Growth of U.S. Industries and Investments in. Information Technology and Higher Education

Transcription

1 reliminary Commens Welcome No for Ciaion wihou ermission of Auhors Growh of U.S. Indusries and Invesmens in Informaion Technology and Higher Educaion Dale W. Jorgenson Harvard Universiy Mun S. Ho Resources for he Fuure Kevin J. Siroh Federal Reserve Ban of New Yor Firs Draf: April This Draf: Ocober Absrac This paper presens new daa on he sources of growh for he U.S. economy over he period The principal innovaion is he incorporaion of deailed informaion for individual indusries including hose involved in he producion of informaion echnology equipmen and sofware. We show ha economic growh is dominaed by invesmens in informaion echnology and higher educaion boh for individual indusries and he economy as a whole. We also show ha a ump in informaion echnology invesmen gains in he employmen of college-educaed worers and he revival of produciviy growh accoun for he resurgence of he U.S. economy since We are graeful o Jon Samuels for excellen research assisance and CRIW conference paricipans especially our discussan Michael Harper and he ediors for helpful commens and useful suggesions for he revision of earlier versions of his paper. Many have generously provided daa and advice -- Jay Berman Charles Bowman Carl Chenrens James Franlin Tom Hale Tom Nardone and Larry Rosenblum (BLS) Kur Kunze (BEA) Eldon Ball (ERS) Mie Dove and Sco Segerman (DMDC). The views expressed are hose of he auhors and do no necessarily reflec hose of he Federal Reserve Sysem or he Federal Reserve Ban of New Yor.

2 I. Inroducion Our obecive in his paper is o quanify he sources of U.S. economic growh for using daa for individual indusries. This boom-up approach complemens he op-down analysis approach employed in our earlier wor. 1 Indusry-level daa enable us o race he sources of U.S. economic growh o heir indusry origins o isolae and analyze he indusries ha produce informaion echnology (IT) and o assess he relaive imporance of produciviy growh and facor accumulaion a boh indusry and economy-wide levels. 2 roduciviy growh in IT-producing indusries has seadily risen in imporance generaing a relenless decline in he prices of informaion echnology equipmen and sofware. This decline in IT prices is rooed in developmens in echnology ha are widely undersood by echnologiss and economiss paricularly he coninuous improvemen in he performance/price raio of semiconducors capured by Moore s Law (Jorgenson (2001)). Informaion echnology has reduced he cos and improved he performance of producs and services embraced by U.S. businesses households and governmens. The enhanced role of invesmen in informaion echnology is a conspicuous feaure of he U.S. economy and a growh revival is under way in many imporan IT-using indusries. The ey IT-producing indusries are compuers communicaions equipmen semiconducors and sofware. These secors are below he usual 2-digi classificaion level used in oher sudies and we have creaed deailed daa for hem in order o characerize IT-producion as precisely as possible. Indusrial Machinery and Equipmen (SIC 35) for example includes Compuers and Office Equipmen (SIC 357) while Elecronic and Elecrical Equipmen (SIC 36) conains Communicaions Equipmen (SIC 366) and Elecronic Componens (SIC 367) mainly semiconducors. Business Services (SIC 73) includes Compuer Services (SIC 737) primarily sofware. This breadown enables us o quanify he impac of IT producion on he U.S. economy more accuraely and represens a subsanial improvemen over earlier sudies using he broader indusry aggregaes. The mechanisms for diffusion of advances in informaion echnology are wo-fold. Firs advances in semiconducors generae coninuing price reducions for a given level of performance. These price reducions drive demands for inermediae inpus in semiconducor-using indusries such as Compuers Communicaions Equipmen and a hos of ohers. Second he indusries ha use semiconducors as inpus generae price declines ha drive invesmens in informaion echnology 1 See Jorgenson and Siroh (2000) Jorgenson (2001) Jorgenson Ho and Siroh (2002) as well as Baily (2002) Congressional Budge Office (2002) Council of Economic Advisors (2002) Gordon (2002) McKinsey Global Insiue (2001) Oliner and Sichel ( ) and Whelan (2002). 2 Baily and Lawrence (2001) and Siroh (forhcoming) provide indusry comparisons ha examine he role of IT and Brynolffson and Hi (2000) survey firm-level resuls. 1

3 equipmen lie compuers and elecommunicaions equipmen. Advances in equipmen producion augmen he downward pressure on prices seadily redirecing he rising IT invesmen flow oward is mos producive uses. 3 On he labor side college-educaed worers are ofen idenified as nowledge worers who mae use of informaion echnology equipmen and sofware so we have divided labor inpu beween college and non-college worers. Obviously no every nowledge worer is a college graduae nor is every college graduae a nowledge worer. A second issue is ha while invesmens in IT ae place wihin he indusries we have idenified invesmens in higher educaion are underaen by fuure college-educaed worers and precede employmen of hese worers someimes by a considerable period of ime. We measure he flow of human capial services from college-educaed worers bu no he accumulaion of he soc of his capial ha aes place in colleges and universiies. Our empirical resuls show ha he more appropriae framewor for analyzing he impac of informaion echnology is a producion possibiliy fronier ha includes oupus of IT-producing indusries as well as inpus of IT capial services compared o he usual aggregae producion funcion. Two advanages of his framewor are ha we incorporae deailed daa from individual indusries including he IT-producing indusries and ha he prices of IT oupus and inpus are lined hrough he prices of IT capial services. Finally we repor deailed resuls for indusry producion accouns and demonsrae he criical imporance of invesmens in IT capial and higher educaion across U.S. indusries. Table 1 summarizes he resuls of a growh accouning decomposiion for value added in he U.S. economy using a producion possibiliy fronier generaed from indusry-level daa. This decomposiion is based on annual observaions for he period as well as he sub-periods and While hese ime periods are convenional a word abou he choice of he periods is useful a his poin. The year 1977 is he firs year in our daa se and he slow growh associaed wih he energy crisis of he 1970 s is readily apparen in he daa. The year 1991 is he end of he las recession in he period we cover and he year 1995 corresponds o a surge in economic growh as well as a ump in he rae of decline of IT prices. Resuls show ha recen resurgence of he U.S. economy has raised he growh rae of value added by 1.85 percenage poins when is compared o Capial inpu conribues 1.02 percenage poins o he pos-1995 revival; a lile more han half of his is due o he surge in IT invesmen while slighly less han half is due o more rapid accumulaion of Non-IT asses. Labor inpu conribues 0.44 percenage poins o he growh resurgence. College-educaed worers conribue abou 3 Models of he ineracions among semiconducor compuer and oher indusries are presened by Dulberger 2

4 a hird of a percenage poin while non-college worers add anoher enh of a percenage poin o he growh resurgence. Faser growh in oal facor produciviy conribues he remaining 0.40 percenage poins. These boom-up resuls are quie comparable o he op-down esimaes menioned earlier. The value of underlying indusry deail however is readily apparen in Table 1 and Figure 1 documening he rising conribuions of IT-producing indusries o U.S. economic growh. Alhough he imporance of hese indusries has seadily increased heir conribuion o growh umps by seveny-five percen afer The conribuion of IT inpus ino producion more han doubles afer 1995 as he pace of IT price declines accelerae. In response o hese price changes firms households and governmens have accumulaed IT equipmen and sofware much more rapidly han oher forms of capial. Non-IT capial however sill predominaes in he conribuion of capial inpu he mos imporan source of U.S. economic growh hroughou he period The conribuion of labor inpu is nex in imporance as a source of U.S. economic growh and plays a vial role in he resurgence of he American economy afer The conribuion of collegeeducaed worers dominaes he growh of labor inpu during he period even hough hese worers are less numerous han non-college worers. This reflecs he facs ha college-educaed worers have higher marginal producs on average as can be seen in he college wage premium and ha he number of college-educaed worers has been growing more rapidly han ha of non-college worers. Boh college and non-college worers however conribue o he growh revival afer As he unemploymen rae fell in he lae 1990 s worers wih a wide variey of levels of educaion and experience enered he rans of he employed labor force. Finally growh in oal facor produciviy (TF) has been he leas imporan of he hree proximae sources of U.S. economic growh capial inpu labor inpu and oal facor produciviy. In fac TF growh essenially disappears during During he pas decade produciviy growh revives modesly during he sub-period and acceleraes considerably afer As an addendum o Table 1 we have divided he conribuion of capial inpu beween he conribuions of capial soc and capial qualiy. The growh of capial qualiy defined as he raio of capial inpu o capial soc reflecs he rise in he relaive imporance of IT equipmen and oher forms of capial wih higher marginal producs and higher capial service prices. Capial soc fails o capure hese differences in marginal producs and has been superseded by a measure of capial inpu as recommended in recen OECD manuals on measuring capial (Blades (2001)) and produciviy (Schreyer (2001)). (1993) Triple (1996) and Oliner and Sichel (2000). 3

5 Similarly we have divided he conribuion of labor inpu beween he conribuions of hours wored and labor qualiy. The growh of labor qualiy defined as he raio of labor inpu o hour wored capures he rise in he relaive imporance of college-educaed worers and oher worers wih higher marginal producs and higher compensaion per hour. Hours wored fails o capure hese differences in marginal producs and has been superseded by a measure of labor inpu as recommended in he Unied Naions (1993) Sysem of Naional Accouns 1993 and Schreyer s (2001) OECD roduciviy Manual. Growh in value added is he sum of growh in hours and growh in average labor produciviy (AL). Table 2 and Figure 2 presen his decomposiion for he period Hours wored predominae rising a 1.68 percen per year while AL grows a 1.39 percen per year. As shown below in Secion II AL growh depends on capial deepening labor qualiy growh and he growh of TF. We have divided capial deepening beween IT and Non-IT capial inpus and labor qualiy among college-educaed and non-college worers and he reallocaion of hours beween hese wo caegories of worers. The resuls reveal he slow growh of labor produciviy in he 1970 s and 1980 s is due o a slump in capial deepening. The growh rae of AL rises only slighly during he firs half of he 1990 s as capial deepening coninues o slump labor qualiy growh remains unchanged and oal facor produciviy growh experiences a modes revival. A subsanial slowdown in he growh of hours wored generaes a furher slide in oupu growh. In previous poswar cyclical recoveries oupu growh had acceleraed during he recovery powered by more rapid growh in boh hours and AL. Acceleraing growh during reflecs a surge in he growh of hours wored of 0.93 percenage poins and a similar rise in AL growh. Tracing his o is sources in Table 2 we see ha capial deepening rises by 0.60 percenage poins accouning for mos of he rise in AL growh. Mos of his 0.51 percenage poins is due o a sharp ump in IT-capial deepening afer The 0.40 percenage poins increase in TF growh is parly offse by a drop in he growh rae of labor qualiy of 0.07 poins. This can be raced o a decline in qualiy growh for non-college worers associaed wih he surge in employmen afer In Table 2 and Figure 3 we also divide growh in TF ino componens associaed wih ITproducing and Non-IT producing indusries. As expeced his reveals a gradual rise in he conribuion of IT-producing indusries ha has coninued hroughou he period roduciviy growh in Non- IT indusries has been negaive on average. Two addiional componens of aggregae TF growh ha capure differences in marginal producs of inpus in differen indusries are reallocaions of capial and labor inpus among indusries. For he period as a whole hese reallocaions are relaively small bu reallocaions of labor inpu flucuae considerably. 4

6 Finally as an addendum in Table 2 we have compared growh in economy-wide value added esimaed from wo indusry-level aggregaion approaches he producion possibiliy fronier and he aggregae producion funcion. The difference beween hese wo measures capures differences in he price of a uni of value added discussed in more deail below. If he producion possibiliy fronier reduces o an aggregae producion funcion his price mus be he same for all indusries. While he differences were modes in size for he period covered by Jorgenson Gollop and Fraumeni (1987) he resuls in Table 2 reveal ha hese differences are no longer small. For he period he reallocaion of value added which measures he divergence beween he wo approaches reaches nearly a full percenage poin. The wide gap beween he producion possibiliy fronier and he aggregae producion funcion can largely be aribued o he more deailed classificaion of IT-producing indusries employed in our sudy. Differences in he growh of value added prices beween hese indusries and Non-IT indusries creae a well-nown fixed-weigh bias. 4 This divergence shows he criical imporance of accouning for relaive price changes hrough an index number approach lie ha currenly uilized in he U.S. Naional Income and roduc Accouns (NIA). We conclude ha he producion possibiliy fronier provides a more appropriae measure of aggregae oupu when using indusry daa and has superseded he aggregae producion funcion. The remainder of he paper is organized as follows. Secion II presens our mehodology for measuring oupu and inermediae inpus. The mos imporan feaure of his mehodology is he use of a consisen ime series of iner-indusry ransacions ables. We use his o allocae he sources of U.S. economic growh among indusries. In Secion III we ouline our mehods for measuring capial inpu. Consan qualiy price indexes for informaion echnology equipmen are essenial for separaing change in performance of his equipmen from he change in price for a given level of performance. The cos of capial is he ey concep for capuring he economic impac of informaion echnology prices. Secion IV oulines our mehods for measuring labor inpu. These incorporae differences in hours wored and wages for worers who differ in age sex and mos imporanly educaional aainmen. In Secion V we ouline a framewor for aggregaing oupu capial labor and inermediae inpus and produciviy over indusries. This framewor was inroduced by Jorgenson Gollop and Fraumeni (1987). A ey role is played by a weighing scheme proposed by Domar (1961) based on he relaive imporance of each indusry in value added as well as he relaive imporance of value added in he indusry s oupu. The Domar weighing scheme capures he impac of sources of growh a he 4 The aggregae producion funcion uses fixed weighs because he value added prices are assumed o be he same. 5

7 indusry level boh in he indusry where growh occurs and in he indusries ha purchase he oupu of his indusry. In Secion VI we presen an analysis of he sources of U.S. economic growh a he indusry level. The conribuions of capial and labor inpus and gains in economy-wide produciviy presened in Tables 1 and 2 and Figures 1-3 reflec he evoluion of he producion srucure of all indusries in he U.S. economy. We aggregae over indusries in order o show how changes in he producion srucure a he indusry level cumulae ino he deerminans of economic growh. We focus special aenion on he role of produciviy growh in he IT-producing indusries invesmens in IT equipmen and sofware and services of he human capial of nowledge worers. Secion VII concludes he paper. II. Measuring Oupu Inermediae Inpu and Value Added. This secion describes our mehodology for measuring indusry oupus inermediae inpus and value added. This mehodology uses a ime series of inpu-oupu (IO) ables and was inroduced by Jorgenson Gollop and Fraumeni (1987 Chaper 5). The resuls were exended and updaed by Jorgenson (1995b). Here we describe he furher updaing and revision of hese sudies. a) Noaion Y Y YTi X i quaniy of oupu of indusry price of oupu o producer in indusry price of oupu o purchasers from indusry quaniy of inpu i ino indusry X i price of commodiy i o buyers X X K L v YC i YC i m i mi YS i M i index of oal inermediae inpu ino indusry price of oal inermediae inpu ino indusry price of oal capial inpu o indusry price of oal labor inpu o indusry value shares quaniy of domesically produced commodiy i price of domesically produced commodiy i quaniy of impors of commodiy I price of impored commodiy i quaniy of oal supply of commodiy i MAKE marix; value of commodiy i made by indusry 6

8 7 b) Mehodology We assume ha he producion funcion for indusry has M disinc inermediae inpus and ha he funcion is separable in hese inpus so ha: (2.1) )... ( ); ( 2 1 M X X X X X T X L K f Y = =. There are M = 44 commodiies corresponding o he primary producs of he indusries lised in Table 3. 5 Under he assumpions of consan reurns o scale and compeiive mares he value of oupu is equal o he value of all inpus: (2.2) + + = i i X i L K Y X L K Y. where we assume ha he price of inermediae inpu X i of commodiy i is he same for all purchasing secors. We define he quaniy of inermediae inpu as a ranslog index of is componens: (2.3) = i i i X v X ln ln where he weighs are he average shares of he componens in he value of inermediae inpu: (2.4) + = i i X i i X i i X i i X i i X X X X v The price index of inermediae inpu X is equal o he value of inermediae inpu divided by he quaniy index X. Noe ha his price is specific o indusry even if he prices of he componen inpus are he same for all indusries since he shares of he componens differ among indusries 6. We require he concep of indusry value added for aggregaion over secors in Secion VI below. Assuming ha he producion funcion is separable in inermediae inpu and value added we define value added V implicily from he equaion: (2.5) V V V v X v Y ln ln ) (1 ln + = where he weighs are shares in gross oupu: (2.6) = Y L K Y L K V Y L K Y L K v. 5 We disinguish 44 separae inpus. Each of hese is an aggregae of many sub-commodiies classified a a finer level of deail in he inpu-oupu accouns. Each indusry purchases a base of hese inermediae inpus. If we were o consruc he price of he base from prices of he sub-commodiies we would obain a differen price index for each purchasing indusry. Our assumpion is ha all indusries face he same price of inermediae inpu i.

9 Value added in nominal erms is V V K K + L = L. The price of value added V is derived by dividing his nominal value by he quaniy index from Equaion (2.5). In order o idenify he impac of informaion echnology we isolae he indusries ha produce IT. In paricular we divide Indusrial Machinery and Equipmen (SIC 35) ino Compuers (SIC 357) and Machinery excluding Compuers (deails are given in Table 3). Similarly we divide Elecronic and Elecrical Equipmen (SIC 36) ino Elecronic Componens (SIC 367 which include semiconducors SIC 3674) Communicaions Equipmen (SIC 366) and Oher Elecrical Machinery. Finally we divide Business Services (SIC 73) ino Compuer Services (SIC 737 which includes sofware) and oher Oher Business Services. This breadown allows us o beer idenify and analyze he impac of IT-producion on he U.S. economy. We derive boh oupus and inermediae inpus from a ime series of iner-indusry ransacions ables. These ables consis of a Use Table ha allocaes he use of each commodiy among inermediae inpus and final demand caegories and a Mae Table ha allocaes he oupu of each commodiy among he indusries ha produce i. These ables are shown schemaically in Appendix Figure 1. The oupu of a given commodiy by all indusries and he inpu of his commodiy by all indusries mus be equal; our sysem of indusry accouns saisfies his accouning ideniy. In he Use Table he h column represens indusry and he ih row represens commodiy i. In nominal erms he sum of he elemens in column is he value of he indusry s oupu. This is equal o he value of his oupu o he producer plus axes paid on his oupu by he purchaser T : (2.7) YT Y Y Y = = Y K Y K + T + L L + i where he price received by he seller is Y and he price paid by he purchaser is YT. The values of capial and labor inpus K K and L L are discussed in he following secions. An indusry may produce several commodiies 7 and a commodiy may be produced by several indusries. The value of he oupu of indusry is equal o he value of all he commodiies i produces: (2.8) YT Y M = i i where M i is he value of commodiy i produced by. This implies ha: (2.9) VC = i YC iyc i M = i i X X i 6 The same subscrip i is used in he numeraor and denominaor of Equaion (2.4) o avoid he proliferaion of symbols; he differen references should be obvious. This applies o similar expressions hroughou he paper. 7 For example he hoel indusry produces he services of boh hoels and resaurans. 8

10 where YC i denoe he quaniy of domesically produced commodiy i and VC i he value. We assume ha each commodiy is an aggregae of he quaniies produced in various indusries and he price of he ih commodiy YCi is given by: M i (2.10) ln YC i ln VC = YT i The Use Table also includes sales o final demand. In Appendix Figure 1 he symbol F i refers o he final demand for commodiy i. This is broen down ino he familiar caegories of personal consumpion expendiures gross privae domesic invesmen governmen purchases expors and impors: (2.11) Fi = ci + i + gi + x i mi where he sum of he elemens in row i of he Use Table is he value of all deliveries of he ih commodiy o inermediae and final demand. Thus he supply-demand balance for commodiy i in value erms is: X X (2.12) YC iyc i = i X i + i Fi We can rewrie his as he oal supply from domesic suppliers and impors which equals oal demand: X X (2.13) YC iyc i + m imi = i X i + i ( ci + ii + gi + xi). We assume ha all buyers purchase he same base of commodiy i ha is he same share of he impored variey. The quaniy of he oal supply of commodiy i of he wo varieies and he price is defined o mae he value ideniy hold: Noe ha his price (2.14) our iner-indusry accouning sysem. c) Daa ln YS X i YS i i = v ln YC = C YC i YC i i + + v m i YS i is assumed o be a ranslog index m m ln m X i is he price paid by producers for heir inpu in Equaion (2.2). This complees We nex describe he sources and mehods for consrucion of our sysem of iner-indusry accouns. The saring poin is he official benchmar U.S. Iner-Indusry Transacions ables produced by he Bureau of Economic Analysis (BEA). These are available for he years and The Office of Employmen roecions of he Bureau of Labor Saisics (BLS) uses hese benchmar ables o generae a ime series of iner-indusry ransacions ables for An earlier i i 8 The laes ables are described in Survey of Curren Business November 1997 p

11 version covered he period These daa are combined wih he ime series of indusry oupus also from he Office of Employmen roecions giving us boh values and prices. 10 The maor difference beween he BEA 1992 benchmar able and he BLS inpu-oupu ables is he reamen of sofware; BLS includes an explici esimae of sofware for each secor. We consolidae and reorganize he BLS iner-indusry ransacions ables from 192 indusries o he 44 indusries covered here. 11 The maor differences are he following: (a) We rea owner-occupied housing as a direc purchase of capial inpu by households raher han a purchase of housing services from he real esae indusry. (b) We consolidae privaely owned elecric uiliies wih publicly owned uiliies in SIC 32 leaving a Governmen Enerprises secor ha does no include elecric uiliies. (c) The Governmen indusry is simplified by consolidaing governmen labor and capial services ino he final demand column for governmen purchases. (d) We impue he service flow from consumers durable asses o obain he consumpion of hese capial services and rea hese as a direc purchase of capial services by households. (e) We rea nonprofi producers symmerically wih he oher producers. Our accouns are hus broader in scope han hose limied o for-profi business secors. (f) We have adused he ables for o mach he GD given in he Survey of Curren Business Augus 2001; he BLS series are based on a previous revision of he NIA. For he period prior o he beginning of he curren BLS ime series of iner-indusry ransacions ables we use a previous version of hese BLS ables for based on he 1987 benchmar ables. We consolidae he earlier ables in a similar manner and lin hem o he curren ables for To mae hem comparable we adus he ables o he new values of indusry oupu produced by he BLS Office of Employmen roecions using he mehod of ieraive proporional fiing discussed by Jorgenson Gollop and Fraumeni (1987 pp. 72-5). Secors such as consrucion oil mining and elecric uiliies are quie differen beween hese wo versions and he previous series are adused o mach he curren one. Our final se of marices for is hus consisen wih he laes esimaes of indusry oupu from BLS and he annual updae of GD published by he BEA in We are graeful o Charles Bowman Carl Chenrens and James Franlin of he BLS for providing hese daa and paienly explaining he deails. The daa are available on he Office of Employmen roecions websie a 10 In an earlier version of his paper we exended he daa se of Jorgenson (1995b) using he benchmar ables of and The aggregaion process involves reallocaing special secors lie scrap res of he world invenory valuaion adusmen general governmen and so on. These are reallocaed o he 44 secors and final demand in accord wih boh Use and Mae marices. 12 Survey of Curren Business Augus

12 The oal of all enries in each column of he Use Table is consisen wih he BLS ime series for Indusry Oupu and Employmen. 13 This daa se provides he value of oupu he price of oupu and employmen for he same indusries for he period We have aggregaed he 192 prices o obain oupu prices for each of our 44 indusries. The excepions o his are Communicaions Equipmen (BLS indusry 53) and Compuer and Daa rocessing Services (BLS indusry 147) where we replace he BLS prices wih BEA prices ha are adused for qualiy change. 14 obained by subracing oupu axes from he purchasers prices as in Equaion (2.7). The prices received by producers are The BLS inpu-oupu daa se also includes he final demand caegories - cigxm - in boh curren and consan prices. Using informaion on impors by commodiies we derive he price for impors mi. We calculae a price index for he oal supply of commodiy i using Equaion (2.14). Finally we derive he prices and quaniies of inermediae inpus. The value of inpu i ino indusry is given by he Use marix. The price X i has been calculaed as described above so ha we can derive he quaniies of iner-indusry ransacions X i. From Equaions (2.3) and (2.4) we calculae he quaniy of inermediae inpu for each indusry. A maor drawbac of he BLS ime series is ha value added is no divided among capial and labor compensaion and indirec business axes as in he BEA benchmar ables. To remedy his deficiency we employ GD by Indusry daa produced by BEA. 15 These daa give for each indusry he componens of Gross roduc Compensaion of Employees roprieors Income Corporae rofis Indirec Business Taxes ec. The value of labor inpu described in Secion IV below is he sum of compensaion of employees and our esimaed value of self-employed labor compensaion. The esimaion of he value of capial inpu is described in Secion III below and includes propery compensaion less he impued value of self-employed labor compensaion plus cerain propery axes. The remainder of GD afer subracing he value of capial and labor compensaion is equal o sales axes ne of subsidies T. d) Issues i) Breadown of Value Added A maor issue is ha he daa on GD by Indusry produced by BEA are no consisen wih he daa on value added in he benchmar iner-indusry ransacions ables. We mainain he oal of value 13 These daa were indly provided by Jay Berman of he BLS. The daa are available a 14 These daa are available from he Gross Oupu by Deailed Indusry file on he BEA's websie The daa are described in Lum and Moyer (2000). 15 These daa are described in Lum and Moyer (2000). The daa are available a 11

13 added for each indusry esimaed in he BLS ables and allocae i in he same proporions as hose in GD by Indusry. This gives us values of capial income labor income and axes - K K L L and respecively - ha sum o he BLS values. The quaniies of capial and labor inpu are hose derived from he GD by Indusry daa or he Census daa described in Secions III and IV below. The prices of capial inpu and labor inpu are derived by dividing hese esimaed values by he quaniies derived from GD by Indusry. ii) Frequency of Iner-Indusry Transacions Tables A second difficuly in consrucing a ime series of iner-indusry ransacions ables is ha he ime series for GD by Indusry published annually are no consisen wih he benchmar iner-indusry ransacions ables published every five years. The magniude and sources of he discrepancies are discussed in BEA (1997). iii) Consisency over Time The 1977 and 1982 benchmar ables are based on he 1972 SIC while 1987 and 1992 ables are based on he 1987 SIC. Similarly he annual GD by Indusry daa have a brea in Daa for GD by Indusry are provided for boh classificaions in 1987 and we have adused he old classificaion o he new one using he shares of each of he old indusries in he new indusries for For he inerindusry ransacions ables we apply he mehod of ieraive proporional fiing o he marices based on he 1972 SIC using indusry oupus based on he 1987 SIC. Our esimaes of indusry oupu and commodiy prices are based on he BLS indusry oupu and impor prices. We assume ha all buyers pay he same price for each commodiy reflecing he absence of daa on prices for differen purchasers. e) Resuls A lis of he indusries included in our sudy is given in Table 3 ogeher wih he definiion of each indusry in he Sandard Indusrial Classificaion. Indusries 6-24 comprise manufacuring while Indusries mae up services. We have sub-divided governmen among governmen enerprises (excluding publicly-owned elecric uiliies) public educaion and general governmen (excluding public educaion). The remaining secors are agriculure hree mining secors consrucion and he household secor. Table 3 gives oupu inermediae inpu and value added for all 44 secors in he year Households and general governmen have no inermediae inpus so ha oupu is equal o value added for hese wo secors. Table 4 gives growh raes of oupu inermediae inpu and value added for all 44 secors for he period T Oupu growh is mos rapid for he IT-producing secors Compuers Communicaions Elecronic Componens and Compuer Services. Growh of inermediae inpu is also 12

14 mos rapid for hese secors. Finance Oher Business Services Communicaions and rofessional and Social Services all inensive users of IT comprise he nex echelon of four indusries in erms of oupu growh. The IT secors also lead in growh of inermediae inpu bu Finance has a sligh edge over Communicaions Equipmen in he growh of value added. In Figure 4 he growh of oupu for each secor is allocaed beween inermediae inpu and value added. Table 5 and Figure 5 give growh raes of oupu for all 44 secors for and Oupu growh is mos rapid for he IT-producing secors during he 1990s bu he growh of Finance oupaces ha of Communicaions Equipmen before The second echelon of four indusries in a leas one of he hree sub-periods includes six indusries indicaing he range of indusries wih relaively rapid growh. Table 6 and Figure 6 give growh raes of inermediae inpu for he hree sub-periods. Again growh is mos rapid for he IT-producing secors during he 1990s bu Finance ousrips Communicaions Equipmen before The second echelon of four indusries in a leas one of he hree sub-periods includes eleven indusries indicaing he widespread imporance of inermediae inpus. Finally Table 7 and Figure 7 give growh raes of value added for he hree sub-periods. The growh of value added in he IT-producing secors is srong for all hree sub-periods bu eroleum Refining leads Communicaions Equipmen and Compuer Services during and Finance leads Communicaions Equipmen during The second echelon of four indusries in a leas one subperiod includes en indusries indicaing he range of indusries wih relaively rapid growh in value added. Our overall conclusion from hese resuls is ha he IT-producing secors sand ou in erms of rapid growh of oupu inermediae inpu and value added for he period as a whole and for he hree sub-periods and Finance surpasses Communicaions Equipmen in growh of value added for he period as a whole and a number of indusries have more rapid growh of inermediae inpu and/or value added during one or more sub-periods. Noneheless he picure ha emerges from hese daa is one of rapid growh of he IT-producing indusries for he period as a whole and acceleraing growh during he period III. Measuring Capial Inpu This secion oulines our mehodology for measuring he flow of capial services in each indusry. The ey obecive is o accoun for subsiuion among asses wih differen marginal producs. The mehodology was originaed by Jorgenson and Griliches (1995) who consruced price and quaniy indexes for capial inpu based on Jorgenson s (1996) model of he corporae cos of capial. These indexes were exended o he indusry level for all hree legal forms of organizaion corporae non- 13

15 corporae and household - by Jorgenson Gollop and Fraumeni (1987 Ch. 4) and updaed and revised by Jorgenson (1995b). We incorporae recen mehodological changes developed by Jorgenson and Siroh (2000). These include he use of asse-specific revaluaion erms in he service price equaion. In addiion capial service flows from new invesmens are assumed o become available in he middle of he year raher han a he end of he year as in our earlier wor. a) Noaion We begin wih noaion for measures of invesmen capial socs and capial services for individual asses and indusry aggregaes. The subscrip refers o he specific asse while refers o he indusry; ime subscrips are suppressed wherever possible. For individual asses we have: I = quaniy of invesmen I = price of invesmen δ = geomeric depreciaion rae Z = quaniy of capial soc I = price of capial soc K = quaniy of capial services K = price of capial services For indusry aggregaes: I = quaniy index of indusry invesmen I = price index of indusry invesmen Z = quaniy index of indusry capial soc Z = price index of indusry capial soc K = quaniy index of indusry capial services K = price of indusry capial services Q K = index of indusry capial qualiy b) Mehodology for Esimaing Capial Service Flows For each indusry we begin wih daa on he quaniy of invesmen in each individual asse I. We assume ha he price index for each asse ransforms nominal invesmen in differen ime periods ino idenical efficiency unis over ime so ha invesmens of differen vinages are perfec subsiues in producion. Improvemens in he performance of capial inpu for example a faser processor in a compuer are incorporaed ino he price index ha ransforms he curren vinage of invesmen ino an equivalen number of efficiency unis of earlier vinages. As a concree example he consan-qualiy 14

16 price index for compuer equipmen ransforms more recen invesmens in faser more powerful compuers ino addiional unis of consan efficiency base-year capial. We ransform daa on he quaniies of invesmen ino esimaes of capial socs for all asses indusries and years hrough he familiar perpeual invenory mehod. This is consisen wih he assumpion of perfec subsiuabiliy across vinages and defines he capial soc for each indusry and asse as: (3.1) Z = Z 1(1 δ ) + I = (1 δ ) τ = 0 τ I τ where he efficiency of an asse is assumed o decline geomerically wih age a he rae Equaion (3.1) has he inerpreaion ha capial soc is a weighed sum of pas invesmens where he weighs are derived from he relaive efficiencies of capial of differen ages capured by he geomeric rae of decline. Noe ha he raes of decline in efficiency δ are indexed by asse. We assume ha hese raes are consan over ime and idenical for all indusries. Finally because all capial is measured in base-year efficiency unis he appropriae price for valuing he capial soc is he invesmen price deflaor I. The insalled soc of capial Z represens he accumulaion of pas invesmens bu we are primarily ineresed in K he flow of capial services from ha soc over a given period. This disincion is no criical for individual asses bu becomes essenial when we aggregae heerogeneous asses o form an indusry or economy-wide aggregae. For individual asses we assume ha new invesmen becomes available for producion a he mid-poin of he year so he flow of capial services for each indusry and each asse is proporional o he arihmeic average of he curren and lagged capial soc: (3.2) K q (.5 Z + 0. Z ) = δ. where q denoes he proporionaliy consan normalized o one. We esimae a price of capial services ha corresponds o he quaniy of capial inpu via he cos-of-capial formula inroduced by Jorgenson (1996). In equilibrium wih no uncerainy invesors are indifferen beween wo alernaives: earning a nominal rae of reurn i on a differen invesmen or buying a uni of capial collecing a renal fee and hen selling he depreciaed asse in he nex period. For invesors purchasing he asse he cos of capial equals he marginal produc of he asse. This implies he familiar cos of capial or user cos for each asse in each indusry: (3.3) K = ( i π ) 1 + δ I 15

17 16 where he asse-specific capial gains erm is 1 1. / ) ( = I I I π and i is he nominal rae of reurn in indusry. The cos of capial accouns for he nominal rae of reurn asse-specific depreciaion and an asse-specific revaluaion erm. An asse wih a higher depreciaion rae has a higher marginal produc and mus receive a higher capial service price as compensaion. Similarly if an invesor expecs a capial loss (π <0) hen a higher service price is required. Jorgenson and Siroh (2000) and Oliner and Sichel (2000) discuss he imporance of incorporaing asse-specific revaluaion erms for informaion echnology asses experiencing rapid downward revaluaions. Tax consideraions are also a ey componen of capial service prices as discussed by Hall and Jorgenson (1996b) and developed in deail by Jorgenson and Yun (2001). We follow Jorgenson and Yun (2001) and Jorgenson and Siroh (2000) in accouning for invesmen ax credis capial consumpion allowances he sauory ax rae propery axes deb/equiy financing and personal axes by esimaing an asse-specific afer-ax real rae of reurn for each asse in each indusry r ha eners he cos of capial formula: (3.4) [ ] = I p I I K r z ITC τ δ τ τ where ITC is he invesmen ax credi τ is he sauory ax rae z is he presen value of capial consumpion allowances for ax purposes τ p is a propery ax rae all for asse a ime. For he corporae secor he rae of reurn r is calculaed as: (3.5) + + = ) )(1 (1 ) (1 ) (1 ) (1 ] ) [(1 g q e q g q i r α α π ρ β π τ β where β is he deb/capial raio i he ineres cos of deb ρ he rae of reurn on equiy α is he dividend payou raio and g q and e q are he ax raes on capial gains and dividends respecively. The asse-specific inflaion rae for asse π allows he rae of reurn r o vary across asses. We assume he afer-ax rae of reurn o all asses in each indusry is he same and esimae ρ as he reurn ha exhauss he value of paymens o capial across all asses in he corporae secor of each indusry. Tha is we esimae he rae of reurn and he capial service prices oinly in order o saisfy he following resricions: (3.6) [ ] = = I p I I K L V K r Z ITC L V K τ δ τ τ

18 17 where r is defined as in Equaion (3.5) and V V is nominal indusry value added he produc of he price of value added V and he quaniy V. 16 Equaions (3.1) hrough (3.6) describe our esimaion procedure for he capial service flow and capial service price K and K respecively for each asse indusry and ime period. We combine capial services for all asses wihin an indusry by means of a ranslog quaniy index; his exacly replicaes a ranslog model of capial services for each indusry as shown by Diewer (1976). The quaniy index of capial inpu is defined as a ranslog aggregae of he services of differen capial asses: (3.7) K v K ln ln = where weighs are he wo-period average of nominal shares of capial income: (3.8) + = K K K K K K K K v The corresponding price index of capial inpus K is defined implicily o mae he value ideniy hold: (3.9) = K K K K Similarly he quaniy of capial soc is defined by: (3.10) K w Z ln ln = where he weighs are he wo-period average nominal shares of capial soc: (3.11) + = I I I I K K K K w The corresponding price index for capial soc Z is defined implicily from he ideniy: (3.12) = I Z K Z. Finally we define capial qualiy Q K for indusry as he raio of capial inpu o capial soc: (3.13) K Z K Q =. I follows ha he growh rae of capial qualiy is defined as he difference beween he growh raes of capial inpu and capial soc: 16 More precisely Equaion (3.6) applies o esimaes for he corporae secor. As discussed in Jorgenson and Yun (2001 Chaper 2) ax consideraions vary by legal form of ownership - corporae non-corporae and household - and our empirical wor aes his ino accoun.

19 (3.14) ln Q K = ln K ln Z. Noe ha quaniy indexes of capial inpus and capial socs aggregae he same asse quaniies K by means of a ranslog index; he difference is he use of service prices versus asse prices as weighs. This implies ha growh in capial qualiy reflecs subsiuion owards asses wih relaively high service prices and high marginal producs. For example large depreciaion raes and rapid downward revaluaions for compuers imply ha hese asses have high marginal producs so heir weigh in an index of capial services grealy exceeds heir weigh in an index of capial asses. Subsiuion oward compuers as compuer prices fall implies ha capial inpu grows faser han capial soc; his is capured by our index of capial qualiy. Second our measure of indusry capial soc is implicily a wo-period average since i aggregaes wo-period averages of capial socs using curren asse prices. Finally o sudy he relaive imporance of informaion echnology (IT) capial and Non-IT capial we define wo furher ses of indexes for capial inpus capial socs and invesmen based on he deailed invesmen daa. The capial services of informaion echnology K IT include he service flows from compuer hardware sofware and communicaions equipmen while he Non-IT capial service flow K NON includes he services from all oher equipmen srucures invenories and land. We creae sub-indexes of capial services as: (3.15) ln K ln K IT = NON IT = v IT IT v ln K NON IT ln K NON where he shares are hose of IT capial and Non-IT capial respecively. c) Daa Our primary daa source for capial inpu is he Tangible Wealh Survey produced by he Bureau of Economic Analysis (BEA) and described in Herman (2000a 2000b). These daa include deailed invesmen by indusry and asse class and conain hisorical cos invesmen and chain-ype quaniy indexes for 61 ypes of nonresidenial asses from 1901 o ypes of residenial asses from 1901 o 2000 and 13 differen ypes of consumers durables from 1925 o Nonresidenial invesmen is available for 62 indusries which we collapse ino 44 indusries including privae households and governmens. We have made several adusmens o he daa worh menioning. Firs for each of he 41 privae indusries we reclassify he BEA daa on 61 nonresidenial asses ino 52 nonresidenial asses. The residenial asses and 13 consumers durable asses are allocaed o he real esae and household indusries. Second we combine invesmen in residenial equipmen wih oher equipmen in he nonresidenial caegory. Third we conrol he oal value of invesmen in maor caegories - equipmen 18

20 and sofware nonresidenial srucures residenial srucures and oal consumer durables - o mach he oals in he U.S. Naional Income and roduc Accouns (NIA). These adusmens lead o a complee ime series of 57 asses in boh curren and chained 1996 dollars for each of he 44 indusries. The invesmen and capial daa are hen allocaed across hree ownership caegories corporae noncorporae and households based on shares provided by BEA. There is no ownership breadown for household and governmen indusry daa. Finally we use prices for each asse from he NIA. Geomeric depreciaion raes for he perpeual invenory calculaions are based on Fraumeni (1997) wih he excepions of compuers and auomobiles. BEA (1999) repors ha depreciaion is nongeomeric and varies over ime for mos compuer componens and peripherals based on he wor of Oliner ( ). We esimaed a bes-geomeric approximaion o he laes depreciaion profile for differen ypes of compuer asses; his generaes an average geomeric depreciaion rae of which we have used for compuer invesmen sofware invesmen and consumer durable purchases of compuers peripherals and sofware. For auomobiles BEA derives a depreciaion profile from new and used car prices. We esimaed a bes geomeric approximaion o he depreciaion profile for auos obaining an esimae of We have colleced daa on invenories and land o complee our capial esimaes. Invenory daa come primarily from he NIA in he form of farm and non-farm invenories allocaed across indusries. These are measured in curren dollars wih a corresponding price index. Invenories are assumed o have a depreciaion rae of zero and do no qualify an invesmen ax credi or capial consumpion allowances for ax purposes so he capial renal price formula is a simplified version of Equaion (3.4). Daa on land are more problemaic. Through 1995 he Federal Reserve Board ( ) published deailed daa on land values and quaniies in is Balance Shees for he U.S. Economy bu he underlying daa became unreliable and are no longer published. We use he limied land daa available in he Flow of Funds Accouns of he Unied Saes and hisorical daa described in Jorgenson (1995b) o esimae a price and a quaniy of privae land. As a pracical maer his quaniy series varies very lile so is maor impac is o slow he growh of capial soc and capial inpu. Lie invenories he depreciaion invesmen ax credi and capial consumpion allowance for land is zero. Finally we have colleced daa on indusry-level value added from he Gross roduc Originaing daabase mainained by he BEA and described in Lum and Moyer (2000) and from he BLS as described above. The BEA daa include he value of oupu value added and inermediae inpus for 62 indusries from 1947 o We have aggregaed hese indusries o mach our 44 indusries. For he esimaion of capial service prices we begin wih value added in he corporae secor and subrac corporae labor income o esimae he amoun of income available o corporae capial. Similarly we 19

21 subrac non-corporae labor income from value added as described in he following secion o obain he value of non-corporae capial income. d) Issues Alhough he mehodology described above conforms o he inernaional sandards recommended by Blades (2001) and Schreyer (2001) of he OECD here are imporan issues relaed o he availabiliy of daa and he plausibiliy of cerain assumpions ha arise in he implemenaion of his mehodology. This subsecion oulines hese issues and describes our soluions. i) Negaive Service rices The inuiion behind our esimaion of capial service prices is ha he value of capial service flows mus exhaus capial income. One problem is ha here is very lile income available o capial in some years and his leads o negaive esimaes of service prices. For example if asse inflaion raes are high and depreciaion raes are low relaive o he ineres rae negaive service prices may resul. Economically his is possible and suggess ha capial gains are higher han expeced so ha a small service price is possible in equilibrium. Bernd and Fuss (1986) discuss his issue in more deail. Empirically however negaive service prices mae aggregaion difficul so we have made adusmens for several asses. Cerain asses showed negaive service prices noably invenories land and srucures in he 1970 s when inflaion was high. Our firs adusmen of he daa was o use a smoohed inflaion rae from he surrounding years raher han he curren inflaion in he cos of capial calculaion. Land showed large capial gains hroughou and has no depreciaion so ha we used he economy-wide rae of asse inflaion for all years. As a las resor we were forced o impue addiional income which added o boh capial income and he value of oupu bu his is a relaively small issue empirically. ii) Deflaors The mehodology described above allows for deflaors for each asse o differ across indusries. In pracice however he indusry-specific deflaors for cerain asses were quie erraic across indusries and ime. The Tangible Wealh Survey repors invesmen in millions of dollars wih no decimal poins so any asse wih a very small value and quaniy in a given year has a deflaor ha is no esimaed precisely. We simply aggregaed each asse across all indusries and used he economy-wide average deflaor o remove he noise. A second concern is our reliance on he deflaors incorporaed in he Tangible Wealh Survey and he NIA. For mos asses his is no a problem bu Jorgenson and Siroh (2000) argue ha he official deflaors do no fully accoun for qualiy change in sofware and communicaions equipmen. For hese asses only a small share of invesmen is associaed wih consan-qualiy deflaors leading o an 20