CAPITAL STOCKS, CAPITAL SERVICES AND MULTI-FACTOR PRODUCTIVITY MEASURES

Transcription

1 OECD Economc Sudes, No. 37, 2003/2 Chaper 1 CAPITAL STOCKS, CAPITAL SERVICES AND MULTI-FACTOR PRODUCTIVITY MEASURES Paul Schreyer TABLE OF CONTENTS Inroducon Capal servces concepual framework Producon funcon Producve sock and capal servces wh geomerc profles Ne (wealh) sock Producve sock and capal servces wh hyperbolc profles Capal servces resuls Capal servces and MFP measures Conclusons Noes Bblography Annex 1. OECD Mehodology The auhor, who s Head of he Prces and Oureach Dvson n he Sascs Drecorae, would lke o hank Drk Pla and Joaqum Olvera Marns for helpful commens on a draf verson of hs paper. 163

2 INTRODUCTION Measures of producvy are cenral o he assessmen of economc growh. Measures of mul-facor (oal facor) producvy or of capal producvy rely on he avalably of sascal seres on he prces and quanes of capal servces ha ener he producon process. Two OECD manuals, Measurng Producvy (2001) and Measurng Capal (2001) have descrbed he concep and measuremen of capal servces and her relaon o he beer-known measures of gross and ne capal sock. Boh manuals are very clear n her recommendaon ha volume ndces of capal servces are he approprae measure of capal npu for acvy and producon analyss. Unforunaely, o dae only a small number of counres produce me seres of capal servces as par of her offcal sascs. 1 The OECD has hus developed a se of capal servce measures for a broader number of counres. Ths paper provdes an overvew of he conceps and mehods underlyng capal servces measures, repors resuls for he G-7 counres and dscusses some of he consequences for measured raes of mul-facor producvy growh. CAPITAL SERVICES CONCEPTUAL FRAMEWORK Capal servces measures are based on he economc heory of producon. The concep relaes back o he work of Jorgenson and Grlches (1967) wh furher developmens manly n he producvy leraure such as Jorgenson (1995), Hulen (1990), Trple (1996, 1998), Hll (2000) and Dewer (2001). 164 In a producon process, labour, capal and nermedae npus are combned o produce one or several oupus. Concepually, here are many faces of capal npu ha bear a drec analogy o measures of labour npu. Capal goods ha are purchased or rened by a frm are seen as carrers of capal servces ha consue he acual npu n he producon process. Smlarly, employees hred for a ceran perod can be seen as carrers of socks of human capal and herefore reposores of labour servces. Dfferences beween labour and capal arse because producers usually own capal goods. When he capal good delvers servces o s owner, no marke ransacon s recorded. The measuremen of hese mplc ransacons whose quanes are he servces drawn from he capal sock durng a perod and whose prces are he user coss or renal prces of capal s one of he challenges of capal measuremen for producvy analyss. 2

3 Capal Socks, Capal Servces and Mul-facor Producvy Measures Producon funcon For any gven ype of asse, here s a flow of producve servces from he cumulave sock of pas nvesmens. Ths flow of producve servces s called capal servces of an asse ype and s he approprae measure of capal npu for producon and producvy analyss. Concepually, capal servces reflec a quany, or physcal concep, no o be confused wh he value, or prce concep of capal. To llusrae, ake he example of an offce buldng. Servce flows of an offce buldng are he proecon agans ran, he comfor and sorage servces ha he buldng provdes o personnel durng a gven perod. Capal servces are an negral par of a durable goods model of producon, self characersed by a producon funcon, say G ha s separable n he servces of dfferen vnages of dfferen ypes of capal goods: Q = 1 G( K [ K, K 2,..., K N ], L, ) [1] 1 2 N In (1), K[ K, K,..., K ] s an aggregaor of capal servces from N dfferen ypes of asses, Q s an aggregae measure of he volume of oupu, and are L labour npus n he producon process. The capal servce measure for each ype of asse say a parcular ype of machne or buldng s self an aggregaor across dfferen vnages of hs asse: K = K [ K,0, K,1,... K ] where K, T, τ s he capal servce flow a me from a τ-year old asse of ype. The assumed separably of K from oher elemens n he producon funcon mples ha he margnal rae of subsuon beween any par of vnages of a parcular ype of asse s ndependen of oher npus. Ths s mporan nsofar as allows consrucng he capal servces measure from he boom up and ndependenly of oher npus n he producon process. The purpose of he emprcal work presened here s herefore o measure capal servces aggregaes for each asse and o derve a oal aggregae of capal servces, noably for s rae of change, K / K 1. Even hough here s lle new abou (1), here are mporan dfferences o more common represenaons of capal n he producon process. Many exbooks and emprcal work sar from a producon funcon G( K, L, ) where K G G s he gross (or somemes he ne) sock of capal. Ths presens n fac a specal case of (1) when here s only one homogenous ype of asse or n he absence of any subsuon possbles beween dfferen ypes of asses. The rae of G change of K would hen equal he rae of change of capal servces, K. In he more general conex dscussed here, he respecve raes of change wll be dfferen beween hese measures, causng poenal bases n producon and producvy analyss f measures of gross or ne socks are used nsead of capal servces. 165

4 OECD Economc Sudes No. 37, 2003/2 Producve sock and capal servces wh geomerc profles For exposonal purposes, and o relae he capal servces approach o oher capal measures, a smplfyng bu wdely-used assumpon wll be made here, namely ha of geomerc age-effcency and age-prce profles. An age-effcency profle descrbes how he producve effcency of an oherwse homogenous asse evolves as he asse ages. An age-prce profle descrbes he relave prce of dfferen vnages of he same asse a a gven pon n me. The geomerc age-prce profle posulaes ha he effcency of asse ype declnes a a consan rae, say δ. Le I be he quany of nvesmen n new asses of ype n 1 year 1. Then, ( 1 δ )I wll be he volume ha remans producvely effcen 1 n year. More generally, he producve sock of asse a me s gven by: 166 τ = 0 τ S = (1 δ ) I τ Implc n he addve presenaon of he producve sock s an assumpon abou he perfec subsuably beween dfferen vnages. 3 Thus, he producve sock s expressed n new equvalen uns of he capal good. I s furher assumed ha he flow of capal servces K s proporonal o he producve sock a he end of he prevous perod: K =λs 1 Wh lle loss of generaly, he proporonaly facor λ s se o uny for all asse ypes. 4 The nex ssue s o consder he prce of renng one un of he producve sock for one perod. If here were complee markes for capal servces, renal prces could be drecly observed. In he case of he offce buldng, renal prces exs and are observable n he marke. Ths s, however, no he case for many oher capal goods ha are owned and for whch renal prces have o be mpued. The mplc ren ha capal good owners pay hemselves gves rse o he ermnology user coss of capal ha s used synonymously wh renal prce n hs paper. 5 To deermne he renal prce, we use he hypohess ha n a funconng asse marke, he purchase prce of a capal good equals he dscouned value of s expeced renals (Box 1). The renal prce/user cos for a new asse a me urns ou o be uc (,0 = q 1, 0 r +δ ζ ). The erm n brackes consues he gross rae of reurn ha one dollar nvesed n he purchase of capal good mus yeld n a compeve marke. The gross rae of reurn self comprses hree erms: A rae of deprecaon δ : deprecaon s he loss n marke value of a capal good due o ageng. In he general case, deprecaon may vary over me and depend on he vnage. In he presen case of geomercally declnng effcency, he prce urns ou o declne a he same geomerc rae. Ths faclaes compuaons sgnfcanly and mples ha he prce rao of a one-year [2] [3]

5 Capal Socks, Capal Servces and Mul-facor Producvy Measures Box 1. Dervng he user coss of capal In a fully funconng asse marke, he purchase prce of an asse wll equal he dscouned flow of he value of servces ha he asse s expeced o generae n he fuure. Ths equlbrum condon s used o derve he renal prce or user cos expresson for asses. Le q, 0 denoe he purchase prce n year of a new (zero-year old) asse of ype, and le u be he renal prce ha hs asse s +τ, τ expeced o fech τ perods laer (frs subscrp o he rgh) when he asse wll be of age τ (second subscrp o he rgh). Wh r as he nomnal dscoun rae vald a me, he asse marke equlbrum condon for a new asse (age zero) becomes: q ( τ + 1), 0 = u = , (1 ) τ τ τ r Ths formulaon mples ha renals are pad a he end of each perod. To solve hs expresson for he renal prce, he prce for a one year old asse n he perod + 1 s compued as ( τ + 1) q+ 1,1 = u and hen subraced from he expresson above o oban u or = , 1(1 ) τ τ τ r + 1,0 = q,0( 1+ r) q+ 1, 1 u whch can be ransformed no., 0 = q 1,0 ( 1+ r) q, 1 u (, 0 = q 1, 0 r + δ ζ + δ ζ ) As n he man ex, he shorhand noaon for deprecaon, δ, and for asse prce changes, ζ, are used. The resul s he user cos expresson shown n he ex alhough he neracon erm δ ζ ha arses n a dscree me formulaon has been lef ou here for exposonal smplcy. Jorgenson and Yun (2001) show how ax consderaons ener he user cos of capal and how hey affec measured economc performance. Due o a lack of avalable daa, such fscal parameers could a presen no be consdered n he OECD se of user coss and capal measures. old asse over a new asse s consan and equal o he prce rao of an s-year q, s s k old asse of an s+1-year old asse: = (1 δ ) where s and k are any wo pons n he servce lfe of asse. q, k A revaluaon or capal gans erm ζ, defned as he expeced asse prce change beween he begnnng and he end of he perod: ζ. q, 0 / q 1, 0 1 Because he revaluaon erm eners no he user cos expresson wh a negave sgn, a fall n asse prces rases user coss. For example, renal prces for personal compuers have o facor n he fall n marke prces and he ensung loss n value of he compuers ha are n use. A ne rae of reurn r he expeced remanng remuneraon for he capal owner once deprecaon and asse prce changes have been aken no 167

6 OECD Economc Sudes No. 37, 2003/2 accoun. The choce of r s a maer of mporance: he value of he user cos erm deermnes he value of capal servces of asse as well as he overall remuneraon of capal. One way o choose r s by seng so ha he resulng value of capal servces exacly exhauss he value of non-labour ncome (gross operang surplus) ha s compued n he naonal accouns. Whle compuaonally convenen, hs procedure requres addonal resrcve assumpons. Anoher possbly s o choose an exernal ne rae of reurn. Whle no exra assumpons are needed here, he resulng value of capal servces does no necessarly add up o gross operang surplus and hs complcaes growh accounng exercses. Also, a choce has o be made as o he exac measuremen of he exogenous rae. Despe hs complcaon, he exogenous approach has been pu forward as he preferred one n he presen exercse. As he prce of capal servces s gven by he user cos of capal, he produc of hs prce and he quany of servces yelds he value of capal servces for asse ype : uc, 0K = uc,0s 1. By aggregang across all asse ypes, one obans he overall value of capal servces uc. K = uc, 0K Jorgenson (1963) and Jorgenson and Grlches (1967) were he frs o develop hese aggregae capal servce measures ha ake he heerogeney of asses no accoun. They defned he flow of quanes of capal servces ndvdually for each ype of asse, and hen appled asse-specfc user cos shares as weghs o aggregae across servces from he dfferen ypes of asses. Because user coss shares reflec he relave margnal producvy of he dfferen asses, hese weghs provde a means o effecvely ncorporae dfferences n he producve conrbuon of heerogeneous nvesmens no he overall measure of capal npu. A cusomary and heorecally recommended ndex number formula o consruc a volume ndex of capal servces s he Törnqvs ndex ha apples average user cos weghs o each asse s rae of change n capal servces: where: + 1 K ) = 0.5( v v )ln( K + ln( K 1 K ) v uc K uc K [4] Ne (wealh) sock 168 I s nsrucve o compare he volume ndex of capal servces and he oal value of capal servces wh he more famlar ne capal sock and s rae of change a curren and consan prces. 6 Whereas he producve sock s desgned o capure he producve capacy of capal goods, and by mplcaon he flow of

7 Capal Socks, Capal Servces and Mul-facor Producvy Measures capal servces, he wealh (ne) sock measures he marke value of capal asses. Wealh sock s somemes consdered a more precse ermnology, however, because here are oher forms of ne sock, n parcular he producve sock whch s a sock ne of effcency declnes n producve asses. In he presen seng, he ne sock a curren prces s obaned by valung each asse s producve sock by he marke prce of he correspondng new asse. The oal value of he ne sock s obaned by addng he ndvdual values of each asse: = q. W q = S 1 q K The rae of change of he ne sock a consan prces depends agan on he ndex number formula chosen for aggregaon across asses. One obvous possbly s o employ agan a Törnqvs-ype formula o oban: where + 1 W ) = 0.5( w w )ln( W + ln( W 1 W ) w q K,0 q,0 K [5] Because he ne sock s a concep ha s well anchored n he sysem of naonal accouns, mos OECD counres publsh daa for a ne sock of fxed asses. However, hese seres are no normally aggregaed hrough Törnqvs ndces: he majory of counres use a Laspeyres-ype volume ndex 7 whch nroduces an addonal dfference beween measures of capal socks avalable from he naonal accouns and measures of capal servces for producvy analyss. To conclude, here are wo key feaures ha dsngush he rae of change of he capal servces measure from ha of he ne capal sock: he weghng scheme and n many cases he ndex number formula used. In perods of rapd change of relave prces and volumes boh elemens conrbue o poenally sgnfcan dfferences beween he me profles of he wo measures. Usage of he ne sock n producvy compuaons nsead of he capal servces measure can hen gve rse o a based sasc of mul-facor producvy. To llusrae, Fgure 1 below compares he wo measures for he Uned Saes and for France and Box 2 provdes a numercal example. Producve sock and capal servces wh hyperbolc profles The use of geomerc paerns o descrbe he effcency and prce profles of asses s compuaonally convenen. Also, here s emprcal evdence for prce profles ha resemble geomerc paerns. Everyday experence suggess ha he prces of asses declne by relavely large absolue amouns n he frs years afer her purchase a 20 per cen drop n he value of a new car durng s frs year of 169

8 OECD Economc Sudes No. 37, 2003/2 Fgure 1. Capal servces and ne capal sock 1 Capal servces Ne capal sock Uned Saes France Based on geomerc age-effcency and age-prce profle and harmonsed ICT deflaors. Aggregaon hrough Törnqvs ndces. Source: Derved from OECD Capal Servces Daabase (Ocober 2003). usage s a well-know emprcal phenomenon. However, s he same paern plausble when comes o descrbng he relave effcency of a vnage produc? For example, does a car loose one ffh of s capacy o generae ranspor servces durng s frs year of usage? Based on a sngle capal em, he answer o hs queson wll ofen be no and hs suggess adopng an approach ha allows for dfferences n he effcency and n he prce profles of asses whle keepng he wo proflesconssen. 170 The OECD capal servces measure s based on a hyperbolc paern for s effcency profle and derves a conssen prce profle. A hyperbolc paern assumes a slow loss n producve effcency over he frs years of an asse s servce lfe and a more rapd declne owards he end of he servce lfe. Ths s shown n Fgure 2. I reproduces he age-effcency profle for ranspor equpmen an asse whose average servce lfe s aken o be 15 years. Neher he hyperbolc nor he geomerc paern breaks off a he 15 years. In he case of he hyperbolc curve, an assumpon has been made ha reremen of a cohor s dsrbued around he medan servce lfe of 15 years. In he case of he geomerc paern, no explc reremen funcon s formulaed. I s assumed ha he geomerc declne capures boh he effecs of wear and ear and reremen.

9 Capal Socks, Capal Servces and Mul-facor Producvy Measures Box 2. Wealh sock and capal servces n he presence of echncal change a numercal example The choce of aggregaon weghs becomes crucal when prces and quanes of dfferen ypes of capal goods evolve a very dfferen raes. Ths s, for example, he case when here s relavely rapd qualy change of one ype of asse compared wh ohers. Aggregaon of asses by way of purchase prces wll generae a serous bas n he capal npu measures because purchase prces wll nadequaely approxmae he margnal producvy of asses whch consue he approprae weghs for aggregaon of capal servces. User coss are desgned o reflec he margnal producvy of asses: capal goods are employed unl her margnal revenue (self dependen on margnal producvy) equals margnal cos (he user cos or renal prce) of an asse. The dfference beween purchase prces (q) and user coss (uc) s he gross rae of reurn (GRR) ha an asse mus yeld per year: uc = q*grr. The gross rae of reurn self s composed of he ne rae of reurn, he rae of deprecaon and rae of revaluaon or asse prce change. Rapd negave prce changes or large raes of deprecaon herefore mply large gross raes of reurn and user coss. Thus, an aggregaon based on user cos weghs wll gve more wegh o asses wh relavely large GRRs as opposed o an aggregaon based on purchase prces, q. Consder he followng example wh wo asses, A and B. In perod = 0, he purchase prce of boh asses equals un bu declnes by 30 per cen n he case of A and rses by 10 per cen n he case of B. Gven he quanes of nvesmen and he (geomerc) raes of deprecaon, a capal sock n perod = 1 can easly be calculaed. In he presen case, wealh and producve sock concde a he level of ndvdual asses. Assume a ne rae of reurn of 5 per cen. The oal user cos s hen compued as 0.55 for Asse A and 0.15 for Asse B. Ths gves rse o a share of Asse A n oal user coss n perod = 0 of 79 per cen and a share of Asse B of 21 per cen que dfferen from he 50 per cen share for each asse when weghs are based on purchase prces. Fnally, consruc a smple Laspeyres quany ndex of capal servces and he wealh sock and s easy o see ha he former rses much faser han he laer. Asse A Asse B Purchase prce = = Quany of Invesmen = = Producve sock/wealh sock = = User coss Ne rae of reurn Deprecaon Revaluaon Toal Weghs = 0 User cos based Purchase prce based Laspeyres quany ndex User cos based 2.15 Purchase prce based

10 OECD Economc Sudes No. 37, 2003/2 Fgure 2. Hyperbolc and geomerc age-effcency paern Average servce lfe 15 years Hyperbolc Geomerc Capal servces measures are sensve o he choce of he age-effcency profle. For example, capal servces measures based on geomerc age-effcency profles rse by 1.5 per cen per year on average n Ausrala over he perod The same varable based on hyperbolc profles grows a 2.2 per cen per year. Smlarly, he geomercally-based seres for he Uned Saes exhbs a 3.4 per cen growh rae over he same perod whereas he hyperbolc paern produces a growh rae close o 4 per cen. In France, he fgures are 2.5 per cen per year (geomerc) and 3.1 per cen per year (hyperbolc). CAPITAL SERVICES RESULTS 172 The followng secon presens a se of capal servce measures for he G-7 counres and Ausrala. The resuls presened are based on a more general model han he one se ou n he second secon of hs paper. In parcular, effcency profles were no assumed o be geomerc. Resuls based on geomerc profles are also avalable from he daabase bu as a specal case. To sar ou, Table 1 shows he volume changes of capal servces, by ype of asse or by ype of produc. A he level of ndvdual asses, he rae of change of capal servces s jus equal o he evoluon of he producve sock. The aggregae ndex of capal servces (Table 2) corresponds o a weghed average of he each asse s ndex of

11 Capal Socks, Capal Servces and Mul-facor Producvy Measures Table 1. Volume growh of capal servces by ype of asse 1 Compound annual percenage changes, oal economy, based on harmonsed deflaors for ICT asses Toal Producs of agrculure meal producs and machnery Hardware Oher on Sofware Oher Communcaon equpmen Oher producs Transpor equpmen Nonresdenal consruc- 1. Usng a hyperbolc age-effcency profle. Source: OECD capal servces daa base (Ocober 2003). Percenages Ausrala Canada n.a n.a n.a. France Germany Ialy Japan Uned Kngdom Uned Saes capal servces where nomnal shares n oal user coss consue he relevan weghs. Raes of change of deflaors can be found n Table 3. To accoun for some of he mehodologcal dfferences beween counres deflaors for nformaon and communcaon echnology producs, he resuls presened here are based on harmonsed deflaors (see Box 3). A frs way of assessng he se of capal servces measures produced here s o compare hem wh smlar daa publshed a he naonal level. Today, hs possbly for comparson exss only for a few counres. These are Ausrala (ABS publshes capal servces daa as par of s annual naonal accouns), he Uned 173

12 OECD Economc Sudes No. 37, 2003/2 Table 2. Volume ndex of capal servces (all asses) = 100, oal economy, based on harmonsed deflaors for ICT asses Ausrala Canada France Germany Ialy Japan Uned Kngdom Uned Saes n.a Usng a hyperbolc age-effcency profle. Source: OECD capal servces daa base (Ocober 2003). Saes (capal servces seres are publshed by he Bureau of Labor Sascs as par of s mulfacor producvy measuremen programme) and he Uned Kngdom where work s underway a ONS and where a frs se of capal servces daa has been publshed a he Bank of England (Oulon 2001). Sascs Canada has also compled a se of capal servces measures (Harchaou and Tarkhan 2002) and work s underway n Span (Mas e al. 2002). 174 A frs comparson of our resuls for Ausrala and hose publshed by he Ausralan Bureau of Sascs 8 reveals wo pons. Frs, he me profle of he OECD seres follows ha of he ABS seres farly closely. A he same me, and hs s he second observaon, here appears o be a sysemac downward bas (5.1 versus 3.7 per cen per year beween 1980 and 1999) of he OECD measures wh regard o he offcal sascs. Ths s, however, due o he fac ha he ABS seres relaes o he busness secor whereas our resuls concern he enre economy. When only prvae secor daa are used n he OECD model, a capal servce measure wh smlar raes of change o hose of he offcal ABS me seres s found. Oher small sources of dfferences n mehodology perss (e.g. ABS chooses

13 Capal Socks, Capal Servces and Mul-facor Producvy Measures Table 3. Prce ndces of capal goods by ype of asse 1 Compound annual percenage changes, oal economy, based on harmonsed ICT deflaors Producs of agrculure, meal producs and machnery Hardware Oher producs Nonresdenal Transpor equpmen consrucon Oher Sofware Oher Communcaon Equpmen 1. Usng a hyperbolc age-effcency profle. Source: OECD capal servces daa base (Ocober 2003). Percenages Ausrala Canada n.a n.a n.a. France Germany Ialy Japan Uned Kngdom Uned Saes an endogenous rae of ne reurn o capal, he OECD seres s based on an exogenous rae, ABS equaes acual and expeced prce changes n her user cos compuaons, OECD uses movng averages for prce expecaons, ec.). Overall, however, he seres f closely when hey relae o he same secor aggregae. A second comparson relaes o he OECD capal servces measures and hose of he Bureau of Labor Sascs. Over he enre perod , US capal npu grew by 3.8 per cen per year accordng o BLS, and by 3.7 per cen accordng o OECD esmaes. Ths small dfference over he enre perod hdes more sgnfcan dfferences over sub-perods ha end o offse on average. The OECD capal servces seres end o show a smooher profle han he offcal BLS 175

14 OECD Economc Sudes No. 37, 2003/2 Box 3. Inernaonal comparably of prce ndces Prce ndces are key n measurng volume nvesmen, capal servces and user coss. Accurae prce ndces should be consan qualy deflaors ha reflec prce changes for a gven performance of nvesmen goods. For example, observed prce changes of compuer boxes have o be qualy-adjused for comparson of dfferen vnages. Wyckoff (1995) was one of he frs o pon ou ha he large dfferences ha could be observed beween compuer prce ndces n OECD counres were lkely much more a reflecon of dfferences n sascal mehodology han rue dfferences n prce changes. In parcular, hose counres ha employ hedonc mehods o consruc ICT deflaors end o regser a larger drop n ICT prces han counres ha do no. Schreyer (2000) used a se of harmonsed deflaors o conrol for some of he dfferences n mehodology. We follow hs approach and assume ha he raos beween ICT and non-ict asse prces evolve n a smlar manner across counres, usng he Uned Saes as he benchmark. Alhough no clam s made ha he harmonsed deflaor s necessarly he correc prce ndex for a gven counry, he possble error due o usng a harmonsed prce ndex s smaller han he bas arsng from comparng capal servces based on naonal deflaors. However, for compleeness and ransparency, boh ses of resuls are avalable from he capal servces daabase. There s a dffculy wh he harmonsed deflaor ha should be noed. From an accounng perspecve, adjusng he prce ndex for nvesmen goods for any counry mples an adjusmen of he volume ndex of oupu. In mos cases, such an adjusmen would ncrease he measured rae of volume oupu change. A he same me, effecs on he economy-wde rae of GDP growh appear o be small (see Schreyer, 2001 for a dscusson). 176 resuls. Parly, hs may be explaned by he fac ha he BLS seres relaes o he prvae secor whereas OECD daa covers he enre economy. The hrd comparson relaes o he Uned Kngdom. Of he four comparsons, hs s clearly he case where dfferences are larges. However, a good deal of he dscrepancy beween OECD measures and Oulon (2001) can be raced back o he fac ha Oulon s esmaes are based on US prce ndces for ICT equpmen goods, adjused for exchange rae effecs. Such exchange rae effecs can be szeable and have been dscussed a greaer lengh n Schreyer (2002). The OECD seres here uses harmonsed deflaors: hey are hus also based on US daa bu no exchange rae adjused. Ths adjusmen for exchange rae movemens beween he UK pound and he US dollar nroduces larger flucuaons n he resulng volume seres. Ths comparson hus pons o he crucal mporance of prce ndces n producng capal servces and capal sock daa. Work s currenly underway n he UK Offce of Naonal Sascs o produce and release a seres of capal servces measures.

15 Capal Socks, Capal Servces and Mul-facor Producvy Measures The fourh comparson concerns Canada. On he face of, he capal servces seres released by Sascs Canada feaure a profle ha s sgnfcanly dfferen from he one obaned by OECD. However, several mporan mehodologcal dfferences accoun for such dscrepancy: frs, he OECD seres relae o he economy as a whole whereas Sascs Canada covers he prvae secor. Secondly, he Canadan seres are based on a geomerc age-effcency profle whereas OECD employs a hyperbolc paern. Thrd, Canada s user cos measures are based on an endogenous rae of reurn, hose compued by OECD on an exogenous rae. Fourh, here are sgnfcan dfferences n he servce lves employed n parcular buldngs and consrucon asses servce lves are sgnfcanly shorer n he offcal seres han n hose compued by OECD. A more dealed analyss can be found n Schreyer e al. (2003) who show ha afer correcon for he mehodologcal dfferences, he OECD model racks he offcal daa que closely: over he perod , Sascs Canada shows growh of capal servces a 3.2 per cen per year. The correspondng and comparable OECD resul s a 3.3 per cen annual growh. The Canadan case clearly shows he rade-off beween usng symmerc and reproducble assumpons for all counres a he nernaonal level, whch helps o mprove nernaonal comparably and he poenally more accurae nformaon for ndvdual counres (such as servce lves for Canadan asses). There s no shor-erm soluon o hs rade-off excep careful documenaon and explanaon of dfferences n he release of daa. CAPITAL SERVICES AND MFP MEASURES The mos mporan usage of capal servces measures s o assess mulfacor producvy (MFP) growh. I s, herefore, of neres o examne how he use of capal servces seres nsead of ne capal sock measures mpacs on he MFP resdual. A complee emprcal analyss would exceed he scope of hs paper 9 bu resuls wll be presened for hree counres by way of llusraon. To derve an MFP measure, 10 assume ha he producon funcon (1) has he 1 2 N form: Q where s a echnology parameer ha shfs = af( K[ K, K,..., K ], L ) a he producon funcon over me. Dewer (1976) showed ha f he npu aggregaor funcon F has a ranslog form, and when producers are prof maxmsng, he rae of echncal change beween perods + 1 and s gven by he rao of a volume ndex of oupu and a Törnqvs ndex of aggregae npus. In logarhmc form hs yelds: a ln Q K K K + 1 L L ( v + v ) ln + ( v + v ) 1 L N = ln = a Q K ln L [6] 177

16 OECD Economc Sudes No. 37, 2003/2 K uc K L w L where v, and v are each npu s share N N n oal cos. = uc K + w L 1 = uc K + w L 1 To assess he mporance of choosng capal servces measures over measures of gross or ne capal sock, we compue (5) n s curren confguraon and wh a ne capal sock measure. For he counres and perods under consderaon, he capal servces measure rses more rapdly han he ne sock measure (Table 4). Ths reflecs he composonal change n he producve capal sock where rapdly-growng asse ypes such as ICT equpmen receve larger weghs han n he ne sock measure. Ths effec s parcularly vsble for he Uned Saes and Ausrala (Table 4). Consequenly, he MFP resdual s lower n he frs case han n he second. Pu dfferenly, usng he ne capal sock as a measure of capal npu would lead o over-esmang MFP growh and under-esmang he conrbuon of capal asses o economc growh. Table 4. MFP growh, oal economy Percenage change a annual raes Ausrala Uned Saes France Oupu Capal servces Ne capal sock MFP based on capal servces MFP based on ne capal sock Based on geomerc age-effcency and age-prce profle and harmonsed ICT deflaors. Aggregaon hrough Törnqvs ndces. Source: Derved from OECD Capal Servces and Producvy Daabases (Ocober 2003). CONCLUSIONS The followng conclusons have emerged from he work on capal servces: 178 Compuaon of capal servces measures does no, n general, requre a larger se of daa or nformaon han he compuaon of gross and ne capal

17 Capal Socks, Capal Servces and Mul-facor Producvy Measures sock seres. Indeed, he dfferen capal measures are and should be all based on he same peces of sascal nformaon. The capal servces approach no only offers a ool for producvy measuremen bu also leads o a conssen eny of measures of he gross sock, he ne sock, prces and volumes of capal servces and consumpon of fxed capal. Somemes, here s a dssocaon of capal servces measures for producvy analyss from deprecaon and ne sock measures n he naonal accouns. Where possble, hese measures should be conssenly derved from he same model. Capal servces esmaes are sensve o he choce of deflaors, n parcular for fas-evolvng hgh-echnology producs. Bu assumpons abou age-effcency funcons and he choce of he rae of reurn also play a role. There s no unque bes way o deal wh some of hese ssues bu s obvous ha more and beer emprcal nformaon could sele a number of ousandng ssues n capal servces measuremen. The presen calculaons rase quesons abou he level of deal a whch OECD member counres publsh nvesmen daa. In parcular, here s a queson abou he level of asse deal ha s avalable. From he perspecve of capal servces measuremen, he separae recognon of ceran nvesmen goods (e.g. IT equpmen) wh large relave prce changes would be desrable. Ceran open quesons also reman: hey are boh of a concepual naure (e.g. he reamen of obsolescence, exogenous and endogenous raes of reurn) and of an emprcal naure (e.g. he form of age-effcency funcons, he choce of servce lves, or he comparably of prce ndces). Some of hese ssues may mer a specfc nernaonal effor o advance n a co-ordnaed manner, ohers wll requre new emprcal sudes a he naonal level o pu capal measures on a more sold emprcal foong. 179

18 OECD Economc Sudes No. 37, 2003/2 NOTES Ths s he case for Ausrala (ABS), he Uned Saes (BLS) and Canada (Sascs Canada). Resuls are forhcomng for Span (Mas e al. 2002). Recenly, work has also been aken up n he Uned Kngdom. 2. There has been a longsandng academc debae abou he naure of capal and s role n producon. One approach, also adoped n hs paper, concenraes on prces and volumes of capal servces. Anoher approach does no consder he servces of he capal good as fundamenal, bu wang,.e. he ac of foregong oday s consumpon n favour of buldng up capal goods and fuure consumpon (see Rymes 1971 for a dscusson). 3. Weaker assumpons han perfec subsuably are possble (Dewer 2001) bu wll no be presened here for ease of exposon. 4. See Schreyer e al. (2003) for a reamen ha does no make hs assumpon. 5. Ths s for smplcy only. In prncple, a dsncon should be made beween renal prces and user coss unless one assumes he added hypoheses of he exsence of complee and fully funconng markes for all ypes and vnages of capal goods. 6. The gross capal sock s anoher sasc frequenly avalable n OECD counres. I represens he cumulave flow of nvesmens, correced for a reremen paern. In he case of geomerc deprecaon/effcency profles, such a reremen funcon s absen because he geomerc paern exends o nfny, mplyng ha capal goods never rere even hough her producve effcency and value become nfnely small. Consequenly, he gross sock does no exs n hs case. Where exss, consues an nermedae sep n he calculaon of a producve sock ha akes accoun of he whdrawal of asses bu does no correc he asses n operaon for her loss n producve capacy. Alernavely, gross capal socks can be consdered a specal case of he producve sock, where he age-effcency profle follows a paern where an asse s producve capacy remans fully nac unl he end of s servce lfe (somemes called one-hoss-shay ). 7. A Laspeyres-ype aggregaon mples W where and 0 + W = w ( W + W ) q 0,0K w s he wegh reference perod. q 0,0K 8. Seres , Ausralan Sysem of Naonal Accouns. 9. See Wölfl (forhcomng) for a sensvy analyss of MFP measures wh regard o he choce of capal npu measures. 10. There s also a concepual ssue ha wll be lef asde here as o exacly whch MFP measure should be chosen n he presence of exogenous raes of reurn.

19 Capal Socks, Capal Servces and Mul-facor Producvy Measures BIBLIOGRAPHY BUREAU OF LABOR STATISTICS (1983), Trends n Mulfacor Producvy, , Bullen DIEWERT, Erwn D. (2001), Measurng he Prce and Quany of Capal Servces under Alernave Assumpons ; Deparmen of Economcs Workng Paper No 01-24, Unversy of Brsh Columba. DIEWERT, Erwn D. (1976), Exac and Superlave Index Numbers ; Journal of Economercs (4). HARCHAOUI, Tarek and Faouz TARKHANI (2002), A Comprehensve Revson of Sascs Canada s Esmaes of Capal Inpu for he Producvy Accouns ; Mehodologcal Noe, Sascs Canada. HARPER, Mchael, Erns R. BERNDT and Davd O. WOOD (1989), Raes of Reurn and Capal Aggregaon Usng Alernave Renal Prces ; n Jorgenson, Dale W. and Ralph Landau (eds.); Technology and Capal Formaon,MIT Press. HILL, Peer (2000); Economc Deprecaon and he SNA ; paper presened a he 26h conference of he Inernaonal Assocaon for Research n Income and Wealh; Cracow, Poland. HULTEN, Charles R. (1990), The Measuremen of Capal ; n Bernd, Erns R. and Jack Trple (eds.) Ffy Years of Economc Measuremen, Unversy of Chcago Press. JORGENSON, Dale W. and Kun-Young YUN (2001); Invesmen Volume 3: Lfng he Burden: Tax Reform, he Cos of Capal and US Economc Growh; MIT Press. JORGENSON, Dale W. (1995), Producvy; Volumes 1 and 2; MIT Press Cambrdge Massachuses and London, England. JORGENSON, Dale W. and Zv GRILICHES (1967), The Explanaon of Producvy Change ; Revew ofeconomc Sudes 34. JORGENSON, Dale W. (1963), Capal Theory and Invesmen Behavour ; Amercan Economc Revew, Vol. 53, pp MAS, Mahlde, Fracsco PEREZ and Ezequel URIEL (2002), Spansh New Capal Sock Esmaes: Mehodology and Resuls. Infrasrucures and ICT ; Paper presened a he IVIE workshop on Growh, capal sock and new echnologes, Valenca. OECD (2001a), Measurng Producvy OECD Manual: Measuremen of Aggregae and Indusry-Level Producvy Growh, Pars. OECD (2001b), Measurng Capal OECD Manual: Measuremen of Capal Socks, Consumpon of Fxed Capal and Capal Servces, Pars. OULTON, Ncholas (2001), ICT and Producvy Growh n he Uned Kngdom ; Bank of England Workng Paper. RYMES, Thomas K. (1971), On Conceps of Capal and Technologcal Change, Cambrdge. 181

20 OECD Economc Sudes No. 37, 2003/2 SCHREYER, Paul, Perre-Emanuel BIGNON and Julen DUPONT (2003), OECD Capal Servces Esmaes: Mehodology and a Frs Se of Resuls ; OECD Sascs Workng Paper. SCHREYER, Paul (2002), Compuer Prce Indces and Inernaonal Growh and Producvy Comparsons ; Revew of Income and Wealh, seres 48 Vol SCHREYER, Paul (2001), Compuer Prce Indces and Inernaonal Growh Comparsons, Economcs of Innovaon and New Technology, Vol. 10. SCHREYER, Paul (2000), The Conrbuon of Informaon and Communcaon Technology o Oupu Growh: a Sudy of he G7 Counres, OECD STI Workng Papers 2000/2. TRIPLETT, Jack (1996), Deprecaon n Producon Analyss and n Income and Wealh Accouns: Resoluon of an old Debae ; Economc Inqury, Vol. 34, pp TRIPLETT, Jack (1998), A Dconary of Usage for Capal Measuremen Issues, presened a he Second Meeng of he OECD Canberra Group on Capal Sock Sascs. WÖLFL, Ana (forhcomng), Growh Accouns for OECD Counres, OECD STI Workng Paper. WYCKOFF, Andrew (1995), The Impac of Compuer Prces on Inernaonal Comparsons of Producvy ; Economcs of Innovaon and New Technology, pp

21 Capal Socks, Capal Servces and Mul-facor Producvy Measures Annex 1 OECD METHODOLOGY Asse ypes. The esmaon of capal servce flows sars wh denfyng N dfferen asses for presen purposes, hese correspond o he asse breakdown currenly avalable from he OECD/Eurosa Naonal Accouns quesonnare, augmened by nformaon on nformaon and communcaon echnology asses where avalable. Only non-resdenal gross fxed capal formaon s consdered, and n parcular, seven ypes of asses or producs: Type of produc/asse Producs of agrculure, meal producs and machnery of whch: IT Hardware Communcaons equpmen Oher Transpor equpmen Non-resdenal consrucon Oher producs of whch: Sofware Oher Colleced n OECD/Eurosa quesonnare Yes No No No Yes Yes Yes No No Invesmen seres. For each ype of asse, a me seres of curren-prce nvesmen expendure and a me seres of correspondng prce ndces are esablshed, sarng wh he year For many counres, hs nvolves a ceran amoun of esmaes, n parcular for he perod Such esmaes are ypcally based on naonal accouns daa pror o he nroducon of SNA93, or on relaonshps beween dfferen ypes of asses ha are esablshed for recen perods and projeced backwards. For purposes of exposon of he mehodology, call curren prce nvesmen seres for asse ype n year IN ( = 1, 2,...7) and he correspondng prce ndex q. Prce ndces are normalsed o he reference year 1995 where =1. q Producve capal socks for each asse ype. For each of he (supposedly) homogenous asse ypes, a producve sock s consruced as follows: S = ( IN / q ) h T τ = 1 τ τ, 0 F τ τ S [A1] 183

22 OECD Economc Sudes No. 37, 2003/2 In hs expresson, he producve sock of asse a he begnnng of perod s he sum over all pas nvesmens n hs asse, where curren prce nvesmen n pas perods, IN τ s deflaed wh he purchase prce ndex of new capal goods, q τ, 0. T represens he maxmum servce lfe of asse ype. Because pas vnages of capal goods are less effcen han new ones, an age-effcency funcon h τ has been appled. I descrbes he effcency me profle of an asse, condonal on s survval and s defned as a hyperbolc funcon of he form used by he Uned Saes Bureau of Labor Sascs (BLS 1983): Alernavely, a geomerc profle can be assumed, along he lnes descrbed n he body of he paper. In he non-geomerc case, has o be aken no accoun ha capal goods of he same ype purchased n he same year do no generally rere a he same momen. More lkely, here s a reremen dsrbuon around a mean servce lfe. In he presen calculaons, a normal dsrbuon wh a sandard devaon of 25 per cen of he average servce lfe s chosen o represen probably of reremen. The dsrbuon was runcaed a an assumed maxmum servce lfe of 1.5 mes he average servce lfe. The parameer F τ s he cumulave value of hs dsrbuon, descrbng he probably of survval over he cohor s lfe span. The followng average servce lves are assumed for he dfferen asses: seven years for IT equpmen, 15 years for communcaons equpmen, oher equpmen and ranspor equpmen, 60 years for non-resdenal srucures, hree years for sofware and seven years for remanng oher producs. The parameer β n he age-effcency funcon was se o 0.8. Servce lves and parameer values follow BLS pracce. Ne rae of reurn. The presen work uses a consan value rr for he expeced real neres rae rr. The consan real rae s compued by akng a seres of annual observed nomnal raes (un-weghed average of neres rae wh dfferen maures) and deflang hem by he consumer prce ndex. The resulng seres of real neres raes s average over he perod ( ) o yeld a consan value for rr. The expeced nomnal neres rae for every year s hen compued as r = (1 + rr)(1 + p ) 1 where p s he expeced value of an overall deflaor, he consumer prce ndex. To oban a measure for p, he expeced overall nflaon, we consruc a fve-year cenred movng average of he rae of change of he consumer prce ndex + = = + where CPI τ ( T τ)( T βτ) h = / s he annual percenage change of he consumer prce ndex. Ths yelds he expeced rae of overall prce change and, by mplcaon, he nomnal ne rae of reurn. Rae of deprecaon. In he case of geomerc profles, he raes of deprecaon are gven by he mehod of double-declnng balances: gven he average servce lfe, he rae of deprecaon s compued as δ =1/ 2T. For he case of non-geomerc profles, see Schreyer e al. (2003) for a dealed descrpon. 184