Output Growth and Inflation Across Space and Time

Transcription

1 Oupu Growh and Inflaion Across Space and Time by Erwin Diewer Universiy of Briish Columbia and Universiy of New Souh Wales and Kevin Fox Universiy of New Souh Wales EMG Workshop 2015 Universiy of New Souh Wales December 4,

2 Inroducion The presen paper will use OECD daa for he years in order o sudy he following wo measuremen problems: How can esimaes of OECD real GDP and associaed measures of OECD inflaion be consruced? How can he OECD annual PPP informaion be used in conjuncion wih member counry daa on real GDP growh o consruc esimaes of member counry real GDP ha are in principle comparable across space and ime? The OECD provides annual PPPs so our sraegy in solving he second problem will be o use OECD aggregae GDP growh raes along wih he annual PPP informaion o produce Harmonized GDP series ha are in principle, comparable across ime and space. 2

3 OECD Ordering of Counries Our firs ask is o use he OECD daa base o form counry GDP volumes. We will use he OECD ordering of counries, which is as follows: 1= Ausralia 2= Ausria 3= Belgium 4= Canada 5= Chile 6= Czech Republic 7= Denmark 8= Esonia 9= Finland 10= France 11= Germany 12= Greece 13= Hungary 14= Iceland 15= Ireland 3

4 OECD Ordering of Counries (con) 16= Israel 17= Ialy 18= Japan 19= Korea 20= Luxembourg 21= Mexico 22= Neherlands 23= New Zealand 24= Norway 25= Poland 26= Porugal 27= Slovak Republic 28= Slovenia 29= Spain 30= Sweden 31= Swizerland 32= Turkey 33= Unied Kingdom 34= Unied Saes. 4

5 Counry Domesic Price and Quaniy Levels P n and Q n The counry values for nominal GDP in he naional currencies for he years can be obained from he OECD elecronic daa base, OECD.Sa. Conver hese esimaes ino billions and denoe he esimae for counry n in year by V n The corresponding volume esimaes can be obained from OECD.Sa TableB1-GE: Gross domesic produc (GDP); Naional currency, consan prices, naional base year, millions, annual daa. Conver hese esimaes ino billions and denoe hese volumes (or quaniies) by Q n for n = 1,...,34 and = 2000,...,2012. The corresponding counry price level for counry n in year is defined as P n V n /Q n for n = 1,...,34 and = 2000,...,2012 5

6 Definiion of OECD Aggregae GDP Inflaion Since he counry volumes Q n are measured in domesic currency unis (which are no comparable across counries), we need o conver he domesic nominal values of GDP ino common currency unis using he average exchange raes for each year. In principle, he numeraire counry could be any of he 34 OECD counries bu i seems reasonable o choose he larges counry as he numeraire counry. The OECD has convenienly done his for us, convering each counry s nominal GDP ino US dollars a he average marke exchange raes for he given year. Conver hese esimaes ino billions and denoe he US dollar esimae for nominal GDP for counry n in year by v n. 6

7 Definiion of OECD Aggregae GDP Inflaion (con) The year, counry n US dollar price level for GDP, p n, is iniially defined as v n /Q n where he counry volumes or real oupus Q n have already been defined using naional daa. The resuling p n were normalized so ha p n 2000 = 1 for n = 1,...,34. The Q n were hen normalized in he opposie direcion so ha US dollar values were preserved. Denoe he resuling normalized Q n as q n for n = 1,...,34 and = 2000,...,2012. These US dollar price levels p n and he corresponding volumes q n are lised in Tables A3 and A4 in he Appendix. These price levels are comparable over ime only; i.e., hey are no comparable across counries. These US dollar (noncomparable across counries) price levels are ploed on he following 3 Chars. 7

8 US Dollar Price Levels; OECD and Counries 1-11 OECD Price Level P and Counry Price Levels in US Dollars PUS1- PUS P PUS1 PUS2 PUS3 PUS4 PUS5 PUS6 PUS7 PUS8 PUS9 PUS10 PUS11 8

9 US Dollar Price Levels; Counries Counry Price Levels in US Dollars PUS12-PUS PUS12 PUS13 PUS14 PUS15 PUS16 PUS17 PUS18 PUS19 PUS20 PUS21 PUS22 PUS23 9

10 US Dollar Price Levels; Counries Counry Price Levels in US Dollars PUS24-PUS PUS24 PUS25 PUS26 PUS27 PUS28 PUS29 PUS30 PUS31 PUS32 PUS33 PUS34 10

11 Aggregae Measures of OECD GDP Growh and Inflaion: Firs Approach We are now in a posiion o calculae aggregae OECD real oupu and he corresponding OECD price level for he years using he (US dollar) price and (domesic) volume daa, p n and q n, as inpus ino he Fisher chained index number formula. Denoe he chained Fisher aggregae OECD volume level for year by Q and he corresponding US dollar year price level by P for = 2000,...,2012. For = 2001,...,2012, define he year OECD Approach 1 volume growh rae and he corresponding OECD US dollar inflaion rae in percenage poins as follows: (10) 100[(Q /Q 1 ) 1] ; (11) 100[(P /P 1 ) 1]. 11

12 Aggregae Measures of OECD GDP Growh and Inflaion: Firs Approach (con) The chained Fisher OECD aggregae price and volume levels, P and Q, for he years are lised in Table 1 along wih he corresponding percenage poin annual growh raes, and, for he years For comparison purposes, we also calculaed he aggregae OECD chained Laspeyres and Paasche indexes over he same period. The resuling Laspeyres and Paasche price levels, P L and P P, are also lised in Table 1. I can be seen ha he chained Fisher, Laspeyres and Paasche price levels are all very close o each oher so ha for his paricular applicaion, he choice of index number formula does no maer very much. Noe he US dollar price level deflaion in 2001, 2009 and 2012 and he large OECD GDP volume decline in

13 Table 1: OECD Annual Aggregae Volumes Q and Price Levels in US Dollars P and Percenage Poin Changes Year Q P P L P P EU P EU P ICP

14 Discussion of Table 1 The sample average growh rae for OECD real GDP was 3.18% per year. The sample average OECD inflaion rae (measured in US dollars a marke exchange raes) was 3.24% per year. I can be seen ha here was only one year where OECD real growh was negaive: 2009 (3.64%). Wha is somewha surprising is ha here were 3 years where OECD inflaion was negaive when measured in US dollars a marke exchange raes: 2001 (2.06%), 2009 (2.69%) and 2012 (1.63%). The deflaion for 2012 is paricularly surprising, given he fairly loose moneary policies across he OECD region in recen years. As menioned before, he choice of Laspeyres, Paasche or Fisher aggregae GDP and price level indexes does no maer much for his applicaion. 14

15 More Discussion of Table 1 The principles used o consruc our OECD aggregae measures of real GDP, Q, are he same principles used o consruc counry wide esimaes of real GDP wihin a counry. The counry esimaes of real GDP aggregae oupu growh over regions wihin he counry use regional price levels as weighs for he regional volumes. In consrucing naional esimaes of real oupu, he naional saisician does no assume ha he quaniies or volumes in each region are comparable across regions: all ha is assumed is ha whaever is being measured a he regional level is comparable over ime. This is he same principle ha is being used in Table 1 o consruc OECD real oupu: here is no assumpion ha he counry unis of measuremen are comparable across counries. 15

16 And Even More Discussion of Table 1 There is one difference in our suggesed mehod for consrucing OECD real GDP as opposed o mehods used o consruc naional esimaes of real GDP: in order o consruc OECD real GDP, we needed o conver naional values of GDP ino a common currency using annual average marke exchange raes. We chose o make his conversion using US dollars as he numeraire currency. In principle, we could have chosen he numeraire currency o be he currency of any one of he 34 member counries. Wha would happen if we chose anoher currency o be he numeraire currency? The uni of measuremen would change, bu he overall OECD growh raes for real GDP would remain he same; i.e., he lised in Table 1 would no change bu he inflaion measures would change; i.e., hey are numeraire dependen. [Compare wih EU ]. 16

17 OECD Growh and Inflaion Measuremen Using Annual PPP Informaion: Approach 2 For many purposes, i is useful o be able o compare he GDP of one counry wih he GDP of anoher counry in comparable unis of measuremen. Thus he OECD (in close cooperaion wih Eurosa) produces an annual series of price indexes (or PPPs) ha enable one o compare he real GDP of member counries wih each oher. The relevan able of PPPs for he 34 counries can be found in OECD.Sa, Table 4: PPPs and Exchange Raes; PPPGDP; Purchasing Power Pariies for GDP; Naional currency per US dollar; Annual; Our second approach o measuring OECD volumes and inflaion uses hese PPPs along wih naional growh raes. 17

18 Counry Shares of Annual OECD Real Oupu Recall ha he counry n nominal value of GDP in year in domesic currency was defined by V n previously. Divide hese nominal values by he corresponding counry n year PPP in order o obain an esimae, r n, of counry n s real GDP in year in volume unis ha are comparable across counries for year : (12) r n V n /PPP n ; n = 1,...,34; = 2000,...,2012. Once he r n have been calculaed, hey can be summed so ha r n=1 34 r n and hen he year counry n share of OECD real oupu can be defined as follows: (13) s n r n /r ; n = 1,...,34; = 2000,...,2012. The counry shares of OECD real GDP are lised in Table 2. 18

19 Harmonizaion Principles Our suggesed soluion o he problem of harmonizing naional growh raes of GDP wih he counry shares of OECD aggregae real GDP ress on wo principles: The resuling harmonized esimaes of counry volumes mus be consisen wih he real annual cross counry volume shares s n lised in Table 2; OECD aggregae real GDP growh mus be equal o he raes of aggregae growh generaed by our recommended Fisher indexes F defined by (16) below. Using he above wo principles, he comparable across ime and space counry GDP volumes will be uniquely deermined (up o a scalar unis of measuremen facor). 19

20 Aggregae OECD Volume Growh: Laspeyres The year growh facor for counry n can be defined as Q n /Q n 1 where Q n is counry n s GDP volume in year. Thus define he OECD Laspeyres ype growh facor (or chain link) for year, L, as he following weighed average of he naional growh facors: (14) L n=1 34 s n 1 (Q n /Q n 1 ) ; = 2001,...,2012. The above measure of OECD GDP volume growh is he mehod used by he OECD o calculae heir official annual measure of OECD volume growh. I cerainly is a sensible measure, using counry (one plus) growh raes going from year 1 o year, Q n /Q n 1, weighed by he counry real volume shares s n 1 for year 1, which were derived using PPPs. 20

21 Aggregae OECD Volume Growh: Paasche and Fisher The counerpar o he Laspeyres ype formula defined by (14) is he following Paasche ype formula (which applies he Laspeyres formula bu reverses he role of ime): (15) P [ n=1 34 s n (Q n /Q n 1 ) 1 ] 1 ; = 2001,...,2012. Since boh indexes have he same logical foundaion, i seems bes o ake a symmeric average of he wo indexes, which leads o he following Fisher ype formula for OECD volume growh for year : (16) F [ L P ] 1/2 ; = 2001,...,2012. The annual Fisher chain links defined by (16) are our preferred esimaes for OECD volume growh using Approach 2. 21

22 Aggregae OECD Volume Growh: Approach 2 Indexes The growh facors (or chain link indexes) defined by (14)- (16) can be muliplied ogeher o generae OECD aggregae volume levels. The growh facors can also be ransformed ino growh raes, L, P and F (in percenage poins), by using he following definiions for = 2001,...,2012: (17) L 100[ L 1] ; P 100[ P 1] ; F 100[ F 1]. The Approach 2 annual OECD volume growh measures defined by (17) as well as our earlier Approach 1 US dollar weighed measures are lised in Table 3 which is reproduced on he nex slide. 22

23 Alernaive Aggregae OECD Volume Growh Measures Year L P F Average

24 Alernaive Aggregae OECD Volume Growh Measures Laspeyres, Paasche and Fisher OECD Growh Raes and Exchange Rae Based Growh Rae GammaL GammaP GammaF Gamma 24

25 Aggregae OECD Volume Growh Measures: Discussion Our preferred Fisher measure of OECD growh in comparable unis across counries, F, grew on average abou 1/10 of a percenage poin more rapidly per year han our preferred measure of OECD GDP growh using US dollar weighs (or more generally, using exchange rae weighed weighs),, ha was explained in he previous secion. Which measure, F or, is bes? Boh and F are essenially share weighed averages of he naional volume growh facors, Q n /Q n 1. However, he shares used in he consrucion of he are counry shares of OECD nominal GDP consruced using exchange raes and he resuling shares are subjec o excessive exchange rae flucuaions. On he oher hand, he shares used o consruc F are real shares of OECD oupu consruced using PPPs and will be more sable. 25

26 Aggregae OECD Inflaion Indexes: Approach 2 The OECD real oupu shares, s n defined by (13), can be used as weighs for naional GDP inflaion raes. Recall ha he naional currency GDP price deflaor for counry n in year was defined as P n. Recall also ha (14)-(16) defined OECD Laspeyres, Paasche and Fisher volume link volume indexes, L, P and F. Use hese definiions wih he naional inflaion facors (P n /P n 1 ) replacing he naional volume growh facors (Q n /Q n 1 ) in order o define he OECD Laspeyres, Paasche and Fisher ICP based chain link price indexes, L, P and F for = 2001,...,2012: (18) L n=1 34 s n 1 (P n /P n 1 ) ; P [ n=1 34 s n (P n /P n 1 ) 1 ] 1 ; F [ L P ] 1/2. 26

27 Aggregae OECD Inflaion Indexes: Approach 2 These chain link indexes can be muliplied ogeher o generae he corresponding OECD aggregae price levels. The inflaion growh facors can also be ransformed ino growh raes, L, P and F in percenage poins, by using he following definiions for = 2001,...,2012: (19) L 100[ L 1] ; P 100[ P 1] ; F 100[ F 1]. The above ICP based inflaion raes (in percenage poins) are lised in he nex slide along wih he earlier US dollar and Euro based inflaion esimaes ha were derived using US dollar and Euro esimaes of counry nominal GDP values and counry volume esimaes, = US and EU. 27

28 Aggregae OECD Inflaion Indexes: Approach 2 Year US EU L P F

29 Aggregae OECD Inflaion Indexes: Approach 2 US and EU Exchange Rae Based Inflaion Raes and ICP Based Laspeyre, Paasche and Fisher OECD Inflaion Raes RhoUS RhoEU RhoL RhoP RhoF 29

30 New Problem: The Consrucion of Comparable Across Counries and Time GDP (Harmonized) Volumes Use he Fisher chain links defined by (16) o define Q H as follows: (18) Q H ; Q H Q H 1 F ; = 2001,...,2012. Now use he counry shares of OECD real GDP s n lised in Table 2 and he aggregae index Q H o define he following preliminary harmonized counry volumes for counry n in year, q Hn, as follows: (19) q Hn Q H s n ; n = 1,...,34 ; = 2000,...,2012. For each year, n=1 34 q Hn = n=1 34 Q H s n = Q H ( n=1 34 s n ) = Q H and so he harmonized volumes saisfy he wo principles lised on slide 19 above. In principle, he counry volumes defined by (19) are independen of counry prices and exchange raes. [Consider he one good case.] 30

31 The Consrucion of Comparable Across Counries and Time GDP Volumes (con) Recall ha he value of counry n s nominal GDP convered ino US dollars a marke exchange raes for year was defined as v n. Thus he corresponding harmonized US dollar price of a uni of (comparable across counries) real GDP for counry n in year is defined as follows: (20) p Hn v n /q Hn ; n = 1,...,34 ; = 2000,...,2012. We impose a normalizaion on he prices defined by (20) ha makes he price level for he US in 2000 equal o uniy; i.e., we divide all prices defined by (20) by a consan ha ses he resuling p H equal o 1 and he quaniies or volumes defined by (19) are all muliplied by his consan. The resuling normalized q Hn and p Hn are lised in Tables 4 and 5. [Compare wih he q n, p n lised in Tables A3 and A4]. 31

32 Discussion of he Counry Comparable Prices and Volumes Lised in Tables 4 and 5 Noe ha q H = q and p H = p = 1 so ha counry GDP volumes are measured as muliples of a bundle of US GDP produced in he year Thus he price levels in Table 5 measure he US dollar value of consan bundle of GDP ha is (in heory) comparable across counries. The price levels in Table 5 are comparable across space and ime, whereas he price levels p n lised in Table A3 of he Appendix are only comparable across ime for each counry. These comparable US dollar price levels are shown in he nex 3 slides. They are (imperfec) indicaors of a counry s compeiveness. [Imperfec because no all commodiies are inernaionally raded plus here are errors in he PPPs]. 32

33 Harmonized OECD Counry GDP Price Levels in Comparable US Dollar Unis of Measuremen p Hn Counries 1-11; US Price Level in 2000 = 1 [Convergence?] AUS AYT BEL CAN CHL CZE DNK EST FIN FRA DEU 33

34 Harmonized OECD Counry GDP Price Levels in Comparable US Dollar Unis of Measuremen p Hn Counries 12-22; US Price Level in 2000 = 1 [Noe ISL!] GRC HUN ISL IRL ISR ITA JPN KOR LUX MEX NLD 34

35 Harmonized OECD Counry GDP Price Levels in Comparable US Dollar Unis of Measuremen p Hn Counries 23-34; US Price Level in 2000 = 1 [Red = USA] NZL NOR POL PRT SVK SVN ESP SWE CHE TUR GRB USA 35

36 Discussion of Harmonized GDP Price Levels in US $ From Table 5, i can be seen ha he counries wih he lowes price levels (in US dollars) in 2012 are counries 13, 21, 25 and 32 (Hungary, Mexico, Poland and Turkey) wih price levels in he 0.76 o 0.77 range. Counries wih relaively high price levels in 2012 are counries 1 (Ausralia, p H = 2.00), 4 (Canada, p H = 1.62), 7 (Denmark, 1.77), 9 (Finland, 1.58), 18 (Japan, 1.76), 20 (Luxembourg, 1.56), 23 (New Zealand, 1.55), 24 (Norway, 2.01), 30 (Sweden, 1.69) and 31 (Swizerland, 1.96). Again, hese price level esimaes are (imperfec) indicaors of he compeiveness of he counry on inernaional markes, wih lower price levels indicaing greaer compeiveness. The Tables 4 and 5 counry volumes and price levels are our preferred comparable across ime and space esimaes. 36

37 Secion 4. OECD Growh and Inflaion Using Counry Annual GDP Volume Growh Raes and Base Period Shares of OECD Real GDP In his secion, we generaed comparable counry GDP volume esimaes for OECD counries covering he period by using he real GDP counry volume shares for 2000, he s n 2000 lised in Table 2 above, along wih he naional growh raes of counry real GDP relaive o 2000, he Q n /Q n 2000 lised in Table A2 of he Appendix. This is a ypical sraegy in forming esimaes of real GDP ha rely on PPPs ha are only produced infrequenly: use he PPP based counry shares of world GDP for a base period and projec hese shares forward using naional GDP volume growh raes. How differen he resuling esimaes are from our preferred harmonized volume esimaes, q Hn, lised in Table 4 above? 37

38 Secion 4 Resuls If we ake each column in Table 5, subrac he corresponding enries in he same column of Table 7 and hen ake he absolue value of he differences, we find ha he average absolue difference grows from 0 in 2000 o 9.4 percenage poins in The maximum absolue difference grows from 0 in 2000 o 54.0 percenage poins in These are massive differences in price levels, which ranslae ino massive differences in GDP levels. The sequence of average absolue differences in percenage poins over he 13 years is as follows: 0, 0.8, 1.6, 2.0, 2.2, 3.8, 5.2, 6.4, 7.6, 6.8, 8.0, 9.3, 9.4. The sequence of maximum absolue differences in percenage poins over he 13 years is as follows: 0, 2.9, 5.2, 6.0, 5.4, 14.0, 25.1, 28.2, 46.9, 24.8, 34.3, 48.5,

39 Secion 5. OECD Growh and Inflaion Using Counry Annual GDP Volume Growh Raes and Final Period Shares of OECD Real GDP In his secion, we generaed comparable counry GDP volume esimaes for OECD counries covering he period by using he real GDP counry volume shares for 2012, he s n lised in Table 2 above, along wih he naional growh raes of counry real GDP relaive o 2000, he Q n /Q n 2000 lised in Table A2 of he Appendix. This mehod for forming comparable counry GDP volumes is used by he World Bank when he Inernaional Comparisons Projec produces a new se of PPPs. The mehodology is sraighforward and follows he approach used in he previous secion excep ha he 2012 counry volume shares are used in place of he 2000 shares. 39

40 Secion 5 Resuls Take each column in Table 5, subrac he corresponding enries in he same column of Table 8 and hen ake he absolue value of he differences. The average absolue difference for 2000 over he 34 counries is 6.0 percenage poins, which increases o 7.9 percenage poins for 2005 and hen gradually decreases o 4.2 percenage poins in Over all observaions, he maximum absolue deviaion is 35.6 percenage poins. The sequence of average absolue differences over he 34 counries in percenage poins over he 13 years is as follows: 6.0, 6.1, 6.2, 7.0, 7.8, 7.9, 6.2, 6.8, 5.9, 5.4, 5.1, 5.2, 4.2. The sequence of maximum absolue differences in percenage poins over he 13 years is as follows: 24.6, 25.9, 32.3, 35.6, 33.1, 27.1, 20.5, 22.0, 16.0, 24.7, 18.7, 12.6, 6.3. Conclusion: exrapolaion does no work well over 13 years 40

41 Secion 6: OECD Growh and Inflaion Using Adjused Counry Annual GDP Volume Growh Raes and OECD Shares of Real GDP for Two Benchmark Years The OECD provides annual PPPs so ha esimaes of relaive GDP volumes can be consruced for all member counries for each year. However, he World Bank s ICP PPPs are only available a infrequen inervals. The quesion arises: how exacly should wo widely separaed benchmark real GDP shares be used along wih annual growh rae informaion o inerpolae beween he benchmark years? We will model his siuaion using our OECD daa base bu will use only he benchmark GDP shares for he years 2000 and 2012 along wih informaion on naional GDP growh raes in order o inerpolae beween he benchmark years. 41

42 The Secion 6 Mehodology We will propose an inerpolaion mehod ha leads o counry shares of real GDP ha are exacly consisen wih he shares s n 2000 for he year 2000 and he shares s n 2012 for he year Sep 1: Consruc counry measures of real GDP ha jump from he year 2000 o he year The long erm growh facor for counry n can be defined as Q n 2012 /Q n 2000 where Q n is counry n s GDP volume in year. Now use hese long erm growh facors along wih he year 2000 counry shares of OECD real GDP, s n 2000, in order o define he OECD Laspeyres ype long erm growh facor, L, as he following weighed average of he naional long erm growh facors: (27) L n=1 34 s n 2000 (Q n 2012 /Q n 2000 ) ; = 2001,...,

43 The Secion 6 Mehodology (con) The counerpar o he Laspeyres ype formula defined by (27) is he following Paasche ype formula ha uses he shares of 2012 and reciprocal long erm growh raes: (28) P [ n=1 34 s n 2012 (Q n 2012 /Q n 2000 ) 1 ] 1 ; = 2001,...,2012. Since boh indexes have he same logical foundaion, i seems bes o ake a symmeric average of he wo indexes, which leads o he following Fisher ype formula for OECD long erm volume growh going from he year 2000 o he year 2012: (29) F [ L P ] 1/2 ; = 2001,...,2012. (29) defines a direc comparison of he daa of 2000 wih he daa of 2012 whereas in secion 3, we used chained Fisher ype indexes o go from 2000 o The chained Fisher index for 2012 relaive o 2000 is equal o , which is very close o is direc counerpar,

44 The Secion 6 Mehodology: Sep 2 Preliminary esimaes of counry GDP volumes in comparable unis for he years 2000 and 2012, q In 2000 and q In 2012 (he index I indicaes ha hese are inerpolaed esimaes), are defined as follows: (30) q In 2000 s n 2000 ; q In 2012 F s n 2012 ; n = 1,...,34. The volumes defined by (30) will be imposed as consrains on our inerpolaion scheme. Define he implied long erm growh facor over he years for counry n, g n, ha is implied by he esimaes of counry levels given by equaions (30): (31) g n q In 2012 /q In 2000 ; n = 1,...,34. 44

45 The Secion 6 Mehodology: Sep 2 (con) These growh facors are no necessarily equal o he naional growh facors G n ha are implied by he naional growh raes defined as: (32) G n Q n 2012 /Q n 2000 ; n = 1,...,34. Thus for each counry n, here is an error facor or discrepancy, E n g n /G n beween he implied growh raes g n defined by (31) and he naional growh raes beween 2000 and 2012, G n defined by (32). We will disribue hese errors in a proporional manner and use he resuling adjused naional growh raes o inerpolae beween he wo benchmark observaions. Thus define he counry n proporional discrepancy facor, n, as follows: (33) n [g n /G n ] 1/12 ; n = 1,...,34. 45

46 The Secion 6 Mehodology: Sep 2 (concluded) The comparable inerpolaed counry volumes q In for nonbenchmark years can now be defined as follows: (34) q In q In 1 (Q n /Q n 1 ) n ; n = 1,...,34 ; = 2001,...,2011. Once he q In have been defined, he corresponding US dollar price levels p In are defined in he usual way: (35) p In v n /q In ; n = 1,...,34 ; = 2001,...,2011. In order o make he volumes and prices defined by (34) and (35) comparable o he harmonized counry prices and volumes expressed in US dollars ha are lised Tables 4 and 5 in secion 3, we impose a normalizaion on he prices defined by (35) ha makes he price level for he US in 2000 equal o uniy..46

47 Secion 6 Resuls The discrepancies beween he new inerpolaed price levels and our preferred harmonized price levels are much reduced as compared o he discrepancies when only one benchmark se of PPPs is used. The overall sample average absolue discrepancy is now only 1.9 percenage poins. Over all observaions, he maximum absolue deviaion is 12.5 percenage poins. The sequence of average absolue differences over he 34 counries in percenage poins over he 13 years is as follows: 0, 1.0, 1.8, 2.0, 2.3, 3.2, 3.0, 3.2, 2.8, 2.6, 1.7, 1.2, The sequence of maximum absolue differences in percenage poins over he 13 years is as follows: 0, 3.9, 9.7, 11.9, 9.4, 10.7, 8.3, 12.5, 12.3, 9.9, 6.1, 3.2, Conclusion: he inerpolaion mehod works fairly well! 47

48 Overall Conclusions The resuls lised in secions 3-5 show ha i is very hazardous for analyss ineresed in comparaive levels of GDP across counries o use naional growh raes and a single cross counry comparison of real GDP levels. If PPP compuaions for a group of counries are only done on an infrequen, hen he inerpolaion mehod explained in secion 6 may prove o be a useful mehod for obaining comparable GDP levels ha are consisen wih he GDP relaive levels for he wo benchmark years. The resuls in secion 6 also indicae ha differen inerpolaion mehods can generae very differen resuls. If a group of counries wan o consruc comparable across counries and ime esimaes of real GDP (or any oher macroeconomic aggregae), hen in order o reduce measuremen errors, i will be necessary o underake PPP exercises on a fairly frequen basis; say every 3-6 years. 48