Measuring Economic Growth in New Zealand

Transcription

1 Measuring Economic Growh in New Zealand Peer Mawson N EW Z EALAND REASUR W ORKING P APER 0/4 S EPEMBER 00

2 NZ REASUR WORKING PAPER 0/4 Measuring Economic Growh in New Zealand MONH/ EAR Sepember 00 AUHOR Peer Mawson he reasury PO Box 374, Wellingon, New Zealand elephone Fax ACKNOWLEDGEMENS he auhor would like o hank Maryanne Aynsley, Iris Claus, Arhur Grimes, Kay Henderson, Dean Hyslop, Nahan McLellan, Gran Scobie, and David Skilling for heir helpful commens and suggesions on various draf versions of he paper. NZ REASUR New Zealand reasury PO Box 374 Wellingon 6008 NEW ZEALAND informaion@reasury.gov.nz elephone Websie DISCLAIMER he views expressed in his Working Paper are hose of he auhor(s) and do no necessarily reflec he views of he New Zealand reasury. he paper is presened no as policy, bu wih a view o inform and simulae wider debae.

3 Absrac his paper examines New Zealand s ranking in he OECD based on real GDP per capia. he fall in ranking experienced by New Zealand implies ha real GDP per capia growh in New Zealand has been relaively poor in comparison o oher OECD counries. he paper examines he hisory of New Zealand s growh rae and explores he differences beween various echniques for measuring average growh raes. he approaches are all shown o be varians of he average annual growh rae bu differ in erms of he weighing srucure used. Ulimaely, he mos appropriae echnique depends on he underlying daa generaing process. he implicaions of daa consrucion echniques for measured growh raes are discussed and differences beween he growh raes obained from differen daa sources are illusraed. he paper also illusraes he sensiiviy of New Zealand growh raes o he sample period chosen. JEL CLASSIFICAION O47 Measuremen of Economic Growh; Aggregae Produciviy C0 Economeric and Saisical Mehods: General KEWORDS Economic Growh; Measuring Growh; Inernaional Comparisons WP 0/4 Measuring Economic Growh in New Zealand i

4 able of Conens Absrac...i able of Conens...ii Lis of ables...ii Lis of Figures...iii Inroducion... New Zealand s place on he OECD ladder... 3 Calculaing Growh Raes Leas Squares Growh Raes Log Difference Model Growh Raes he Average Annual Growh Rae Geomeric Average Growh Raes he four approaches summarised Choice of Mehod... 4 Daa Consrucion echniques and Measured Growh Raes Changes in he way New Zealand real GDP is measured Differen approaches o consrucing real GDP series (Chain versus Fixed weighs) Measured New Zealand growh raes over ime Conclusion...3 References...4 Appendix A:...5 A. Weighing Scheme of he OLS Growh Rae Esimaor... 5 A. Obaining he growh rae esimaor in a log-difference model... 6 A.3 he geomeric Average Growh Rae... 7 A.4 Proof ha Log Difference Regression and Geomeric Growh Raes are Equal... 8 Appendix B - New Zealand real GDP per capia series...9 Appendix C New Zealand average annual change growh raes from differen daa sources...30 Appendix D New Zealand growh raes and growh rae rankings from alernaive daa sources...3 Lis of ables able New Zealand s GDP per Capia Ranking Amongs OECD Counries... 3 able four echniques o consruc a growh rae... 9 able 3 A comparison of New Zealand growh raes using he alernaive echniques o consruc a period growh rae... 0 able 4 - Uni Roo ess on he naural log of New Zealand real GDP per capia series... able 5 Sources of New Zealand real GDP per capia daa used in his paper... 3 WP 0/4 Measuring Economic Growh in New Zealand ii

5 able 6 Example of a Laspeyres Index... 7 able 7 Example of a Paasche Index...7 able 8 Comparison of annual growh raes for fixed weigh real gross domesic expendiure series wih differen base years... 8 able 9 - New Zealand Growh Raes for Differen Window Endpoins and Window Lenghs based on OECD daa... 0 able 0- New Zealand s growh rae ranking in he OECD for a number of differen subperiods based on OECD daa... able D - New Zealand Growh Raes for Differen Window Endpoins and Window Lenghs based on PW daa... 3 able D- New Zealand s growh rae ranking in he OECD for a number of differen subperiods based on PW daa... 3 able D3 - New Zealand Growh Raes for Differen Window Endpoins and Window Lenghs based on Maddison 00 daa able D4- New Zealand s growh rae ranking in he OECD for a number of differen subperiods based on Maddison 00 daa able D5 - New Zealand Growh Raes for Differen Window Endpoins and Window Lenghs based on Haugh s Calibraed daa Lis of Figures Figure New Zealand s Real GDP per Capia Ranking Amongs OECD Counries... Figure Weighing Scheme for OLS growh rae esimae (0)... 6 Figure 3 Maximum/Minimum Weigh Raio for ime series of lengh... 6 Figure 4 -A comparison of differen growh rae consrucion echniques (NZ growh raes measured over differen 0 year windows)... Figure 5 A comparison of New Zealand s growh raes obained from differen daa ses (NZ growh raes measured over differen 0 year windows)... 4 Figure 6 A comparison of New Zealand s growh raes obained from differen daa ses (NZ growh raes measured over differen 0 year windows)... 5 WP 0/4 Measuring Economic Growh in New Zealand iii

6 Measuring Economic Growh in New Zealand Inroducion Recenly here has been increased ineres in New Zealand s income posiion relaive o oher counries, in paricular counries in he Organisaion for Economic Co-operaion and Developmen (OECD). he increased ineres reflecs concerns ha New Zealand s relaive income posiion has been falling since he 950s. For example Growing an Innovaive New Zealand (New Zealand Governmen, 00) released in February saed ha New Zealand s relaive income declined over much of he pos-war period. New Zealand s real per capia income fell from among he highes in he world in he 950s, o jus under he OECD average in 970, o 0 h in he OECD by 999. o address such concerns he previous Governmen (999-00) adoped a goal of reurning New Zealand s per capia income o he op half of he OECD. Our economic objecive is o reurn New Zealand s per capia income o he op half of he OECD and o mainain ha sanding. his will require New Zealand s growh rae o be consisenly above he OECD average growh rae for a number of years. ha will require susained growh raes in excess of our hisorical economic performance. (New Zealand Governmen, 00) While such goals focus on New Zealand s per capia income, he income measure generally used has been Gross Domesic Produc (GDP) per capia. his paper highlighs a number of issues ha are relevan when measuring economic growh over ime and when making inernaional comparisons on he basis of ranking in real GDP per capia. Secion examines New Zealand s ranking wihin a group of OECD counries, based on our level of real GDP per capia, when several differen daa sources are used. his highlighs ha New Zealand s ranking is o some exen influenced by he daa source used (hough all sources are consisen wih New Zealand sliding down he ladder over ime). he fall in our ranking implies ha New Zealand s growh rae in real GDP per capia mus have been relaively poor over periods of ime. his leads o he quesion of wha has been New Zealand s average growh rae since he 950s and how does his compare wih he experience of oher counries? However, prior o addressing his quesion, here are several issues relaing o he consrucion of average growh raes ha are imporan For example New Zealand Governmen (00) illusraes New Zealand s relaive decline in per capia income by way of a graph showing New Zealand s GDP per head. WP 0/4 Measuring Economic Growh in New Zealand

7 o highligh if a counry s performance is o be accuraely assessed. One of hese issues is how o measure average growh over any given period of ime. his issue is discussed in Secion 3. Daa consrucion echniques can have imporan ramificaions for he esimaed growh rae. he impac of daa consrucion echniques on measured growh raes are discussed in Secion 4. Wih he issues raised in Secions 3 and 4 borne in mind, Secion 5 examines New Zealand s hisorical growh performance based on several daa sources. Finally, Secion 6 concludes by briefly summarising some of he key poins. New Zealand s place on he OECD ladder Figure presens New Zealand s ranking in he OECD, in erms of real GDP per capia, based on daa from hree differen sources. hese differen daa sources are OECD (00), Maddison (00), and Penn World ables (PW) 3. he rankings on which Figure is based are displayed in able. Figure New Zealand s Real GDP per Capia Ranking Amongs OECD Counries 0 5 Ranking 0 5 OECD ($US) OECD (PPP) PW Maddison(00) ear Regardless of which daa source is used, New Zealand s ranking has dropped over ime. Noe ha in Figure he values on he verical axis are displayed in reverse order, ie higher numbers (lower rankings) are below lower numbers (higher rankings). Consequenly a negaive slope is associaed wih a worsening in he ranking over ime. However, here is a degree of variaion in New Zealand s relaive ranking across he differen daa sources. his implies ha daa consrucion and collecion echniques can influence he paricular ranking ha New Zealand aains. 4 I is also ineresing o Daa from wo ables of his publicaion were used. OECD($US) rankings are based on able A.9 of OECD(00) which presens GDP per head a he price levels and exchange raes of 995 (US dollars). OECD(PPP) ranking are based on able B.7 of OECD(00) which presens GDP per head a he price levels and PPPs of 995 (US dollars). In boh cases daa was obained elecronically via OLISNE o enable annual daa from 970 hrough o 000 o be used. he Czech Republic, Hungary, Poland and he Slovak Republic are excluded from he sample due o he incomplee ime coverage of heir daa. 3 Alan Heson, Rober Summers, Daniel Nuxoll and Beina Aen, Penn World ables Version 5.6, Cener for Inernaional Comparisons a he Universiy of Pennsylvania, January Differences in he number of counries included in he various daases may also lead o differen daases suggesing differen rankings. he OECD daa displays a ranking ou of 6 counries, he PW daa displays a ranking ou of 5 counries, and he WP 0/4 Measuring Economic Growh in New Zealand

8 observe ha New Zealand s GDP per capia ranking based on OECD daa was subsanially higher when 995 purchasing power pariies (PPPs) are used raher han he 995 exchange rae agains he Unied Saes dollar. able New Zealand s GDP per Capia Ranking Amongs OECD Counries year PW year PW OECD ($US) OECD (PPP) Maddison (00) OECD ($US) OECD (PPP) Maddison (00) he OECD daases used in his paper include he following 6 counries (lowes ranking possible is 6): Ausralia, Ausria, Belgium, Canada, Denmark, Finland, France, Germany, Greece, Iceland, Ireland, Ialy, Japan, Korea (Souh), Luxembourg, Mexico, Neherlands, New Zealand, Norway, Porugal, Spain, Sweden, Swizerland, urkey, Unied Kingdom, and he Unied Saes. he Penn World able (PW) daase used in his paper is made up of 5 counries (lowes ranking possible is 5). hese are he same as for he OECD daases wih he exclusion of Germany. he Maddison daase used in his paper is made up of 4 counries (lowes ranking possible is 4). hese are he same as for he OECD daases wih he exclusion of Iceland and Luxembourg. Ulimaely, i appears here will always be a degree of uncerainy as o New Zealand s acual GDP per capia ranking for any paricular individual year back o 950 (and prior) due o differen daa sources or differences in he unis in which GDP per capia is expressed providing differen rankings. his uncerainy also applies o pinpoining subperiods where New Zealand s ranking decline has been he greaes. hree ou of he four series for New Zealand s GDP per capia ranking display subsanial falls in he mido-lae 970s. 5 For example, he series based on PW daa shows ha New Zealand Maddison daa displays a ranking ou of 4 counries (as oulined in able ). hese differences in counry numbers are no sufficien o explain he differences beween he rankings obained when using he differen daases, implying ha daa consrucion and collecion echniques also play a role. 5 he series based on OECD($US) daa also displays a falling ranking over his period, alhough he loss of places is no as grea in his series. WP 0/4 Measuring Economic Growh in New Zealand 3

9 dropped from 7 h in 975 o 5 h in 980. Likewise he series based on OECD PPP daa shows ha New Zealand dropped from 6 h in 974 o 8 h in 979. he Maddison series also shows a sizable decline over his period. he enry of Briain ino he European Union and he resuling loss of free enry o Briish markes for dairy producs, and he oil price shocks of he 970s are poenial explanaions for New Zealand s relaive fall in he real GDP per capia rankings during his period. Based on he daa shown in able, here may be a case for arguing ha he mid o lae 960s was also a period in which New Zealand s ranking fell significanly. For example, in 966 he Maddison series ranked New Zealand 3rd, whereas in 970 New Zealand s ranking had slipped o 9 h. he collapse of wool prices in 967, due o increased compeiion from synheic fibres, coincides wih he fall in ranking ha occurred during his period. Oher economiss have expressed alernaive views as o which periods are mos significan in New Zealand s slide down he OECD s rankings. For example, Brian Eason saes ha he economy mainly los is placing following wo major shocks in he lae 960s when he price of wool collapsed, and he lae 980s when here was a grossly overvalued real exchange rae. 6 As already discussed, he firs of hese wo explanaions is o some exen apparen in he daa displayed in Figure. he laer explanaion is no really suppored by hree of he four series used in his paper, alhough he PW series does show ha New Zealand s ranking slipped from h in 984 o 8 h in 988. I is clear ha daing key periods is iself dependen on he paricular daa series chosen. Falls in New Zealand s ranking wihin he OECD resul from relaively poor growh in real GDP per capia in comparison o oher OECD counries over ime. herefore i would be of ineres o know wha has been New Zealand s average growh rae since he 950s and how does his compare wih he performance of oher OECD counries? As is he case for deermining New Zealand s ranking in he OECD, i is likely ha differen people will obain differen esimaes of New Zealand s growh rae over a period. hese esimaes are likely o differ due o: he approach aken o measuring he average growh rae over a period; he real GDP series used; he unis in which he series is expressed; and he paricular ime period used. he nex secion discusses four possible ways of measuring he average growh rae of real GDP per capia over a period of ime. 3 Calculaing Growh Raes For a given ime series of annual real GDP per capia daa, how should he average growh rae for he enire daa period, or a paricular sub-period of ineres, be calculaed? 7 here are a number of poenial ways of consrucing an average growh rae for a paricular period. his paper focuses on four alernaives: (a) leas squares growh raes; (b) a differenced logarihmic model; (c) he average annual growh rae; and (d) he geomeric average growh rae. his secion explains he procedures involved in compuing growh raes using hese alernaive echniques. As will be shown, deriving hese alernaive growh rae esimaors algebraically highlighs ha he differen esimaes obained from hese mehods are all some varian of he average of he annual growh raes. he alernaive approaches differ in erms of he averaging echnique used on hese annual growh raes. he annual growh rae for a series of annual observaions, say,, 3,,, is defined as: 6 Eason(00) "Of roas pork - reasury debaes he economy." Lisener. 7 he discussion ha follows is equally relevan for esimaing he growh rae in any series. he daa does no necessarily need o be annual; wha is imporan is ha i is available for regular inervals over ime. WP 0/4 Measuring Economic Growh in New Zealand 4

10 a () where is he observaion for year Leas Squares Growh Raes One common approach o measuring growh raes is he Leas Squares or Ordinary Leas Squares (OLS) approach. In fac Kakwani (997) noes ha his is he mos commonly used procedure for esimaing growh raes. he OLS approach is based on he compound growh formula: ( + r) () he compound growh formula saes ha he value of real GDP per capia a ime is equivalen o he value of real GDP per capia a ime grown a a consan annual rae r (wih compounding occurring annually over - years). aking naural logs of () gives: ln ln ln( + r) + ln( + r) (3) Adding a disurbance erm ε, and leing equaion (4): ln ln( + r) α and ln( + r ) β yields ln α + β + ε (4) By regressing ln on (ime) using OLS we obain an esimae of he slope coefficien ( βˆ ) ha provides an esimae of he insananeous growh rae ( ln( + r) ). he compound rae of growh can be obained as follows 9 : ˆ β r OLS e (5) I can be shown (see Appendix A.) ha he OLS esimaor of β can be expressed as: ˆβ k s ln s (6) s where k s 6( s + )( s ) ( + )( ) ha is, βˆ is a weighed average of he lns s wih he k s s serving as weighs. As s s lns lns lns he OLS esimaor for β approximaes a weighed s average of he proporional changes in he series of ineres (eg, in he case of annual daa, a weighed average of he annual growh raes). 8 I is possible o consruc - annual growh raes from series ha has annual observaions. 9 Solving + ) β ln( r for r gives e r β hence equaion (5). WP 0/4 Measuring Economic Growh in New Zealand 5

11 However, i is worh focusing on he weighs. Noe ha he formula for he weighs ( k s ) is a quadraic in s. his weighing scheme means ha he weighs on he annual growh raes firs increase wih s, unil reaching a maximum when s +, and hen decrease symmerically unil s. o illusrae he differing weighs applied o he (approximaions of) he annual growh raes, Figure plos he weighs ha would apply if one was working wih sample of size 0. When 0, he weigh given o he annual growh rae in he middle of he sample is 5.6 imes he weigh given o he growh raes a he end poins of he sample. In general he raio of he highes weigh used o he lowes weigh used is. he 4( ) raio of he highes weigh o he lowes weigh for values of beween and 00 are shown in Figure 3. Figure Weighing Scheme for OLS growh rae esimae (0) k(s) s Figure 3 Maximum/Minimum Weigh Raio for ime series of lengh 30 5 Max/Min Weigh WP 0/4 Measuring Economic Growh in New Zealand 6

12 3. Log Difference Model Growh Raes As jus discussed, he commonly used leas square regression approach resuls in a quadraic weighing scheme. he use of a differen model enables us o obain an esimaor based on a simpler weighing scheme. Consider he model: ln β + ε (7) By noing ha his is equivalen o o be rewrien as: ln + β + ε, recursive subsiuion enables (7) ln ln ln + β ( + ε (8) ) s s Noe ha he model shown in equaion (8) is idenical o he model shown in (4) excep for he error erm 0. herefore, he argumen (based on manipulaing he compound growh formula) ha β can be inerpreed as a growh rae also holds for his model. In he model shown in (8) he error erm is described by a moving average process. he OLS esimaor of β in he model described by equaion (7) can be expressed as (see Appendix A.): ˆβ ln (9) So βˆ is jus an average of he - equal weighing of. ln erms, wih each ln erm being given an As was he case in secion., he esimae of he slope coefficien ( βˆ ) provides an esimae of he insananeous growh rae. he compound rae of growh can be obained as follows: ˆ β r LD e (0) 0 Equaion (4) is ln α + β + ε where ln ln( + r) α and ln( + r) β hus equaion (4) can be wrien as ln ln ln( + r) + ln( + r) + ε ln + ( ) ln( + r) + ε ln + β ( ) + ε which is he same as equaion (8) excep for he error erm. WP 0/4 Measuring Economic Growh in New Zealand 7

13 3.3 he Average Annual Growh Rae Noing ha ln approximaes he annual growh rae implies ha βˆ in equaion (9) is approximaely equal o he average of he annual growh raes. In fac, using he acual annual growh raes raher han heir ln counerpars gives us anoher simple way of calculaing he annualised rae of growh over a period. his approach is referred o as he average annual growh rae (AAGR) approach. he average annual growh rae can herefore be specified as: r AAGR () 3.4 Geomeric Average Growh Raes Anoher way of calculaing he average growh rae for a period when an annual ime series of daa ( o ) is available is o direcly uilise he compound growh formula by using he daa poins and as follows: ( + r) () solving he expression in () for r gives: r GEO (3) Here r is he rae of growh required o grow so ha i equals in - years when compounding occurs annually. his approach is referred o as he geomeric average approach. he fac ha his approach only uses he values of he wo endpoins of he series of ineres is ofen considered a weakness. he reason for referring o his approach as he geomeric average approach is ha i is possible o express +r as follows (see appendix A.3 for deails): r + GEO (4) + he expression shown in (4) saes ha + rgeo is he geomeric average of one plus he annual growh raes obainable from he daa. 3.5 he four approaches summarised Secions 3. o 3.4 have idenified four approaches ha can be used o measure he average growh rae over a period or sub-period of ineres. able summarises how hese approaches measure he growh rae as a funcion of he ime series observaions of he series for which average growh raes are being consruced. WP 0/4 Measuring Economic Growh in New Zealand 8

14 able four echniques o consruc a growh rae echnique Consrucion ˆ.OLS ( r OLS ) e β r OLS where ˆβ s 6( s + )( s ) ln ( + )( ) s.log Difference Regression ( r LD ) ˆ β r LD e where ˆβ ln 3.Average Annual Growh Rae ( r AAGR ) raagr 4.Geomeric Average ( r GEO ) r GEO For he ime series {,, 3,, } I is possible o show ha echniques and 4 are equivalen so ha r LD rgeo (see appendix A.4 for deails). ha is, he average growh rae for a period calculaed by he log difference regression echnique would be he same as he average growh rae calculaed by he geomeric average approach. Anoher poin worh noing is ha he log difference regression rae is approximaely equal o he βˆ used in is consrucion. I was noed ha βˆ esimaed in he log difference regression approximaely equals he average annual growh rae and herefore he average annual growh rae is approximaely equal o he log difference growh rae (and subsequenly he geomeric average growh rae). ha is: r GEO r r (5) LD AAC I is widely recognised ha ln( + x) x when x is small. his implies ha e x x and herefore r LD ˆ β e ˆ β. hus rgeo rld βˆ raac WP 0/4 Measuring Economic Growh in New Zealand 9

15 able 3 A comparison of New Zealand growh raes using he alernaive echniques o consruc a period growh rae Real GDP per ear capia Window ha Growh is Average Growh Rae (% per annum) Difference compared o AAGR Measured over AAGR GEO OLS LD GEO & LD OLS Noe: he GDP per Capia series is GDP per head a he price levels and exchange raes of 995 (US dollars) as published in (OECD 00). Daa was obained elecronically o 3 decimal places and daa o his level of accuracy was used in he growh rae calculaions. AAGR, GEO, OLS and LD refer o he growh rae obained using he Average Annual Growh Rae, Geomeric Average, Ordinary Leas Squares and Log Difference echniques respecively. able 3 illusraes he resuls obained by using he four growh rae echniques oulined earlier. Esimaes of he average growh rae in New Zealand real GDP per capia over a number of differen 0-year windows are compued as well as he average growh rae of he enire period ( ). his means ha for each window a sub-series of daa poins is used. No surprisingly, he growh raes calculaed using he geomeric average and log difference echniques are idenical and only differ o he average annual growh raes by up o 5 one hundredhs of a percen. here is subsanial variaion beween he growh rae compued using he OLS echnique and he oher hree echniques. In some cases he difference beween he growh raes obained using he OLS echnique and he average annual growh rae echnique is greaer han he average annual growh rae value. he quadraic weighing scheme used in he OLS echnique resuls in he OLS WP 0/4 Measuring Economic Growh in New Zealand 0

16 growh raes being maerially differen from he growh raes obained using he oher echniques, even when he raes are calculaed over he enire sample. Figure 4 -A comparison of differen growh rae consrucion echniques (NZ growh raes measured over differen 0 year windows) Average growh rae (%) over period AAGR GEO(LD) OLS Window endpoin Source: Auhor s growh rae calculaions based on OECD daa as shown in able 4. Figure 4 provides an alernaive represenaion of he daa in able 3 and plos he average growh rae in New Zealand s real GDP per capia for moving 0-year periods as measured using he differen growh rae approaches. hus he firs growh rae ploed for each series is for he period 970 o 980, he second for he period 97 o 98 and so on. Figure 4 again highlighs ha he growh rae esimaes for a paricular period can vary significanly depending on he echnique used, wih he OLS growh rae a imes differing subsanially from he raes obained using oher approaches. 3.6 Choice of Mehod Secion 3.5 highlighed ha growh raes obained from he OLS approach someimes differed subsanially o hose obained from he oher 3 mehods. Given his, wha is he mos appropriae way of calculaing a growh rae? his depends on he daa generaing process underlying he daa being used. In he case ha he log of GDP per capia is saionary around a deerminisic rend and hence does no conain a uni roo, hen i is appropriae o use he OLS approach. On he oher hand when he log of GDP per capia is inegraed of order one (I()) he log difference approach is more appropriae. As he log difference approach provides he same resuls as he geomeric average approach, and is approximaely equal o he average annual growh approach, here is lile in i when choosing beween hese hree approaches. he average annual growh rae approach involves a weighing srucure (sandard arihmeic weighs) ha makes i inuiively simple. he geomeric average approach (and consequenly log difference approach) is also quie inuiive and has he advanage ha if one akes he value of real GDP per capia a he sar of he sample period of ineres and grow i a he geomeric average growh rae for he appropriae number of years, he value obained will be ha of he final value of real GDP per capia in he sample period of Regression analysis based on ime series daa implicily assumes ha he underlying daa is saionary. When a series is inegraed of order (I()) aking he firs difference will resul in a saionary series. WP 0/4 Measuring Economic Growh in New Zealand

17 ineres. In general his will no be he case when he oher growh rae approaches are used. As shown in able 4, he naural log of all he New Zealand real GDP per capia series used in his paper are inegraed of order (I()). Wha his means is, ha wih New Zealand daa a leas, he use of he OLS approach o calculae an average growh rae should be avoided and one of he oher 3 approaches used. Due o is simpliciy, when growh raes are compued in he res of his paper he average annual growh rae has been used. able 4 - Uni Roo ess on he naural log of New Zealand real GDP per capia series Real GDP per capia series ADF es on log of series (levels) ADF es on log of series (firs difference) Order of Inegraion OECD (PPP) () -3.4** (0) I() OECD ($US) () -3.4** (0) I() Calibraed (0) -.630* (0) I() Maddison (00) -.69 () ** (0) I() Penn World ables () ** (0) I() Preliminary PW () ** (0) I() Boh a consan and rend were included in he Augmened Dickey-Fuller (ADF) ess when conduced on levels daa. Numbers in brackes in he second and hird columns indicae number of lags used in hese ess. he lag lenghs were deermined using he Schwarz crierion. * signifies a uni roo null is rejeced a he 5% significance level ** signifies a uni roo null is rejeced a he % significance level 4 Daa Consrucion echniques and Measured Growh Raes Secion 3, examined differen echniques o esimae an average growh rae over a paricular period. Figure 4 highlighed ha when hese differen echniques were applied o a common daa series, he OLS approach could resul in average growh esimaes ha looked quie differen o hose obained from he oher approaches. ha is, he choice of average growh rae esimaion echnique can be quie imporan. Anoher facor ha mus be borne in mind is wha daase o use when calculaing average growh raes over a period. For example, here exis several poenial series for New Zealand s real GDP per capia and hese series differ in he lengh of heir coverage and how real GDP per capia has been measured 3. his secion illusraes he differences in New Zealand s growh rae in real GDP per capia when differen daa ses are used. Six daa ses are used in his illusraion. heir deails are shown in able 5. 3 For some longer series he way in which GDP per capia is measured may no be consisen across he whole series, raising doubs abou he validiy of some comparisons across ime. WP 0/4 Measuring Economic Growh in New Zealand

18 able 5 Sources of New Zealand real GDP per capia daa used in his paper Daase Source Coverage Addiional Deails OECD($US) OECD(PPP) Calibraed chain-weighed real producion GDP per capia series Maddison(00) ear beginning April 970 o year beginning April 000 ear beginning April 970 o year beginning April 000 ear beginning April 978 o year beginning April 999 ear beginning April 950 o year beginning April 998 GDP per capia a he price levels and exchange raes of 995 (US dollars) As published in OECD(00) alhough daa obained elecronically hrough OLISNE GDP per capia a he price levels and purchasing power pariies (PPP) of 995 (US dollars) As published in OECD(00) alhough daa obained elecronically hrough OLISNE Annual real GDP series obained by aggregaing Haugh (00) s quarerly series. Per capia adjusmen made using populaion daa. GDP per capia in 990 Geary- Khamis dollars. As published in Maddison (00). Penn World ables (PW5.6) o 99 he variable RGDPCH is used. his is Real GDP per capia in consan dollars (Chain Index) expressed in inernaional prices, base 985. Preliminary Penn World ables (PW6.0) o 997 he variable RGDPCH is used. his is defined as Real per capia GDP chain mehod (996 prices). his daase is ye o be finalised bu updaes and exends he ime coverage of he previous PW release. he New Zealand series described in his able are presened in Appendix B. For each of hese series New Zealand s average growh rae over every possible en-year window has been calculaed using he average annual growh rae (AAGR) approach oulined in Secion 3. As he series are of differen lenghs he number of possible windows for each series also differs. Figure 5 shows he average growh rae for each en-year period ploed agains he window endpoin. 6 his means ha a value for, say, 990 represens he average growh rae over he period 980 o 990. Likewise, a value 4 Alan Heson, Rober Summers, Daniel Nuxoll and Beina Aen, Penn World ables Version 5.6, Cener for Inernaional Comparisons a he Universiy of Pennsylvania, January Alan Heson, Rober Summers and Beina Aen, Penn World able Version 6.0, Cener for Inernaional Comparisons a he Universiy of Pennsylvania, December 00 6 Appendix C provides he numerical values ploed in Figures 5 and 6. WP 0/4 Measuring Economic Growh in New Zealand 3

19 for 970 represens he average growh rae over he period 960 o 970. Figure 5 illusraes he variaion beween he average growh rae for a en-year period when differen daa ses are used. One feaure of Figure 5 is ha here appears o be more variabiliy in he growh raes obained using differen daa ses earlier on in he sample. his is paricularly he case if one omis he preliminary Penn World able daa ha is ye o be finalised. However, i is worh poining ou ha as he graph displays he average growh rae for a en-year period even small differences would resul in maerial differences in real GDP per capia over ime. For example, even when we exclude he preliminary Penn World able daa, he average growh rae for he period ending 99 (ie 98 o 99) differs beween daa sources by up o a bi under 0.5% per annum. If acual performance was o differ by his much hen real GDP per capia would have increased by nearly 5% more over he en year period when comparing performance for his period under he highes and lowes growh esimaes. Figure 5 A comparison of New Zealand s growh raes obained from differen daa ses (NZ growh raes measured over differen 0 year windows) 4 Annual average growh rae (%) Window Endpoin Calibraed Maddison0 OECD PW5.6 Prelim. PW6.0 Noe: he average annual growh rae mehod was used o obain he average growh raes presened in his figure. WP 0/4 Measuring Economic Growh in New Zealand 4

20 Figure 6 A comparison of New Zealand s growh raes obained from differen daa ses (NZ growh raes measured over differen 0 year windows) Calibraed Maddison OECD PW Prelim. PW6.0 Noe: he average annual growh rae mehod was used o obain he average growh raes presened in his figure. Verical axis displays annual average growh rae (%) Horizonal axis displays year of window endpoin Figure 6 illusraes he growh raes for each series shown in Figure 5 separaely (using consisen scales). Casual observaion of he Maddison and PW plos in Figure 6 could sugges a downward rend over ime in New Zealand s average growh rae. However such a conclusion is likely o be misleading due o changes over ime in he way in which real GDP for New Zealand has been measured. WP 0/4 Measuring Economic Growh in New Zealand 5

21 4. Changes in he way New Zealand real GDP is measured Over ime here have been effors o improve he way real GDP is measured. Unforunaely, however, hese improvemens mean ha real GDP series consruced on a consisen basis and covering a long hisorical ime period are no available. Consequenly long ime series of annual GDP daa eiher end o include daa consruced in several differen ways or require a considerable proporion of he series o be based on esimaed raher han measured values. Saisics New Zealand released upgraded naional accouns a he end of 000 and in mid 00. hese inroduced a number of imporan changes, including moving from a fixed weigh o a chain linked calculaion of consan price (real) daa, he adopion of he inernaional accouning sandard, Sysem of Naional Accouns 993 (SNA93), and he Ausralia New Zealand Sandard Indusrial Classificaion (ANZSIC). Real GDP figures back as far as he June quarer of 987 are available on his consisen basis. hese new SNA93 chain linked series are now New Zealand s official daa series and replace he previous official series ha was based on a differen accouning sandard called Sysem of Naional Accouns 968 (SNA68). he previous official series was also a fixed weigh raher han chain weighed series (more deails of wha his means are provided below). he previous official fixed weigh series was available from Sepember Wha his means is ha real GDP series ha provide esimaes of New Zealand s real GDP for ime inervals ha include 977 are likely o include daa ha is consruced in several differen ways. When his is he case, esimaes of economic performance for differen sub periods are probably no sricly comparable and unforunaely here is no easy way around his. 4. Differen approaches o consrucing real GDP series (Chain versus Fixed weighs) and heir influence on growh raes Annual GDP series measure he oal value of goods and services produced in an economy over a -monh period. Nominal GDP series simply sum over all possible goods and services he oal value of each ype of good or service produced in he monhs. For each good or service, he oal value is he number of unis of he good or service produced, muliplied by he price of a uni of ha good or service for ha year. An increase in nominal GDP from one year o he nex can herefore be aribued o an increase in prices, an increase in he volume of goods and services produced, or mos probably, some combinaion of hese wo. For example, if in year all prices are 0% higher han hey were in year, and he same quaniy (volume) of each good or service is produced, hen nominal GDP will be 0% higher. If hese goods and services mus be shared amongs he same number of people in each year, is he counry beer off? he answer is no as in aggregae people have he same quaniy of goods and services available for consumpion. Real GDP series overcome his problem by removing he impac of price changes. Consequenly, changes in real GDP reflec changes in he volume or quaniy of goods and services produced. Such a series is commonly referred o as being expressed in consan prices or real erms. here are several approaches o doing his, wih he approaches differing in he choice of which year s prices are used in he consrucion of 7 he calibraed real GDP series produced by Haugh (00) comprises of Saisics New Zealand s quarerly chain series from June 987 onwards appended o a calibraed chain series for he period back o Sepember 997. he laer is derived by exploiing he saisical relaionship beween he period of overlapping chain and fixed series (987: o 000:). (Buckle, Haugh and homson, 00) WP 0/4 Measuring Economic Growh in New Zealand 6

22 he index. 8 As is illusraed below, he choice of which year s prices are used has implicaions for he growh raes ha can be obained from he series. his secion begins by considering he difference beween wo ypes of volume indexes (he Laspeyres and Paasche indexes). A Laspeyres index calculaes he oal value of GDP holding prices consan a heir firs year levels. able 6 presens a heoreical example of real GDP in he firs and second year consruced using he Laspeyres mehod (noe he oal value of each commodiy for each year uilises he firs year s prices). In he example, real GDP has grown by 8.%. able 6 Example of a Laspeyres Index ear ear Quaniy q Price p Value p q Quaniy q Value p q Commodiy A B C oal (real GDP) Source: Saisics New Zealand (998) - wih very minor amendmens A Paasche index calculaes he oal value of GDP holding prices consan a heir second (or las) year levels. able 7 presens a heoreical example of real GDP in he firs and second year using he Paasche mehod (noe he oal value of each commodiy for each year uilises he las (second) year s prices). In he example, real GDP has grown by 5.4%. able 7 Example of a Paasche Index ear ear Quaniy q Value p q Quaniy q Price p Value p q Commodiy A B C oal (real GDP) Source: Saisics New Zealand(998) - wih very minor amendmens Clearly he growh rae is dependen on which approach (Laspeyres or Paasche) is used. he resul ha he growh rae of he Laspeyres index is greaer han he growh rae shown by he Paasche index is no jus due o he consrucion of he example 9. he reason why Laspeyres indexes end o exhibi higher growh han Paasche indexes is due o he subsiuion effec ha occurs when relaive price changes occur. People end o purchase more of goods ha have become relaively cheaper and less of goods ha have become relaively more expensive. Consequenly goods ha have become relaively cheaper end o have faser growh (in erms of numbers of unis produced and consumed) and goods ha have become relaively more expensive end o have slower growh. By using firs year prices (before he relaive price changes), he Laspeyres approach gives a higher weigh o fas growing commodiies and a smaller weigh o slow growing commodiies. 8 his discussion relies heavily on Saisics New Zealand (998). 9 Noe ha he physical quaniies of he goods produced are he same in boh ables 6 and 7. WP 0/4 Measuring Economic Growh in New Zealand 7

23 In erms of wha drives differences in he growh raes obained from he wo approaches, Saisics New Zealand (998) saes Wha maers is he exen o which he paern of relaive prices (ie he raio of he price of one commodiy o anoher) changes over ime and no he general rae of inflaion. If all prices were o increase a he same rae he wo volume indices would be equal, bu if some prices go up faser han ohers, and especially if some go down while ohers go up, he wo volume indices will diverge. he more variaion here is in he price changes, he more he volume indexes will diverge. hings become even more complex when one is ineresed in consrucing values for real GDP over more han periods. here are wo general approaches. he firs is known as he fixed weigh index approach and uses he prices of jus one period. Real GDP for each period in he series is calculaed by muliplying he price of each commodiy (in he chosen base year) by he quaniy of he commodiy produced in he year for which real GDP is being calculaed. Unil recenly, his is he approach ha Saisics New Zealand used and when using his approach 99/99 was chosen as he base year s prices o be used. For each year, he quaniy of a paricular commodiy produced was muliplied by ha commodiy s 99/99 price. Summing his produc over all commodiies gave a value for real GDP expressed in 99/99 prices. Consequenly, he values of real GDP prior o 99/99 are consruced using he Paasche index approach (as he 99/99 prices being used relae o a laer period han he quaniies of commodiies produced). On he oher hand, values of real GDP for years afer 99/99 uilise he Laspeyres index approach. As a Laspeyres index ends o regiser higher growh raes han a Paasche index, his means ha i is likely ha growh prior o 99/9 (based on a Paasche index) would be undersaed o growh pos 99/99 (based on a Laspeyres index). One issue ha arises wih fixed weigh series is ha he growh raes beween consecuive years are sensiive o he choice of base year chosen. In general, moving he base year forward in ime will end o reduce growh raes previously recorded so ha hey have o be revised downwards. Hisory is rewrien. (Saisics New Zealand, 998) Saisics New Zealand (998) provides an illusraion of his by comparing annual growh raes for oal real gross domesic expendiure when 99/9 prices were used wih he growh raes when 98/83 prices are used. 0 able 8 reproduces a able summarising he resuls. As can be seen from he able he differences in annual growh raes are quie subsanial. able 8 Comparison of annual growh raes for fixed weigh real gross domesic expendiure series wih differen base years ear ended March Published base- Published base- Difference weighed series in 98/83 prices: percen growh from previous year weighed series in 99/9 prices: percen growh from previous year Source: Based on able C from Saisics New Zealand (998) he second general approach o obaining real GDP values for muliple years is known as he annual chain-linked approach and his mehod updaes he price weighs used every 0 Unforunaely his is no a pure experimen as changes o mehodology and revisions o componen series also conribue o differences in growh raes. WP 0/4 Measuring Economic Growh in New Zealand 8

24 year. For he period 987 o 000, he chain-linked real GDP series is derived by calculaing he (percenage) change beween 987 and 988 using 987 prices o value he quaniies in 987 and 988. he change beween 988 and 989 is calculaed using 988 prices o value he quaniies in 988 and 989 and so on. o obain a series of real GDP figures based on 995 prices he following approach is used. For each year a measure of he oal change beween he year of ineres and he year 995 is obained by muliplying ogeher he annual changes beween consecuive years. For years prior o 995, he value of 995 real GDP (which will equal he nominal GDP for 995 as 995 prices are being used) is divided by he by he appropriae oal change figure. For years pos 995 he 995 value for real GDP is muliplied by his amoun. Noe ha he above approach o obaining a chain-linked series is known as a Laspeyres chain linked approach as for each pair of years he prices of he earlier year are used. If he laes year s prices were used for each pair he resuling index would be a Paasche chain index. If relaive prices change monoonically using chain weighs insead of fixed weighs end o resul in a growh rae somewhere beween ha of a fixed Laspeyres or fixed Paasche index. As oulined above, Saisics New Zealand has upgraded New Zealand s Naional Accouns by moving from fixed o (Laspeyres) chain weighs. heoreically his should increase growh raes prior o 99/9 as a chain Laspeyres index will produce higher growh raes han a fixed Paasche. he upgrade would also heoreically reduce growh raes afer 99/99 as a chained Laspeyres index will resul in lower growh raes han a fixed Laspeyres index. Experimenal work by Saisics New Zealand based on real (expendiure based) GDP series showed ha when moving from a fixed weigh mehod o a Laspeyres chain weighed mehod for consrucing real GDP series he differences in (annual) growh raes are less han 0.3 percenage poins alhough he annual growh rae beween he 994 and 995 March years was as high as 0.6 percenage poins (see Saisics New Zealand (998) for more deails). he key poin o be aken from his secion is ha here are a number of measuremen issues associaed wih measuring real GDP and consequenly wih measuring he growh in real GDP per capia. As a resul here probably does no exis a definiive or rue calculaed value for he hisorical rae of growh in a paricular period. Differen approaches o measuring or consrucing real GDP series have resuled in he various series for real GDP per capia ha are available no being idenical. herefore, he average growh rae for a period of ineres will end o vary across series. Consider he following example. 99 GDP measured in 99 prices is 5% higher han 99 GDP. 993 GDP measured in 99 prices is 4% higher han 99 GDP. 994 GDP measured in 993 prices is 6% higher han 993 GDP. 995 GDP measured in 994 prices is % higher han 994 GDP. Consequenly 995 real GDP is.05 x.04 x.06 x.0.69 imes as grea as 99 real GDP. If GDP in 995 was $00 billion hen 99 real GDP would be $85.54 billion. Noe ha he Saisics New Zealand publicaion inerpres he difference beween, say,.% and.4% as being percenage poins. A more common inerpreaion of a percenage poin would be he difference beween, say, % and 3% and herefore he difference beween.% and.4% would be regarded as 0. percenage poins. In his paper I have used his more common inerpreaion and herefore have amended he percenage poin differences presened in he Saisics New Zealand publicaion accordingly. WP 0/4 Measuring Economic Growh in New Zealand 9

25 5 Measured New Zealand growh raes over ime One poin ha should be noed when considering New Zealand s average growh rae over a paricular sub-period is ha he growh rae can be quie sensiive o he endpoins (or ime period) chosen. able 9 shows New Zealand s growh rae based on OECD daa for a number of differen lengh sub-periods. o illusrae he sensiiviy of he average growh rae for a period, consider he average growh rae for he period 988 o 994 (a 6 year window wih window endpoin 994). he average growh rae for his sub-period is 0.63 percen. Compare his o he growh rae for he period 987 o 993. he average growh rae for his period was -0.0 percen per annum. hese growh raes differ significanly ye he sar and end of he six year period under consideraion differ by only one year. able 9 - New Zealand Growh Raes for Differen Window Endpoins and Window Lenghs based on OECD daa Window endpoin Window lengh Max Growh Raes calculaed using average annual change mehod. Example: he growh raes wih window endpoin 999 and window lengh 8 is calculaed using real GDP daa for he years 99 hrough o 999. Highlighed figures show he highes average growh rae for each window lengh. For example if one focuses on growh raes for sub periods ha are 7 years long, he highes growh rae for any period of his lengh was.5% and his relaes o he period 99 o 999. WP 0/4 Measuring Economic Growh in New Zealand 0