UNSW Business School Working Paper

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1 Business School / School of Economics UNSW Business School Working Paper UNSW Business School Research Paper No ECON 14 Alernaive User Coss, Produciviy and Inequaliy in US Business Secors W. Erwin Diewer Kevin J. Fox This paper can be downloaded wihou charge from The Social Science Research Nework Elecronic Paper Collecion: hps://ssrn.com/absrac=

2 Alernaive User Coss, Produciviy and Inequaliy in US Business Secors W. Erwin Diewer and Kevin J. Fox 1 30 May, 2017 Absrac Using he new Bureau of Economic Analysis (BEA) Inegraed Macroeconomic Accouns as well as oher BEA daa, we consruc produciviy accouns for wo key secors of he US economy: he Corporae Nonfinancial Secor (Secor 1) and he Noncorporae Nonfinancial Secor (Secor 2). Calculaing user coss of capial based on, alernaively, ex pos and prediced asse price inflaion raes, we provide alernaive esimaes for capial services and Toal Facor Produciviy growh for he wo secors. Raes of reurn on asses employed are also repored for boh secors. In addiion, we compare raes of reurn on asses employed and TFP growh raes when he land and invenory componens are wihdrawn from he asse base. Finally, implicaions for labour and capial shares from using alernaive income conceps are explored. Key Words User cos of capial, Toal Facor Produciviy, rae of reurn on asses, Inegraed Macroeconomic Accouns, Bureau of Economic Analysis, ex pos and ex ane asse inflaion raes, US Nonfinancial Secor, Ausrian model of producion, balancing raes of reurn, inequaliy. Journal of Economic Lieraure Classificaion Numbers B25, C43, C82, D24, E22, E43. 1 W. Erwin Diewer: Vancouver School of Economics, Universiy of Briish Columbia, Vancouver B.C., Canada, V6T 1Z1 and he School of Economics, UNSW Ausralia, Sydney 2052, ( erwin.diewer@ubc.ca) and Kevin J. Fox: CAER & School of Economics, UNSW Ausralia, Sydney 2052 ( K.Fox@unsw.edu.au). The firs auhor graefully acknowledges he financial suppor of he SSHRC of Canada, and boh auhors graefully acknowledge he financial suppor of he Ausralian Research Council (LP , DP ).

3 1. Inroducion The US Bureau of Economic Analysis (BEA), in conjuncion wih he Bureau of Labor Saisics (BLS) and he Board of Governors of he Federal Reserve, have developed a new se of producion accouns, he Inegraed Macroeconomic Accouns, for wo major privae secors of he US economy: he Corporae Nonfinancial Secor (which we will call Secor 1) and he Noncorporae Nonfinancial Secor (which we will call Secor 2). For boh secors we work ou he rae of reurn on asses employed back o 1960 and compue esimaes of Toal Facor Produciviy (TFP) growh. In addiion o comparing resuls across he secors, we are paricularly ineresed in deermining wheher raes of reurn and TFP growh have declined in recen years compared o he long run rends. Anoher conribuion is o documen wha can happen o user coss when ex pos asse inflaion raes are used in he user cos formula. Dale Jorgenson and his coworkers have advocaed he use of ex pos inflaion raes in a user cos formula and so we call he resuling user coss Jorgensonian. We show ha for many asses, Jorgensonian user coss can be quie volaile and even negaive a imes which means ha hey canno be used in many conexs. We advocae he use of prediced asse inflaion raes in he user cos formula and we sugges a very simple moving average mehod for forming hese prediced asse inflaion raes, which we implemen and compare wih heir Jorgensonian counerpars. We use Jorgensonian and prediced user coss o consruc alernaive measures of capial services and TFP growh for our wo secors of he US economy and, somewha surprisingly, we find ha here was lile difference in he resuling rend measures of TFP growh, even hough here are very large differences in he wo ses of user coss. An addiional conribuion is he examinaion of wha happens o ex pos raes of reurn on asses employed and on TFP growh as we wihdraw asses from he asse base. This research has relevance for exising esimaes of raes of reurn and TFP growh since many produciviy sudies exclude land and invenories from heir asse base. We find ha excluding hese asses leads o exaggeraed esimaed raes of reurn on he remaining asses (as could be expeced) bu he effecs on esimaes of TFP growh are more variable. For our Secor 1, we found ha excluding land and invenories had lile effec on measured TFP growh bu in Secor 2, he exclusion of land dramaically lowered measured TFP growh. Finally, we use our daa se o provide evidence on he debae regarding growing inequaliy due o a falling labour share in income. We find ha moving from value added shares o (Hayekian) income shares provides sronger evidence of falling labour shares, indicaive of growing inequaliy, for boh our secors. Our accouning framework is laid ou in he following secion and he empirical resuls for he above measuremen exercises follow in he subsequen secions. 2 2 The Appendix in Diewer and Fox (2016) explains in deail how we used he Inegraed Macroeconomic Accouns o consruc our daa se for he wo secors of he US economy. 1

4 2. The Accouning Framework, User Coss and Raes of Reurn on Asses Following Jorgenson and Griliches (1967), he Toal Facor Produciviy growh of a firm or indusry of a secor is generally measured as an oupu index divided by an inpu index. The basic ingrediens ha go ino an index number formula are wo price vecors and wo quaniy vecors ha lis he oupu quaniies and heir prices (or he inpu quaniies and heir prices) produced or used for he producion uni for he wo observaions being compared. Compiling prices and quaniies for oupus and nondurable inpus for each period or observaion is generally sraighforward, bu deermining he flow price for a durable inpu is no sraighforward. In order o accomplish he laer ask, we will use a model of producion ha is due o he economis Hicks (1961) and he accounans Edwards and Bell (1961). 3 In each accouning period, he business uni combines he capial socks and goods in process ha i has inheried from he previous period wih flow inpus purchased in he curren period (such as labour, maerials, services and addiional durable inpus) o produce curren period flow oupus as well as end of he period depreciaed capial sock and invenory componens which are regarded as oupus from he perspecive of he curren period (bu will be regarded as inpus from he perspecive of he nex period). The model could be viewed as an Ausrian model of producion in honour of he Ausrian economis Böhm-Bawerk (1891) who viewed producion as an aciviy which used raw maerials and labour o furher process parly finished goods ino finally demanded goods. 4 The beauy of his model is ha a complex ineremporal producion model wih many periods can be reduced o a sequence of single period models. Using his one period framework, we can now explain how user coss arise. Consider a producion uni which produces quaniies q O of a single oupu, uses q I unis of an inermediae inpu, uses q L unis of labour services during say period and purchases q K unis of a capial sock a he beginning of he period. Afer using he services of he capial inpu during period, he producion uni will have q u K unis of used (depreciaed) capial on hand a he end of period. We suppose ha he producion uni faces he posiive prices P O, P I, P L for is oupu and variable inpus during period and i faces he beginning of period price for unis of he capial inpu equal o P K and he price P +1u K for (used) unis of he depreciaed capial good a he end of period. Finally, we assume ha he producion uni has a one period financial opporuniy cos of capial a he beginning of period (i.e., a beginning of he period nominal ineres rae) equal o r. We also assume ha he period producion possibiliies se for his producion uni is he se S. Using all of hese assumpions, he producion uni s (compeiive) one period profi maximizaion problem is he following consrained opimizaion problem: (1) max * qo, qi, ql, qk, qk {P O q O P I q I P L q L P K q K + (1+r ) 1 P K +1u q K * : (q O,q I,q L,q K,q K u ) S }. Noe ha (1) assumes ha all oupus and all variable inpus are paid for a he beginning of period, as is he paymen for he iniial capial sock, which is an inpu. The depreciaed 3 This model can be raced back in par o Walras (1954; ) and Böhm-Bawerk (1891; 342) and more explicily o von Neumann (1945; 2). 4 For more on his Ausrian model of producion and addiional references o he lieraure, see Diewer (1977; ) (1980; 473) (2010) (2014). 2

5 capial sock q K u is an oupu ha is produced a he end of period and is end of period marke value, P K +1u q K u, is discouned by (1+r ) o accoun for he opporuniy cos of ying up financial capial in he asse over period. We make some addiional assumpions a his poin in order o furher simplify he consrained opimizaion problem defined by (1). Firs we assume ha he capial inpu depreciaes a he consan geomeric rae δ per period. The geomeric model of depreciaion has been advocaed by Jorgenson (1989) and his coworkers and i is currenly used by he BEA o consruc US business secor capial socks. The geomeric model of depreciaion implies ha he depreciaed quaniy of end of period capial, q K u, is relaed o he corresponding beginning of he period capial sock, q K, by he following equaion: 5 (2) q K u = (1 δ)q K where δ is he geomeric rae of depreciaion and saisfies he inequaliies 0 δ < 1. Le P K +1 be he end of period price of a uni of he capial sock ha has he same qualiy as he beginning of he period uni of he capial sock. Define he consan qualiy asse inflaion rae over period, i, by he following equaion: (3) 1+ i P K +1 /P K. Thus i is he consan qualiy inflaion rae for he capial sock componen from he beginning of period o he end of period. We assume ha he anicipaed end of period price for he used beginning of he period capial sock is equal o he end of period price for a consan qualiy uni of he capial sock, i.e., we assume ha P +1u K = P +1 K and hus we have he following equaion: (4) P K +1u = (1+i )P K. Our final addiional assumpion is ha all revenues and variable inpu coss are received and paid for a he end of period insead of he beginning of period. Wih hese changes, he producer s consrained opimizaion problem becomes: (5) max qo, qi, ql, qk {(1+r ) 1 [P O q O P I q I P L q L + (1+i )(1 δ)p K q K ] P K q K : (q O,q I,q L,q K ) S * }. The erms involving q K (he beginning of he period capial sock) in he objecive funcion of (5) simplify o f K (1+r ) 1 [1+r (1+i )(1 δ)]p K. Thus f K is he discouned o he beginning of period user cos of capial using he geomeric model of depreciaion. 6 However, insead of discouning end of period cash flows o he beginning of period, we 5 The assumpion of equaion (2) allows us o replace he iniial producion possibiliies se S wih a new se S * which is he feasible se of (q O,q I,q L,q K ). 6 This simple discree ime derivaion of a user cos (as he ne cos of purchasing he durable good a he beginning of he period and selling he depreciaed good a an ineres rae discouned price a he end of he accouning period) was developed by Diewer (1974; 504), (1980; ), (1992; 194). Simplified user cos formulae (he relaionship beween he renal price of a durable inpu o is sock price) dae back o Babbage (1835; 287) and o Walras (1954; ). The original version of Walras in French was published in The early indusrial engineer, Church (1901; ) also developed a simplified user cos formula. 3

6 could ani-discoun or appreciae beginning of he period cash flows o he end of period. 7 This can be accomplished by muliplying he objecive funcion in (5) by (1+r ). If we do his, we obain he following one period profi maximizaion problem: (6) max qo, qi, ql, qk {[P O q O P I q I P L q L u K q K : (q O,q I,q L,q K ) S * } where he end of period user cos of capial u K is defined as follows: (7) u K [1+r (1+i )(1 δ)]p K = [r i + (1+i )δ]p K. This formula for he user cos of capial was obained by Chrisensen and Jorgenson (1969; 302) for he geomeric model of depreciaion. I plays a fundamenal role in our analysis. 8 There are wo versions of he user cos formula u K defined by (7) ha we will use in his paper: (i) An ex pos version ha uses he acual beginning and end of period consan qualiy asse prices, P K and P +1 K, in order o define he asse inflaion rae as i (P +1 K /P K ) 1; and (ii) an ex ane version ha uses he acual beginning of period consan qualiy asse price, P K, and an anicipaed price for he asse a he end of period, P +1* K, in order o define an anicipaed asse inflaion rae as i * (P +1* K /P K ) 1. Jorgenson (1995) (1996) and his coworkers 9 have endorsed he use of ex pos user coss, arguing ha producers can perfecly anicipae fuure asse prices, and so we refer o he user coss defined by (7) when ex pos asse inflaion raes are used in he formula as Jorgensonian user coss. On he oher hand, Diewer (1980; 476) (2005a; ) and Hill and Hill (2003) endorsed he ex ane version for mos purposes, since hese ex ane user coss will end o be smooher han heir ex pos counerpars and hey will generally be closer o a renal or leasing price for he asse. 10 We will use our secoral daa on he US corporae and noncorporae financial secor o compue capial services aggregaes and he resuling raes of TFP growh using boh Jorgensonian and smoohed user coss ha use prediced asse inflaion raes. 7 Assuming ha all of he flow ransacions wihin he accouning period are realized a he end of each period is consisen wih radiional accouning reamens of asses a he beginning and end of he accouning period and he cash flows ha occur during he period; see Peasnell (1981; 56). The idea of ani-discouning o he end of he period o form end of period user coss u K (as opposed o he usual discouned o he beginning of period user coss f K ) was explicily suggesed by Diewer (2005; 485). Ani-discouning is implici in he derivaion of he user cos of an asse using he geomeric model of depreciaion ha was made by Chrisensen and Jorgenson (1969; 302). 8 We have ignored ax complicaions in deriving (6). Any specific capial axes (such as propery axes on real esae asses) should be added o he user cos formula for he relevan asses. In our empirical work, we were no able o obain a breakdown of propery axes ino land and srucure componens and so propery ax raes are missing in our user coss ha we consruc in he following secions of his sudy. Business income axes ha fall on he gross reurn o he asse base can be absorbed ino he cos of capial, r, so ha r can be inerpreed as he before income ax gross reurn o he asse base used by he producion uni. For maerial on he consrucion of user coss for more complex sysems of business income axaion, see Diewer (1992) and Jorgenson (1996). 9 See in paricular Jorgenson and Griliches (1967) (1972) and Chrisensen and Jorgenson (1969). 10 Of course, he problem wih using ex ane user coss is ha here are many mehods ha could be used o predic asse inflaion raes and hese differen mehods could generae very differen user coss. For empirical evidence on his poin, see Harper, Bernd and Wood (1989), Diewer (2005a) and Schreyer (2012). 4

7 We now discuss he issues surrounding he choice for he cos of capial, r, in he user cos formula. There are many mehods for choosing r ha have been suggesed in he lieraure bu he mehods break down ino wo classes: hose ha choose exogenous esimaes for r and hose ha choose r endogenously as he rae of reurn which will jus make he value of inpus used during he period (including capial services) equal o he value of oupus produced during he accouning period. We will use endogenous esimaes for he cos of capial in his sudy. 11 In order o explain how he cos of capial is deermined endogenously, we need o consider he case where he producion uni uses N ypes of capial. Le P Kn and P +1 Kn be he beginning and end of period prices for a new asse of ype n, le 0 δ n < 1 be he associaed geomeric depreciaion rae, le i n (P +1 Kn /P Kn ) 1 be he associaed period ex pos asse n inflaion rae over period and le r be he endogenously deermined period ex pos rae of reurn on he asse base for he producion uni. The ex pos end of period user cos for asse n is defined as: (8) u Kn [1+r (1+i n )(1 δ n )]P Kn = [r i n + (1+i n )δ n ]P Kn ; n = 1,...,N. The period echnology se for he producion uni is now he se of feasible producion vecors (q O,q I,q L,q K1,q K2,...,q KN ) ha belong o a period producion possibiliies se S *. Le q O,q I,q L denoe he period oupu produced, inermediae inpu used and labour used for he producion uni and le (q K1,q K2,...,q KN ) denoe he vecor of beginning of period capial socks used by he producion uni during he period. The ex pos rae of reurn on he period asse base, r, is defined as he soluion o he following (linear) equaion which ses he value of period oupus equal o he value of period inpus where capial inpus are valued a heir ex pos user coss: (9) 0 = P O q O P I q I P L q L Σ n=1 N u Kn q Kn = P O q O P I q I P L q L Σ n=1 N [1+r (1+i n )(1 δ n )]P Kn q Kn. The ex pos cos of capial mehod for deermining he opporuniy cos of capial ha is based on solving equaion (9) for r is due o Jorgenson and Griliches (1967) (1972) and Chrisensen and Jorgenson (1969). This mehod has been used frequenly in he regulaory conex. The mehod can be applied o boh a single enerprise as well as o he economy as a whole. Naional saisical agencies ha have programs ha measure he produciviy of marke secor indusries generally use his mehod. 12 From a naional income accouning perspecive, his mehod has he grea advanage for saisical agencies ha i preserves he srucure of he Sysem of Naional Accouns 1993 (SNA 1993); i.e., he resuling user cos values jus sum o he Gross Operaing Surplus ha was already in SNA Thus his mehod can be viewed as a sraighforward elaboraion of he presen sysem of accouns which does no change is 11 The problem wih he exogenous mehod is ha i is difficul o deermine exacly he appropriae exernal cos of financial capial. In paricular, i is difficul o esimae he risk premium ha is associaed wih invesing in a producion uni ha generaes variable ex pos raes of reurn on is asse base over ime. Neverheless, he exogenous mehod is probably he preferred mehod from a heoreical poin of view. These issues are discussed more fully in Schreyer, Diewer and Harrison (2005) and Schreyer (2009) (2012). 12 The Bureau of Labor Saisics in he U.S. was he firs o inroduce an official program o measure Mulifacor Produciviy or Toal Facor Produciviy in 1983; see Dean and Harper (2001). Oher counries wih TFP programs now include Canada, Ausralia, he UK and New Zealand. 5

8 basic srucure; i only provides a decomposiion of Gross Operaing Surplus or Cash Flow ino more basic componens. 13 In he following secions of his sudy, we will calculae hese ex pos raes of reurn on asses for our Secors 1 and 2 and also use he Jorgensonian user coss defined by (8) when we calculae TFP growh raes for our wo secors. The major disadvanage of using Jorgensonian user coss is heir volailiy and heir endency o become negaive for a leas some periods when asse inflaion raes for paricular asses (such as land) are high. These volaile and someimes negaive user coss do no approximae corresponding asse renal prices (when hey exis), which do no exhibi he same volailiy. Moreover, if hese bouncing user coss are used in producion funcion sudies where he underlying echnology is esimaed using derived supply and demand funcions, he resuling esimaed parameers are unlikely o be reliable. Finally, if saisical agencies repor hese volaile user coss in heir sysem of produciviy accouns, users are likely o be skepical of hese esimaes. Thus here is a need o produce smooher user coss for a variey of reasons. Our approach o producing smooher user coss will be o use prediced asse inflaion raes, say i n *, in he user cos formula insead of he acual ex pos asse inflaion raes, i n. The mehod for calculaing hese prediced asse inflaion raes will be explained more fully in subsequen secions bu he prediced raes are basically simple long run geomeric averages of pas ex pos inflaion raes. Once he smoohed or ex ane asse inflaion rae for asse n in period, i n *, has been defined for n = 1,...,N, he ex ane or smoohed end of period user cos for asse n in period, u Kn *, is defined as: (10) u Kn * [1+r * (1+i n * )(1 δ n )]P Kn = [r * i n * + (1+i n * )δ n ]P Kn ; n = 1,...,N where he smoohed balancing rae of reurn for period, r *, is defined as he soluion o he following equaion (which is linear in r * ): (11) 0 = P O q O P I q I P L q L Σ n=1 N u Kn * q Kn = P O q O P I q I P L q L Σ n=1 N [1+r * (1+i n * )(1 δ n )]P Kn q Kn. The smoohed rae of reurn r * can be viewed as a planned rae of reurn on asses ha is expeced on he beginning of he period value of he capial sock used by he producion uni, provided expeced asse inflaion raes, he i n *, are realized. 14 The smoohed user coss defined by (10) will also provide a decomposiion of Gross Operaing Surplus ino meaningful componens. As we shall see, he ex ane user coss are considerably smooher 13 This mehod for decomposing Gross Operaing Surplus ino explanaory facors (ha are useful when measuring TFP growh), was endorsed in he Sysem of Naional Accouns, 2008; see Schreyer, Diewer and Harrison (2005) for a discussion of he issues. 14 Period prediced prices for oupu, inermediae inpu and labour, say P * O, P * I and P * L, should be used in equaion (11) in order o calculae he period prediced rae of reurn, r *, insead of he acual ex pos prices for oupu, inermediae inpu and labour, P O, P I and P L. However, i is he usual convenion in producion heory o assume ha acual ex pos uni value prices for variable oupus and inpus are equal o heir prediced counerpars. 6

9 han heir Jorgensonian counerpars. 15 Noe ha boh of our user cos models use endogenous raes of reurn. One of he main purposes of his sudy is o deermine wheher he choice of user cos formula affecs our esimaes of TFP growh. We conclude his secion by discussing some of he problems associaed wih he valuaion of invesmens made by he producion uni during period and wih he sales of asses ha migh have occurred during period. We discuss hese issues in he conex of equaion (9) bu a similar discussion holds for he accouning framework defined by equaion (11). Consider he second equaion in (9). Upon noing ha (1+i n )P Kn is equal o he end of period price of a new uni of he nh capial sock componen, P Kn +1, (9) can be rewrien as follows: (12) 0 = P O q O P I q I P L q L Σ n=1 N (1+r )P Kn q Kn + Σ n=1 N P Kn +1 (1 δ n )q Kn. Recall our Ausrian one period model of producion where he beginning of period capial socks are regarded as inpus and he end of period capial socks are regarded as oupus. The iniial value of he capial sock, Σ N n=1 P Kn q Kn, is appreciaed o end of period values by muliplying his iniial capial sock value by (1+r ) so ha he ani-discouned price for inpu asse n is (1+r )P Kn. Looking a (12), we see ha he erm Σ N n=1 (1+r )P Kn q Kn is (minus) he cos of he beginning of period capial sock a end of period prices. The oher prices on he righ hand side of (12) are also expressed in end of period prices. The firs hree erms on he righ hand side of (12) correspond o he value of oupus produced during period, less he N value of inermediae and labour inpus used during he period. The final se of erms, Σ n=1 P +1 Kn (1 δ n )q Kn, is he end of period value of he depreciaed beginning of he period capial sock. Thus (1 δ n )q Kn is he depreciaed quaniy of he beginning of he period capial sock for asse n ha is lef over a he end of period. Bu his quaniy is no he enire end of period capial sock for asse n: during period, here may have been invesmens in asse n. Suppose q GIn is he gross invesmen in asse n during period (and he average price ha he saisical agency assigns o his invesmen is P GIn ) for n = 1,...,N. Thus he acual end of period quaniy of asse n ha he producion uni has a is disposal is q +1 Kn q GIn + (1 δ n )q Kn and according o our accouning convenions, i should be valued a he end of period asse price P +1 Kn. Hence he erms Σ N n=1 P +1 Kn q GIn seem o be missing from he righ hand side of (12). There is an explanaion for his apparen puzzle. Suppose asse n is a reproducible capial sock; i.e., an asse which is produced inernally by he producion uni or purchased from anoher producer. In his case, he value of he gross invesmen in asse n during period, P GIn q GIn, will be par of he period value of oupu for 15 There is a problem wih inerpreing hese smoohed user coss as renal prices ha migh be anicipaed a he beginning of he accouning period. When here is a severe recession in he economy in say period, boh r defined by solving (9) and r * defined by solving (11) will become unusually low (or even negaive) and i is unlikely ha he resuling low (or negaive) user coss defined by (10) could be anicipaed in pracice. This limiaion of our analysis should be kep in mind, paricularly when looking a he user coss for This suggess ha exogenous esimaes for he cos of capial may be a more appropriae sraegy for forming user coss ha more closely approximae renal prices. If an exogenous r * is used, hen equaion (11) will no hold in general and i will be necessary o include pure profis (or losses) as a balancing iem in he SNA. However, we do no pursue his line of inquiry in he presen sudy. 7

10 he producion uni; i.e., i should be included as par of P O q O. This resolves he puzzle for reproducible capial sock componens. 16 Now suppose asse n is an invenory sock. Exernal purchases of he invenory sock will be par of inermediae inpu purchases, P I q I. Sales of he invenory iem will be refleced in he value of gross oupu, P O q O. Bu a he end of period, here will be a ne change in invenory socks equal o q Kn +1 q Kn. Hence i appears ha he erm P Kn +1 (q Kn +1 q Kn ) is missing on he righ hand side of (12). Noe ha since asse n is an invenory iem, we assume δ n 0 and so he erm P Kn +1 (1 δ n )q Kn = P Kn +1 q Kn is presen on he righ hand side of (12) and adding P Kn +1 (q Kn +1 q Kn ) o his erm gives us he end of period value of invenory socks, P Kn +1 q Kn +1, which is he righ answer from he perspecive of he Ausrian approach o producion heory. Bu saisical agencies rea invenory change over a period as par of secoral oupu and so he missing erm P Kn +1 (q Kn +1 q Kn ) should be included as a par of he value of gross oupu, P O q O. 17 This resolves he puzzle for invenory componens of he capial sock. Suppose asse n is a ype of land asse. As was he case for invenory iems, we assume ha he land depreciaion rae is δ n = 0 and again, we find ha he erm P Kn +1 (q Kn +1 q Kn ) is missing on he righ hand side of (12). This erm now represens he value of ne purchases of land of ype n over period, q Kn +1 q Kn, valued a end of period price for his ype of land, P Kn +1. Saisical agencies ypically do no rea land as an oupu or an inermediae inpu so in his case, he ne quaniy of land purchases over period, valued a end of period land prices, will no appear as par of he gross oupu (if land was sold during period ) or inermediae inpu of he secor (if land was purchased during period ). Thus we need o rea hese ne purchases as an inpu cos iem, so P Kn +1 (q Kn +1 q Kn ) should be added o he righ hand side of (12), bu his ne cos value is offse by he increase in he value of land holdings a he end of he period, so +P Kn +1 (q Kn +1 q Kn ) should be added o he righ hand side of (12). These wo enries cancel and so his resolves he puzzle for he land componens of he capial sock However, o make he accouning precisely consisen wih he Ausrian model of producion, we require ha he price used o value gross invesmens in asse n during period, P GIn, be equal o he end of period impued value for a uni of he nh capial sock. Seing P +1 Kn = P GIn will ensure consisency. In our empirical work, we used he BEA end of period price for reproducible unis of he capial sock which may be slighly differen from he corresponding invesmen price for he asse. 17 The BEA in paricular does include he value of invenory change as par of he gross oupu of an indusry. However, hey may no value he change in invenories a end of period prices of he invenory iem and so again here may be a sligh inconsisency in our empirical work due o his pricing difference. For a more complee reamen of he accouning problems associaed wih he reamen of invenories in he Ausrian model of producion, see Diewer (2005b). 18 Suppose some land is purchased during period a he price P * Kn where his purchase price is no equal o he end of period price of land, P +1 Kn. The quaniy of new land purchased will be equal o q +1 Kn q Kn. Then he erm P * Kn (q +1 Kn q Kn ) should be added o he righ hand side of (12) as a purchase of a primary inpu (a cos iem) and a he same ime, we should add he erm P +1 Kn (q +1 Kn q Kn ) o he righ hand side of (12) o value his land purchase a he end of period price of his ype of land (a revenue iem). Thus in principle, we should add he erm (P +1 Kn P * Kn )(q +1 Kn q Kn ) o he righ hand side of (12). If some land is sold during he period a he price P * Kn, hen q +1 Kn q Kn is negaive and is equal o minus he quaniy sold. In his case, we should sill add he erm (P +1 Kn P * Kn )(q +1 Kn q Kn ) o he righ hand side of (12) o make he accouning consisen wih our Ausrian model of producion. In our empirical work, we did no make hese adjusmens o he accouning ideniy given by (12); we simply assumed ha P * Kn is equal o our end of period price for he asse, P +1 Kn. 8

11 Real moneary balances are no regarded as producive inpus by naional income accounans. However, we rea real moneary balances as being necessary for producion. 19 Our accouning reamen of real balances is enirely analogous o our reamen of land and, as was he case wih land, he accouning decomposiion given by (9) or (12) is consisen wih our Ausrian heory of producion. Equaions (9) and (12) provided an accouning reamen of producion using ex pos asse prices. As menioned above, i is possible o build a similar accouning reamen of producion using ex ane asse prices; i.e., insead of using equaion (9) as our saring poin for our accouning decomposiion, we could have used equaion (11). The consisency of equaion (11) wih he Ausrian view of producion is similar o our analysis of he consisency of equaions (9) and (12) wih he Ausrian approach o producion heory. We conclude his secion wih an imporan observaion. Alhough we do no hink ha he Jorgensonian ex pos user coss are useful in all conexs, we do hink ha hey are he righ user coss o use in he conex of finding he ex pos rae of reurn on asses for a producion uni. Ex pos raes of reurn are exremely imporan indicaors of economic efficiency (along wih TFP growh raes) and i is imporan o measure hese raes of reurn accuraely o guide he allocaion of resources beween secors. 20 Before we use he daa ha are described in he Appendix o consruc ex pos raes of reurn on asses and TFP growh raes, in he following secion we describe he use of our daa base o consruc esimaes for real wages and labour produciviy. 3. Real Wages and Labour Produciviy Growh in Secors 1 and 2 In his secion, we draw on our daa base in order o calculae real wages and labour produciviy for he wo secors. 21 We sar wih he daa for Secor 1, he Nonfinancial Corporae Secor of he US economy. Value Added of Secor 1 in year, V VA1 (in billions of dollars), and he corresponding year price index, P VA1 are lised in Table 1. Define he year real value added of Secor 1 as Q VA1 V VA1 /P VA1 for = 1960,...,2014. The price and quaniy of employee labour in Secor 1, are P L1 and Q L1 and define he value of labour inpu in Secor 1 for year as V L1 P L1 Q L1. The labour series V L1 and P L1 are also lised in Table 1. The value of capial services in Secor 1 for year, V KS1, can be defined residually by subracing he value of labour inpu from value added; i.e., V KS1 V VA1 V L1. The shares of labour and capial services in value added are defined as s L1 V L1 /V VA1 and s KS1 V KS1 /V VA1. These Secor 1 value added shares along wih he value of capial services are also lised in Table This is consisen wih he cash-in-advance, or vending machine model of he demand for money consider by Fischer (1974). For a more exensive discussion of he issues surrounding money in he producion funcion, see Diewer and Fox (2015). 20 See Harberger (1998) on he imporance of he rae of reurn on asses. 21 This daa base is described in more deail in he Appendix of Diewer and Fox (2016). 9

12 A beginning of year price index for personal consumpion expendiures, P C, for = , is convered o a cenered consumer price index for year, P C *, by averaging P C and P C +1 ; i.e., define P C * (1/2)(P C + P C +1 ) for = 1960,..., This series, along wih he wage rae index P L1, was used o define he Secor 1 real wage for year, defined as follows: (13) RW 1 P L1 /P C * ; = 1960,...,2014. Finally, Secor 1 Labour Produciviy in year (relaive o he level in 1960), ProdL 1, is defined as follows (and is lised in Table 1): (14) ProdL 1 [Q VA1 /Q L1 ]/[Q VA /Q L ] ; = 1960,...,2014. The price of (value added) oupu in Secor 1 grew 4.56 fold over he sample period while employee wages grew fold. The geomeric raes of growh were 3.61% per year for oupu and 5.00% per year for wages. Real wages grew 2.25 fold over he sample period while labour produciviy grew 3.41 fold (he corresponding geomeric raes of growh were 1.51% and 2.30% per year). The sample average labour and capial services shares were 68.6% and 31.4% respecively. The upward rend in he capial services share is noiceable in Figure 1 which plos he series s L1, s KS1, P VA1, RW 1 and ProdL 1. Noe ha he capial services share finishes up a 36.7%, well above is long erm average of 31.4%. I can be seen ha real wages have grown very slowly since Noe also ha real wage growh was fairly similar o labour produciviy growh unil 1982 and hen labour produciviy grew subsanially faser han real wages. Finally, i can be seen ha labour produciviy in Secor 1 is sill growing fairly seadily since 2006 a he geomeric average rae of 1.20% per year bu his rae is lower han he hisorical average rae of 1.51% per year. We urn our aenion o Secor 2, he Nonfinancial Noncorporae Secor of he US economy. Value Added of Secor 2 in year, V VA2 (in billions of dollars) and he corresponding year price index, P VA2 are lised in Table 2. Define he year real value added of Secor 2 as Q VA2 V VA2 /P VA2 for = 1960,...,2014. The value and price of labour in Secor 2, V L2 and P L2 are lised in Table 2. The value of capial services in Secor 2 for year, V KS2, can be defined residually by subracing he value of labour inpu from value added; i.e., V KS2 V VA2 V L2. The shares of labour and capial services in value added for Secor 2 are defined as s L2 V L2 /V VA2 and s KS2 V KS2 /V VA2. These Secor 2 value added shares along wih he value of capial services are also lised in Table 2. Again, we use he consumpion price series P C * along wih he Secor 2 wage rae index P L2 o define he Secor 2 real wage for year, RW 2 P L2 /P C * for = 1960,...,2014. This series also appears in Table 2. Finally, Secor 2 Labour Produciviy of Secor 1 in year (relaive o he level in 1960), ProdL 2, is defined as follows (and lised in Table 2): (15) ProdL 2 [Q VA2 /Q L2 ]/[Q VA /Q L ] ; = 1960,..., This series was normalized o equal 1 in Noe ha he Secor 1 wage rae series P L1 is also normalized o equal 1 in

13 Table 1: Secor 1 Value Added V VA1, Value of Labour Inpu V L1, Value of Capial Services V KS1, Value Added Shares of Labour and Capial Services, s L1 and s KS1. Price of Labour P L1, Real Wage RW 1 and Labour Produciviy ProdL 1 for Year Year V VA1 V L1 V KS1 s L1 s KS1 P VA1 P L1 RW 1 ProdL Noe: All values are in billions of dollars. 11

14 Table 2: Secor 2 Value Added V VA2, Value of Labour Inpu V L2, Value of Capial Services V KS2, Value Added Shares of Labour and Capial Services, s L2 and s KS2. Price of Labour P L2, Real Wage RW 2 and Labour Produciviy ProdL 2 for Year Year V VA2 V L2 V KS2 s L2 s KS2 P VA2 P L2 RW 2 ProdL Noe: All values are in billions of dollars. 12

15 13

16 The price of (value added) oupu in Secor 2 grew 7.71 fold over he sample period (much higher han he Secor 1 price growh of 4.56 fold) while wages grew fold. The geomeric raes of growh were 3.61% per year for real value added, 3.86% per year for he value added deflaor and 4.81% per year for wages. Real wages grew 2.04 fold over he sample period while labour produciviy grew 2.36 fold, much lower han he 3.41 fold of labour produciviy in Secor 1. The long run average geomeric raes of growh of real wages and labour produciviy for Secor 2 were 1.33% and 1.61% per year while he corresponding growh raes for Secor 1 were 1.51% and 2.30% per year. Thus real wage growh and labour produciviy growh in Secor 2 were subsanially below heir Secor 1 counerpars. The sample average labour and capial services shares in Secor 2 were 56.7% and 43.3% (68.6% and 31.4% in Secor 1). I can be seen ha Secor 2 is much more capial inensive han Secor 1. The upward rend in he capial services share is very noiceable in Figure 2, which plos he series s L2, s KS2, P VA2, RW 2 and ProdL 2. Noe ha he capial services share finishes up a 50.4%, well above is long erm average of 43.3%. I can be seen ha real wages have grown very slowly since Noe also ha real wage growh sagnaed afer 2007 while labour produciviy coninued o grow. I can be seen ha he srucure of producion is enirely differen in he noncorporae nonfinancial secor as compared o he corporae nonfinancial secor. In he following secion, we will calculae price and quaniy indexes for he capial socks used in boh secors as well as he corresponding real and nominal capial oupu raios for he wo secors. 4. Capial socks and Capial Oupu Raios for Secors 1 and 2 We consruced chained Fisher capial sock price and quaniy indexes for Secor 1 using price and quaniy informaion for each of he nine asses ha are used as inpus, which are as follows: 1 = Equipmen; 2 = Inellecual propery producs; 3 = Nonresidenial srucures; 4 = Residenial srucures; 5 = Residenial land; 6 = Farm land; 7 = Commercial land; 8 = Beginning of year invenory socks, and 9 = Beginning of he year real holdings of currency and deposis. Denoe he resuling period price and quaniy indexes as P K1 and Q K1 for = 1960,...,2015. Define he Secor 1 capial sock value a he beginning of year as V K1 P K1 Q K1. Now define he year nominal and real capial oupu raios as V K/O,1 V K1 /V VA1 and Q K/O,1 Q K1 /Q VA1. V K1, Q K1, P K1, V K/O,1 and Q K/O,1 are lised in Table 3. I can be seen ha he Secor 1 aggregae capial sock price P K1 increased 7.36 fold over he sample period. The average geomeric growh raes for he price and quaniy of he Secor 1 capial sock were 3.70% per year and 2.74% per year respecively. The real capial oupu raio, Q K/O,1, declined more or less seadily from 2.47 in 1960 o 1.59 in The nominal capial oupu raio, V K/O,1, did no decline nearly as much due o increasing land prices We consruced chained Fisher land price and quaniy indexes for Secor 1 and hen compared he value of land o value added and he quaniy of land o he quaniy of oupu. The nominal land o oupu raio wen from 36.7% in 1960 o a peak of 51.2% in 2006, declined o 22.0% in 2012 and finished up in 2014 a 30.4%. The corresponding real land o oupu raio declined seadily from 36.7% in 1960 o 9.8% in The inclusion or exclusion of land from he producive asse base does make a significan difference o capial oupu raios. 14

17 The nominal capial oupu raio sared a 2.47 and ended up a 2.52 wih many flucuaions in beween (V K/O,1 had a low of 2.00 in 1966 and a high of 2.80 in 2009). We similarly consruced chained Fisher capial sock price and quaniy indexes for Secor 2 using he price and quaniy informaion for each of he foureen asses ha are used as inpus, 24 which are as follows: 1 = Equipmen held by sole proprieors; 2 = Equipmen held by parners; 3 = Equipmen held by cooperaives; 4 = Inellecual propery producs held by sole proprieors; 5 = Inellecual propery producs held by parners; 6 = Nonresidenial srucures held by sole proprieors; 7 = Nonresidenial srucures held by parners; 8 = Nonresidenial srucures held by cooperaives; 9 = Residenial srucures held by he noncorporae nonfinancial secor; 10 = Residenial land held by he noncorporae nonfinancial secor; 11 = Farm land held by he noncorporae nonfinancial secor; 12 = Commercial land held by noncorporae nonfinancial secor; 13 = Beginning of he year invenories held by he noncorporae nonfinancial secor, and 14 = Beginning of he year real holdings of currency and deposis by noncorporae nonfinancial secor. Denoe he resuling beginning of period price and quaniy indexes as P K2 and Q K2 for = 1960,...,2015. Define he Secor 2 capial sock value a he beginning of year as V K2 P K2 Q K2. Now define he year nominal and real capial oupu raios for Secor 2 as V K/O,2 V K2 /V VA2 and Q K/O,2 Q K2 /Q VA2. V K2, Q K2, P K2, V K/O,2 and Q K/O,2 are lised in Table 3. I can be seen ha he Secor 2 aggregae capial sock price P K2 increased fold over he sample period whereas he Secor 1 capial sock price increased only 7.36 fold. The average geomeric growh raes for he price and quaniy of he Secor 2 capial sock were 5.02% per year (3.70% per year for Secor 1) and 1.44% per year (2.74% per year for Secor 1) respecively. This large difference in growh raes beween secors is explained by he relaively very large land componen in he Secor 2 capial sock. 25 The price of land ends o grow more rapidly and he quaniy less rapidly han oher asses. The real capial oupu raio for Secor 2, Q K/O,2, increased (erraically) from 3.43 in 1960 o 4.01 in 1983 and hen declined o 2.07 in The corresponding nominal capial oupu raio, V K/O,2, did no decline nearly as much, due o increasing land prices. The nominal capial oupu raio sared a 3.43 and remained roughly consan unil 1969 and hen increased rapidly o hi a peak of 5.83 in 1982 and hen fell o 3.48 in 2012 and increased a lile o end up a 3.80 in I can be seen ha he real and nominal capial oupu raios are in general, much larger in Secor 2 han in Secor 1. The nominal and real capial oupu raios for Secors 1 and 2 are ploed in Figure 3, where he overall decline in he real capial oupu raios from 1983 is visible. The much higher capial oupu raios for Secor 2 over Secor 1 are also apparen. 24 The BEA Fixed Asse Tables are organized somewha differenly for he Nonfinancial Noncorporae Secor as compared o Secor 1, wih a decomposiion of Secor 2 ino subsecors. This led us o organize he capial sock daa for Secor 2 ino foureen raher han nine componens. 25 The average share of residenial land in Secor 2 value of he capial sock is 28.2%, farm land is 16.4% and commercial (nonresidenial and nonfarm) land is 7.1%. Thus he overall average land share in he oal value of Secor 2 asses is 51.6% and for reproducible asses is 48.4%. The average land share of asse value in Secor 1 is only 14.4% and he corresponding reproducible asse share is 85.6%. 15