Online Appendix: Labor Share Decline and Intellectual Property Products Capital

Transcription

1 *NOT FOR PUBLICATION Online Appendix: Labor Share Decline and Inellecual Propery Producs Capial By Dongya Koh, Raül Sanaeulàlia-Llopis and Yu Zheng 1

2 Conens A The Daa 1 A.1 The Consrucion of Aggregae Daa Series A.1.1 The Source of Daa A.1.2 Depreciaion Rae by Type of Capial A.1.3 Invesmen by Type of Capial A.1.4 Relaive Price of Invesmen by Type of Capial A.1.5 Sock of Capial in Efficiency Unis by Type of Capial A.1.6 Rae of Reurn o Capial by Type of Capial A.1.7 Aggregae, Tradiional and Oher Counerfacual Labor Shares A.2 The BEA-NSF s Capializaion of R&D Expenses B Furher Insighs on IPP Capial 9 C A Broader Hisorical Perspecive: IPP Capializaion and he U.S. Labor Share, D The Corporae Secor and he BLS Labor Share 13 D.1 The Corporae Secor D.2 The BLS Labor Share E IPP Capial and Labor Share by Indusry 17

3 A The Daa A.1 The Consrucion of Aggregae Daa Series A.1.1 The Source of Daa All daa series are rerieved from he Bureau of Economic Analysis for he period Naional Income and Produc Accouns (NIPA-BEA) 1. NIPA 1.7.5: Gross Naional Produc (GNP), Consumpion of Fixed Capial (CFC), Saisical Discrepancy (SDis). 2. NIPA 1.12: Compensaion of Employees (CE), Proprieors Income (PI), Renal Income (RI), Corporae Profis (CP), Ne Ineres (NI), Taxes on Producion (Tax), Subsidies (Sub), Business Curren Transfer Paymens (BCTP), Curren Surplus of Governmen Enerprises (GE). 3. NIPA 2.3.3: Real Personal Consumpion Expendiures on Nondurable Goods (excluding Gasoline and Oher Energy Goods) (QCONS ND ) and Services (QCONS SV ). 4. NIPA 2.3.5: Personal Consumpion Expendiures on Nondurable Goods (excluding Gasoline and Oher Energy Goods) (CONS ND ) and Services (CONS SV ). 5. NIPA 3.9.5: Governmen Gross Invesmen on Srucures (IG ST ), Equipmen (IG EQ ), Inellecual Propery Producs (IG IP P ), Sofware (IG Sofware ), Research and Developmen (IG RD ). 6. NIPA 5.3.4: Price Indices for Privae Fixed Invesmen on Nonresidenial Equipmen (OPI EQ,NRes ), Residenial Equipmen (OPI EQ,Res ), Inellecual Propery Producs (OPI IP P ), Sofware (OPI Sofware ), Research and Developmen (OPI RD ), Enerainmen, Lierary and Arisic Originals (OPI En ) NIPA 5.3.5: Privae Fixed Invesmen on Nonresidenial Srucures (IP ST,NRes ), Residenial Srucures (IP ST,NRes ), Nonresidenial Equipmen (IP EQ,NRes ), Residenial Equipmen (IP EQ,Res ), Inellecual Propery Producs (IP IP P ), Sofware (IP Sofware ), Research and Developmen (IP RD ), Enerainmen, Lierary and Arisic Originals (IP En ). 8. NIPA A/B: Governmen Gross Fixed Invesmen on Residenial Srucures (IG ST,Res ). Fixed Asses Accouns (FAT-BEA) 1. FAT 1.1: Curren-Cos Ne Sock of Privae Fixed Asses for Nonresidenial Equipmen (K P,EQ,NRes ), Nonresidenial Srucures (K P,ST,NRes ), Inellecual Propery Producs (K P,IP P ), Residenial (K P,Res ); Curren-Cos Ne Sock of Governmen Fixed Asses for Nonresidenial Equipmen (K G,EQ,NRes ), Nonresidenial Srucures (K G,ST,NRes ), Inellecual Propery Producs (K G,IP P ), Residenial (K G,Res ); Consumer Durables (K CD ). 2 1 The price of governmen invesmen in equipmen and IPP is available for using NIPA Tables 5.9.A and 5.9.B. Unforunaely, he price of residenial governmen invesmen is no available, alhough here is separae informaion on he iems of residenial invesmen from he governmen in (1) srucures/federal/naional defense/new buildings/residenial, (2) srucures/federal/nondefense/new buildings/residenial, and (3) sae and local/new/buildings/residenial. For his reason, we have decided o use he privae secor prices for governmen invesmen in equipmen, IPP, and residenial invesmen. We have checked ha prices for each ype of invesmen are very similar across he privae and he governmen secor. 2 Consumer durables are no par of our benchmark analysis as hey are no capialized in NIPA. We have found ha an exension of our exercise ha incorporaes consumer durables lowers he level of he LS bu does no affecs is rend. 1

4 2. FAT 1.3: Curren-Cos Depreciaion of Privae Fixed Asses for Nonresidenial Equipmen (DEP P,EQ,NRes ), Nonresidenial Srucures (DEP P,ST,NRes ), Inellecual Propery Producs (DEP P,IP P ), Residenial (DEP P,Res ); Curren-Cos Depreciaion of Governmen Fixed Asses for Nonresidenial Equipmen (DEP G,EQ,NRes ), Nonresidenial Srucures (DEP G,ST,NRes ), Inellecual Propery Producs (DEP G,IP P ), Residenial (DEP G,Res ); Consumer Durables (DEP CD ). 3. FAT 2.1: Curren-Cos Ne Sock of Privae Fixed Asses for Sofware (K P,Sofware ), Research and Developmen (K P,RD ), Enerainmen, Lierary and Arisic Originals (K P,En )). 4. FAT 2.4: Curren-Cos Depreciaion of Privae Fixed Asses for Sofware (DEP P,Sofware ), Research and Developmen (DEP P,RD ), Enerainmen, Lierary, and Arisic Originals (DEP P,En )). 5. FAT 7.1 A/B: Curren-Cos Ne Sock of Governmen Fixed Asses for Sofware (K G,Sofware ), Research and Developmen (K G,RD ). 6. FAT 7.3 A/B: Curren-Cos Depreciaion of Governmen Fixed Asses for Sofware (DEP G,Sofware ), Research and Developmen (DEP G,RD ). A.1.2 Depreciaion Rae by Type of Capial We consruc he ne sock of capial and depreciaion of capial for radiional capial and for IPP capial. The ne sock of radiional capial is he sum of privae- and governmen-secor nonresidenial srucures, equipmen, and residenial capial. The ne sock of IPP capial is only in nonresidenial. The ne sock of capial by ype of capial: Privae IPP: Governmen IPP: Privae Tradiional: Governmen Tradiional: K P,IP P = K P,IP P K G,IP P = K G,IP P K P,T = K P,ST,NRes + K P,EQ,NRes + K P,Res K G,T = K G,ST,NRes + K G,EQ,NRes + K G,Res The depreciaion by ype of capial: Privae IPP: Governmen IPP: Privae Tradiional: Governmen Tradiional: DEP P,IP P = DEP P,IP P DEP G,IP P = DEP G,IP P DEP P,T = DEP P,ST,NRes + DEP P,EQ,NRes + DEP P,Res DEP G,T = DEP G,ST,NRes + DEP G,EQ,NRes + DEP G,Res The capial depreciaion rae by ype of capial is hen: δ IP P = DEP P,IP P + DEP G,IP P K P,IP P + K G,IP P and δ T = DEP P,T + DEP G,T K P,T + K G,T A.1.3 Invesmen by Type of Capial We consruc he nominal invesmen in radiional capial, sofware capial and IPP, and he associaed invesmen shares, which will be used in he consrucion of price indices in Secion A.1.4: 3 3 In more deail, firs, invesmen accouns in srucures include nonresidenial and residenial srucures, see Table in NIPA. Nonresidenial srucures include (i) commercial and healh care (i.e., office buildings (excep 2

5 Srucures: Equipmen: Inv EQ Tradiional: Inv T = Inv ST Sofware: Inv ST = IP ST,NRes = IP EQ,NRes + IP ST,Res + Inv EQ. Inv Sofware = IP Sofware. IPP: Inv IP P = IP IP P + IG IP P Aggregae: Inv = Inv T + Inv IP P Shares of Invesmen: + IP EQ,Res.. s i = Invi Inv, for i {T, IP P }. + IG ST. + IG EQ Aggregae invesmen appears in he expendiure-measure of oupu, GDP (see NIPA Table 1.1.5). GDP consiss of (a) personal consumpion expendiures ha includes goods (durable and nondurable) and services, (b) gross domesic privae invesmen ha is disaggregaed in his able as fixed invesmen 4 and change in privae invenories, (c) ne expors of goods and services, and (d) governmen consumpion expendiures and gross invesmen. 5 Furher, noe ha while changes in privae invenories are capialized as hey ener he invesmen accoun, his is no he case for governmen invenories since hey are included in governmen consumpion expendiures (see foonoe 2 in NIPA Table 3.9.5). 6 The ime series of he nominal invesmen in radiional and IPP capial in panel (a) of Figure 2. In 1947, he nominal invesmen in radiional capial is abou 50 billion USD and ha in IPP capial is negligible. By 2013, he invesmen in radiional capial has reached 250 billion USD, and ha in IPP capial almos 100 billion USD. In erms of he relaive imporance of invesmen in radiional capial and IPP (panel (b) of Figure 2), he share of IPP invesmen rises from 10% of he oal invesmen o 30% from 1947 o hose consruced a manufacuring sies and hose consruced by power uiliies for heir own use), hospials and medical buildings, mulimerchandise shopping, food and beverage esablishmens, warehouses, and oher commercial), (ii) manufacuring, (iii) power and communicaion, (iv) mining exploraion, shafs and wells (i.e., peroleum and naural gas and mining), and (v) oher srucures (religious, educaion and vocaional, lodging, amusemen and recreaion, ransporaion, farm, oher, brokers commissions on sale of srucures, and ne purchases of used srucures). Residenial srucures include (i) permanen sie (i.e., single-family and mulifamily srucures) and (ii) oher srucures (i.e., manufacured homes, dormiories, improvemens, brokers commissions and oher ownership ransfer coss and ne purchases of used srucures). Second, he invesmen accouns in equipmen include (i) informaion processing (i.e., compuers and peripheral equipmen, communicaion equipmen, medical insrumens, nonmedical insrumens, phoocopy and relaed equipmen, and office and accouning equipmen), (ii) indusrial equipmen (i.e, fabricaed meal producs, engines and urbines, mealworking machinery, special indusry machinery, general indusrial equipmen, including maerials handling, elecrical ransmission, disribuion, and indusrial apparaus), (iii) ransporaion equipmen (i.e., rucks, buses, and ruck railers, auos, aircrafs, ships and boas, railroad equipmen), and (iv) oher equipmen (i.e, furniure and fixures, agriculural machinery, consrucion machinery, mining and oilfield machinery, service indusry machinery, elecrical equipmen, and oher) less sales of equipmen scrap (excluding auos), see Table in NIPA. Third, he invesmen accouns in IPP include (i) sofware (i.e., prepackaged excluding sofware embedded, or bundled, in compuers and oher equipmen, cusom and own accoun), (ii) R&D in businesses manufacuring (i.e., pharmaceuical and medicine manufacuring, chemical manufacuring, semiconducor and oher elecronic componens, moor vehicles, bodies and railers, and pars, aerospace producs and pars, and oher manufacuring), in business nonmanufacuring (i.e., scienific research and developmen series, and all oher nonmanufacuring) and in nonprofi insiuions serving households (i.e., universiies and colleges, and oher nonprofi insiuions), and (iii) enerainmen, lierary, and arisic originals (i.e., hearical movies, long-lived elevision programs, books, music and oher), see Table in NIPA. 4 Fixed invesmen is displayed in erms of nonresidenial invesmen (in srucures, equipmen and IPP) and residenial invesmen. 5 Noe ha governmen consumpion and invesmen are recorded in he same accoun in Table This accoun is furher broken down ino federal (naional defense and nondefense) and sae and local. 6 Noe also ha consumer durables are no capialized in NIPA. Then, if we wan o include hem in our accouning exercise we mus exend our measure of oupu o include he income generaed by consumer durables.. 3

6 Furher, we define various shares of invesmen for laer use in Secion A.1.4: Nonresidenial Equipmen: Residenial Equipmen: Srucures: Equipmen: s P,EQ,NRes = s P,EQ,Res s ST = s EQ Inv ST IP EQ,NRes IP EQ,NRes = 1 s P,EQ,NRes Inv ST = 1 s ST +Inv EQ +IP EQ,Res A.1.4 Relaive Price of Invesmen by Type of Capial We consruc he relaive price of invesmen in radiional capial and in IPP capial. In addiion, we also consruc he relaive price of invesmen in sofware capial, o be used in one of he counerfacual exercises. The price of he consumpion good is he numèraire. We firs consruc he price of invesmen in srucures, equipmen, radiional capial, IPP capial and he componens in IPP capial separaely. (a) Price of Invesmen in Srucures: Price index for consumpion, P C, is used as a proxy for he price of srucures invesmen. 7 We use a Törnqvis price index aggregae 8 for nondurable consumpion (excluding gasoline and oher energy goods) and services. Le P C,i be he price index for nondurable goods and service good i in year, compued as he raio beween nominal consumpion of good i, CONS i, and he quaniy index of good i, QCONS i, i.e. P C,i = CONSi, for i {ND, SV }. Le s C,i CONS QCONS i = i be CONS ND +CONS SV he corresponding nominal share of good i in period. Le he growh rae of a variable x be denoed as λ(x ) = x x 1 1 ln( x x 1 ). Then, he growh rae of he Törnqvis price index for consumpion is λ(p C ) = i s C,i + s C,i 2 1 λ(p C,i ). The level of he consumpion price index is recovered recursively, P C = P C 1 [1 + λ(p C )] = P I,ST where P C 0 is normalized o 1 a he iniial period. (b) Price of Invesmen in Equipmen: In compuing he price index of equipmen invesmen, we use a Törnqvis price index for privae residenial equipmen invesmen, P I,EQ,Res = OP I EQ,Res, and privae non-residenial equipmen invesmen, P I,EQ,NRes = OP I EQ,NRes, from NIPA Table Then, he 7 As is sandard in he lieraure, we use he consumpion deflaor as he price index for invesmen in srucures (see Fisher (2006) and Canova e al. (2010)). The consumpion deflaor has he advanage over an oupu deflaor when applied o he srucures, since i does no involve price changes of equipmen invesmen. In addiion, we find no major difference in he resuls if we use he price of srucures derived from FAT. 8 The Törnqvis price index specifies, for a variey of producs indexed by j, P P 1 = Π j ( P j P j 1 ) 1 2[s j +sj 1], (A-1) where s j is he share of he value of he variey j. 9 We do no use he U.S annual series provided by Cummins and Violane (2002) in his exercise because hose series incorporae he sofware as par of equipmen while he curren NIPA accouns caegorize sofware ino R&D. We assume ha he hedonic mehods used o compue he official price index have correcly qualiy-adjused mos ypes of equipmen invesmen now. 4

7 growh rae of he price index of equipmen is ( ) s P,EQ,Res λ(p I,EQ ) = + s P,EQ,Res 1 2 λ(p I,EQ,Res ) + ( s P,EQ,NRes ) + s P,EQ,NRes 1 λ(p I,EQ,NRes ), 2 where s P,EQ,Res and s P,EQ,NRes are he share of privae residenial and non-residenial equipmen invesmen of oal equipmen invesmen defined in Secion A.1.3. (c) Price of Invesmen in Tradiional Capial: In compuing he price index of radiional invesmen, we use a Törnqvis price index for srucures and equipmen consruced above in (a) and (b). Then, he growh rae of he price index of he radiional invesmen is ( s λ(p I,T ST + s ST ) 1 ) = λ(p I,ST ) + 2 ( s EQ ) + s EQ 1 λ(p I,EQ ), 2 where s ST and s EQ are he share of srucures and equipmen invesmen of oal radiional invesmen defined in Secion A.1.3. (d) Price of Invesmen in IPP: This is available only for non-residenial invesmen. We use he price index for IPP Invesmen, P I,IP P = OP I IP P, available in NIPA Table Likewise, we use he price indexes for he subcaegories of IPP, such as sofware (P I,Sofware = OP I Sofware ), R&D (P I,RD = OP I RD ), and Enerainmen (P I,En = OP I En ), from NIPA Table Then, he level of he price indices of invesmen in radiional capial is recovered recursively as P I,T = P I,T I,T 1 [1 + λ(p )] where P I,T 0 is normalized o 1 a he iniial period. We furher normalize he price index of he IPP invesmen P I,IP P and he price index of he sofware invesmen P I,Sofware o 1 a he iniial period. Finally, he relaive price of invesmen (using he consumpion as numèraire) is defined as p j = P I,j P C, and is inverse, v j = 1, is he invesmen-specific echnical change, for j {T, IP P, Sofware}. p j A.1.5 Sock of Capial in Efficiency Unis by Type of Capial Define he invesmen in efficiency unis by he nominal invesmen deflaed by he price of invesmen for radiional capial and IPP: x j, = Inv j /P I,j, for j {T, IP P, sofware}. Then, we can recursively compue he sock of capial in efficiency unis, k x,j applying he capial accumulaion equaion in (3): by k x j,+1 = x j, + (1 δ j, )k x j,, (A-2) for j {T, IP P, sofware}. We se kj,0 x = 850 by argeing he annual capial-oupu raio of 12. 5

8 A.1.6 Rae of Reurn o Capial by Type of Capial We impue he ne rae of reurn by using he equaions (4) and (5) wih he pos-revision daa: [ k x ] T, (1 LS )y + v T, (1 δ T, ) + kx IP P, v IP P, (1 δ IP P, ) r = 1, (A-3) kt, x v T, 1 + kx IP P, v IP P, 1 where LS is he labor share compued by using pos-revision naional income daa in Secion 3.1 and y is real GNP deflaed by he price of consumpion in he pos-revision daa. Assuming he ne rae of reurn o capial, r, is idenical across ypes of capial, we can compue gross rae of reurn from he equaion R j,+1 = 1 v j, (1 + r +1 ) 1 v j,+1 (1 δ j,+1 ), (A-4) for j {T, IP P, sofware}. A.1.7 Aggregae, Tradiional and Oher Counerfacual Labor Shares Wihin his model, we compue a radiional labor share ha only uses capial income from radiional capial o evaluae he effec of IPP capializaion. In addiion, we compue a labor share ha incorporae only radiional capial income and sofware income. Finally, in he decomposiion exercise, we compue a labor share seing he IPP depreciaion o zero. Aggregae labor share: If we follow he consrucion of δ j,, P I j,, v j,, x j,, k x j,, r, R j, in he way specified in Secions A.1.2 hrough A.1.6 and compue he labor share according o (1), we will have, by consrucion, recovered he labor share in he pos-revision daa exacly. We compue he capial income by ype of capial and he labor income, which are he inpus o panel (a) of Figure 8: Tradiional Capial Income: y T, = R T, kt, x. IPP Capial Income: y IP P, = R IP P, kip x P,. Labor Income: w H = ry R T, kt, x R IP P,kIP x P,. Tradiional labor share: Given he series of depreciaion raes, prices of invesmen and invesmen for radiional and IPP capial as well as he ne raes of reurn o capial, we compue he radiional labor share according o (2). Labor share wih radiional capial and sofware: This is he labor share ploed in panel (b) in Figure 6, labeled + Sofware. To he radiional capial income, we add he sofware income o compue he labor share wih radiional capial and sofware: R T kt x LS T +Sofware = 1 + R sofwareksofware x y R IP P kip x P + R sofwareksofware x. Labor share wihou IPP depreciaion: This he labor share ploed in Figure 7, labeled Aggregae wihou IPP Depreciaion. Firs we compue he ne IPP capial income as: ( 1 + yip ne r P, = 1 ) kip x v IP P, 1 v P,. IP P, 6

9 Then he labor share wihou IPP depreciaion is compued as: LS IP P depreciaion = 1 R T,kT, x + yne IP P, y δ. IP P, v IP P, kip x P, A.2 The BEA-NSF s Capializaion of R&D Expenses The major componen of he 2013 NIPA revision is he capializaion of he R&D expendiures from he business, governmen and non-profi insiuions serving households (NPISH). In his secion, we firs describe he definiion of he R&D adoped by he BEA and he mehodology of evaluaing he invesmen, oupu and depreciaion of he R&D. Second, we discuss he pracical implicaions ha his capializaion has had on he axonomy of he fixed asses ables (FAT). The definiion of he R&D adoped by BEA is essenially he same as ha used by he Naional Science Foundaion (NSF) in is annual Business Research and Developmen and Innovaion Survey (BRIDS) 10 and he Survey of Research and Developmen Expendiures a Universiies and Colleges. The NSF definiion is consisen wih he broad Frascai definiion of R&D, while in pracice he business secor s R&D is he repored R&D expendiures in naural sciences and engineering and he governmen and NPISH s R&D includes repored expendiures on he social sciences in addiion o naural sciences and engineering, bu excludes he humaniies. 11 The expendiure on R&D is hen he sum of he inpu coss minus he consumpion of oher fixed asses and sofware o produce R&D, repored on he performer basis in he NSF surveys. Nex, he BEA aribues he ownership of he R&D capial o he funder of he R&D projec. In oher words, he measure of he annual R&D invesmen in he business, governmen and NPISH secors in NIPA are he aggregae expendiures on R&D funded by hese secors respecively. The measuremen of he R&D oupu is also a delicae issue. Since mos R&D invesmen is conduced for in-house uses, here is no an observable marke price of R&D. The radiional cos-based approach o value non-markeed producs and asses (such as he oupu of governmens and NPISHs and he asses in he ownaccoun consrucion in he language of he accounans) fails o capure he increase in he produciviy of R&D, conradicing he micro evidence of a much higher rae of reurn o R&D han o oher invesmens. 12 Concepually, he oupu of R&D is he discouned presen value of he fuure gains he company or organizaion derives from R&D. 13. The BEA seles wih an alernaive approach which bases he value of R&D oupu on he prices of producs produced by R&D-inensive indusries. The BEA developed an R&D price index from he indusry value-added price indexes for he four indusries ha perform he mos R&D, radio and TV receiving equipmen, drugs and medicines, office, compuing and accouning machines, and aircraf and missiles, weighed by he indusry s share of oal performer-based R&D expendiures. 10 The BRIDS is he successor o he Survey of Indusrial Research and Developmen (SIRD or RD-1), which colleced daa on R&D domesically performed by indusry from 1953 o See Okubo e al. (2006), p Ibid., pp The value of R&D should be deermined in erms of he economic benefis i is expeced o provide in he fuure., see Chaper 10 in hp://unsas.un.org/unsd/naionalaccoun/docs/sna2008.pdf for a discussion of he reamen of R&D capializaion Inellecual propery producs include he resuls of research and developmen (R&D). Research and [experimenal] developmen consiss of he value of expendiures on creaive work underaken on a sysemaic basis in order o increase he sock of knowledge, including knowledge of man, culure and sociey, and use of his sock of knowledge o devise new applicaions. This does no exend o including human capial as asses wihin he SNA. The value of research and developmen (R&D) should be deermined in erms of he economic benefis i is expeced o provide in he fuure. This includes he provision of public services in he case of R&D acquired by governmen. In principle, R&D ha does no provide an economic benefi o is owner does no consiue a fixed asse and should be reaed as inermediae consumpion. Unless he marke value of he R&D is observed direcly, i may, by convenion, be valued a he sum of coss, including he cos of unsuccessful R&D, as described in chaper 6. 7

10 The depreciaion of R&D capures he idea ha he R&D capial loses value due o obsolescence and/or echnology diffusion. The fac ha we canno observe he price in he resale marke for differen vinages of R&D asses makes he convenional mehod of calculaing depreciaion inapplicable o he R&D. The BEA esimaes he depreciaion ogeher wih he profi impac from R&D from a forward-looking profi model wih a gesaion lag using he firm- and esablishmen-level daa (Li (2012)). Consider a firm s R&D invesmen problem in period : J d q +j+d I(RD )(1 δ) j max π = RD + RD (1 + r) j+d, (A-5) j=0 where he profi impac from R&D lass unil period J, he gesaion lag, or he ime from invesmen o he sar of he profi impac, is d, he sales revenue in period j is q j, he profi rae increase due o vinage- R&D is I(RD ) every period saring + d, he cos of capial is r and he depreciaion rae is δ. I is assumed ha I(RD ) akes a paricular funcional form: I(RD ) = I Ω (1 exp[ RD θ ]), (A-6) which an increasing and concave funcion in RD ha approaches an upper bound I Ω in he limi. This is a simple funcion wih wo parameers, I Ω and θ. The former measures he full long-run poenial of he R&D and he laer governs he effeciveness of he vinage- R&D o achieve he full poenial impac on he profi rae. We will see laer ha in he acual implemenaion, he raio RD θ is se up o be relaively sable over ime. Noe ha θ is fixed for a paricular vinage of R&D, bu is allowed o differ across vinages. The opimaliy condiion in he firm s R&D invesmen problem ses he basis of he esimaion: θ I Ω exp( RD θ ) J d j=0 q +j+d (1 δ) j (1 + r) j+d = 0. (A-7) The value of d is se o 2, ha of J is se o 20 (excep for he pharmaceuical indusry where i is se o 25), and he value of I Ω and r are boh se o 8.9%, i.e. he long-run average rae of reurn on all asses for non-financial corporaions. The esimaion of he depreciaion rae δ proceeds in hree seps. Firs, five years sales revenue daa before year are used in an auoregressive model o predic he fuure sales revenues, q +j+2 for j = 0,...J 2. Second, he process of θ is modeled o follow a process: logθ = logθ α( 2000), (A-8) where 2000 is he base year and α is he coefficien in he linear regression of log(rd ) on a consan and he year. This implicily assumes ha (logged) θ grows a he same rae as (logged) R&D invesmen, which implies ha he raio RD θ is more or less consan across years. In he hird sep, a leas-square fiing is performed in which he program searches for he values of δ and θ 2000 o minimize T 5 θ (θ 2000 ) [ I Ω exp( RD θ ) (θ 2000) =1 J d j=0 q +j+d (1 δ) j (1 + r) j+d ] 2, (A-9) assuming δ is relaively consan wihin he T 5 years. The 5 years subraced are used in he revenue forecasing One can repea he above exercise for subses of indusries and ime periods o recover indusry- and imevarying discoun raes. 8

11 B Furher Insighs on IPP Capial This secion provides furher insighs on he invesmen, he price of invesmen and he depreciaion rae of he subcaegories of he IPP capial, i.e. sofware, R&D and arisic originals. Invesmen The levels of nominal invesmen by subcaegory of IPP capial are ploed in panel (a) in Figure B-1 and he share of aggregae invesmen of each subcaegory of IPP capial are ploed in panel (b) in Figure B-1. The sofware invesmen share has increased from zero in he 1950s exponenially o 11% of oal invesmen by 2013; he R&D invesmen share shows an increase from 5% in he lae 1940s o roughly 12-13% since he mid-1960s; and he arisic originals invesmen share shows a sligh increase from 2% in 1947 o 3% in Relaive Price of Invesmen The relaive prices of invesmen by subcaegory of IPP capial are ploed in panel (c) Figure B-1. The relaive prices of invesmen in sofware, R&D and arisic originals all decline bu a differen raes. The relaive prices of R&D and arisic originals fall somewha mildly o 70% of he price of consumpion by 2013, whereas he relaive price of invesmen in sofware declines sharply, reaching 50% by he early 1980s and 10% by Depreciaion Raes The depreciaion raes by subcaegory of IPP capial are ploed in (d) in Figure B-1. Clearly, sofware is he IPP componen wih he highes depreciaion rae saring around 0.30 in he early 1960s and going up o 0.34 in he 2000s; R&D capial depreciaion is roughly around 0.17 since he 1970s; and arisic originals have he lowes depreciaion rae wih an average around 0.14 since he 1970s. 9

12 Figure B-1: Subcaegories of IPP Capial (a) IPP Componen Invesmen Levels (b) IPP Componens Invesmen Shares (c) Relaive Price of Invesmen in IPP Componens (d) Depreciaion Rae of IPP Componens Noes: IPP capial includes sofware, R&D and arisic originals (see Secion 2). The invesmen shares are in erms of aggregae invesmen ha includes boh privae and governmen invesmen. The depreciaion rae of and he relaive price of sofware are available since The consrucion of invesmen, invesmen price, and depreciaion rae is discussed in Secion 2.

13 C A Broader Hisorical Perspecive: IPP Capializaion and he U.S. Labor Share, Here, we exend he hisorical perspecive of our analysis o he U.S. sample from 1929 o 2013, as early as NIPA allow us o race back o. 15 Visual inspecion of labor share suggess ha he labor share decline is a phenomenon ha sars primarily afer WWII (see panel (a) of Figure C-1). This secular decline in labor share clearly coincides wih he increase in he relaive imporance of IPP invesmen. Unil 1930, IPP invesmen represens less han 3% of aggregae invesmen. I sars o grow almos linearly since he 1930s, reaching a value above 20% in he 2000s and close o 30% in he las few years. See Figure C-1b. Finally, panel (c) in Figure C-1 shows he effecs of IPP capializaion. There, we redo he exercise described in Secion 3, bu wih his larger sample saring from We find ha he radiional labor share is basically fla ha is, exending our analysis back o 1929 does no change our main finding ha he labor share decline can be explained by IPP capializaion. The coefficien of he linear rend for he sample from 1929 o 2013 is an insignifican (he orange dashed line) a 10% significance level. 15 Noe ha while NIPA provides daa since 1929, FAT provides daa including he invesmen series ha we describe nex since 1901.

14 Figure C-1: Labor Share, Invesmen Shares, and IPP Capial, U.S (a) US Aggregae Labor Share, BEA (b) Invesmen Shares in Tradiional and IPP Capial, (c) Aggregae and Tradiional Labor Share, Noes: Panel (a) shows he aggregae labor share as described in Secion 3.1, exending he analysis o Panel (b) provides radiional invesmen and IPP invesmen as a share of aggregae invesmen including privae and governmen invesmen and residenial and nonresidenial invesmen, exending he analysis o Panel (c) shows he radiional labor share and he aggregae labor share consruced as described in Secion 3, exending he analysis o 1929.

15 D The Corporae Secor and he BLS Labor Share We conduc robusness of our main findings using he corporae secor labor share and he labor share consruced by he Bureau of Labor Saisics (BLS). D.1 The Corporae Secor There are a leas wo moivaions for invesigaing he LS in he corporae secor only. 16 Firsly, by focusing on he corporae secor, we purge ambiguous income from he compuaion of he LS (i.e., here is no proprieors income), see he discussion in Karabarbounis and Neiman (2014). 17 Secondly, he corporae secor does no include eiher he housing secor or he governmen secor, where he measuremen of LS is subjec o criicism (Gomme and Ruper, 2004, 2007). 18 The corporae LS is shown in panel (b) of Figure D-1. 19,20 This LS remains seady around a value of 0.63 from he lae 1940s o he lae 1970s and, as noed by Karabarbounis and Neiman (2014), i exhibis a decline from 0.63 in 1975 o 0.56 in 2013, wih an acceleraed decline saring in he early 2000s. 21 Noe ha he corporae secor fixed invesmen consiss of privae nonresidenial fixed invesmen and asses. 22 Panel (a) of Figure D-1 shows he invesmen share of radiional capial and IPP in he corporae secor. The share of invesmen in IPP has increased from 9% in he lae 1940s o 27% in he lae 1990s, reaching 33% in The IPP figures are larger for he corporae secor han for he enire economy, suggesing a larger IPP capial inensiy in he corporae secor. Par of he reason of his observaion is ha he corporae secor does no include residenial invesmen. The FAT decomposes he fixed asses of he corporae secor ino srucures, equipmen, and IPP (see online Appendix G of he longer version of he paper). This allows us o assess he effecs of IPP capial on corporae secor LS in a wo-secor model analogous o Secion 3. The invesmen prices are hose for he enire economy already compued in Appendix A.1.4. The counerfacual radiional labor share is shown in panel (b) of Figure D-1. The IPP capial compleely explains he LS decline in he corporae secor. The radiional LS (orange line in panel (b) of Figure D-1) wihou IPP capial income displays no visible rend afer To summarize, as for he enire economy, he decline of he corporae secor LS is accouned for by IPP capial. The corporae secor radiional labor share remains rendless hroughou he sample period. Noice ha 16 The corporae secor represens 55% of GNI in 1948 and 65% in I increases o 71% in he early 1980s and decreases o 65% in he 2000s. 17 See also earlier reamens of he corporae LS in Boldrin and Perala-Alva (2009) (among ohers). 18 See Appendix G of he longer version of he paper for an analysis of he housing and governmen secors for he enire economy. 19 We compue he corporae LS by dividing he compensaion of employees (i.e., he income accruing o employees, such as wages, salaries, employers conribuions for social insurance, and oher labor income) by he gross value added, which consiss of he consumpion of fixed capial, compensaion of employees, axes on producion and impors less subsidies, and ne operaing surplus, and, in urn, ne operaing surplus consiss of ne ineres and miscellaneous paymens, business curren ransfer paymens, and corporae profis. 20 Here we focus on he join LS behavior of financial and nonfinancial corporae businesses. See online Appendix A.3 of he longer version of he paper for he corporae secor daa sources and consrucion. The LS behavior of he enire corporae secor and he nonfinancial corporae secor are similar because he financial corporae secor is relaively small. The gross value added of he financial corporae secor accouns for 4% of he corporae gross value added; his proporion slowly increases o 12% oward he end of he sample. 21 Our corporae LS is idenical o he updaed LS daa supplied by Karabarbounis and Neiman (2014) for he subperiod 1975 o 2012 (i.e., he green line in panel (b) of Figure D-1). 22 Tha is, he corporae secor does no include componens associaed wih residenial invesmen and/or governmen invesmen. I also excludes non-corporae privae invesmen. 23 If a all, LS seems o slighly increase by 2 LS poins from he lae 1940s o he mid-1970s.

16 he radiional labor share mirrors he aggregae labor share in erms of cyclical flucuaions. In paricular, he recen decline since 2001 of he corporae radiional labor share does no represen a break from he (insignifican) secular rend. In fac, he corporae radiional labor share peaked (above is secular average) in Formally, we have compued sandard Bai-Perron ess and found ha hey do no pick any sign of srucural change for he radiional labor share from 1975 o Therefore he decline of he corporae labor share in he 2000s is more likely o be of cyclical (or medium-run) naure. D.2 The BLS Labor Share In a recen analysis of he US LS, Elsby e al. (2013) discuss in deail he wo main LS consrucs provided by he Bureau of Labor Saisics (BLS). The headline measure of he LS provided by he BLS, and available from he Major Secor Produciviy Coss division, correcs for he amoun of ambiguous income (mainly, proprieor s income) using he raio of self-employed o employed in he US economy. This carries he implici assumpion ha he wages ( earned (per uni of work) by he employed is idenical o ha of he self-employed, basically LS = CE N+SE ) Y N where CE is he compensaion of employees, Y is oupu, N is he amoun of employees, and SE is he amoun of self-employed. However, Elsby e al. (2013) noed ha under his definiion of he LS he oal amoun of labor income in he proprieors secor can and does exceed (from 1981 o 1991) he oal amoun of proprieors income, which implies he pahological phenomenon ha LS exceeds one in he proprieors secor or ha he capial share (or he marginal produc of capial) are negaive in ha secor. In ligh of his resul, Elsby e al. (2013) sugges wo preferred measures of LS. The firs is he economywide basis measure which corresponds o our benchmark LS described in Secion 3.1 in he main ex, and also implemened by previous lieraure on LS dynamics (Cooley and Presco, 1995; Gomme and Ruper, 2004, 2007; Ríos-Rull and Sanaeulàlia-Llopis, 2010). The second is he BLS measure available from he Major Secor Mulifacor Produciviy (MSMP) division ha is consruced under he assumpion ha he reurns o capial (user-cos based) are he same for proprieors income han for he res of he economy. The laer is labeled as he asse basis measure of proprieors income. Ineresingly, in he compuaion of he asse basis measure he BLS MSMP division uses he reurns o capial from he corporae secor (see BLS (2007)), which implies ha he asse basis and he corporae LS mus bear resemblance, a conjecure ha is largely confirmed by Figure D-2 ha plos he wo measures side by side. This way, our findings for he corporae secor LS described in Appendix D.1 also apply o he asse basis LS provided by he BLS. In paricular, noe ha wihou IPP income LS is rendless. Ineresingly, afer removing IPP income, he acceleraion of he LS decline since 2001 (see he discussion in Elsby e al. (2013) and in our Appendix D.1) does no seem o represen a secular break, bu more likely a cyclical or medium-run phenomenon a conjecure ha deserves furher exploraion and ha will become more ransparen as he sample grows afer 2013.

17 Figure D-1: Effecs of IPP Capial on Corporae Labor Share (a) Tradiional and IPP Inv. Shares, Corporae Secor, BEA (b) Aggregae and Tradiional Labor Share, Corporae Secor, BEA Noes: Panel (a) shows he share of nominal invesmen by ype of capial. In Panel (b) he reference scenario is he benchmark labor share for he corporae secor from he pos-revision daa (i.e. he blue line). This measure of labor share is idenical o he updaed labor share daa supplied by Karabarbounis and Neiman (2014) for he subperiod 1975 o 2012 (i.e. he green line). The consrucion of he aggregae and radiional labor share follows closely he mehodology in Secion 3, applied o he corporae secor only.

18 Figure D-2: Corporae Labor Share (BEA) vs Asse Basis Labor Share (BLS) Noes: The corporae LS is compued using BEA daa as described in our main ex (Secion D.1) and is idenical o ha consruced from he updaed pos-2013 BEA revision series of Karabarbounis and Neiman (2014). The asse basis LS is consruced by he Major Secor Mulifacor Produciviy (MSMP) division a he BLS. For comparison purposes he average of boh series is normalized o one. The counerfacual LS series labeled Tradiional is compued as described in he main ex.

19 E IPP Capial and Labor Share by Indusry In his secion, we invesigae which indusries are becoming more inense in IPP capial and wheher he decline of LS a he indusry level can be explained by indusry-wide IPP capial inensiy. To sar, we plo he oupu shares of 12 main indusries from 1947 o 2013 in Figure E Of all indusries, only services, informaion, and FIRE (finance, insurance, real esae, renal and leasing) are growing relaive o oher indusries, so heir oupu shares increase, see panel (a) of Figure E-1. The fases-growing indusry is services which sars a 13.1% of he oal oupu in 1947 and grows o 30%, almos a hreefold facor, by FIRE also shows an imporan increase in oupu share from around 12% in 1947 o 22.6%, almos a wofold facor, in Informaion sars low, around 3.2% and increases by abou a 1.5-fold reaching an oupu share ha is sill small, 5.5%, compared wih he oher growing indusries. The oupu shares of indusries ha sagnae or decline are found in panel (b) of Figure E-1. The indusry wih he larges decline is clearly manufacuring. The durable goods manufacuring share of oupu drops from nearly 18% in he early 1950s o 7.6% in 2013, and he nondurable goods manufacuring share of oupu drops from 14.3% in 1947 o 6.9% in In relaive erms, i is also imporan o noe he drop in he agriculural share of oupu from 9.3% in 1947 o 1.4% in In shor, oupu is moving o services, FIRE and informaion, and he indusries wih sagnan or decreasing oupu shares by 2013 ha sill represen a large share of oupu are manufacuring (in durables and nondurables), reail rade, and wholesale rade. We sar by showing he evoluion of radiional (i.e. srucures and equipmen) and IPP invesmen shares for 12 main (i.e., 2 digi NAICS) indusries. Figure E-2 shows he indusries wih high IPP invesmen. Informaion and (durables and nondurables) manufacuring are he indusries wih he larges shares of IPP invesmen. For hese indusries, he IPP invesmen accouns for 60% of he indusry-specific aggregae invesmen in 2013, represening he larges ype of invesmen. For he informaion indusry, he IPP invesmen sars a 30% of oal invesmen in he lae 1940s and remains seady unil he mid-1970s, afer which i sars o linearly increase o 60% in The IPP share in he invesmen of durables manufacuring sars a 20% in he lae 1940s and linearly increases o 30% in he early 1960s and furher 60% in he early 2010s. The IPP share in he invesmen of nondurables manufacuring is somewha lower han ha of durables, saring around 10% in he lae 1940s and increases o reach a plaeau around 20% in he 1960s and he 1970s and hen linearly increases from he early 1980s o reach roughly 60% in The IPP invesmen share in services is slighly below 10% before he 1970s, and i rises from he 1980s o reach roughly 40% in The IPP invesmen in wholesale rade remains nil unil he 1970s, afer which i shows an exraordinary growh ha reaches 40% of invesmen by The rend of he IPP share of invesmen in reail rade resembles ha in wholesale rade. The growh in he IPP share in he invesmen in reail rade sars only in he mid-1970s and i increases o around 20% in he 2010s. We observe ha hese high IPP indusries demonsrae he growh of IPP invesmen share associaed by he decline of invesmen share in radiional capial. Nex, we use addiional indusry-level daa of invesmen, price of invesmen, and depreciaion from he FAT o consruc indusry LS. 25 We apply ha formula separaely o each indusry under he assumpion ha he ne reurn o capial is idenical across NAICS indusries. The main reason o use his LS consruc, in addiion o ensure consisen indusry classificaion under NAICS hroughou he period, is ha i allows us o sudy he effecs of IPP capial on he LS a he indusry level, in he same manner ha we explored hese effecs 24 We recognize 12 main indusries, 11 of which correspond o he 2-digi Norh American Indusry Classificaion Sysem (NAICS) codes: agriculural, foresry, fishing and huning, mining, uiliies, consrucion, durable goods manufacuring, nondurable goods manufacuring, wholesale rade, reail rade, ransporaion and warehousing, informaion, and finance, insurance, real esae, renal and leasing. We addiionally consruc services as he welfh indusry, which includes he following se of 2-digi NAICS code indusries: professional and business services, educaional services, healh care and social assisance, ars, arisic originals and recreaion, accommodaion and food services, and oher services. In he Appendix of, we furher describe he source and sample periods of indusry daa and some adjusmen mehods ha we apply o he value added daa by indusry. 25 A nice feaure of he FAT is ha, unlike NIPA, hey consisenly use NAICS codes from 1947 o The change in he indusry classificaion in NIPA makes he consrucion of a consisen measure of LS over ime from NIPA alone unfeasible for some indusries, for lack of disaggregaed subindusry daa.

20 a he aggregae level in he main ex. 26 A he same ime, we consruc he indusry IPP capial inensiy by dividing he IPP capial sock by he oal capial sock in each indusry. We invesigae he relaionship beween LS and he IPP capial inensiy by indusry for wo subsample periods, and in panel (a) in Figure E This exercise explores wheher indusries ha have grown more in IPP capial inensiy have also experienced a decline in LS. There are hree observaions o highligh. Firs, in erms of IPP capial inensiy, he indusries wih he highes inensiy are also hose ha experience larger growh in IPP capial inensiy in he 2000s. In addiion, hese indusries consis of six of he seven indusries wih he highes oupu share in These indusries include informaion and services ha is, wo of he hree growing indusries idenified in Figure E-1 ha respecively grow by abou 0.05 and 0.06 IPP capial inensiy poins from he firs o he second subperiod, nondurables and durables manufacuring which respecively grow by and IPP capial inensiy poins, and wholesale and reail rade, which respecively grow by and IPP capial inensiy poins. Some of hese indusries, such as nondurables and durables manufacuring and informaion, have a relaively high level of IPP capial inensiy above 0.10 before 2000, and ohers such as wholesale rade and services sar from IPP capial inensiy below 0.06 before Second, in erms of LS, he larges decline occurs in durables manufacuring by 0.15 LS poins, in nondurables manufacuring by 0.08 LS poins, in boh informaion and reail rade by 0.07 LS poins, and in wholesale rade by 0.04 LS poins from he firs o he second subperiod. These resuls represen he firs direc empirical evidence of he relaionship beween he larges growh in IPP capial inensiy and he larges declines in LS a he indusry level. The larges increases in IPP capial inensiy and declines in he LS occur for indusries wih large iniial LS values. Insead, indusries wih relaively low LS such as agriculure, FIRE, and uiliies, barely experience an increase in IPP capial and declines in he LS. Finally, only wo of he 12 main indusries exhibi a posiive relaionship beween IPP capial inensiy and LS, ransporaion and mining. We also disaggregae he 12 main indusries ino 46 subindusries (3 and 4-digis NAICS) for he period See Table E-1 for indusry codes and names. 29 For each of hese subindusries, panel (b) in Figure E-3 repors on he verical axis he difference (i.e., changes in levels) in LS beween he pre- and pos-2000 years and on he horizonal axis he difference in IPP capial inensiy beween he pre- and pos-2000 years. Our sample largely populaes he boom-righ quadran of ha panel suggesing ha mos subindusries display a decline in heir LS associaed wih an increase in heir IPP capial inensiy, wih very few indusries showing a decline in IPP capial inensiy and/or an increase in LS (e.g., peroleum and coal producs (Sub-24)). For example, chemical producs (Sub-25) shows an increase in IPP capial inensiy by.26 poins and a decline in LS by.06 poins and compuer and elecronic producs (Sub-13) shows an increase in IPP capial inensiy by.15 poins and a decline in LS by.17 poins. The general paern is ha increases in IPP capial inensiy go hand in hand wih decreases in LS a he subindusry level; a simple regression weighed by subindusries oupu shares implies ha for a.100 poins increase in IPP capial inensiy, LS declines by.020 poins. In all, even wih a finer indusry classificaion, we find a negaive relaionship beween LS and IPP capial inensiy ha is consisen wih ha for 2-digi NAICS indusries. As we consruc radiional LS for each indusry in he same fashion as described in he main ex, we confirm ha he radiional LS of indusries ha inves in IPP flaens ou. These resuls are shown in Figure E-4 for he 26 For he subperiod we also consruc he NAICS indusry LS compued direcly from he naional income componens in NIPA according o secion 3.1; his is no feasible for he pre-1997 years because he NIPA indusry classificaion for hose years is based on he Sandard Indusrial Classificaion (SIC). We plo indusrylevel LS consruced from he FAT daa agains indusry-level LS compued from NIPA in he Appendix of he large version of his paper (available online). By and large, he wo consrucs of LS correspond well. Since our model is fricionless, he difference of he model-based LS and he daa-based LS is an indicaor of fricions beyond wha is facored ino he price series of invesmen. 27 The poin break of 2000 is moivaed by he fac ha, since he ealry 2000s, we find IPP invesmen has reached a seady srucure of is componens, ha is, he share of sofware, R&D, and arisic originals in oal IPP invesmen has remained relaively sable afer year 2000; see he discussion in online Appendix B. 28 Only FIRE is missing wih a high oupu share bu low IPP capial inensiy. 29 Our sample increases o 57 subindusries if we resric he aenion o he pos-1970 years, wihou providing addiional insighs in our resuls.

21 main indusries ha inves in IPP ha is, informaion, services, nondurable and durable goods manufacuring, wholesale rade and reail rade. 30 The effecs of IPP on LS are larges for he manufacuring secor. Using he pos-revision daa, he aggregae LS of nondurable goods manufacuring and ha of durable goods manufacuring declines by, respecively, 0.20 and 0.25 LS poins from 1947 o 2013, represening he wo larges LS declines in all indusries. Furher, a he same ime, hese wo indusries have also invesed heavily in IPP, especially in he pos-2000 period, suggesing a poenial relaionship beween IPP capial and LS. The LS decline miigaes wih he radiional LS. For nondurables manufacuring, he radiional LS decreases by 15 percenage poins from 1947 o 1984, bu i acually increases by 5 percenage poins from 1985 o 2013, neing a 10% decline over he enire sample. For durable goods manufacuring, he radiional LS declines by 10 percenage poins from 1947 o 1983 and hereafer remains consan unil he end of he sample. IPP capial drives he LS of he manufacuring indusries down. Finally, he effecs of IPP capial on he LS in informaion indusry are also large. The aggregae LS in informaion declines from 0.68 in 1947 o 0.50 in 2013, a drop of 0.18 LS poins. In conras, he radiional LS drops in informaion reduces o 0.06 LS poins from 0.71 in 1947 o 0.65 in 2013, and he LS displays an increase from 0.60 in he mid-1980s o 0.65 in For he services indusry he LS sars a 0.86 in The aggregae LS in services falls o 0.82; he radiional LS remains essenially fla and ends a he same 0.86 in We find similar effecs of IPP capial on he LS in wholesale rade and reail rade. 30 For indusries ha do no inves in IPP he difference beween aggregae and radiional LS is, obviously, negligible.

22 Figure E-1: US Oupu Shares by Indusry, BEA (a) Growing Indusries (b) Declining Indusries Noes: The oupu shares by indusry are compued using NAICS classificaion.

23 Figure E-2: Srucures, Equipmen and IPP Invesmen Shares, High IPP Indusries (a) Informaion (b) Services (c) Manufacuring: Nondurable goods (d) Manufacuring: Durable goods (e) Wholesale Trade (f) Reail Trade Noes: In each panel we plo he radiional and IPP invesmen shares of indusry-specific aggregae invesmen for 2-digi NAICS indusries ha we caegorize as having high IPP invesmen.

24 Figure E-3: Labor Share and IPP Capial Inensiy by Indusry: Pre- and Pos-2000s (a) Main Indusries (b) Sub-Indusries Noes: Labor share is compued by indusry using NAICS classificaion. IPP capial inensiy is he share of IPP capial in oal capial by indusry (or subindusry). The size of he poins refers o he indusry-specific share of oupu in he aggregae economy.