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1 *NOT FOR PUBLICATION Online Appendix: Labor Share Decline and Inellecual Propery Producs Capial By Dongya Koh, Raül Sanaeulàlia-Llopis and Yu Zheng 1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 2 A.1 The Consrucion of Aggregae Daa Series A.1.1 The Source of Daa A.1.2 Labor Share from Naional Income Daa A.1.3 Aggregae Capial Depreciaion Rae A.1.4 Aggregae Invesmen A.1.5 Relaive Prices of Invesmen in Srucures, Equipmen and IPP A.1.6 Relaive Price of Invesmen A.1.7 Sock of Capial in Efficiency Unis A.1.8 Rae of Reurn o Capial A.1.9 Labor Share from One-Secor One-Capial Model A.2 The Consrucion of Labor Share by Indusry A.2.1 The Source of Daa A.2.2 Adjusmen of Value Added in GDP-by-indusry Daa A.3 The Consrucion of Corporae Secor Daa Series A.3.1 The Source of Daa A.3.2 The Corporae Secor Labor Share from Naional Income Daa A.3.3 The Corporae Secor Labor Share from One-Secor Model A.4 The BEA-NSF s Capializaion of R&D Expenses B Effecs of he 2013 BEA Revision on Labor Share: Pre- vs. Pos-Revision Daa By Naional Income Componens 14 C Furher Insighs on Aggregae Capial and Is Types 16 D The Capial Share of Income for he US Corporae Secor: Srucures, Equipmen and IPP 23 E A Broader Hisorical Perspecive: IPP Capializaion and he U.S. Labor Share, F A Three-Secor Model 27 G Removing Housing and Governmen Secor from he Aggregae Economy 29 H The BLS Labor Share 31

3 I Furher Insighs on he Effecs of IPP Capializaion on Labor Share by Indusry 33 J Exending IPP Invesmen in BEA Accouns wih Adverising 39 1

4 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 analisys 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. 2

5 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 Labor Share from Naional Income Daa We consruc our labor share by using Naional Income Daa. Firs, we define unambiguous capial income and unambiguous income. This gives us he proporion of unambiguous capial income o unambiguous income. We assume ha ambiguous capial income akes he same proporion agains ambiguous income. Combining ambiguous and unambiguous capial income wih consumpion of fixed capial (depreciaion of fixed asses) yields he oal capial income. Then our definiion of labor share is simply one minus he raio beween oal capial income o aggregae oupu. 1. Unambiguous Capial Income (UCI) = Renal Income (RI) + Corporae Profis (CP) + Ne Ineres (NI) + Curren Surplus of Governmen Enerprises (GE) 2. Unambiguous Income (UI) = UCI + Consumpion of Fixed Capial (CFC) + Compensaion of Employees (CE) 3. Proporion of Unambiguous Capial Income To Unambiguous Income: θ = UCI+DEP UI. 4. Ambiguous Income (AI) = Proprieors Income (PI) + Taxes on Producion (Tax) - Subsidies (Sub) + Business Curren Transfer Paymens (BCTP) + Saisical Discrepancy (SDis) 5. Ambiguous Capial Income (ACI) = θ AI. Then, capial income, Y K, is compued as, Y K = UCI + CFC + ACI, which we use o consruc our baseline labor share as, Labor Share = 1 Capial Share = 1 Y K Y, where aggregae oupu, Y, is he gross naional produc (GNP), ha is, he sum of oal unambiguous facors income and ambiguous income, Y = UI + CE + AI GNP. 3

6 A.1.3 Aggregae Capial Depreciaion Rae We consruc ne sock of capial and depreciaion of capial for privae and governmen wih and wihou IPP by summing up nonresidenial srucures, equipmen, and IPP and residenial capial: 3 Privae wih IPP: Governmen wih IPP: Privae wihou IPP: Governmen wihou IPP: K P,wIP P = K P,ST,NRes + K P,EQ,NRes + K P,Res + K P,IP P K G,wIP P = K G,ST,NRes + K G,EQ,NRes + K G,Res + K G,IP P K P,NoIP P = K P,ST,NRes + K P,EQ,NRes + K P,Res K G,NoIP P = K G,ST,NRes + K G,EQ,NRes + K G,Res Privae wih IPP: Governmen wih IPP: Privae wihou IPP: Governmen wihou IPP: DEP P,wIP P = DEP P,ST,NRes + DEP P,EQ,NRes + DEP P,Res + DEP P,IP P DEP G,wIP P = DEP G,ST,NRes + DEP G,EQ,NRes + DEP G,Res + DEP G,IP P DEP P,NoIP P = DEP P,ST,NRes + DEP P,EQ,NRes + DEP P,Res DEP G,NoIP P = DEP G,ST,NRes + DEP G,EQ,NRes + DEP G,Res We compue he aggregae capial depreciaion rae wih IPP as and δ wip P = DEP P,wIP P + DEP G,wIP P K P,wIP P + K G,wIP P δ NoIP P = DEP P,NoIP P + DEP G,NoIP P K P,NoIP P + K G,NoIP P A.1.4 Aggregae Invesmen We consruc he nominal invesmen in srucures, equipmen, sofware and IPP and he invesmen shares, which will be used in he consrucion of price indices in Secion A.1.6: 4 3 In FAT daa, residenial capial for privae secor is no disaggregaed ino srucures and equipmen. Also noe ha IPP capial is only in nonresidenial. 4 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 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 4

7 Srucures: Equipmen: Sofware: IPP: Aggregae wih IPP: Aggregae wihou IPP: Aggregae wihou Non-Sofware IPP: Shares wih IPP: Shares wihou IPP: Shares wihou Non-Sofware IPP: Inv ST Inv EQ Inv Sofware Inv IP P Inv wip P = IP ST,NRes = IP EQ,NRes + IP ST,Res = IP Sofware. + IG IP P = IP IP P Inv NoIP P Inv wsofware = Inv ST = Inv ST = Inv ST Inv,wIP P,i s = Invi Inv wip P Inv,NoIP P,i s = Invi s Inv,wSofware,i = + IP EQ,Res. + Inv EQ + Inv EQ Inv NoIP P Inv i. + IG ST. + IG EQ + Inv IP P.. + Inv EQ + Inv Sofware, for i {ST, EQ, IP P }., for i {ST, EQ}. Inv wsofware., for i {ST, EQ, Sofware}. Furher, we define he share of privae nonresidenial and residenial equipmen invesmen for laer use in Secion A.1.5 (b). Nonresidenial Equipmen: Residenial Equipmen: s P,EQ,NRes = s P,EQ,Res IP EQ,NRes IP EQ,NRes = 1 s P,EQ,NRes +IP EQ,Res 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 5 and change in privae invenories, (c) ne expors of goods and services, and (d) governmen consumpion expendiures and gross invesmen. 6 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). 7 The ime series of he nominal invesmen wih and wihou IPP are in Figure 5a. In 1979, nominal invesmen wih or wihou IPP sands a abou 500 billion USD. By 2014, he oal invesmen has reached 2500 billion USD of which one-hird is IPP invesmen. The amoun of IPP invesmen rises over ime from almos zero o 50% of he invesmen in srucures and equipmen. In erms of he relaive imporance of srucures, equipmen and IPP invesmens, recall Figure 2. The share of IPP invesmen rises from 10% of he oal invesmen o 35% from 1947 o 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. 5 Fixed invesmen is displayed in erms of nonresidenial invesmen (in srucures, equipmen and IPP) and residenial invesmen. 6 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. 7 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. 5

8 A.1.5 Relaive Prices of Invesmen in Srucures, Equipmen and IPP (a) Price of Invesmen in Srucures: Price index for consumpion, P C, is used as a proxy for he price of srucures invesmen. 8 We use a Törnqvis price index aggregae 9 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 λ(p I,EQ ) = 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 growh rae of he price index of equipmen is ( ) ( s P,EQ,Res s P,EQ,NRes + s P,EQ,Res 1 2 λ(p I,EQ,Res ) + ) + 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.1.4. (c) 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 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. 9 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], (1) where s j is he share of he value of he variey j. 10 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. 6

9 A.1.6 Relaive Price of Invesmen In compuing he price index of invesmen, we use a Törnqvis price index for srucures, equipmen, and IPP invesmen, each of which is consruced above. The growh rae of he price index of invesmen is calculaed as Wih IPP: Wihou IPP: Wihou Non-Sofware IPP: λ(p I,wIP P ) = i {ST,EQ,IP P } λ(p I,NoIP P ) = s i {ST,EQ} λ(p I,wSofware ) = i {ST,EQ,Sofware} Inv,wIP P,i Inv,wIP P,i s +s 1 2 λ(p I,i Inv,NoIP P,i Inv,NoIP P,i +s 1 2 λ(p I,i ). s Inv,wSofware,i ). +s Inv,wSofware,i 1 2 λ(p I,i ). where s Inv,j,i are he shares of invesmen defined in Secion A Then, he level of he price index of invesmen is recovered recursively for he case wih IPP, wihou IPP and wihou non-sofware IPP, P I,j = P I,j I,j 1 [1 + λ(p )] where P I,j 0 is normalized o 1 a he iniial period, for j {wip P, NoIP P, wsofware}. 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 {wip P, NoIP P, wsofware}. p j A.1.7 Sock of Capial in Efficiency Unis Define he aggregae invesmen in efficiency unis by he nominal invesmen deflaed by he price of invesmen: x j = Inv j /P I,j, for j {wip P, NoIP P, wsofware}. Then, we can recursively compue he sock of capial in efficiency unis, k x,j by applying he capial accumulaion equaion in (2): k x,j +1 = xj + (1 δ j )k x,j, (2) for j {wip P, NoIP P, wsofware}. We se k x,j 0 = 850 by argeing he annual capial-oupu raio of We also conduc several counerfacual experimens in subcaegories of IPP in Secion 3.5, saring from wihou IPP as a benchmark, (1) adding Enerainmen, (2) adding R&D, and (3) adding sofware. For hese experimens, we consruc he growh rae of he price index in he following way: (1) λ(p I ) = i {ST,EQ,En} (2) λ(p I ) = i {ST,EQ,En,RD} (2) λ(p I ) = i {ST,EQ,En,RD,Sofware} s Inv,i +s Inv,i 1 2 λ(p I,i ) s Inv,i +s Inv,i 1 2 λ(p I,i ) s Inv,i +s Inv,i 1 2 λ(p I,i ) where he share of invesmen in each experimen is compued ou of corresponding oal invesmen, i.e. (1) Inv 1 = Inv ST + Inv EQ + Inv En, (2) Inv 2 = Inv 1 + Inv RD, and (3) Inv 3 = Inv 2 + Inv Sofware. 7

10 A.1.8 Rae of Reurn o Capial We impue he ne rae of reurn by using he equaions (3) and (4) wih he pos-revision daa: [ ] r = (1 LS ) ywip P k x,wip P + 1 v wip P (1 δ wip P ) v 1 wip P 1, (3) where LS is he labor share compued by using pos-revision naional income daa in Secion 2 and y wip P real GNP deflaed by he price of consumpion in he pos-revision daa. is Assuming he ne rae of reurn o capial, r, is idenical across capial composies, we can compue gross rae of reurn from he equaion R j +1 = 1 v j (1 + r +1 ) 1 v j (1 δ j +1 ), (4) +1 for j {wip P, NoIP P, wsofware}. A.1.9 Labor Share from One-Secor One-Capial Model Labor share from our one-secor one-capial model, which is equaion (4), is reproduced here: ls = 1 R k x y. (5) Wihin his model, we compue a number of counerfacual labor shares o evaluae he effec of IPP capializaion as follows., P I,wIP P, v wip P, x wip P, k x,wip P Labor share wih IPP: If we follow he consrucion of δ wip P, r, R wip P in he way specified in Secions A.1.3 hrough A.1.8 and compue he labor share according o (5), we will have, by consrucion, recovered he labor share in he pos-revision daa exacly. We compue he capial income in his case, yk wip P = R wip P k x,wip P, since i will be used in he consrucion of he wo counerfacual labor shares ha follow. Labor share wihou IPP: We firs consruc δ NoIP P, P I,NoIP P, v NoIP P, x NoIP P, k x,noip P, and R NoIP P in he way specified in Secions A.1.3 hrough A.1.8. Noice ha in deriving R NoIP P we use he same r as ha in he case wih IPP. We compue he capial income yk NoIP P = R NoIP P k x,noip P. The effec from IPP capializaion on real oupu is hen he difference in capial income from including IPP or no: IP P = yk wip P yk NoIP P. We adjus he oupu down by his difference: y NoIP P = y wip P IP P. We can now compue he labor share according o (5) using R NoIP P, k x,noip P and y NoIP P. Labor share wihou non-sofware IPP: We firs consruc δ wsofware, and R wsofware k x,wsofware, P I,wSofware in he way specified in Secions A.1.3 hrough A.1.8. Noice ha in, v wsofware, x wsofware, deriving R wsofware we use he same r as ha in he case wih IPP. We compue he capial income y wsofware k = R wsofware k x,wsofware. The effec from sofware capializaion on real oupu is hen given by Sofware = yk wip P y wsofware k. We adjus he oupu down by his difference: y wsofware = y wip P Sofware. We can now compue he labor share according o (5) using R wsofware, k x,wsofware and y wsofware. A.2 The Consrucion of Labor Share by Indusry We idenify 12 main indusries by he 2-digi Norh American Indusry Classificaion Sysem (NAICS). The codes and names of he indusries a differen levels of aggregaion used in he analysis are found in Table I-1. In mos of 8

11 he BEA indusry daa, he indusry classificaion sysem underwen a change in Before 1997, he indusries are classified under he Sandard Indusrial Classificaion (SIC), while afer 1997, hey are classified under he Norh American Indusry Classificaion Sysem (NAICS). Due o his change, he indusry NIPA daa, even a is leas disaggregaed level, is no direcly comparable over ime. The FAT indusry daa, however, are an excepion. The indusry daa in FAT follows he NAICS since For his reason, o compue labor share by indusry we apply o each indusry he mehod we developed using he invesmen model in secion 3.1. To his end we use daa on he invesmen flows and depreciaion raes for each indusry available a he FAT. We assume he ne rae of reurn and he price of invesmen are idenical o hose in he aggregae economy. We furher need he indusry value added under a consisen NAICS classificaion. Firs, we obain he indusry value added since 1997 from he regional daa accouns in BEA, which is under NAICS and is revised during he 2013 BEA revision. Second, we obain he indusry value added under NAICS for years 1947 o 1997 from he GDP-by-Indusry Table in NIPA-BEA a hp: // (as of April 15, 2015). Noe ha his able was las updaed in 2011, which is before he revision ha capializes he non-sofware componens of IPP. We revise he indusry value added before 1997 o incorporae he full capializaion of he IPP in secion A.2.2. To validae our measures of he indusry labor share compued from our invesmen model (secion 3.1) using FAT indusry daa, we also compue he benchmark labor share (as described in secion 2.1) separaely for each indusry using daa from Table 6 in NIPA-BEA (NAICS Classificaion ). We provide a dicussion of his comparison in Appendix I. 12 A.2.1 The Source of Daa All indusry level daa used in he analysis is rerieved from he following four sources. Indusry Daa from FAT-BEA (NAICS Classificaion ) 1. FAT 3.1: Curren-Cos Ne Sock of Privae Equipmen (K EQ,i ), Srucures (K ST,i ), and Inellecual Propery Producs (K IP P,i ) for each indusry i. 2. FAT 3.4: Curren-Cos Depreciaion of Privae Equipmen (DEP EQ,i ), Srucures (DEP ST,i ), and Inellecual Propery Producs (DEP IP P,i ) for each indusry i. 3. FAT 3.7: Invesmen in Privae Equipmen (Inv EQ,i ), Srucures (Inv ST,i ), and Inellecual Propery Producs (Inv IP P,i ) for each indusry i. Indusry Daa (GDP-by-Indusry) in BEA (Non-Ineracive Table, NAICS Classificaion ) GDPbyInd VA NAICS for each indusry i: Indusry value added before 1997 in NAICS classificaion. Indusry Daa from Regional Daa in BEA (NAICS Classificaion ) 1. GDP in curren dollars : Indusry value added afer 1997 in NAICS classificaion. 12 One cavea from compuing indusry labor shares from NIPA-BEA is ha he consumpion of fixed capial and renal income are no available by indusry, a feaure ha our compuaion of indusry labor share from FAT daa helps circumven. Alernaively, indusry daa from NIPA ha includes consumpion of fixed capial and renal income (under gross operaing surplus) are also available from he GDP-by-Indusry Table in NIPA- BEA a hp:// ha uses NAICS classificaion from 1947 o Aside from being of less qualiy (see he echnical documenaion in hp:// iedguide.hm#gdpia_ou), hese daa are no updaed by he 2013 BEA revision, which limis heir use o assess he effecs of IPP on he labor share by indusry. 9

12 Indusry Daa from NIPA-BEA (NAICS Classificaion ) 1. NIPA 6.2: Compensaion of Employees (CE i ) for each indusry i 2. NIPA 6.12: Nonfarm Proprieors Income (PI NF,i ) for each indusry i NIPA 6.15: Ne Ineres (NI i ) for each indusry i 4. NIPA 6.16: Corporae Profis (CP i ) for each indusry i NIPA 6.17: Corporae Profis Before Tax (CPbTax i ) for each indusry i 6. NIPA 6.19: Corporae Profis Afer Tax (CPaTax i ) for each indusry i 7. NIPA 1.5.5: Gross Domesic Produc (GDP), Gross Privae Domesic Invesmen in Research and Developmen, and Enerainmen Lierary and Arisic Originals (Non-sofware conribuion o GDP) 8. NIPA Governmen Gross Invesmen in Research and Developmen. A.2.2 Adjusmen of Value Added in GDP-by-indusry Daa We explore wo approaches o adjus he indusry value added for he full effec of he IPP capializaion, each involving a differen underlying assumpion. In he firs approach, we assume in each year he impac from he IPP capializaion on indusry-level oupu is he same as he impac from he IPP capializaion on he aggregae oupu (i.e. GDP), for all indusries. In he second approach, we assume for each indusry, he impac from he IPP capializaion on indusry-level oupu for all years before 1997 is idenical o ha in In oher words, he firs approach allows for heerogeneous oupu impacs over ime, while he second approach allows for heerogeneous oupu impacs across indusries. The resuls we repor in he paper are obained by adoping he second approach. We confirm ha he wo approaches produce qualiaively similar resuls and he unrepored resuls are available upon reques. We deail he wo approaches in wha follows. Firs Approach. We revise up all indusry value added by a facor equal o he raio beween GDP o GDP wihou non-sofware IPP capializaion. Le Y B be GDP in year for he sample period , aken from NIPA Table Le Y A be he GDP in year for he sample period wihou aking ino accoun he non-sofware IPP capializaion, which is obained by subracing from Y B he gross privae domesic invesmen in R&D and Enerainmen, Lierary and Arisic Originals and governmen gross invesmen in R&D, available from NIPA Tables and Then define he raio = Y B, which is he facor ha we muliply o he Y A indusry value added from 1947 o 1997 in he GDP-by-Indusry Table. Second Approach. We revise up an indusry value added by a facor equal o he raio beween he indusry oupu o he indusry oupu wihou non-sofware IPP capializaion of ha indusry in Le Y B,i 1997 be he value added of indusry i in 1997 from he (revised) Regional Daa. Le Y A,i 1997 be he oal value added of indusry i in 1997 from he GDP-by-Indusry Table. Then we can compue for each indusry he raio, i 1997 = Y B,i 1997, which is he facor ha we muliply o he indusry value added from 1947 o 1997 from he GDP-by-Indusry Table. A.3 The Consrucion of Corporae Secor Daa Series One benefi of using he corporae secor daa o compue labor share is ha here is no need o divide Proprieors Income beween labor and capial. For his reason, i is commonly used in he sudies of labor share. We also examine he effec of IPP capializaion on he corporae secor labor share in he paper. 13 We obain Farm Proprieor s income from NIPA Table 1.12 and add o he proprieor s income in Agriculure. 14 This Table does no include Agriculure, Mining, Consrucion, and Services. Y A,i

13 A.3.1 The Source of Daa 1. NIPA 1.14: Gross Value Added of Corporae Business (GVA C), Consumpion of Fixed Capial (CFC C), Compensaion of Employees (CE C), Taxes on Producion and Impors Less subsidies (TaxLessSub C), Ne Operaing Surplus (NOS C) 2. FAT 4.1: Curren-Cos Ne Sock of Privae Nonresidenial Fixed Asses (KC) for Equipmen (KC EQ), Srucures (KC ST), and Inellecual Propery Producs (KC IPP) 3. FAT 4.4: Curren-Cos Ne Sock of Privae Nonresidenial Fixed Asses (DEP C)for Equipmen (DEP C EQ), Srucures (DEP C ST), and Inellecual Propery Producs (DEP C IPP) 4. FAT 4.7: Invesmen in Privae Nonresidenial Fixed Asses (IC) for Equipmen (IC EQ), Srucures (IC ST), and Inellecual Propery Producs (IC IPP) A.3.2 The Corporae Secor Labor Share from Naional Income Daa To compue he corporae secor LS, we use NIPA Table 1.14, which conains he informaion abou he gross value added of corporae business and nonfinancial corporae business. LS is compued by dividing he compensaion of employees (i.e. he income accruing o employees, such as wages, salaries, employer s conribuions for social insurance, and oher labor income) by he gross value added which consiss of consumpion of fixed capial, compensaion of employees, axes on producion and impors less subsidies, and ne operaing surplus. A.3.3 The Corporae Secor Labor Share from One-Secor Model The FAT daa allows us o decompose he fixed asses of corporae business, boh in financial and nonfinancial secor, ino equipmen, srucures, and inellecual propery producs. Hence we can conduc he analysis of IPP capializaion and counerfacuals by using one-secor one-capial model. The procedure is analogous o ha of aggregae labor share in secion A.1.3 hrough A.1.9. To recover he ne rae of reurn o capial, we use he labor share compued from he naional income daa in secion A.3.2. Furher, we se he iniial capial sock o be equal o he Curren-Cos Ne Sock of Privae Nonresidenial Fixed Asses in A.4 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) 15 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. 16 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 15 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

14 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. 17 Concepually, he oupu of R&D is he discouned presen value of he fuure gains he company or organizaion derives from R&D. 18. 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. 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, (6) 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 ]), (7) 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. 17 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. 12

15 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. (8) 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), (9) 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, (10) 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. 13

16 B Effecs of he 2013 BEA Revision on Labor Share: Pre- vs. Pos- Revision Daa By Naional Income Componens Here, we explore he effecs of he 2013 BEA revision on he LS. To his end, firs, we compue he benchmark LS described in Secion 2.1 using pre-revision daa and se his as a reference LS. Then, we replace each naional income componen (i.e., compensaion of employees, consumpion of fixed capial, ec.) wih is pos-revision counerpar one by one and compue he counerfacual LS again. The resuls are shown in panels (a) o (l) of Figure B-1. Of all componens of he GNP, only he revision of he consumpion of fix capial (CFC) has sizable effecs on he LS (see panel (c)). This feaure is consisen wih he descripion in Secion

17 Figure B-1: Effecs of he 2013 BEA Revision on Labor Share: By Naional Income Componen (a) GNP (b) CE (c) CFC (d) SDis (e) PI (f) RI (g) CP (h) NI (i) Tax (j) Sub (k) BCTP (l) CSGE Noes: All variables used in he compuaion are in nominal erms. The componens of GNP ha are used in he consrucion of he labor share are: Compensaion of Employees (CE), Consumpion of Fixed Capial (CFC), Saisical Discrepancy beween GNP and Naional Income (SDis), Proprieors Income (PI), Renal Income (RI), Corporae Profis (CP), Ne Ineres (NI), Taxes on Producion (Tax) and Subsidies (Sub), Business Curren Transfer Paymens (BCTP), and Curren Surplus of Governmen Enerprises (CSGE). 15

18 C Furher Insighs on Aggregae Capial and Is Types This secion provides furher insighs on depreciaion and invesmen shares by ype of capial including srucures, equipmen and IPP. We also invesigae he BEA componens of IPP. Price of Invesmen The hisorical series of he relaive price of invesmen in srucures, equipmen and IPP relaive o consumpion are in panel (a) of Figure C-1. The price of invesmen in srucures is se o be he price of consumpion compued in Secion A.1.5. The relaive prices of invesmen in equipmen and IPP boh decrease, where equipmen reaches 30% and IPP reaches 50% of he price of consumpion by Boh he invesmen prices of equipmen and IPP have subsanially decreased in parallel since he lae 1940s wih equipmen acceleraing is decline since he 1980s. The decomposiion by IPP componens in panel (b) of Figure C-1 shows ha he relaive prices of invesmen in sofware, R&D and arisic originals 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 Panel (a) of Figure C-2 shows he hisorical series of he depreciaion rae of srucures, equipmen and IPP described in secion The depreciaion rae of srucures is he lowes, roughly 3% for he enire sample period. The depreciaion rae of equipmen capial is also roughly consan beween 13 and 14% (i.e., 4 o 5 imes larger han ha of srucures), while he depreciaion rae of IPP capial is he highes and increases wih ime saring around 15% in he lae 1940s and increasing o roughly 22% in he 2000s. The depreciaion of each ype of he IPP capial is in panel (b) of Figure C-2. Clearly, sofware is he IPP capial wih he larges 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. Invesmen and Capial The invesmen shares of srucures, equipmen and IPP are ploed in panel (a) of Figure C-3. The invesmen share of srucures declines over ime from around 55% in 1947 o 40% in 2013; he equipmen share mildly decreases from 38% o 34%; and he IPP share goes up from 7% o 26%. The invesmen shares of IPP componens in panel (b) of Figure C-3 shows ha he sofware invesmen share has increased 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 Panels (c) and (d) of Figure C-3 show he shares in aggregae capial of, respecively, srucures, equipmen and IPP, and of IPP componens. The share of IPP capial increases from 2% in 1947 o 8% in The share is compensaed by mild declines in srucures (from 81% o 78%) and a somewha larger decline in equipmen (from 18% o 14%). Tha is, despie he larger decline in he invesmen shares of srucures, his does no ranslae ino declines in he share of srucures in aggregae capial, largely due o a low depreciaion rae compared wih oher ypes of capial. The opposie occurs o IPP. In erms of IPP componens, he share of sofware capial in aggregae capial increases o 1.5% by 2013, he share of R&D capial in aggregae capial increases from roughly 1.2% in 1947 o 5.2% since he mid-1960s, and he share of arisic originals in aggregae capial is roughly consan a 1%. Nonresidenial Invesmen and Capial Panel (a) of Figure C-4 shows he invesmen shares in srucures, equipmen and IPP invesmen in aggregae nonresidenial invesmen. Tha is, we remove from aggregae invesmen residenial srucures (and equipmen). Wihou residenial invesmen, equipmen and IPP gain imporance relaive o srucures. Equipmen invesmen accouns for 53% of aggregae invesmen in lae 1940s and around 40% in he 2000s, reaching 41% in 2013, while IPP invesmen accouns for 10% of aggregae invesmen in lae 1940s and roughly 31% in he 2000s, reaching 32% in Wihou residenial invesmen, srucures sars around 40% in he 1940s and reach 27% in Tha is, in invesmen shares, IPP invesmen has already surpassed srucures, and rends up o overake equipmen. This is no he case ye in erms of aggregae capial. Panel (b) of Figure C-4 shows srucures capial in aggregae capial represening 70% in

19 o a somewha seady 65% since he mid-1950s. The share of equipmen capial goes down from 30% in he mid 1950s o 23% by 2013, which is offse by he rise in IPP capial from a share of 3% in 1947 o 12% o Privae and Governmen IPP Invesmen and Capial Panel (a) of Figure C-5 shows he invesmen shares of sofware, R&D and arisic originals invesmen in aggregae invesmen separaely for he privae and he governmen secor. The privae sofware invesmen accouns for he highes share of aggregae invesmen wih an exponenial rise since he early-1960s from zero o 9.3% by This rend diverges from ha of governmen sofware which invesmen remains low and accouns for roughly 1.2% of aggregae invesmen since he 1980s. The privae R&D invesmen share increases from 2.5% in 1947 o 8.7% in The governmen R&D invesmen share is larger han he privae share before he 1980s, ha peaks a 8% of oal invesmen by he early 1960s, while since he 1980s his accoun represens around 4.5% of oal aggregae invesmen. Arisic originals are only presen in he privae secor represening a sligh increase from 1.7% in 1947 o 2.5% in The share of each ype of IPP capial in he privae and governmen secors is in panel (b) of Figure C-5. Due o he higher depreciaion rae of sofware capial, he share of privae sofware capial represens 1.3% of aggregae capial by 2013, while he governmen counerpar accouns for barely 0.2% by Tha is, he privae sofware capial basically represens he enire amoun of sofware capial in he economy. The share of aggregae R&D, which depreciaes a a rae beween 3 and 4 imes less han sofware, has remained in he governmen secor above ha of he privae secor unil he lae 1990s, afer which he privae secor share of R&D capial is 2.8% and he governmen secor share is 2.3%. Arisic originals are only presen in he privae secor and represen roughly 1% of aggregae capial. 17

20 Figure C-1: Relaive Price of Invesmen, BEA (a) Relaive Price of Invesmen in Srucures, Equipmen and IPP (b) Relaive Price of Invesmen in IPP Componens Noes: In panel (a) and (b) we use he relaive price of invesmens consruced as described, including daa sources, in secion A

21 Figure C-2: Depreciaion Raes, BEA (a) Depreciaion Raes of Srucures, Equipmen and IPP (b) Depreciaion Raes of IPP Componens Noes: In panel (a) and (b) he depreciaion raes by ype of capial are consruced using curren-cos depreciaion and curren-cos ne sock from FAT, see secion A.1.1. These compuaions include privae and governmen capial, and boh residenial and nonresidenial capial. 19

22 Figure C-3: Invesmen and Capial, BEA (a) Sruc., Equip. and IPP Invesmen Shares (b) IPP Componen Invesmen Shares (c) Sruc., Equip. and IPP in Aggregae Capial (d) IPP Componens in Aggregae Capial Noes: In panel (a) and (b) we compue invesmen shares including privae and governmen invesmen, and residenial and nonresidenial invesmen. Analogously, in panel (c) and (d) we compue he capial inensiy, by ype of capial, in aggregae capial. See secion A.1.1 for daa sources. 20

23 Figure C-4: Nonresidenial Invesmen and Capial, BEA (a) Srucures, Equipmen and IPP Invesmen Shares (b) Srucures, Equipmen and IPP Capial Inensiy Noes: In panel (a) and panel (b) he invesmen shares include nonresidenial privae and governmen capial. Tha is, residenial invesmen is no included in aggregae invesmen. See secion A.1.1 for daa sources. 21

24 Figure C-5: Privae and Governmen Invesmen and Capial, BEA (a) IPP Componen Invesmen Shares (b) IPP Componens in Aggregae Capial Noes: In panel (a) we compue invesmen shares of IPP componen in aggregae invesmen. Aggregae invesmen includes privae and governmen invesmen, and residenial and nonresidenial invesmen. Analogously, in panel (b) we compue he capial inensiy, by ype of IPP capial, in aggregae capial. See secion A.1.1 for daa sources. 22

25 D The Capial Share of Income for he US Corporae Secor: Srucures, Equipmen and IPP The aggregae capial share of income is he sum of he respecive shares of srucures, equipmen, and IPP. In secion 3.3 we showed he behavior of each ype of capial share for he aggregae US economy. Of he aggregae capial share of income, he capial share of IPP has played an increasing role, while ha of srucures and equipmen has remained relaively consan. We reproduce hese resuls in panel (a) of Figure D-1. For compleeness, we show in panel (b) of Figure D-1 he respecive capial shares of income for each ype of capial in he US corporae secor. In he corporae secor, we find ha while he capial share of srucures decreases from 24% in 1947 o 13% in 2000, i also rebounds up by 5 LS poins from 13% in 2001 o 18% in 2013, which helps explain he acceleraion of he LS decline in he 2000s. The corporae capial share of equipmen is 16% on average wih a ligh increase from an average share slighly above 15% before he 1970s o slighly below 17% afer he 1980s. Finally, i is clearly he capial share of IPP wih a linear increase from 2% in 1947 o 9% in 2013 ha explains he secular decline of he corporae LS.

26 Figure D-1: Capial Share of Income: Srucures, Equipmen and IPP, US (a) Aggregae Economy (b) Corporae Secor Noes: Panel (a) reproduces he resuls in he main ex ploed in Figure 7. Panel (b) reconducs he analogous excercise for he corporae secor as described in secion 5. In he corporae secor, he sum of hese hree capial shares by ype of capial adds up o one minus he benchmark labor share (blue line) compued in panel (c) of Figure 13, and he sum of he capial share of srucures and equipmen adds up o one minus he he counerfacual LS Wihou IPP (orange line) ploed in (c) of Figure 13.

27 E 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. 20 Visual inspecion of labor share suggess ha he labor share decline is a phenomenon ha sars primarily afer WWII (see panel (a) of Figure E-1). This secular decline in labor share clearly coincides wih he increase in he relaive imporance of IPP invesmen. Unil he 1930s, IPP invesmen represens less han 3% of aggregae invesmen. I sars o grow almos linearly since he 1930s, reaching he value above 20% in he 2000s and close o 30% in he las few years, see panel (b) of Figure E-1. On he oher hand, invesmen in srucures represens around 70% of aggregae invesmen in he early 20h cenury and his share declines hereafer coninuously o he curren level of roughly 40% in he 2000s. The share of invesmen in equipmen sars a 20% in he early 20h cenury and increases during he firs half of he 20h cenury unil i reaches he value around 35% in he 1950s and remains a ha level since hen. 21 Specifically, consisen wih Figure 2 in he main ex, he share of equipmen invesmen has remained relaively seady and he increase in he share of invesmens in IPP is offse by he decline in he share of invesmen in srucures from he 1950s. Finally, panel (c) of Figure E-1 shows he effecs of IPP capializaion. There, we redo he same exercise described in Secion 3.3 bu wih his larger sample saring from We find ha wihou IPP capializaion labor share basically flaens ou 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. 20 Noe ha while NIPA provides daa since 1929, FAT provides daa including he invesmen series ha we describe nex since We also noe ha during he WWI and WWII here is a clear subsiuion beween invesmen in srucures and equipmen ha raises he share of equipmen invesmen above ha of invesmen in srucures.