Extended Business Sector Data on Outputs and Inputs for the U.S.:

Transcription

1 1 Exended Business Secor Daa on Oupus and Inpus for he U.S.: W. Erwin Diewer, 1 Discussion Paper 13-01, School of Economics, Universiy of Briish Columbia, Vancouver, Canada, V6T 1Z1. diewer@econ.ubc.ca January 2, 2013 Absrac Using recen daa from he Bureau of Economic Analysis (BEA), he Bureau of Labour Saisics (BLS), he Board of Governors of he Federal Reserve Sysem (or Federal Reserve Board or FRB) and he US Deparmen of Agriculure (USDA), he paper consrucs a op down daa se ha covers he oupus produced and inpus used by an Exended Business Secor of he US economy for he years The Exended Business Secor consiss of he enire US economy less he inpus used and oupus produced by he Public Adminisraion secor and less he US housing secor, boh rened and owned. The consruced daa se is suiable for measuring he Toal Facor Produciviy (TFP) or Mulifacor Produciviy (MFP) of his Exended Business Secor. Journal of Economic Lieraure Classificaion Numbers C43, C67, C82, D24, E22, E43. Keywords Toal Facor Produciviy, Mulifacor Produciviy, measuremen of capial, measuremen of invenory change, user coss, real ineres raes. 1 School of Economics, Universiy of Briish Columbia and he School of Economics, Universiy of New Souh Wales. The financial assisance of he SSHRC is graefully acknowledged.

2 2 1. Inroducion The Toal Facor Produciviy (TFP) of a producion secor is defined as he real oupu produced by he secor divided by he real inpu uilized by he secor. TFP growh is defined as (one plus) oupu growh divided by (one plus) inpu growh; i.e., i is usually defined as an oupu quaniy index divided by an inpu quaniy index. 2 When naional saisical agencies consruc TFP growh esimaes for an aggregae of firms or indusries such as he enire privae secor of he economy, hey ake a boom up approach; i.e., hey form esimaes for he real oupu produced and real inpu used by he indusry and hen ake he raio of oupu o inpu o form an esimae of he indusry s TFP. The indusry TFP growh raes are hen weighed appropriaely and aggregaed up o form naional esimaes of TFP growh. I is also possible o form esimaes of naional TFP growh using a op down approach. This approach uses final demand daa for he economy o form naional oupu measures and uses economy wide labour and capial services inpus o form naional inpu measures. Thus he op down approach provides no indusrial deail. From a purely mehodological poin of view, he boom up approach is preferable. If wage raes and user coss were consan across indusries, here would be lile difference beween he wo approaches. However, wage raes for he same ype of labour generally differ across indusries and user coss for he same ype of capial also differ across indusries (due o differing coss of capial across indusries) and he boom up approach can adjus for hese variaions while he op down approach canno. Thus he op down approach will usually be subjec o some aggregaion bias. 3 However, here are wo reasons why i is useful o implemen a op down approach o measuring a naion s produciviy performance: Using he op down approach, i is easy o measure he effecs of changes in a counry s erms of rade; i.e., using his approach, i is possible o measure changes in he prices of expors and impors on he real income generaed by he producion secor of he economy. 4 The effecs of produciviy growh and growh of primary inpus can be measured along wih hese erms of rade effecs in a unified framework. 2 This index number definiion of TFP growh daes back o Jorgenson and Griliches (1967). The BLS (1983) (2012) calls TFP growh Mulifacor Produciviy growh (MFP growh). For a comprehensive Manual on how o measure Mulifacor Produciviy, see Schreyer (2001). 3 Gu (2012) explains he problem in some deail. There will generally be some uni value aggregaion bias in he labour and capial services esimaes consruced by he op down approach; see Jorgenson (2012), Jorgenson and Schreyer (2012), Diewer (2012) and Schreyer (2012) for addiional discussion on his poin. For a comprehensive discussion of uni value bias, see Diewer and von der Lippe (2010). 4 Sudies ha use varians of his approach include Diewer and Morrison (1986), Morrison and Diewer (1990), Kohli (1990) (2004) (2006), Fox and Kohli (1998), Diewer and Lawrence (2000) (2006), Diewer, Mizobuchi and Nomura (2005), Cho, Kim and Schreyer (2012) and Diewer and Yu (2012).

3 3 The op down approach can generae more reliable measures of a naion s TFP han he boom up approach if here is a considerable amoun of measuremen error in he secoral daa. 5 The problem is ha i is difficul o consruc accurae secoral daa on inpus. Saisical agencies generally do no have accurae surveys for he prices and quaniies of inermediae inpus used by indusries. Furhermore, he allocaion of labour and capial o indusries is no a rivial ask. Inaccurae esimaes of secoral inpus can be largely avoided by he use of he op down approach since he inersecoral allocaion of inpus does no maer using his approach. In his paper, we will consruc a suiable daa base so ha he op down approach can be implemened for he U.S. economy for he years In his paper, we will consruc esimaes of TFP growh (or Mulifacor Produciviy growh) for our concep of an Exended Marke Secor for hese years and compare our op down esimaes wih he boom up esimaes for he Privae Business Secor provided by he Bureau of Labor Saisics (2012); see secion 7 below. Our Exended Marke Secor covers he enire economy excep he Public Adminisraion Secor (or General Governmen Secor) and he Housing Secor (including boh rened and owned housing). 7 Noe ha he oupu concep used by he BLS for he Privae Business Secor is equal o GDP less he oupu of household workers, nonprofi insiuions, he gross housing produc of Owner Occupied Housing, he renal value of nonprofi insiuional real esae and he oupu of Governmen Enerprises. 8 In secion 2 below, we develop preliminary esimaes for consumpion, invesmen, deliveries of our Exended Marke Secor o he General Governmen secor, expors and impors. In secion 3, we use more deailed BEA daa o disaggregae expors and impors of goods. In secion 4, he consrucion of our labour inpu daa is described while secion 5 describes he consrucion of reproducible capial socks, invenory socks and business and farm land. Secion 6 consrucs user coss of capial. Secion 7 consrucs TFP esimaes for our Exended Marke Secor and compares hem o he corresponding BLS Mulifacor Produciviy esimaes for he U.S. Privae Business Secor. Secion 8 concludes. Our primary source of daa is he Bureau of Economic Analysis (BEA) bu we also make use of Bureau of Labor Saisics (BLS) daa, U.S. Deparmen of Agriculure daa and balance shee daa from he Board of Governors of he Federal Reserve. 5 A sufficien condiion for he exisence of secoral measuremen error is he exisence of unreasonable balancing Inernal Raes of Reurn for he secor. 6 NAICS daa for hese years is readily available on he inerne. 7 The BLS privae business secor covers rened housing bu no he services of Owner Occupied Housing (OOH). We have excluded OOH as well as rened housing because accurae informaion on he sock of renal housing and he land occupied by renal housing is no available. Informaion on he sock of all residenial housing and he value of residenial land is available bu no a breakdown ino he rened and owned pars. 8 See he BLS (2012).

4 4 2. Esimaes of U.S. Final Demand Expendiures for he Exended Business Secor: Consumpion, Invesmen, Deliveries o General Governmen, Expors and Impors Our primary daa source is he ineracive websie of he Bureau of Economic Analysis (2012). Using his source, from Table1.1.5: Gross Domesic Produc, (las revised on Ocober 26, 2012), we can find annual daa on he Gross Domesic Produc for he U.S., V GDP, for he years = This same able has value daa for he expendiure componens of GDP: V PC = personal consumpion expendiures; V PI = gross privae domesic invesmen; V GCI = governmen consumpion expendiures and governmen gross invesmen; V XG = expors of goods; V XS = expors of services; V MG = impors of goods and V MS = impors of services. Price indexes for he above value aggregaes, P GDP, P PC, P PI, P GCI, P XG, P XS, P MG and P MS, can be found in BEA Table 1.1.4: Price Indexes for Gross Domesic Produc; Index numbers. 9 The corresponding quaniy indexes, Q GDP, Q PC, Q PI, Q GCI, Q XG, Q XS, Q MG and Q MS, can be obained by dividing each value series by he maching price index. Noe ha invesmen ha ends up in he governmen secor is in he governmen value aggregae V GCI. We will remove hese invesmen expendiures from his governmen value aggregae. In order o accomplish his ask, we use BEA Table 3.9.5: Governmen Consumpion Expendiures and Gross Invesmen. This Table has value informaion on governmen consumpion expendiures, V GC, ha are produced by he governmen and valued a heir cos of producion. This Table also liss governmen invesmen expendiures, V GI, for he years Corresponding quaniy series for governmen invesmen expendiures for he years can be found in BEA 5.8.3A: Real Gross Governmen Fixed Invesmen by Type, Quaniy Indexes. Anoher quaniy series for governmen invesmen expendiures ha covers he years can be found in BEA Table 5.8.6B: Real Gross Governmen Fixed Invesmen by Type, Chained Dollars. The wo quaniy series were linked o form he quaniy series Q GI ha covered he enire sample period, The implici price series, P GI, was formed by dividing V GI by Q GI. Having consruced he privae secor invesmen price and quaniy series, P PI and Q PI, and he governmen secor invesmen price and quaniy series, P GI and Q GI, we can consruc an aggregae price of invesmen P I and an aggregae quaniy of invesmen Q I series as chained Fisher aggregaes of he wo componen invesmen series. The corresponding aggregae value of invesmen, V I, is se equal o P I Q I. We can also consruc indirec price and quaniy series for governmen consumpion expendiures, P GC and Q GC, as follows: consruc chained Fisher index aggregaes of P GCI and Q GCI and P GI and Q GI, which we denoe by P GC and Q GC. 10 Thus we have he following final expendiure decomposiion of U.S GDP in year : (1) V GDP = V PC + V I + V GC + V XG + Q XS Q MG Q MS 9 These price indexes coincide wih heir chained Fisher (1922) index counerpars, which are available for he period in various BEA Tables. 10 We noe ha he corresponding indirec value of governmen consumpion series, P GC Q GC, agrees wih he governmen value of consumpion series, V GC, which was downloaded earlier.

5 5 and we have companion price and quaniy series for each value aggregae in equaion (1). The BEA provides he following alernaive aggregae producion secor decomposiion of GDP for year which we will find useful: (2) V GDP = V BB + V HP + V NI + V GG where V BB = gross domesic produc excluding gross value added of households and insiuions and of general governmen (and hus his is a broad measure of business secor oupu), V HP = he value of household producion, V NI = he value of producion for nonprofi insiuions and V GG = value added of general governmen; i.e., his aggregae is equal o he compensaion of general governmen employees plus general governmen consumpion of fixed capial. Informaion on hese producion secor componens of GDP are available for from BEA Table 1.3.5: Gross Value Added by Secor. This same Table has as an Addendum iem, he Value of Gross Housing Value Added, V H. 11 Chained quaniy indexes ha correspond o hese value aggregaes, Q BB, Q HP, Q NI, Q GG and Q H may be found in BEA Table 1.3.6: Real Gross Value Added by Secor, Chained Dollars. The corresponding implici price indexes, P BB, P HP, P NI, P GG and P H can be calculaed by dividing each value aggregae by he maching quaniy index. Wha is he relaionship of he value of governmen consumpion expendiures, V GC, and he value added of he general governmen secor, V GG? The value of governmen consumpion expendiures should equal general governmen value added V GG plus he value of inermediae inpu purchases by he general governmen secor, 12 V G ; i.e., we have: (3) V GC = V G + V GG. We have price and quaniy series for V GC and V GG and so i is possible o consruc implici chained Fisher price and quaniy indexes for he governmen inermediae inpu value aggregae, P G and Q G, by forming chained Fisher indexes using he wo price series, P GC and P GG, and he wo quaniy series, Q GC and Q GG. We noe ha V G P G Q G also equals he value aggregae V G defined implicily in equaion (3). In wha follows, we will inerpre V G as he (ne) value of deliveries of goods and services o he general governmen secor by he res of he economy. 11 This value aggregae includes he value of housing rens and he impued renal services of Owner Occupied Housing. The impued services of OOH and mos rens are included in V B bu some housing rens are included in he oher secors. 12 Acually, V G is equal o inermediae inpu purchases by he general governmen secor, less he value of goods and services sold o he res of he economy by he general governmen secor. Thus V G is equal o ne general governmen inermediae inpu purchases from he res of he economy. Conversely, V G is equal o he ne value of goods and services supplied o he general governmen secor from he res of he economy.

6 6 We require one addiional definiion before we define he scope of our exended business secor aggregae. Noe ha he gross value of housing expendiures, V H, is par of he value of personal consumpion expendiures, V PC. Our consumpion aggregae, V C, will ne ou hese housing expendiures: (4) V C V PC V H. As usual, we have price and quaniy series for V PC and V H and so i is possible o consruc implici chained Fisher price and quaniy indexes for our consumpion aggregae ha excludes housing services, P C and Q C, by forming chained Fisher indexes using he wo price series, P PC and P H, and he wo quaniy series, Q PC and Q H. We noe ha V C P C Q C also equals he value aggregae V C defined by equaion (4). We define he value of our exended business secor oupu, V B, o be he GDP of he enire economy in year less he gross value of housing services V H less general governmen value added V GG ; i.e., 13 (5) V B V GDP V H V GG = V PC + V I + V GC + V XG + Q XS Q MG Q MS V H V GG = (V PC V H ) + V I + (V GC V GG ) + V XG + Q XS Q MG Q MS = V C + V I + V G + V XG + Q XS Q MG Q MS using (1) using (3) and (4). We have indicaed how price and quaniy indexes for each of he value aggregaes on he righ hand side of he las equaion in (5) can be consruced. These value aggregaes are he basic building blocks for our exended business secor measure of oupu. The prices ha are mached o quaniies in he subaggregaes ha make up V B are final demand prices. From he viewpoin of producion heory, i is more appropriae o adjus hese final demand prices ino prices ha producers face for heir oupus and inpus. 14 This involves subracing various commodiy axes from he price of consumpion and adding axes on impors of goods. Thus we now make a brief deour and describe various axes ha are available in BEA ables. From BEA Table 3.2: Federal Governmen Curren Receips and Expendiures, we can read he annual year values following ypes of Federal axes: V TFP = Federal personal curren axes; V TFE = Federal excise axes; V TFCD = Federal cusoms duies; V TFCI = Federal axes on corporae income and VT FSI = Federal conribuions for governmen social insurance. From BEA Table 3.1: Governmen Curren Receips and Expendiures, we can obain informaion on axes paid by all levels of governmen for he following ypes of ax: V TP = Toal personal axes; V TPI = Toal axes on producion and impors; V TCI = Toal axes on corporae income and V S = Value of subsidies. Finally we can obain sae and local governmen ax informaion from BEA Table 3.3: Sae and Local 13 This is acually a preliminary definiion; we will make some commodiy ax adjusmens o his definiion shorly. 14 This observaion daes back o Jorgenson and Griliches (1972).

7 7 Governmen Curren Receips and Expendiures: V TSLPT propery axes. = Sae and local governmen We will define he value of propery axes in year as V TPROP = V TSLPT and we define axes on he impors of goods as V TMG = V TFCD. We will assume ha oal commodiy axes on our consumpion aggregae, V TC, are equal o oal axes on producion and impors less cusoms duy less propery axes; i.e., (6) V TC = V TPI V TMG V TPROP. The key series on ax revenues and subsidies are lised below in Table 1. Table 1: Key Tax Series for he US Economy; Year V TC V TPROP V TMG V TP V TCI V TFSI A consumpion ax rae can be generaed as C V TCS /V C for = 1987,...,2011 and a new producer price series for our consumpion aggregae for year can be se equal o (1 C )P C. 15 The quaniy of consumpion remains he same a Q C and he new value of V S 15 This is only an approximaion o a bes pracice mehodology which would disaggregae consumpion ino ax homogeneous caegories, make adjusmens for consumpion axes for each caegory and hen aggregae up he componens wih he new more appropriae producer prices ino an overall consumpion aggregae. However, since U.S. consumpion axes are so small in general, he aggregaion error involved in our approximae procedure is probably small.

8 8 consumpion is equal o (1 C )P C Q C. We will abuse noaion and denoe he new producer consumpion price by P C in Table 2 below (and he new producer value of consumpion will also be denoed by V C ). In a similar manner, we can adjus he price index for impored goods for rade axes. Define an aggregae impor ax rae on goods as MG V TMG /V MG for = 1987,...,2011 and a new producer price series for our impored good aggregae for year can be se equal o (1+ MG )P MG. 16 The quaniy of impored goods remains he same a Q MG and he new value of impored goods is equal o (1+ MG )P MG Q MG. We will abuse noaion and denoe he new producer impor price series by P MG in Table 2 below (and he new producer value of impored goods series will be denoed by V MG ). Tables 2 and 3 below lis he price and quaniy indexes for he oupu componens of our Exended Business Secor of he U.S. Economy. 17 Table 2: Price Indexes for Oupu Componens of he U.S. Exended Business Secor; Year P C P I P G P XG Table 3: Quaniy Indexes for he Oupu Componens of he U.S. Exended Business Secor; P XS 16 Again, here will be some aggregaion bias in our procedure unless all impored goods are axed a he same rae (which is no he case). 17 All price indexes have been normalized o equal uniy in 1987 and he quaniy indexes have also been normalized so ha he produc of price imes quaniy equals value (in billions of U.S. dollars). The las 3 columns in Tables 2 and 3 lis some supplemenary series of ineres. P MG P MS P H P GC P GG

9 9 Year Q C Q I Q G Q XG Q XS In he following secion, we will disaggregae he componens of expors and impors of goods ino addiional componens using various BEA Tables. Q MG Q MS 3. Disaggregaed Componens of U.S. Expors and Impors of Goods We can obain he values for 8 classes of expors of goods for he years from BEA Table 4.2.5: Expors and Impors of Goods and Services by Type of Produc. The 8 classes of expor produc are as follows: V X1 = Value of foods, feeds and beverages; V X2 = Value of indusrial supplies and maerials; V X3 = Value of capial goods: civilian aircraf, engines and pars; V X4 = Value of capial goods: compuers, peripherals and pars; V X5 = Value of capial goods: oher; V X6 = Value of capial goods: auomoive vehicles, engines and pars; V X7 = Value of consumer goods, excep auomoive; V X8 = Value of oher expors. The corresponding price indexes, P Xn, can be found in BEA Table 4.2.4: Price Indexes for Expors and Impors of Goods and Services by Type of Produc; Index numbers. Expor quaniy indexes, Q Xn, can be obained by dividing each value series by he corresponding price index; i.e., Q Xn V Xn /P Xn for n = 1,...,8 and = 1987,...,2011. The Q H Q GC Q GG

10 10 disaggregaed price and quaniy series for expors are lised below in Tables 4 and I can be seen ha here is some degree of variabiliy in he componen price indexes. Table 4: Price Indexes for Eigh Classes of Goods Expors; Year P X1 P X2 P X3 Table 5: Quaniy Indexes for Eigh Classes of Goods Expors; P X4 Year Q X1 Q X2 Q X3 18 All of he price indexes have been normalized o equal uniy in 1987 wih offseing normalizaions o he quaniy indexes o preserve values. Q X4 P X5 Q X5 P X6 Q X6 P X7 Q X7 P X8 Q X8

11 We can obain values for 9 classes of impors of goods for he years from BEA Table 4.2.5: Expors and Impors of Goods and Services by Type of Produc. The 9 classes of impors are as follows: V M1 = Value of foods, feeds and beverages; V M2 = Value of indusrial supplies and maerials, excep peroleum and producs; V M3 = Value of peroleum and producs; V M4 = Value of capial goods: Civilian aircraf, engines and pars; V M5 = Value of capial goods: Compuers, peripherals and pars; V M6 = Value of capial goods: Oher; V M7 = Value of auomoive vehicles, engines, and pars; V M8 = Value of consumer goods, excep auomoive; V M9 = Value of oher impors. The corresponding price indexes, P * Mn, can be found in BEA Table 4.2.4: Price Indexes for Expors and Impors of Goods and Services by Type of Produc; Index numbers. Impor quaniy indexes, Q Mn, can be obained by dividing each value series by he corresponding price index; i.e., Q Mn V Mn /P * Mn for n = 1,...,8 and = 1987,...,2011. Recall ha we defined an aggregae impor ax rae on goods in he previous secion as MG VT MG /V MG for = 1987,...,2011. We use ha ax rae here and define new ax adjused price series for our disaggregaed impored good componens P Mn equal o (1+ MG )P * Mn for n = 1,...,9. The disaggregaed price and quaniy series for impors are lised below in Tables 6 and Table 6: Price Indexes for Nine Classes of Goods Impors; Year P M1 P M2 P M3 P M4 P M5 P M6 P M7 P M8 P M9 19 As usual, we normalized all price series o equal uniy in 1987.

12 Table 7: Quaniy Indexes for Nine Classes of Goods Impors; Year Q M1 Q M2 Q 3 Q M4 The BEA uses chained Fisher (1922) indexes o form higher level aggregaes. We will use chained Törnqvis indexes 20 o form higher level aggregaes. However, he chained Törnqvis price index of he impor componens lised in Tables 6 and 7 above is very close o he corresponding chained Fisher index and hence o he aggregae index P MG ha was repored in Table 2 above and similarly, he chained Törnqvis price index of he expor componens lised in Tables 4 and 5 above is very close o he corresponding chained Fisher index and hence o he aggregae index P XG ha was also repored in Table 2 above. 21 Q M5 Q M6 Q M7 Q M8 Q M9 20 See Diewer (1976) for a definiion of hese indexes and heir connecion wih producion heory. 21 Diewer (1978) showed heoreically why superlaive indexes (like he Fisher and Törnqvis) approximae each oher so closely. Empirically, chained Fisher indexes generally closely approximae heir chained Törnqvis counerpars when using annual macroeconomic daa.

13 13 We now urn our aenion o he developmen of measures of labour inpu ino our Exended Business Secor. 4. Measures of Labour Inpu for he Exended Business Secor The BEA makes esimaes of he compensaion of employees (paid workers) across all secors of he economy so ha i is possible o obain esimaes of labour compensaion for our definiion of he Exended Business Secor. However, he BEA does no make esimaes for he value of self employmen labour inpu or he inpu of unpaid family workers. The BLS does make esimaes for boh employee labour income and impue labour income for he self employed and i provides a qualiy adjused wage rae for all ypes of labour. Thus he BLS measures of labour inpu and compensaion would be ideal for our purpose excep ha he definiion of he BLS Privae Business Secor does no coincide wih our definiion of he Exended Business Secor. The BLS (2012) defines he scope of is privae business secor as follows: BLS Privae Business Secor = Gross Domesic Produc (GDP) oupu of general governmen oupu of household workers oupu of nonprofi insiuions gross housing produc of owner occupied dwellings renal value of nonprofi insiuional real esae oupu of governmen enerprises. The scope of our business secor is defined as follows: Exended Business Secor = Gross Domesic Produc (GDP) oupu of general governmen gross housing produc of all residenial dwellings, boh rened and owned. Thus he scope of our business secor is broader han he BLS scope in ha we include he oupus of households, nonprofis and governmen enerprises bu i is narrower in ha we exclude all housing services, no jus owner occupied housing services. 22 Our saring poin for developing esimaes for he price and quaniy of labour inpu ino he Exended Business Secor is he BLS esimaes for he price and quaniy of labour inpu ino heir Privae Business Secor. For laer comparison purposes, we will also lis he BLS oupu and capial services measures in his secion. The basic source is following Table on he BLS (2012) websie: Table; Ne Mulifacor Produciviy and Cos, ; SIC linked o NAICS ; Privae Business Secor Excluding Governmen Enerprises; Basic Measures; Levels. From his 22 There is good reason o exclude he services of owner occupied housing from a produciviy sudy since impued oupu in his secor will be equal o inpu and hence here is no possibiliy of produciviy gains in his secor. We exclude he services of rened dwelling unis because of he difficulies in obaining accurae informaion on he price and quaniy of land and srucure inpus used in he renal secor.

14 14 Table, we can download informaion for on: Mulifacor Produciviy for year MFP ; real value added oupu Q YBLS ; curren dollar oupu V YBLS, labour inpu Q LBLS ; labour compensaion in curren dollars V LBLS ; capial services Q KBLS and capial income in curren dollars V KBLS. 23 Implici price indexes for oupu and he wo inpus for he years can be obained by dividing he values by he corresponding quaniy indexes; i.e., P YBLS V YBLS /Q YBLS, P LBLS V LBLS /Q LBLS and P KBLS V KBLS /Q KBLS. The resuling price series were normalized o equal one in 1987 and he unis of measuremen for he quaniy indexes were changed so as o preserve values. The resuling BLS price and quaniy series along wih he BLS Mulifacor Produciviy series are lised in Table 8 below. Table 8: BLS Price and Quaniy Indexes for U.S. Oupu, Labour and Capial Services Inpu and Mulifacor Produciviy: Year P YBLS P LBLS P KBLS Q YBLS Q LBLS Q KBLS V YBLS V LBLS V KBLS MFP GAG The las row in Table 8 gives (one plus) he Geomeric Average Growh (GAG) rae for he variable in ha column going from 1987 o 2010 for he price and value series and going from 1987 o 2011 for he quaniy series. These raes of growh apply o he Privae Business Secor of he BLS and can be compared laer wih he corresponding raes of growh for our Exended Business Secor lised in Tables 29 and 30 below. Looking a he las 3 columns in Table 8, i can be seen ha he BLS esimae for he value of oupu in year, V YBLS, is somewha greaer han he value of inpus for he 23 The hree value series do no conain esimaes for 2011.

15 15 same year, V LBLS + V KBLS. 24 The BLS generally uses balancing Inernal Raes of Reurn o make he value of inpus equal o he value of oupus for each indusry. However, if he indusry IRR looks unreasonable, an exogenous IRR is subsiued for i. 25 Thus i may be he case ha several indusries had unreasonably high IRRs and so he BLS subsiued lower raes in heir user cos formulae, leading o lower esimaes of he oal value of inpus as compared o he corresponding oal value of oupus. We wan o exend he BLS wage rae series o 2011 and we will use he movemen in a relaed wage index o accomplish his ask. From BEA Table 6.2C: Compensaion of Employees by Indusry, we can find he compensaion of employees for all domesic indusries for he years BEA Table 6.2D coninues his compensaion series for he years BEA Table 6.5D: Full-Time Equivalen Employees by Indusry, has an employmen series for he years for all domesic indusries. Thus we can form an economy wide wage rae for employees by dividing oal compensaion of employees by he number of full ime equivalen employees for he years We use he rae of change in his wage rae o exend he BLS wage rae series P LBLS o We will relabel he resuling wage rae series as P L and we will use i as our measure of qualiy adjused wage raes for he Exended Business Secor. The remaining problem is o find esimaes for he value of labour inpu for he household, nonprofi and governmen enerprise secors. We will add esimaes for hese value aggregaes o he BLS labour value aggregae, V LBLS, in order o obain an esimae of he value of labour services for he Exended Business Secor, which we will denoe by V L. From BEA Tables 6.2C and 6.2D, we can obain he compensaion of employees by indusry for he wo periods and As pars of hese Tables, he compensaion of federal governmen employees and sae and local employees of governmen enerprises is lised. We sum up hese esimaes and denoe he resuling compensaion series as V LG for general governmen employees and V LGE for governmen enerprise employees. The laer series will be our measure of labour compensaion for he governmen enerprise secor. From BEA Table 1.3.5: Gross Value Added by Secor, we obained esimaes of he value added generaed by households and nonprofi insiuions serving households, V HP and V NI respecively; recall equaion (2) above. BEA Table 6.2C: Compensaion of Employees by Indusry, has an Addendum iem: Compensaion of Employees by Indusry; Households and insiuions for he years , which we label as V LHI. Unforunaely, his addendum series was no coninued in BEA Table 6.2D. However, when we formed he raio of V LHI o V HP + V NI for he years , we found ha he raio was quie sable a Thus he raio of employmen compensaion in he household and nonprofis indusries o value added in hose indusries was reasonably 24 The excess value of oupu is $220.4 billion in 1987 and his increases o $759.3 billion in See Harper, Nakamura and Zhang (2012) for a descripion of he BLS reamen of abnormal IRRs.

16 16 sable a 37%. We exended V LHI o he years by seing i equal o 0.37(V HP + V NI ) V LHI. Finally, we approximae 26 he oal value of labour inpu used by he Exended Business Secor, V L, as follows: (7) V L V LBLS + V LHI + V LGE. Thus he value of labour inpu ino he Exended Business Secor (EBS) is se equal o he BLS value of labour services V LBLS plus an esimae of he value of labour inpu by he household and nonprofi insiuion secors V LHI plus he value of labour inpu ino he governmen enerprise secor V LGE. We approximae he EBS wage rae by he BLS Privae Secor wage rae P L. The quaniy of labour inpu ino he EBS is se equal o Q L V L /P L. The price, quaniy and value series for EBS labour inpu can be found in Table 9 below along wih he value of labour inpu for he household and nonprofi insiuion, he governmen enerprise and he general governmen secors. Table 9: Exended Marke Secor Wage Rae, Quaniy and Value of Labour Inpu, Value of Household and Nonprofi Insiuions, Governmen Enerprise and General Governmen Labour Inpu Year P L Q L V L V LHI V LGE V LG 26 A beer approximaion would subrac off he labour inpu associaed wih he renals of dwelling unis.

17 17 We urn now o he developmen of capial sock daa for he Exended Business Secor. 5. Reproducible Capial Sock and Land Esimaes for he Exended Business Secor Our source of informaion on he socks of reproducible asses held by he EBS is he BEA, which has done an excellen job in providing informaion on reproducible capial sock componens for he U.S. economy. Our main source of informaion for he values of ne capial socks held by he Privae Secor a he end of each year (or he beginning of he following year) is BEA Table 2.1: Curren Cos Ne Sock of Privae Fixed Asses, Equipmen and Sofware and Srucures by Type in Billions of dollars. Using his Table, we obained beginning of he year esimaes for he for he Privae Secor of he U.S. economy for he following capial sock componens for = 1988,...,2012: V K1 = Capial sock value of compuers and peripheral equipmen; V K2 = Capial sock value of sofware; V K3 = Capial sock value of communicaion equipmen; V K4 = Capial sock value of medical equipmen and insrumens; V K5 = Capial sock value of nonmedical insrumens; V K6 = Capial sock value of phoocopy and relaed equipmen; V K7 = Capial sock value of office and accouning equipmen; V K8 = Capial sock value of indusrial equipmen; V K9 = Capial sock value of ligh rucks (including uiliy vehicles); V K10 = Capial sock value of oher rucks, buses, and ruck railers; V K11 = Capial sock value of auos; V K12 = Capial sock value of aircraf; V K13 = Capial sock value of ships and boas; V K14 = Capial sock value of railroad equipmen; V K15 = Capial sock value of oher equipmen; V K16 = Capial sock value of office buildings; V K17 = Capial sock value of healh care buildings including hospials; V K18 = Capial sock value of muli-merchandise shopping buildings; V K19 = Capial sock value of food and beverage esablishmens; V K20 = Capial sock value of warehouses; V K21 = Capial sock value of oher commercial buildings; V K22 = Capial sock value of manufacuring srucures; V K23 = Capial sock value of power and communicaion srucures; V K24 = Capial sock value of mining exploraion, shafs and wells; V K25 = Capial sock value of oher srucures; V KRS = Capial sock value of residenial srucures and V KNS = Capial sock value of nonresidenial srucures (equals sum of V K16 o V K25 ). We will emporarily define V K26 V KRS (he value of Privae Secor Residenial Srucures) and V K27 V KNS (he value of Privae Secor Nonresidenial Srucures). The saring capial socks for 1987 are missing in BEA Table 2.1. We will obain esimaes

18 18 for hese missing socks laer. The capial socks ha are lised in Table 2.1 are for he Privae Secor of he U.S. economy. Thus only he capial socks for he Governmen Secor are excluded in his Table. However, he Governmen Secor consiss of he General Governmen Secor (we wan o exclude he capial socks used by his secor) and he Governmen Enerprise Secor (we wan o include he capial services used by his secor 27 ). There is addiional informaion on various subcomponens of he above capial sock componens V Kn lised in BEA Table For some componens of he capial sock, we used he mos disaggregaed daa in Table 2.1 while for oher componens, we used higher level aggregaes. The reason for his asymmeric reamen of asse classes is as follows. We sared wih relaively few capial sock componens bu when we compared he componen capial sock price wih he corresponding invesmen price for he same componen, we someimes found large differences in he wo price series. When his occurs, his is a sign of asse heerogeneiy; i.e., he prices of he iem asse classes in he componen did no move proporionally over ime, leading o differences beween he componen invesmen price index and he componen sock price index. Thus when his difference in asse prices versus invesmen prices occurred for an aggregaed asse class in Table 2.1, we abandoned he aggregae and worked wih he componen series lised in Table Quaniy indexes ha correspond o he above capial sock values are available in BEA Table 2.2: Chain-Type Quaniy Indexes for Ne Sock of Privae Fixed Asses, Equipmen, Sofware and Srucures by Type; Index numbers, 2005=100; Las Revised on Augus 15, Table 2.2 lised he quaniy indexes Q Kn for he 27 asse classes lised above and corresponding price indexes P Kn ha covered he years were calculaed as P Kn V Kn /Q Kn for n = 1,...,27 and = 1988,...,2012. The value of annual invesmens in he above asses V In ha are delivered o he privae secor for he years = 1987,...,2011 can be found in BEA Table 2.7: Invesmen in Privae Fixed Asses, Equipmen and Sofware and Srucures by Type. Chained Fisher quaniy indexes Q In for hese invesmens can be found in BEA Table 2.8: Chain-Type Quaniy Indexes for Invesmen in Privae Fixed Asses, Equipmen and Sofware and Srucures by Type; Index numbers, 2005=100. The corresponding implici invesmen price indexes P In can be formed by dividing V In by Q In ; i.e., P In V In /Q In for n = 1,...,27 and = 1987,..., We compared he invesmen prices P In o he corresponding asse prices P Kn for he years = 1988,...,2011 and hey corresponded sufficienly well ha we se he asse prices for 1987 equal o he corresponding invesmen prices; i.e., we se P 1987 Kn P 1987 In for n = 27 We will form esimaes for he capial socks used by he Governmen Enerprise Secor laer. 28 Table 2.1 liss daa on some 75 componens and subcomponens of he U.S. Privae Secor reproducible capial sock. 29 The asse price series for he firs 26 asses lised above ended up being quie close o he corresponding invesmen price series for he same asses.