc headngs were aggregated usng natonal accounts expendture data as weghts, resultng n PPPs for the constructon category. The Eurostat-OECD approach to estmatng constructon and cvl engneerng PPPs dffers from the ICP approach, 11 and thus several economes n the Eurostat-OECD comparson conducted the ICP survey, whch provded a lnk for constructon between the Eurostat-OECD economes and the rest of the world. Because of the peculartes of the avalable nput data, a modfed approach was used for lnkng: Prces collected for the machnery and equpment tems were used to calculate reference PPPs for the equpment hre subheadng at the global level. Regonal GCL prces n local currency were used to calculate lnkng factors nstead of prces converted to a common regonal numérare wth the regonal PPPs, as s done n the standard lnkng approach. More concretely, economes' PPPs were calculated by applyng the unrestrcted, unweghted CPD method. Lnkng factors for the basc headngs were calculated as the geometrc mean of the subheadng PPPs for the economes n a regon. 12 Nonstandard Partcpaton Followng TAG's recommendaton, the two sngleton economes (the Islamc Republc of Iran and Georga), the CIS economes, the Carbbean 458 Operatonal Gudelnes and Procedures for Measurng the Real Sze of the World Economy

5 economes, Cuba, and the Pacfc Islands were ncluded n the global lnkng process n a way that had no effect on the multlateral PPPs for all other economes n the global comparson. Ths was acheved by the specal lnkng approaches, as explaned n the sectons that follow. Sngleton Economes: The Islamc Republc of Iran and Georga PPPs for the Islamc Republc of Iran (IRN) and Georga (GEO) were calculated by means of a blateral comparson wth Turkey (TUR), a partcpant of the Eurostat-OECD comparson, and Armena (ARM), a CIS economy, respectvely. The Islamc Republc of Iran s thus lnked n the global comparson through Turkey's results and Georga through Armena's results. The Eurostat-OECD tem lst was used as the bass for the IRN-TUR comparson, 13 and the CIS 2011 lst was used as the bass for the GEO-ARM comparson. 14 Natonal annual average prces for the Islamc Republc of Iran and Georga were computed based on the prce surveys. These prces were used for the calculaton of blateral IRN-TUR and GEO-ARM BH PPPs. Blateral PPPs for the Islamc Republc of Iran and Georga were brdged to the global comparson usng Turkey's and Armena's results n the global comparson, whch were derved usng the "standard" approach descrbed earler. Calculaton of the blateral BH and aggregated PPPs requres the followng steps: Step C1. Use the Eurostat-OECD tem lst as the bass for the IRN-TUR comparson. Reclassfy the tems from the Eurostat lst prced by the Islamc Republc of Iran and Turkey to follow the ICP BH classfcaton. 15 Carry out a smlar procedure for the GEO- ARM comparson. Step C2. Calculate blateral PPPs for the IRN- TUR and GEO-ARM comparsons on the bass of the natonal annual average prces n natonal currency from step C1 usng the EKS* method. 16 Turkey s the numérare n the IRN-TUR blateral comparson (.e., Turkey's PPPs equal 1). Smlarly, Armena s the numérare n the GEO-ARM blateral (.e., Armena's PPPs equal 1). Step C3. Aggregate the blateral BH PPPs for the IRN-TUR and GEO-ARM comparsons usng the GEKS procedure for each level of aggregaton up to GDP and for ICP analytcal categores. Turkey s the numérare n the IRN-TUR comparson, and Armena s the numérare n the GEO-ARM comparson. The followng steps are needed to lnk the blateral aggregated PPPs (from step C3) for the Islamc Republc of Iran and Georga to the global comparson: Step D1. Obtan the BH and aggregated PPPs for the Islamc Republc of Iran and Georga n the global comparson by usng Turkey's and Armena's fnal PPPs from step B6 n the global comparson (after the CAR- redstrbuton) as a brdge to the Islamc Republc of Iran's and Georga's PPPs from step C3. The Islamc Republc of Iran's global PPP s thus the blateral PPP wth Turkey multpled by Turkey's global PPP n the global comparson (world 1). Georga's global PPP s the blateral PPP wth Armena multpled by Armena's global PPP n the global comparson (world 1). Step D2. Calculate s for the Islamc Republc of Iran and Georga by dvdng the nomnal expendtures n natonal currency by the PPPs obtaned from step D1. For the Islamc Republc of Iran, the lnkng method just descrbed was possble for the GDP components for whch the brdge economy, Turkey, followed the same comparson approach. An alternatve lnkng method was requred for housng and constructon and cvl engneerng because Turkey followed the Eurostat approach, whereas the Islamc Republc of Iran followed the ICP approach. For these components, the Islamc Republc of Iran was lnked through economes usng the ICP housng and constructon and cvl engneerng surveys. Commonwealth of Independent States The CIS economes were lnked to the global comparson va Russa. Russa partcpated n both the CIS and Eurostat-OECD comparsons. Because of the need for regonal fxty, whch s mpossble for dual partcpants, n accordance wth an agreement the results for Russa from the Eurostat-OECD comparson were used as offcal results. The CIS economes, except Lnkng and Calculaton of Global Results 459

6 Russa, were excluded from the calculaton of the nterregonal lnkng factors. The followng steps are requred to calculate the regonal and aggregate level PPPs: 17 Step E1. Calculate the PPPs for the CIS on the bass of the natonal annual average prces n natonal currency usng the EKS* method. For nonstandard ICP BHs, aggregate the specfc CIS BH PPPs usng the EKS procedure, wth the respectve natonal accounts expendtures as weghts, to follow the ICP BH classfcaton. Russa s the numérare (.e., Russa 1). Step E2. Calculate the aggregated PPPs for the CIS by applyng an unrestrcted GEKS aggregaton to the BH PPPs obtaned from step E1 for each level of aggregaton up to GDP. The followng steps are requred to lnk at the aggregate level: Step F1. Obtan the BH and aggregated PPPs for the CIS economes n the global comparson by usng as a brdge Russa's PPPs from step B6 n the fnal global comparson, after the CAR- redstrbuton s used as a brdge. Global PPPs for the CIS economes are thus ther PPPs from the CIS comparson (Russa 1) multpled by Russa's global PPPs n the global comparson (world 1). Step F2. Calculate the s for the CIS economes by dvdng the nomnal expendtures n natonal currency by the PPPs obtaned from step F2. The Carbbean The Carbbean was lnked to the global comparson va the Latn Amercan economes. As an ntal step, the 22 Carbbean economes were lnked to the 16 Latn Amercan economes at the basc headng level. Lnkng at the basc headng level was carred out by calculatng separate sets of CPD-W PPPs for Latn Amerca and the Carbbean, by subsequently calculatng a combned set of respectve PPPs, and fnally by rendexng the combned set of PPPs n accordance wth the ntraregonal results (the CAR-PPP approach 18 ) n order to mantan fxty of both the Latn Amerca and Carbbean basc headng PPPs. Lnkng at the aggregate level was carred out usng the CAR- approach. The GEKS aggregaton was carred out frst for Latn Amerca and the Carbbean separately and then for the combned set of data. Fnally, subregonal totals of real expendtures were redstrbuted n accordance wth the economes' real expendture shares from separate Latn Amerca and the Carbbean aggregatons n order to mantan fxty of both the Latn Amerca and the Carbbean results at all aggregate levels. As for the standard ICP regons, the aggregated PPPs were calculated ndrectly by dvdng the nomnal expendtures by the real expendtures. Ths approach enabled regonal lnkng of the Carbbean economes, usng the Latn Amercan economes as a base, whle mantanng base economy nvarance and fxty of results for both subregons. As a second step, the Carbbean results were lnked to the global comparson usng Latn Amerca's global results as a brdge. Cuba Cuba was lnked to the Latn Amerca comparson va Peru for household consumpton, government compensaton, machnery and equpment, and constructon. For housng, Cuba was lnked va Repúblca Bolvarana de Venezuela, whch had a typcal housng ndex per capta for the Latn Amerca comparson as well as the dwellng stock quantty and qualty data needed for the blateral comparson. The prce and expendture data used for Cuba n the calculatons were expressed n convertble pesos. The lnkng steps for the PPPs were smlar to those descrbed for the Islamc Republc of Iran and Georga. 19 The Pacfc Islands The Pacfc Islands partcpated n ICP 2011 on a lmted bass. Twenty slands provded prce data on some 87 household consumpton tems. No specfc natonal accounts actvtes were conducted, but there was an opportunty to use exstng household ncome and expendture survey (HIES) data for the purpose of complng consumpton data. The Pacfc Islands were brdged to the ICP va economes partcpatng n other regons: Fj partcpated n both the Asa and the Pacfc and the Pacfc Islands comparsons. New Zealand and Australa partcpated n both the OECD and ICP Pacfc Islands comparsons. 460 Operatonal Gudelnes and Procedures for Measurng the Real Sze of the World Economy

7 The weghted geometrc mean of PPPs to the brdge economes was used n the lnkng (the weghts were Fj, 0.5; Australa and New Zealand, 0.25) n order to have symmetry between Asa and the Pacfc and the OECD n regonal nfluence. Dual Partcpaton In ICP 2011, Russa partcpated n both the CIS and Eurostat-OECD comparsons. To preserve the fxty of Russa's results wthn the Eurostat- OECD regon, t was agreed that for the global comparson Russa would be ncluded only n the Eurostat-OECD regon. Thus Russa's dual partcpaton dd not pose any computatonal ssues. Egypt and Sudan requred specal treatment because both the Afrca (AF) and Western Asa (WA) regons ncluded these economes n ther regonal results. Because t was not possble to mantan fxty for these economes n both regonal comparsons, a suggested approach was to use geometrc averages from the regonal results as was done for Egypt n the 2005 round of the ICP. Two sets of prce data for Egypt and Sudan for each regon were ncluded n the computatons of the nterregonal BH PPPs (lnkng factors) usng the CPD-W method. One set ncluded ther GCL prces expressed n the AF numérare on the bass of the BH PPPs from the AF comparson. Another set ncluded ther GCL prces expressed n the WA numérare on the bass of the BH PPPs from the WA comparson. The use of these two sets was logcal n the regonal approach because both economes partcpated n both comparsons, and all nterregonal PPPs should be based on nput data from both regonal comparsons for Egypt and Sudan. The global PPPs from regons were calculated for Egypt and Sudan usng the standard approach as follows: PPP 1 "Egypt/ PPP "Egypt/ AF" PPP "AF/ [nterregonal lnkng factor] The geometrc means of PPP 1 and PPP 2 were consdered fnal global BH PPPs for Egypt: PPP "Egypt/ (PPP 1 "Egypt/ PPP 2 "Egypt/ ) 1/2 The same procedure was carred out for Sudan: PPP 1 "Sudan/ PPP 2 "Sudan/ PPP "Sudan/ AF" PPP "Sudan/ WA" PPP "AF/ [nterregonal lnkng factor] PPP "WA/ [nterregonal lnkng factor] The geometrc means of PPP 1 and PPP 2 were consdered fnal global BH PPPs for Sudan: PPP "Sudan/ (PPP 1 "Sudan/ PPP 2 "Sudan/ ) 1/2 Ths was a symmetrcal way to nclude Egypt and Sudan n the global comparson at the basc headng level on the bass of nput data from both regons. The CAR- approach was used for the global lnkng at the aggregate level. Therefore one set of nput data for each economy n queston was used n the unrestrcted GEKS method to avod these economes havng a double mpact on the global lnkng through use of the CAR- approach. Egypt and Sudan had the same natonal accounts expendture data n both regons. BH-PPPs were derved as descrbed earler. Aggregated PPPs for Egypt and Sudan from the unrestrcted global GEKS were used n the further computatons. Regonal s for both regons, AF and WA, were calculated wth the ncluson of Egypt and Sudan, and two s from both regons were calculated for Egypt and Sudan usng the standard procedure. Aggregated s for Egypt and Sudan were then obtaned as follows: PPP 2 "Egypt/ PPP "Egypt/ WA" PPP "WA/ [nterregonal lnkng factor] 1 "Egypt" "AF" share "Egypt/AF" Lnkng and Calculaton of Global Results 461

8 2 "Egypt" 1 "Sudan" 2 "Sudan" "WA" "AF" "WA" share "Egypt/WA" share "Sudan/AF" share "Sudan/WA" Geometrc means from 1 and 2 were consdered s n the global comparson for Egypt and Sudan: "Egypt" "Sudan" ( 1 "Egypt" ( 1 "Sudan" 2 "Egypt") 1/2 2 "Sudan") 1/2 The ndrect global PPPs for Egypt and Sudan were derved after ths n the standard way as PPPs expendtures n natonal accounts/ s. 462 Operatonal Gudelnes and Procedures for Measurng the Real Sze of the World Economy

9 Annex A Weghted Country Product Dummy Method The weghted country product dummy (CPD-W) method uses explct weghts. 20 Representatve/mportant tems receve hgher weghts, such as 2 or 3, than the weghts, such as 1, assgned to nonrepresentatve/less mportant tems. 21 The unweghted orgnal country product dummy (CPD) derves estmators of regresson parameters (26A.1) through mnmzaton of the squares n logarthmc terms usng a standard least squares procedure: j 2 ln ( plj ) j n k ; 1 j 1 l 1 (26A.1) α 0; β 0. n r c α β j1 1 Representatve/mportant tems and nonrepresentatve/less mportant tems receve the same weght, 1, n the unweghted CPD. The CPD-W approach suggests that each prce correspondng to a product n a gven economy n a regon be gven a prespecfed weght n the least squares estmaton dependng on the representatvty/mportance of the product. Suppose w s a set of weghts for representatve/mportant (w repr ) and nonrepresentatve/less mportant (w nonrepr ) tems to be appled to the prce p lj (Rao 2004). The weghted least squares (WLS) approach appled to (26A.1) can then be presented as j 2 w ln ( plj ) j n k ; 1 j 1 l 1 (26A.2) ' α 0; β 0. n r c α β j1 1 ' It s often declared that the advantage of the stochastc CPD approach s that t allows one to derve standard errors for the CPD estmates of PPPs, common prces, and so forth. 22 However, t s not easy to mplement these standard errors n the analyss because there are numerous problematc ponts. 23 In effect, standard errors of the CPD parameters are not used n the ICP. Therefore, to make the CPD method more transparent and understandable for a broad array of users, the CPD-W method s presented n the equatons that follow n a more tradtonal ndex form specfc to the Geary-Khams (GK) method n geometrc (logarthmc) terms (Dewert 2002; Sergeev 2004): 1/ r q R Nr jr ( ) q jr π Pjr/ PPPr ; r 1 j 1 1,2,, M and PPPr where 1/ q M Nr jr ( ) qjr [ Pjr/ π ] ; 1 j 1 r 1,2,, R 1( PPP 1) R (26A.3) (26A.4) p s the nternatonal average prce of tem n the currency of the numérare regon (here regon R); p s an analogue of a from the CPD regresson; PPP r s the PPP of regon r relatve to the base regon R (PPP R 1); PPP r s an analogue of b r from the CPD regresson; R s the number of regons; N(r) s the number of economes n regon r; M s the number of products wthn a basc headng; P jr s the prce for product n economy j from regon r n the regonal numérare (by economy's regonal PPPs); q jr s the weght for product n economy j from regon r the approprate values can be 3 (for mportant products) and 1 (for less mportant products); rsq jr s the cumulatve value of the mportance of tem among all economes n all regons; and Sq jr s the cumulatve value of the mportance of tems prced n all economes of regon r. The average "nternatonal prce" of the -th tem (p ) s presented as an mplct quanttyweghted geometrc average of the PPP-adjusted natonal prces (ndcators of mportance are used as weghts). 24 The PPP for the j-th regon (PPP j ) s presented as the geometrc average (mplct expendture weghted) devaton of ts regonal prces from the nternatonal prces. Lnkng and Calculaton of Global Results 463

10 The system shown n (26A.3) and (26A.4) can be effcently solved by an teratve method. 25 The geometrc mean of the prce ratos or smply the exchange rates of the economy selected as the base can be used as an ntal set of unknown PPPs. Annex B Usng the GEKS Method for Aggregaton The Gn-Éltetö-Köves-Szulc (GEKS) method was recommended by the ICP's Techncal Advsory Group for calculatng aggregatons wthn the regons as well as for the global comparson. 26 All calculatons by the GEKS method are carred out for each aggregated headng separately. Frst, calculate the blateral Fsher PPPs (F-PPPs) 27 for all pars of economes. For any two economes j and k, the bnary F-PPP (prce ndex) s computed as P Fjk, pq j k pq k k j k pq pq j j 1/2. (26B.1) Second, average geometrcally all drect and ndrect F-PPPs (equally, all F-PPPs of economy j to all other economes) to obtan the transtve GEKS-PPPs. The GEKS-PPP s computed as PGEKS PF / P jk, j, l F k, l, (26B.2) l 1/K where K s the total number of economes. The respectve s calculated as j j j j Q p q / P. (26B.3) Economes wthn and across regons can be very dfferent. The blateral ndexes for the economes wth dfferent prce and quantty structures can be unrelable. 28 In ths aspect, analyss of the Paasche-Laspeyres spread (PLS) s very mportant for detals, see Vogel (2013). Annex C The Country Aggregaton wth Redstrbuton (CAR) Method of Lnkng above the Basc Headng Level The Techncal Advsory Group of the Internatonal Comparson Program (ICP) recommended that the country aggregaton wth redstrbuton (CAR-) approach 29 serve as the offcal ICP 2011 method (Sergeev 2011). In ths method, the unrestrcted global Gn- Éltetö-Köves-Szulc (GEKS) purchasng power partes (PPPs) for the aggregates are used to recalculate the economy aggregates n natonal currences (NCs) nto s (real expendture) measured n a world numérare. Economy s are summed up by the regon, and these regonal s are redstrbuted n accordance wth the economy shares of s n the regonal comparsons to preserve the regonal fxty: "economy n the "regon n the share "economy/ regon" Because the ndcator share of an economy wthn the regon can be also consdered the ndex "economy/regon" and the share of a regon wthn the world total can be consdered the ndex "regon/world," ths procedure can also be presented n the form of ndexes (VIs): VI "economy/ VI "regon/ VI "economy/ regon" The respectve PPPs (wth fxty) are calculated n an ndrect way as PPPs "natonal currency/ world numérare" Notes expendtures n NC/s. 1. Annex A descrbes the CPD-W method. 2. These PPPs were suppled by the regons. 3. When dfferent, the regon-specfc and ICP BH classfcatons have herarchcal relatons. Therefore regon-specfc basc headngs can be aggregated to the ICP basc headng usng the Gn- Éltetö-Köves-Szulc (GEKS) procedure (wth natonal accounts expendture weghts). For example, f the regonal 464 Operatonal Gudelnes and Procedures for Measurng the Real Sze of the World Economy

11 classfcaton has three separate basc headngs for coffee, tea, and cocoa, but the ICP Classfcaton has only one combned basc headng, t s possble to run the GEKS procedure for these three basc headngs n order to obtan the regonspecfc PPPs for the ICP basc headng coffee, tea, and cocoa. In addton, n ICP 2011 treatment of nonproft nsttutons servng households (NPISHs) had some specfctes. NPISH expendtures were dstrbuted among the respectve household consumpton expendture categores n the global comparson. However, to mantan regonal fxty, the fnal lnkng steps were carred out usng expendtures as per the regonal practce for dstrbuton. 4. Annex B descrbes the GEKS method. 5. The GEKS method was recommended by TAG for the aggregaton wthn the regons as well as for the global comparson. However, t s lkely that the dfferences n the regonal methodologes and the classfcatons wll have some margnal mpact on the (n)comparablty of the global results wth fxty. 6. For example, the Eurostat-OECD program used fxty for the 37 economes n ts comparson. 7. These PPPs were suppled by the regons. 8. In total seven basc headngs, of whch one was under the household consumpton expendture, and the remanng sx were under the ndvdual government consumpton expendture. 9. An equal way would be use of the same PPPs for the educaton total of all educaton BHs. 10. Much of the former data were used n the Eurostat-OECD approach for example, all prces of pharmaceutcals, medcal products, and outpatent medcal servces by prvate provders were used for the respectve basc headngs. The mpact of the new approach on GDP PPPs was generally not very hgh. 11. The CIS apples a dfferent regonal approach, however. The CIS economes were lnked va Russa n the Eurostat-OECD exercse. 12. Ths approach s smlar to the country approach method wth the rendexaton of PPPs (CAR-PPP). See note 33 n annex C for further nformaton. 13. The BH classfcaton used n the Eurostat- OECD comparson dffers from the ICP BH classfcaton. 14. The CIS BH classfcaton s based on the Eurostat-OECD classfcaton, but t has a few dfferences. 15. Because natonal accounts expendture data for the Islamc Republc of Iran are avalable only for the ICP BH classfcaton, the ICP BH PPPs are calculated by reclassfyng the tems rather than by aggregatng the BH PPPs. 16. The EKS* method was selected because t s the offcal PPP calculaton method of the Eurostat-OECD and CIS programs. 17. These PPPs were provded by the regon. 18. See note 33 n annex C for further nformaton on the CAR-PPP approach. 19. Volumes were not calculated for Cuba because of peculartes n the natonal accounts expendture data. 20. The verson used n regonal lnkng an economy's prces n regonal numérares as an nput bass s presented here. Ths annex s based on Sergeev (2011), wth nputs from Yur Dkhanov. 21. The weghts 3 and 1 were recommended by the ICP's TAG. The weghts 1 and 0 are applcable to the EKS* method 1 for representatve tems wth an astersk (*) and 0 for nonrepresentatve tems wthout an astersk. The weghts are not applcable, however, to the CPD method because the tems wth 0 weghts are tems not prced, and they are elmnated from the calculatons. 22. It s unclear how the stochastc estmatons should be used n practce. In addton, the estmatons of errors depend on the regresson specfcaton. 24. Theoretcally, quantty weghts should be used here, but ths nformaton s not avalable. 25. The numercal results by (26A.3) and (26A.4) are dentcal to the results by (26A.1) and (26A.2). 26. Ths annex s based on Sergeev (2011) wth nputs from Yur Dkhanov. 27. The same can be appled to the / quantty ndexes because the Fsher ndex s Lnkng and Calculaton of Global Results 465

12 relatvely symmetrcal to varables (prces and quanttes). The product of PPP(F) and Q(F) s the expendture rato. In prncple, each blateral ndex (e.g., Tornqvst) can be used n the GEKS procedure. The Fsher ndexes, but not the Törnqvst ndexes, are used tradtonally because the product of PPP(T) and Q(T) s not equal to the expendture rato. 28. The so-called selectve GEKS procedure can be used to elmnate the mpact of "weak" blateral lnks. In accordance wth ths, blateral F-PPPs wth a hgh PLS and a PLS of less than 1 are elmnated and replaced by ndrect PPPs calculated va a thrd economy. Such an approach was used durng the lnkng of Group I and II n the 1993 round of the European Comparson Program. For detals, see Unted Natons Economc Commsson on Europe (1997). 29. Ths method s descrbed n chapter 15 of the ICP 2005 Methodologcal Handbook as calculaton of the regonal lnkng factors (betweenregon PPPs) by the weghted harmonc mean method (World Bank 2007). It s also possble to use the country approach method wth the rendexaton of PPPs (CAR-PPP method), n whch regonal PPPs from the global comparson are combned wth the economy's regonal PPPs: PPP "economy/ PPP "economy/ regon" PPP "regon/ PPP "regon/ s calculated as the unweghted geometrc mean from the economy's PPPs belongng to the regon. Ths method was descrbed n chapter 15 of the ICP 2005 Methodologcal Handbook as calculaton of the regonal lnkng factors (between-regon PPPs) by the unweghted geometrc mean method (World Bank 2007). Also, a modfcaton of the CAR-PPP method s used n the Eurostat Organsaton for Economc Co-operaton and Development (OECD) comparson n order to preserve the fxty of the Eurostat comparson. Both CAR methods (CAR- and CAR-PPP) mantan the fxty of the regonal results, but the between-regon results obtaned by these methods can be slghtly dfferent. References Dewert, E "Weghted Country Product Dummy Varable Regressons and Index Number Formulae." /product_dummy_varable.doc. Rao, D. S. Prasada "The CPD Method: A Stochastc Approach to the Computaton of PPPs n the ICP." Paper presented at SSHRC Conference on Index Numbers and Productvty Measurement, Vancouver, June 30 July 3. /ICPINT /Resources/Country-Product-Dummy _Method.doc. Sergeev, Sergey "The Use of Weghts (Indcaton of Representatvty) wthn the CPD and EKS Methods at the Basc Headng Level." ste resources.worldbank.org/icpint/resources/use _of _Weghts.doc "Implementaton of the Parallel Computatons for Lnkng the Regons wthn the 2011 ICP." Paper presented at sxth meetng of Techncal Advsory Group, Internatonal Comparson Program, World Bank, Washngton, DC, October 3 4. Unted Natons Economc Commsson on Europe Internatonal Comparson of GDP n Europe New York/Geneva: Unted Natons. Vogel, Frederc A "Valdaton of Basc Headng and Aggregated PPPs: When Does Valdaton End and Estmaton Begn?" In Measurng the Real Sze of the World Economy: The Framework, Methodology, and Results of the Internatonal Comparson Program (ICP). ces/ / / 10_ICPBook_Valdaton_F.pdf. World Bank ICP 2005 Methodologcal Handbook. STATISTICS/ICPEXT/0,,contentMDK: ~page PK: ~pPK: ~theStePK :270065,00.html. 466 Operatonal Gudelnes and Procedures for Measurng the Real Sze of the World Economy