INDUSTRY-LEVEL PRODUCTIVITY MEASUREMENT AND THE NATIONAL ACCOUNTS. by Dale W. Jorgenson and Paul Schreyer 1. Draft 15 July 2010

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1 IDUSTRY-LEVEL RODUCTIVITY MEASUREMET AD THE ATIOAL ACCOUTS by Dale W. Jorgenson and aul Schreyer Inroducon Draf 5 July 200 Implcly or explcly, producvy measuremen has long been lnked o he naonal accouns. aonal accouns daa have consued he key source for he componens of producvy sascs measures of he volume of oupus produced and he volume of npus used n an economy, a secor or an ndusry. The 993 Sysem of aonal Accouns acknowledged he lnk o producvy measures bu n a cursory way only and wh reference o measures of labour producvy raher han mul-facor producvy. A parcular concepual gap was he absence of he noon of capal servces. Ths s he dea ha here s no only a flow of labour servces and nermedae npus bu also a flow of capal servces no producon. Ths flow can be measured as an negral par of he naonal accouns, very much n he same way as labour (a leas n s smplfed measure of hours worked) has long made s way no he naonal accouns. The 2008 Sysem of aonal Accouns (2008 SA, Uned aons e al. 2009)) made a decsve sep by recognsng capal servces as an negral elemen n he new sysem of naonal accouns, hereby openng he way for fully arculaed ses of oupu, npu and producvy sascs 2. In so dong, he SA as an offcal accounng sandard follows a pah ha has long been pursued by he academc communy. Landmarks of hese effors nclude endrck (96), Chrsensen and Jorgenson (973), and Jorgenson, Gollop, and Fraumen (987). More recenly, Jorgenson and Landefeld (2006) have presened a prooype sysem ha negraes he U.S. naonal ncome and produc accouns wh producvy sascs generaed by he U.S. Bureau of Labor Sascs and balance shees produced by he Federal Reserve Board. Jorgenson and Landefeld s prooype sysem descrbes he Acknowledgemens: Fnancal suppor for Jorgenson s parcpaon n hs research was provded by he Alfred. Sloan Foundaon hrough a gran o Harvard Unversy. We are grealy ndebed o Mun Ho and Jon Samuels for asssance n preparaon of he ndusry-level and economy-wde daa used o llusrae he concepual framework presened n hs paper. These daa are dscussed n much greaer deal n Jorgenson, Ho, and Samuels (200). We are also graeful o Ankur ael for exceponally capable research asssance. The usual dsclamer apples. 2 A companon produc o he 2008 SA, he new OECD (2009) Manual on Measurng Capal provdes he necessary reference for he compuaon of capal and capal servces measures. I complemens he OECD (200) Manual on Measurng roducvy ha descrbes n some deal he consrucon of producvy sascs a he aggregae and ndusry levels.

2 accounng relaons a he aggregae level of he economy and for he man nsuonal secors. The prooype sysem has been updaed by Jorgenson (2009b) Jorgenson, Gollop, and Fraumen (987) provde he framework for ndusry-level producvy accouns and her lnk o aggregae measures of producvy change. Fraumen, Harper, owers, and Yuscavage (2006) ake hs dscusson forward and show how ndusry and producvy accouns n U.S. sascal agences can be negraed no a conssen se. Dsaggregang he producon accoun by ndusral secor requres an negraed sysem of npu-oupu accouns and accouns for gross produc orgnang by ndusry, descrbed by Lawson, Moyer, Okubo, and lanng (2006), and Moyer, Rensdorf, and Yuskavage (2006). Donahoe, Morgan, Muck, and Sewar (200) presen daa for he U.S. sysem of ndusry accouns for on he bass of he orh Amercan Indusry Classfcaon Sysem (AICS). Our own conrbuon bulds on hs work and adds o n wo ways. Frs, we se ou an negraed sysem of ndusry and economy-wde producvy accouns n complance wh 2008 SA accounng sandards. The reference o he ermnology and conceps of he 2008 SA should encourage researchers and sascal offces o develop ndusry and aggregae producvy accouns as hey mplemen he new sandard. Snce we lm ourselves o he boundares and convenons of he 2008 SA, hs pus us a varance wh Jorgenson and Landefeld s (2006) prooype accounng sysem n he reamen of consumer durables and n capal servce measures for governmen-owned asses. Our second conrbuon consss n lnkng and nerpreng wo varans of Jorgenson s (966) producon possbly froner. We show how aggregae producvy measures defned under boh varans relae o each oher and o measures of ndusry-level producvy growh. A parcular pon n hs conex, noed by oher auhors as well, arses from he exsence of axes on producs ha drve a wedge beween he oal value of oupus and he oal value of npus. We deal wh hs wedge by reang axes as he prce of a fxed npu and show how can be aken no he accoun n he de-composon of economy-wde producvy growh. The Canadan roducvy Accouns, publshed by Sascs Canada, provde a leadng example of producvy accouns negraed wh a sysem of naonal accouns. 3 The ndusry accouns are based on AICS and ncorporae a me seres of npu-oupu ables for he perod The npu-oupu ables are negraed wh he expendure sde of he Canadan Sysem of aonal Accouns 4 and hese ables are conssen wh measures of capal and labour npus, as well as mulfacor producvy. 5 Snce 2007 Sascs eherlands has publshed a sysem of ndusry-level producvy accouns ha s negraed wh sysem of naonal accouns for The eherlands. 6 Sascal agences n Ausrala, Belgum, Denmark, Fnland, and Ialy also publsh ndusry-level producvy sascs whn he framework of he naonal accouns. 3 See Baldwn, Gu, and Macdonald (200) for a recen summary of he Canadan roducvy Accouns. 4 See Wlson (2006) for deals on he Canadan Sysem of aonal Accouns and s relaonshp o 993 SA (Uned aons, e al., 993).. 5 Inegraon of producvy measures wh he Canadan Sysem of aonal Accouns s dscussed by Baldwn and Harchaou (2006). 6 See van der Bergen, van Rooen-Horsen, de Haan, and Balk (200). 2

3 Indusry-level: accounng relaonshps We sar by seng ou he accounng relaonshps a he ndusry level,.e., for a se of producng uns (for nsance, esablshmens) grouped by her prmary acvy along an ndusry classfcaon such as he Inernaonal Sandard Indusry Classfcaon or he orh Amercan Indusry Classfcaon. Esablshmens produce one or more producs bu her prmary produc deermnes he allocaon o a parcular ndusry. We consder a se of J dfferen ndusres, a se of I producs ha are produced domescally or mpored from abroad. On he oupu sde of he producon accoun of ndusry one has he sum over he value of all oupus produced, he value self beng he produc of he prces and quanes of each produc. In he naonal accouns, oupu s valued a basc prces, excludng axes rased on producs sold bu ncludng any subsdes receved by he producer. On he npu sde of he ndusry producon accoun one fnds he value of nermedae producs enerng producon and value added, self composed of compensaon of employees, gross operang surplus (profs), mxed ncome (he ncome of self-employed persons) and axes ha are rased on producon. Inermedae npus can eher be purchased from oher ndusres n he counry or can be mpored from abroad. The valuaon of npus s a purchasers prces, reflecng all axes leved on hese producs and all subsdes pad on hese producs. More formally, he ndusry-level producon accoun 7 s hen presened as: ~ Q X + VA wh,2,... ndusres and Q ~ X Q ~ X VA CE + GOS + MI + T where Q : Quany (volume) of produc produced n ndusry : Basc prce of produc produced n ndusry X : Quany (volume) of produc used n ndusry ~ : urchasers prce of produc produced n ndusry VA Value added (a basc prces) of ndusry CE Compensaon of employees n ndusry GOS : Gross operang surplus n ndusry MI : Mxed ncome n ndusry T : Taxes on producon leved n ndusry J From he frs lne n equaon () can easly be seen ha value added equals gross oupu mnus nermedae npus. Value added s a measure of prmary ncome ha combnes labour ncome, propery ncome and axes on producon. A crucal sep n he developmen of producvy measures wll be he () 7 To be precse, he SA dsngushes beween he producon accoun and he prmary dsrbuon of ncome accoun bu o keep hngs smple and whou much loss of nformaon we combne hese wo accouns no one producon accoun. 3

4 decomposon of hese ncome componens no a prce and a quany or volume componen, of whch more laer. Supply-use ables: accounng relaonshps across ndusres and producs The above accounng relaonshps can be brough ogeher n supply-use ables (also called make-use ables). Today, an ncreasng number of counres use supply-use ables as he organsng and balancng framework for her naonal accouns. The key mer of such ables s ha hey sysemacally rack flows of producs hrough he economy, along wh he value added generaed n her producon. As wll be shown below, supply-use ables are also a key elemen n he consrucon of ndusry-level producvy measures and her lnks o aggregae producvy ndcaors. Much can be sad abou he consrucon and mehodology of supply-use ables bu for he purpose a hand suffces o ndcae ha he supply able shows whch ndusry produces whch producs, he use able shows wheher hese producs are delvered o oher ndusres (and f so o whch ndusres) or wheher hese producs go o fnal demand (and f so, wheher s he consumpon, nvesmen or expor componen of fnal demand). 8 The supply able s bes presened as a marx wh producs along rows and ndusres producng hem along columns. To domescally produced oupus have o be added mpored producs Q M, a prces M, o characerse oal supply for each ype of produc 9, he sum of each row of he supply marx. Each ndusry s oal producon s gven by he sum of each column of he supply marx J Toal domesc supply of produc a basc prces Q;,2,... producs Impors: supply from abroad a basc prces (c..f.) Q M M I Toal domesc supply by ndusry a basc prces Q;,2,... J ndusres (2) I was menoned earler ha oupu (and herefore supply) of producs are valued a basc prces whereas npus (and herefore demand) are valued a purchasers prces, one of he dfferences beng ne axes on producs. To ensure balance of supply and use of producs, he value of ne axes on producs has hus o be added o he value of supply. There s anoher em ha needs o be aken no accoun, namely rade and ranspor margns: he purchaser s prce ncludes any ransporaon charges needed for delvery a he requred me and place. If such ransporaon coss are pad separaely by he purchasers, hey form par of he purchaser s prce bu no par of he basc prce,.e., he prce relevan for he suppler. Transpor margns reflec he value of a servce and along wh axes on producs hey have o be added o he value of producon a basc prces o oban a measure of oal supply of a produc a purchasers prces. However, as dsnc from axes on producs {T }, ransporaon margns are only re-allocaed across ndusres and her sum remans zero. The use able sars from oal supply a purchasers prces whch equals oal demand a purchasers prces and hen racks he desnaon of each produc n he economy. For every ype of produc (he rows of he use marx), he dfferen desnaons are shown n he columns of he use marx: nermedae npus o oher ndusres and fnal demand (consumpon, nvesmen and expors), denoed {FD } n equaon (3) below. 8 For more deals, see Beuel (2008). 9 See Chaper 4 of he 2008 SA for a dscusson how o conver sascal nformaon on mpors from rade classfcaons o produc classfcaons. 4

5 Toal supply of produc a basc prces J + + ne axes + ranspor margns J T + TM Toal demand of produc a purchasers prces ~ J X + FD for,2,... I producs Q + M Q M (3) Each column n he use marx furher reproduces he ndusry-level producon accoun as n equaon n (): nermedae npus a purchasers prces plus value added a basc prces equals gross oupu a basc prces. For he economy as a whole, GD a basc prces s he sum over ndusry value added a basc prces. In urn, GD a basc prces equals fnal demand a purchasers prces mnus he value of mpors mnus ne axes on producs. Gross oupu mnus nermedae npus J I J Q Value added (GD) a basc prces VA Fnal demand mnus mpors mnus ne axes FD MQM J ~ X T (4) Fgure Supply and use ables roduc 2. Toal supply from Impors Taxes on Trade and Toal supply a 2 J domesc producon producs ranspor margns { Q } Indusry J Q,, M,Q M, T TM purchasers' prces J, Q, + M,Q M, + T + TM.. I Q J, J, M,Q M, T TM I Gross oupu I Q,Q, Q J J, Q J, J MQM M,QM, 0 J I J, Q, + Q + T + TM M, M, I J Q M,Q M, T TM 5

6 Toal supply a Delveres o Indusry Delveres o J Q purchasers' prces + M Q M + T + TM 2 I fnal demand FD roduc. 2. ~ { X } J I, Q + Q + T + TM I, M, I M, I I I J Q M,Q M, T TM I. J Inermedae npus ~,X, ~ X ~,J, J FD Value-added: VA VA J Compensaon of employees CE CE J Gross operang GOS GOS J surplus Mxed ncome MI MI J Taxes on producon T T J Gross oupu Q JQ J Indusry-level volume measures of oupus, npus and producvy All he relaonshps so far have been defned n curren prces and are accounng denes. However, producvy measuremen deals wh he volumes of oupus, npus and how hey relae o each oher and conssen measuremen of volume and prce aggregaes requres some backng n producon heory. A he ndusry level, we evoke he exsence of a perod ndusry producon funcon f ha relaes he aggregae volume of ndusry oupu Q o labour npu L, capal npu and nermedae npus X. More specfcally, f s he maxmum oupu Q producble n perod, gven a se of labour, capal and nermedae npus: Q f (L,,X ) for,2,... J ndusres. (5) The volume of oupu Q s self a funcon g of he varous producs produced by ndusry : Q g (Q,Q2,...Q ). More specfcally, f g I s he mnmum amoun of aggregae npu 0 requred o produce he vecor of oupus ( Q,Q2,...Q ), he se of effcen producon possbles a he ndusry I level can be represened as 0 For he mahemacal properes of hs facor requremens funcon see Dewer (976). 6

7 g (Q,Q2,...,Q ) f (L,,X ) for,2,... I J ndusres. (6) The producon possbles ses a ndusry-level form he sarng block for he specfcaons of ndces of oupus, npus and producvy. We consder hese n urn. Oupu For ndusry gross oupu, he frs sep n volume measuremen consss of applyng a producer prce ndex (I) o he value change of gross oupu a he mos dsaggregaed produc level. Is are ypcally developed by produc bu a he lowes level of aggregaon no necessarly wh an ndusry-specfc componen. I s herefore common pracce o apply he same prce ndex across a sngle row of he supply able. In oher words, he assumpon s made ha he prce change of he same ype of produc s ndependen of he ndusry where s produced. In erms of he presen se-up, hs mples ha he volume change of ndusry s gross oupu of produc ype beween perod - and, s obaned by deflang he value change of ndusry oupu by he produc-specfc I 2, / - : Q Q Q / Q / /. ( ) ( ) Gven a se of volume changes for each ndusry-produc combnaon, {Q /Q - } and he producon values for each of hese combnaons, he queson arses whch ndex number formula o choose n he consrucon of an ndusry-level volume ndex of gross oupu. Chrsensen and Jorgenson (973) were frs o conssenly apply Törnqvs or ranslog quany ndces n measurng he changes n he volume of oupu, npu and producvy. In erms of he producon heorec se-up above, hs means ha he change n he oupu aggregaor g s measured as g (Q,Q2,...,Q I Δ I ) ln Q ln s Δ Q ln Q for,2,... J ndusres g (Q,Q2,...,Q ) (7) and Q where s 0.5( s + s ) Q s. The aggregaon weghs s reflec he share of produc ype n ndusry s oal gross oupu. The ranslog aggregaon formula has a number of desrable properes. In parcular, Dewer (976) showed ha f g has a ranslog funconal form, and gven revenue maxmsng behavour of producers, he ranslog aggregaon formula s superlave n ha exacly represens he shf n g. oe also ha he ranslog funconal form allows for dfferen degrees of subsuon beween producs produced by an ndusry. 3 Usng ranslog formulae rases, however, an ssue of conssency wh curren naonal accouns oe ha even f an ndusry-specfc deflaor were avalable for each ype of produc would sll be mpossble o se up a fully conssen deflaon procedure for he supply and he use able unless here s nformaon abou he demand desnaon of each elemen of ndusry-produc specfc supply. A fully-fledged nformaon se requres a se of saelle marces ha map he produc-specfc delvery srucure beween ndusres. Ths s developed n much greaer deal n Chaper 8 of IMF (2004). A smlar reamen wh an emphass on foregn rade can be found n Chaper 20 of IMF (2009). 2 Ths may enal a bas when he acual produc composon below he mos dealed level a whch Is are used n he supply-use ables vares srongly beween ndusres and when componen prces below hs level exhb dfferen prce changes. 3 The ranslog funconal form was nroduced by Chrsensen, Jorgenson, and Lau (973). 7

8 pracce: n concep, boh he 993 and he 2008 SA favour he use of superlave ndex numbers he focus n he SA s on he Fsher Ideal Index raher han on he ranslog or Törnqvs ndex number formula. Ths would appear o be a mnor emprcal ssue as has been shown ha he ranslog and he Fsher ndex approxmae each oher closely (Dewer 978). Only a mnory of counres acually uses Fsher Ideal ndex numbers n her naonal accouns. A much more pervasve formula s he chaned Laspeyres ndex for volume measures. In he comparson beween perods and -, he Laspeyres ndex uses perod -weghs only and s resuls can dverge from hose of superlave ndex number formulae. We are hus facng a suaon where aggregaes of oupus (and npus see below) derved for purposes of producvy measuremen may dffer from he same aggregaes shown n he naonal accouns. There s no general rule abou he quanave mporance of hs dfference. If relave prces change lle beween comparson perods, dfferences may urn ou o be small. If, on he oher hand, here are large shfs n relave prces, he ensung bas from he use of a smple Laspeyres-ype ndex may urn ou o be szeable. Inpus On he npu sde, before dsenanglng prce from volume changes, some exra work on curren prce daa s necessary. I wll be remembered ha oal coss conss of nermedae npus, compensaon of employees, mxed ncome, gross operang surplus and axes on producon. Whle compensaon of employees s whou doub a paymen for labour servces, and whle gross operang surplus wll largely or enrely reflec paymen for capal servces, hs s less clear for mxed ncome and for axes on producon. Mxed ncome beng essenally he ncome of self-employed persons, some of wll be compensaon of labour servces and some wll be compensaon of capal servces. A common mehod s o assume ha average remuneraon of he self-employed n an ndusry equals he average remuneraon of oher workers of smlar qualfcaon n he same ndusry 4. Smlarly, axes on producon have o be allocaed o eher labour or capal. In some cases hs may be possble by examnng he naure of axes (for example a propery ax would be added o gross operang surplus as concerns srucures or land or a payroll ax would be allocaed o compensaon of employees) bu n some cases he allocaon wll reman somewha arbrary. Consderaon has also o be gven o gross operang surplus. A case can be made o assume ha all of GOS s remuneraon for capal servces bu a case can also be made o spl GOS up no remuneraon for capal and no resdual or wndfall prof or loss, n parcular f markes are no aken as fully compeve 5. For he presen exposon we shall assume ha GOS plus any added values from mxed ncome and from axes on producon exacly equal remuneraon of capal servces. In erms of he noaon adoped earler, we shall denoe he value of oal labour npu n ndusry as W L CE +α MI +β T where α s he share of mxed ncome ha has been allocaed o labour and where β s he share of ne axes on producon ha has been allocaed o labour. Smlarly, we shall denoe he value of oal capal servces n ndusry as, GOS +(-α )MI +(-β )T. I follows ha value added a basc prces n ndusry corresponds o he sum of labour and capal ncome: VA L + for,2,... J ndusres. (8) L 4 See, for example Jorgenson, Ho, and Sroh (2005), Chaper 6, or OECD (200). 5 For a dscusson, see OECD (2009), Dewer and akamura (2007) or Schreyer (20XX). 8

9 In (8), L sands for he prce of labour npu L, and, sands for he prce of he flow of capal servces. VA was nroduced earler and denoes curren-prce value added n ndusry. Toal coss n ndusry are he sum of prmary npus and nermedae npus and hey equal he value of gross oupu: ~ Q L + + X TC for,2,... J ndusres (9) L X Volume of nermedae npus Inermedae npus are an ndusry s purchase of oupus from oher ndusres. In our supply-use ~ framework hey correspond o cell enres X for each of he,2,.. I producs and,2,.. J ndusres. Inermedae npus as well as prmary npus are valued a purchaser s prces,.e., hey nclude ne axes on producs. Ths s conssen wh an npu perspecve by producers usng nermedae npus and consues he heorecally correc valuaon n producvy accouns 6. Bu he mplcaon s also ~ ha, a leas n prncple, here should be separae deflaors for each, a condon rarely me n pracce where ofen a sngle deflaor s used across enre rows of he supply-use ables. We consruc a volume aggregaor of nermedae npus X X (X,X 2,...X, ) purchased by ndusry and apply he same reasonng as n he case of oupu aggregaon 7 o oban a ranslog ndex of nermedae npus: I Δ ln X s Δ X ln X for,2,... J ndusres ~ where sx, 0.5( sx, + sx,) and s X, ~ X. X (0) Volume of labour npu eher capal nor labour are homogenous npus, and measurng labour npu by smply addng hours worked gnores dfferences n labour qualy ha arse as a consequence of educaon, sklls, or work experence. 8 L should herefore be undersood as an aggregaor across L dfferen ypes of labour: L L (L, L 2,...L L, ) and he oal value of compensaon as he sum of compensaon across dfferen ypes of labour: L LL LL. Here, L s he hourly compensaon of he -h ype of labour n ndusry and L s he correspondng number of hours. By applyng he same reasonng as n he case of oupu aggregaon, he quany change of labour npu can be measured as a ranslog ndex of he volume changes of dfferen ypes of labour npu: L L Δ ln L s Δ ln L for,2,... J ndusres () 6 See Jorgenson, Gollop and Fraumen (987) and OECD (200) for deals on he consrucon of ndusry-level producvy accouns. Deals on he consrucon of a me seres of npu-oupu ables are gven by Jorgenson, Ho, and Sroh (2005), Chaper 4. 7 The aggregaor X s aken as a homogenous ranslog funcon n s componens and producers behave as cos mnmzers. 8 See Jorgenson, Gollop, and Fraumen (987), Chapers 3 and 8, and Jorgenson, Ho, and Sroh (2005), Chaper 6. 9

10 L L, L, L, and L, LL where s 0.5( s + s ) L s. The ndex number () can also be nerpreed as he quany ndex of labour ncome. The log dfference beween he quany ndex of labour ncome and a smple ndex of hours worked ha does no accoun for dfferen ypes of labour qualy s an ndex of labour qualy. Labor qualy capures changes n he composon of he work force by he characerscs of ndvdual workers, as suggesed by BLS (993). A more dealed descrpon of he sources and mehods for hese esmaes s provded by Jorgenson. Ho, and Sroh (2005), Chaper 6. Volume of capal npu For a long me naonal accounng sandards reaed labour and capal dfferenly here was explc recognon of a prce and quany of labour npu bu no such recognon of a prce and quany of capal npu. Ths changed wh he 2008 SA, whch explcly acknowledges capal servces, hereby permng a prce-volume spl of all ncome componens. Akn o labour npu, s recognsed ha here are dfferen ypes of capal servces, each proporonal o dfferen ypes of capal socks. Aggregae capal npu no ndusry, combnes dfferen ypes of capal socks: (, 2,..., ) and he oal value of compensaon for capal servces s he sum of compensaon across dfferen ypes of capal:. Here, s he prce of he -h ype of capal servces n ndusry per un of, he correspondng quany. By applyng he same reasonng as n he case of oupu aggregaon, he quany change of capal npu can be measured as a ranslog ndex of he volume changes of dfferen ypes of capal npu: Δ ln s Δ ln for,2,... J ndusres where s 0.5( s + s ) s.,,, and, (2) We shall only brefly dwell on he man feaures of capal measuremen, for more deal, he reader s referred o Hulen (990), Jorgenson, Ho, and Sroh (2005), Chaper 5, OECD (2009), SA 2008 (2009), Chaper 20, or Dewer and Schreyer (2009). The frs queson relaes o he consrucon of me seres of ndusry and asse-specfc capal socks { }. For mos purposes, hese are developed by cumulang me seres of ndusry and asse-specfc nvesmen expendure, deflaed such ha hey are expressed n consan qualy uns of nvesmen. To each nvesmen seres, an age-effcency and reremen profle s appled ha akes accoun of he loss of producve capacy of capal goods and of her scrappng as hey age. In he smples case, he combned age-effcency/reremen profle exhbs a geomerc form,.e., he cohor of asses loses effcency and reres a a consan rae. Wh me seres of ndusry- and assespecfc capal socks a hand, he assumpon s made ha he flow of capal servces s proporonal o he sze of he ndvdual socks. roporonaly mples ha he ndex of capal npu as n (2) can be nerpreed as an ndex of capal servce flows. The second man ngreden of capal servces measuremen s he prce of hese servces. Capal servce prces are renal prces and hey may be observable when owners of capal goods ren hem ou o users for one or several perods of me. Gven such daa on marke renal prces by class of asse, he mplc renal values pad by owners for he use of her propery can be mpued by applyng hese renal raes as prces. Ths mehod s ofen used o esmae he renal value of owner-occuped dwellngs. The man obsacle o broader applcaon of hs mehod s he lack of daa on marke renal prces. An alernave approach for mpuaon of renal prces s o exend he perpeual nvenory mehod o nclude 0

11 prces of capal servces. For each ype of capal perpeual nvenory esmaes are prepared for asse prces, servce prces, deprecaon, and revaluaon. Under he assumpon of geomercally declnng relave effcency of capal goods, he asse prces declne geomercally wh vnage 9. For a secor no subec o eher drec or ndrec axes, a common specfcaon for he capal servce prce s: ( r + δ ( + ) ) ~ for asse ype and,2,... J ndusres, (3) ~ where s he purchaser s prce, a he begnnng of perod, of a new asse of ype acqured by ndusry, r s he nomnal rae of reurn prevalng for ndusry, δ s he consan rae of deprecaon for ~ asse ype n ndusry and / ~ + s he rae of nflaon n he acquson prce of new capal goods beween he begnnng and he end of perod. Servce prces for each class of asses held by each ndusry comprse machnery, equpmen, resdenal and nonresdenal srucures, land and several oher ypes of naural resources (see he dscusson on he scope of capal below). More elaborae versons of he user cos expresson nclude erms for ncome axes and deprecaon allowances and we refer o Jorgenson and Yun (200) for a more dealed exposon. In prncple, all he erms n (3) are observable excep for he rae of reurn r (and he expeced rae of asse prce change f (3) s nerpreed as an ex-ane erm). OECD (2009) provdes a dscusson on he varous alernaves for esmang hese erms. For reasons of space, we only refer o one of hem here. Ths approach s based on ex-pos prce changes and compues he rae r afer equang he remuneraon of capal wh gross operang surplus and he capal par of mxed ncome: ( r ) + δ( + ) ~ for,2,... J ndusres. (4) oe wo complcaons n he case of ndusres wh non-marke producers, n parcular governmen. As non-marke producers offer her producs a a prce ha covers only par or none of he coss of producon, revenues canno serve as a measure of he value of oupu. The SA herefore foresees ha he value of oupu s esmaed as he sum of coss ncurred n s producon. Concernng capal remuneraon, no observable measure of gross operang surplus exss so r canno be compued as n (4). Jorgenson and Landefeld (2006), Jorgenson and Yun (200) and OECD (2009) show alernaves for dealng wh hs complcaon. A second, more serous ssue arses from he fac ha he 2008 SA recognzes capal servces for asses owned by marke producers bu no by non-marke producers. Capal coss for governmen producers are solely measured as he value of deprecaon, hus gnorng ha par of ~ coss of capal servces ha reflec he opporuny coss of capal and revaluaon: ( ) r. The asymmerc reamen of asses used n marke and n non-marke producon resuls eher n an ncomplee esmae of capal npus or n a devaon from naonal accouns convenons. Anoher naonal accouns convenon s he reamen of consumer durables as fnal consumpon expendure and no as nvesmen. On concepual grounds, ceran consumer durables consue capal goods ha provde a flow of capal servces, n parcular n he producon of servces ha households produce for her own consumpon, for nsance washng machnes n he process of launderng. For manly praccal reasons, hs producon s ousde he SA producon boundary and accordngly, consumer durables are ousde he SA asse boundary. Jorgenson and Landefeld (2006) show how prces and quanes of capal servces for all producve asses can be ncluded n a naonal accouns framework and hs ncludes a conssen reamen of consumer durables and governmen asses 9 See Fraumen (997) for he compuaon of deprecaon n he U.S. naonal accouns and OECD (2009) for a general dscusson.

12 Indusry-level producvy measures Havng deal wh he measuremen of aggregaes of npus and oupus, s now only a shor sep owards he measuremen of ndusry producvy. The sarng pon s (6) and we defne he famly of mul-facor producvy ndces of ndusry as he shf n he producon possbly effcen se beween perods and -, gven a reference se of npus: π f (,L, X ) / f (, L,X ) for,2,... J ndusres. (5) Dewer (976) showed ha f he npu and oupu aggregaors n (6) are ranslog funconal forms, f he echnology exhbs consan reurns o scale and f producers ac as cos mnmsers and revenue maxmsers under compeve condons, an exac represenaon of (5) s he Törnqvs or ranslog producvy ndex: ln π Δ ln Q v Δ ln v Δ ln L v Δ ln X for,2,... J ndusres. L wh v 0.5( v + v ), v 0.5( v + v ); v 0.5( v + v ) v k k k L L L X X X and ~ LL XX ; v L ; v X. Q Q Q X (6) Ths producvy measure s based on gross oupu and allows for subsuon beween prmary and nermedae npus. roducvy growh s hus defned as he capacy o produce a larger bundle of gross oupu gven a se of prmary and nermedae npus 20. ong ha ndusry value added equals ndusry gross oupu mnus nermedae npus consumed by he ndusry, a volume ndex of value added n ndusry, ΔlnV, s mplcly defned hrough he de-composon of he volume ndex of gross oupu no a volume ndex of value added and a volume ndex of nermedae npus: Δ ln Q v Δ ln V + v Δ ln X or Δ ln V VA v X v Δ ln Q v X Δ ln X VA VA VA VA VA and VA VA Q wh v 0.5( v + v ) v for,2,... J ndusres. Expressons (6) and (7) can now be combned o yeld a de-composon of he rae of growh of real value added n ndusry : (7) VA ( v Δ ln + v Δ ln L + π ) Δ ln V L. v (8) 20 An alernave formulaon of producvy change s n erms of value added and a shf of a prmary npu funcon over me. Whle he wo ypes of producvy measures can be lnked, hey represen dfferen assumpons abou echnology and, more specfcally, dfferen assumpons abou he pah-ndependence of producvy change (see Hulen 973). 2

13 Toal economy producvy measures The sarng pon for lnkng ndusry-level producvy measures o economy-wde producvy measures s Jorgenson s (966) producon possbly froner (F). The F relaes an economy s oupu of fnal demand producs (consumpon, nvesmen, expors) o he se of npus avalable n he economy. The key feaure of he F s he explc role provdes for changes n he relave prces of fnal demand componens. In wha follows, we shall presen wo ypes of he F, each correspondng o somewha dfferen assumpons abou he economy s echnology. Value-added based producon possbly froner We characerse a value-added based F as he effcen se of volume measures of value added, produced by he se of prmary npus labour and capal avalable n he economy: H(V, V 2,...,V ) Z (L,) (9) J Expressons (4) and (8) provde he curren-prce accounng relaonshp n accordance wh (9): J VA VA L + L (20) If H and Z are approxmaed by ranslog funconal forms, and assumng prof-maxmsng behavour of producers, compeve markes and consan reurns o scale, he shf n he value-added based producon possbly froner ρ Z (L,)/Z - (L,) s exacly represened by he dfference beween a ranslog ndex of he volume of value added and a ranslog ndex of he volume of labour and capal npus. The resulng expresson s a wdely-used measure of economy-wde growh of mul-facor producvy, orgnally nroduced by Jorgenson and Grlches (967): ln ρ Δ ln V w Δ ln L w Δ ln where J L VA Δ ln V w Δ ln V : share-weghed growh of ndusry value added Δ ln w Δ ln : share-weghed growh of dfferen ypes of capal L L Δ ln L w Δ ln L : share-weghed growh of dfferen ypes of labour wh w w w w w ( w + w ) L L 0.5 L L, L ( w + w ) 0.5, ( w + w ) L w, L LL VA LL, L L for,2,... I ndusres w, VA VA 0.5 VA VA and VA ( w + w ) 0.5 and ( w + w ) L L 0.5 L L and L for,2,... I ndusres VA w for,2,... I ndusres, VA w for,2,... ypes of capal, VA L w for,2,... L ypes of labour. VA (2) 3

14 We follow Jorgenson, Ho and Sroh (2005), Chaper 8, and compue he economy-wde labour and capal shares w L and w as well as he share-weghed growh of labour and capal npu under he assumpon of a sngle prce for a parcular ype of npu, ndependen of he ndusry n whch s used. Ths s anamoun o a op-down compuaon whou any ndusry-specfc nformaon. The assumpon of a sngle npu prce consues a benchmark, achevable under full mobly of facors n compeve facor markes. Below hs benchmark wll be compared wh npu aggregaes ha allow for npu-specfc npu prces, gvng rse o a reallocaon erm. Imporanly, he assumpon of a sngle prce does no carry over o he oupu sde he prce of value added s allowed o vary across ndusres as here s no reason o assume ha each ndusry produces he same ype of value added. Indeed, he ndusry-specfc prce of value added s a cenral feaure of Jorgenson s (966) producon possbly froner. When (8) s nsered no (2), we oban he lnk beween economy-wde producvy growh as defned hrough he value-added based producon possbly froner and ndusry-level gross-oupubased producvy growh: J ln ρ wh REALL REALL L w v VA VA π + REALL v L + REALL L w Δ VA ln L w L J L vva v w Δ VA ln w J L vva w w L Δ ln L 4 Δ ln Equaon (22) s dencal o expresson (3) n Jorgenson, Ho, and Sroh (2005), Chaper 8, wh hree sources of economy-wde producvy growh. The frs source s a weghed average of ndusry producvy growh raes. Each ndusry s producvy growh ges weghed by wo coeffcens: w VA, he ndusry share n oal value added and v VA, each ndusry s value-added share n gross oupu. One dvded by he oher corresponds o he rao of ndusry gross oupu o economy-wde value added, he se of Domar (96) weghs. These weghs sum o more han uny and pck up he fac ha producvy ncrease n an ndusry ha delvers nermedae producs o anoher ndusry has boh drec and ndrec effecs on economy-wde producvy growh. Two reallocaon effecs can also be denfed hrough equaon (22). They quanfy he deparure from he assumpons on npus requred for he producon possbly froner: he frs em n he reallocaon erms capures aggregae labour or capal npu when aggregaon s carred ou across ndusres, allowng for ndusry-specfc prces of labour or capal servces. The second em s aggregae labour or capal npu under he assumpon of equal npu prces across ndusres. The reallocaon erm wll be posve f npus grow qucker n hose ndusres ha pay hgher prces for hese npus han oher ndusres. Fnal producs-based producon possbly froner An alernave pah owards characersng echnology n he economy s o defne he F as he effcen se of he volume of fnal producs, produced by prmary npus labour and capal as well as by mpors avalable n he economy. oe he symmery of hs se-up wh our specfcaon of he ndusrylevel producon echnology: n boh cases, oupu s undersood as delveres of producs o uns ousde he secor, and npu s undersood as all purchases of producs and prmary facors of producon enerng he secor. For he economy as a whole, oupu s he se of fnal producs {Q FD }, composed of consumpon goods and servces, nvesmen goods and expors. Inpus comprse labour, capal and mpors. (22)

15 h(qfd,qfd2,...,qfd, ) z (L,,QM ) (23) J To derve he accounng denes n accordance wh hs specfcaon, we sar by expressng he vecor of fnal demand delveres measured a purchasers prces n he supply-use able above n basc prces. Ths s necessary because purchasers prces reflec an npu perspecve. In he presen specfcaon, fnal demand producs are consdered he economy s oupu and should hus be valued a basc prces (us as value added, he alernave oupu measure n (9) was valued a basc prces). Le ~ { FD } sand for he basc prces of fnal producs, { FD } for he purchasers prces of fnal producs, {T FD } for he ne axes on fnal producs and {TM FD } for he ransporaon margns on fnal producs, hen he followng relaon holds: FD + FDQFD FDQFD ~ ( T + TM ) FD Expresson (4) can now be employed o relae he value of fnal demand o value added and o he se of prmary npus: FD (24) J VA + T + FDQFD + T + FD TM FDQFD + FD MQM J ( ) FD VA + + T M L + + LL ~ MQ M T DX Q and M (25) Where ( ) I T I T T TM T DX FD FD M TM M In he las lne of (25) we used (20) o express economy-wde value added as he sum of paymens o capal and labour and we used T DX as a shorhand for he produc axes and ranspor margns on domesc nermedae producs: T DX equals oal axes on producs plus ransporaon margns mnus axes and ransporaon margns on fnal demand producs (T FD +TM FD ) mnus axes and ransporaon margns on mpors (T M +T MM ). Impors are consdered an npu n he presen se-up of he producon possbly froner and hence have o be valued a purchasers prces. The hrd lne n expresson (25) s he accounng deny a curren prces ha corresponds o he F (24). However, a comparson of he npu sde of he producon possbly froner wh he accounng relaonshp (25) shows ha he ax erm T DX has no quany correspondence as an npu no producon. To deal wh hs cos em, we re-defne he producon possbly froner wh an addonal fxed npu 2 whose quany s equal o one and whose prce s equal o T DX : h(qfd,qfd2,...,qfd, ) z~ (L,,QM,) (26) J We are now ready o formulae he measure of producvy growh ha corresponds o hs characersaon of echnology. Applyng he same reasonng as before, we fnd ha f h and z~ are approxmaed by a ranslog funconal form, and f we assume prof-maxmsng behavour of producers, compeve markes and consan reurns o scale n he fnal producs-based F, he producvy shf Π z~ (L,,Q,) / z~ (L,,Q,) s exacly represened by he dfference beween a ranslog ndex of M M 2 See Dewer and akamura (2007) for a more formal demonsraon of hs echnque n he conex of a cos funcon and as a way o deal wh decreasng reurns o scale. 5

16 he rae of change of fnal producs and a ranslog ndex of he volume of labour, capal, mpored npus and one fxed npu. ln Π Δ ln Q v Δ ln L v Δ ln v Δ ln Q where FD L I FD Δ ln Q s Δ ln Q : share-weghed growh of fnal producs wh s FD ( + s ) FD FD FD FD 0.5 sfd FD, FD v v v ( v + v ) L L 0.5 L L, L 0.5, M M Q s for,2,... I producs FD M L w, L LL FD LL, L L for,2,... I ndusres ( v + v ) v FD for,2,... I ndusres M M 0.5( vm + vm ) ~ Q, vm I MQM FD MQM (27) As a fnal sep, we shall now lnk he economy-wde producvy growh rae Π based on a fnal demand concep o he economy-wde producvy growh rae ρ based on value added and va ρ o he raes of ndusry-level producvy growh ρ (,2,... ). Ths s acheved by usng he expresson for value added based producvy growh (2), nserng no (27) and collecng erms: ln Π vva ln ρ + VAL + IDEX where J lnρ and VA w v VA VA π + REALL L + REALL VA ( vva + vva ); vva FD Δ ln Q s Δ ln Q J w v Δ v 0.5 VAL s IDEX FD FD M M VA L L VA L VA ln V ( w v v ) Δ ln L + ( w v v ) Δ ln VA (28) Equaon (28) shows ha economy-wde producvy growh ln Π s he sum of he followng componens: a share-weghed average of ndusry-level producvy growh ln π. The compose share v w / v for each ndusry s bes nerpreed by lookng a he rao of he same VA VA VA shares when no averaged over wo perods: VA VA VA Q v VAw VA / vva /. FD VA Q FD Thus, each ndusry s rae of producvy growh eners he economy-wde producvy change wh a wegh ha reflecs he ndusry s gross oupu n relaon o economy-wde fnal demand. Ths s a dfferen verson of a sysem of Domar weghs, scaled up from he Domar weghs ha provded he lnk beween he se of {π } and he value-added based producvy measure n (22); 6

17 wo reallocaon erms REALL L and REALL descrbed earler; a valuaon effec VAL: hs valuaon effec arses from he presence of axes on producs and ransporaon margns ha drves a wedge beween he growh rae of GD a purchasers prces, measured from he expendure sde of he accouns ( sfdδ ln QFD smδ ln QM ) and he growh rae of economy-wde value-added a basc prces ( J w Δ VAvVA ln V ); an ndex number effec IDEX ha s a smple consequence of he fac ha raos of arhmec averages are no equal o arhmec averages of raos. Indeed, had Fsher deal ndces been employed for he dervaons above, hs erm would be dencally zero. Because Fsher and ranslog ndces approxmae each oher, hs effec s lkely o be small n pracce. Toal economy and ndusry-level producvy and he U.S. naonal accouns. To llusrae he conceps presened n hs paper we gve prooype oal-economy and ndusrylevel producon accouns for he U.S. aonal Income and roduc Accouns (As) for he perod To smplfy he presenaon we focus on he value-added based producon possbly froner and ndusry-level gross-oupu-based producvy growh presened n (22) above. 22 We have sub-dvded he me perod a 995 and 2000 o focus on he IT nvesmen boom of , whch ended wh he do-com crash of We defne he conrbuon of an ndusry o U.S. economc growh as he growh rae of real value added n he ndusry, weghed by he share of he ndusry n he GD. Table gves he conrbuons of egh maor ndusry groups o economc growh durng he perod Table 2 presens he underlyng growh raes and shares n nomnal GD for all egh groups. The conrbuons of sx of hese groups ncreased durng he IT nvesmen boom of , relave o he perod , whle he conrbuons of seven groups decreased durng he perod of slower growh followng he do-com crash of The prces of capal npus are essenal for assessng he conrbuon of IT equpmen and sofware o economc growh. Ths conrbuon s he relave share of IT equpmen and sofware n he value of oupu, mulpled by he rae of growh of IT capal npu. A subsanal par of he growng conrbuon of capal npu n he U.S. can be raced o he change n composon of nvesmen assocaed wh he growng mporance of nformaon echnology. The conrbuons of college-educaed and non-college-educaed workers o U.S. economc growh s gven by he relave shares of hese workers n he value of oupu, mulpled by he growh raes of her hours worked. Table shows ha he growh of producvy was far less mporan han he conrbuons of capal and labour npus as sources of U.S. economc growh for he perod roducvy growh accouns for us under eleven percen of U.S. economc growh, consderably less han he ffeen percen of growh for esmaed by Jorgenson and Grlches (967). The conrbuon of capal npu accouns for 53 percen of growh durng he perod , whle labour npu accouns for 36 percen. In he Domar (96) weghng scheme he producvy growh rae of each ndusry s weghed by he rao of he ndusry s gross oupu o aggregae value added. A dsncve feaure of Domar weghs 22 Ths llusraon employs he 65-secor classfcaon of ndusres based on AICS and presened n he As. A dealed breakdown of he IT-producng secors s provded by Jorgenson, Ho, and Samuels (200). Ths s essenal for analyzng he economc mpac of nformaon echnology. 7

18 s ha hey sum o more han one, reflecng he fac ha an ncrease n he rae of growh of he ndusry s producvy has wo effecs. The frs s a drec effec on he ndusry s oupu and he second an ndrec effec va he oupu delvered o oher ndusres as nermedae npus. The rae of growh of aggregae producvy (22) also depends on he reallocaons of capal and labour npus among ndusres. Table 3 gves he decomposon of he rae of growh of producvy presened n Table above. The Domar-weghed sum of ndusry producvy growh raes for he perod s 0.34 percen, he same as he aggregae producvy growh rae n Table. The posve reallocaon of capal npu of precsely offses he negave reallocaon of labor npu. We conclude ha he ndusry-level raes of producvy growh are he man sources of aggregae producvy growh over long perods of me, as shown by Jorgenson, Gollop, and Fraumen (987), Chaper 9. For he relavely shor sub-perods of and , he reallocaons are quanavely sgnfcan and are no muually offseng. Table 4 gves conrbuons of he 65 ndvdual ndusres o aggregae value added, usng valueadded weghs, and producvy growh for he oal economy, usng Domar weghs. Real esae, wholesale rade, and real rade are he larges conrbuors o value added, reflecng her large shares n value added. The compuer and elecronc producs ndusry s a maor conrbuor o boh value added and producvy growh, despe s relavely modes share n value added and s small Domar wegh. Table 5 gves conrbuons of hese ndusres o aggregae growh of IT- and on-it capal npu and College and on-college workers. Conclusons By recognzng capal servces as an negral elemen he 2008 SA has cleared he way o ncorporaon of producvy no sysems of naonal accouns Ths resolves long-sandng conroverses and has led o a very sgnfcan convergence of vews. The OECD (2009) Manual on Measurng Capal provdes dealed mehodology for he consrucon of measures of capal servces, usng daa avalable from he naonal accouns. Ths complemens he OECD (200) Manual on Measurng roducvy, presenng he mehodology for consrucng producvy sascs a he ndusry and economy-wde levels. Incorporaon of ndusry-level and oal economy measures of producvy no he naonal accouns has he advanages of nernaonal sandardzaon ha have long accrued o measures of oupu and ncome. Sascal offces, led by Canada and The eherlands and ncludng Ausrala, Belgum, Denmark, Fnland, and Ialy, are producng offcal ndusry-level and oal-economy esmaes of producvy whn he framework of he naonal accouns. Sandardzaon ress on an exensve body of concepual and emprcal research. We have conrbued o hs effor by seng ou a sysem of producvy accouns whn he framework of he 2008 SA. Jorgenson, Ho, and Samuels (200), he EU (European Unon) LEMS (capal, labor, energy, maerals, and servces) proec descrbed by O Mahony and Tmmer (2009), and he sudes presened n Jorgenson (2009a), The Economcs of roducvy, have presened ndusry-level daa on producvy whn he framework of naonal accouns. The EU LEMS sudy was compleed on June 30, Ths landmark sudy presens producvy measuremens for 25 of he 27 EU members, as well as Ausrala, Canada, Japan, and orea, and he U.S. 23 Effors are underway o exend he EU LEMS framework o mporan developng and ranson economes, ncludng Argenna, Brazl, Chle, Chna, Inda, Indonesa, Mexco, Russa, Turkey, and Tawan For curren nformaon on he parcpang counres, see he EU LEMS webse a hp:// 24 Addonal nformaon s avalable on he World LEMS webse a hp:// 8

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