US TFP Growth and the Contribution of Changes in Export and Import Prices to Real Income Growth

Transcription

1 US TFP Growh and he Conribuion of Changes in Expor and Impor Prices o Real Income Growh Erwin Diewer (UBC; UNSW) Paper Prepared for he IARIW-UNSW Conference on Produciviy: Measuremen, Drivers and Trends Sydney, Ausralia, November 26-27, 2013 Session 1: Perspecives on Inernaional Produciviy Performance Time: Tuesday, November 26, 10:30-11:00

2 1 US TFP Growh and he Conribuion of Changes in Expor and Impor Prices o Real Income Growh June 9, 2013 W. Erwin Diewer 1 Discussion Paper School of Economics Universiy of Briish Columbia Vancouver, Canada, V6T 1Z1 erwin.diewer@ubc.ca 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 and he US Deparmen of Agriculure, he paper calculaes he Mulifacor Produciviy (MFP) Growh for an Exended Business Secor of he US economy for he years The Exended Business Secor (EBS) consiss of he enire US economy less he inpus used and oupus produced by he Public Adminisraion secor and less he US housing secor. The sudy found ha Mulifacor Produciviy growh in he EBS averaged 1.157% per year, somewha higher han BLS MFP growh in he Privae Secor which averaged 0.962% per year. The sudy also produced esimaes of MFP where a ne oupu concep was used. Finally, he effecs of changes in he prices of US expors and impors on real income growh was calculaed using a ranslog model based on he work of Diewer and Morrison and Kohli. Key Words US Mulifacor produciviy growh, oal facor produciviy growh, ranslog gross and ne produc model, real income growh, erms of rade effecs. Journal of Economic Lieraure Classificaion Numbers C43, C67, C82, D24, E22, E43. 1 School of Economics, Universiy of Briish Columbia and School of Economics, Universiy of New Souh Wales. The financial assisance of he SSHRC is graefully acknowledged as are helpful commens by Ulrich Kohli and an unknown referee.

3 2 1. Inroducion This special issue of he Journal of Produciviy Analysis is devoed o honor he memory of Caherine Morrison-Paul, who died June 30, 2010 from complicaions resuling from leukemia. She was a leading exper in he measuremen of produciviy, producion heory and resource economics, wih over 60 journal aricles o her credi. She was a long ime conribuor o his Journal. My own connecion o Cahy daes back o working wih her while she did her Ph.D degree a he Universiy of Briish Columbia, which was compleed in While I was no her hesis advisor (who was Keizo Nagaani), I worked closely wih her because her hesis was on cos funcions and dualiy heory. Cahy and I wen on o work on research of muual ineres over he years wih hree published papers o show for our join effors. The firs published paper was Diewer and Morrison (1986) and he presen paper merely adaps he heory developed here in a relaively sraighforward way. This firs paper aemped o develop a producion heoreic framework where he conribuions of Toal Facor Produciviy (TFP) growh and changes in he erms of rade could be joinly evaluaed in a welfare oriened framework. In his firs paper, we used exac index number echniques in he conex of a ranslog echnology. In our second paper, Morrison and Diewer (1990a), we addressed he same issues of TFP growh and he effecs of changes in he erms of rade bu we developed a nonparameric approach o hese measuremen issues ha involved he use of averages of firs order approximaions o changes in various exogenous variables. In his second paper, we applied our firs and second approaches o hese measuremen quesions using Japanese daa and showed ha he wo approaches agreed reasonably well. Finally, in our hird paper, Morrison and Diewer (1990b) which appeared in he firs volume of he Journal of Produciviy Analysis, Cahy laid ou a general mehodological approach ha she used in many of her previous and subsequen papers. The radiional index number approach o he measuremen of TFP growh assumes compeiive price aking behavior, no fixed inpus and consan reurns o scale. Cahy showed how his radiional index number approach o TFP measuremen could be modified o deal wih he above complicaions, provided ha one could use addiional informaion obained by he use of economeric mehods o modify he radiional index number esimaes. Many observers have noed ha an improvemen in a counry s erms of rade has effecs ha are similar o an improvemen in a counry s produciviy growh. However, i is no sraighforward o work ou he exac magniude of each source of gain. Diewer (1983), Diewer and Morrison (1986), Morrison and Diewer (1990a) and Kohli (1990) (2004) (2006) developed producion heory mehodologies which enable one o obain index number esimaes of he conribuion of each ype of gain. In paricular, Kohli (2006)

4 3 criicized he Diewer and Morrison (1986) approach o his problem if rade was no balanced. Mehodologies ha could deal wih unbalanced rade were developed by Diewer, Mizobuchi and Nomura (2005) and Kohli (2004) (2006) and his approach will be followed in he presen paper. Thus secions 2 and 3 below presen he deails of his exac index number mehodology. In Diewer (2013), an annual daa base for an Exended Business Secor (EBS) was developed for he U.S. economy for he years This daa base is described and i is used o calculae he Toal Facor Produciviy (TFP) growh 2 of he U.S. EBS for he years A radiional user cos approach o he measuremen of capial services was used in his secion. Secion 6 reurns o he heoreical model developed in secions 2 and 3 and implemens i using U.S. daa; i.e., he real (gross) income generaed by he U.S. business secor is decomposed ino he produc of 6 explanaory facors. Secion 7 moves o a ne income framework; i.e., depreciaion is subraced from gross oupu o form ne oupu and real ne income generaed by he U.S. Exended Business Secor is decomposed ino explanaory facors. Secion 7 concludes. 2. The Producion Theory Framework In his secion, we presen he producion heory framework which will be used in his paper. 3 The main reference is Diewer and Morrison (1986). 4 Assume ha he business secor of he economy produces quaniies of M (ne) 5 oupus, y [y 1,...,y M ], which are sold a he posiive producer prices P [P 1,...,P M ]. We furher assume ha he business secor of he economy uses posiive quaniies of N primary inpus, x [x 1,...,x N ] which are purchased a he posiive primary inpu prices W [W 1,...,W N ]. In period, we assume ha here is a feasible se of oupu vecors y ha can be produced by he business secor if he vecor of primary inpus x is uilized by he business secor of he economy; denoe his period producion possibiliies se by S. We assume ha S is a closed convex cone ha exhibis a free disposal propery. 6 2 This is he erm used by Jorgenson and Griliches (1967) used o describe a concep ha is essenially oupu growh divided by inpu growh. The Bureau of Labor Saisics (1983) (2012) uses he equivalen erm Mulifacor Produciviy (MFP) growh. 3 Diewer, Mizobuchi and Nomura (2005), Diewer and Lawrence (2006), Diewer and Yu (2012) and Cho, Kim and Schreyer (2012) have used varians of his mehodology for Japan, Ausralia, Canada and Korea. 4 The heory also draws on Diewer (1983; ), Kohli (1990) (2003) (2004) (2006), Morrison and Diewer (1990a), Fox and Kohli (1998) and Chaper 24 in he IMF, ILO, OECD, Eurosa, UNECE and he World Bank (2009). 5 If he mh commodiy is an impor (or oher produced inpu) ino he marke secor of he economy, hen he corresponding quaniy y m is indexed wih a negaive sign. We will follow Kohli (1978) (1991) and Woodland (1982) in assuming ha impors flow hrough he domesic producion secor and are ransformed (perhaps only by adding ransporaion, wholesaling and reailing margins) by he domesic producion secor. The recen exbook by Feensra (2004; 76) also uses his approach. 6 The assumpion ha S is a cone means ha he echnology is subjec o consan reurns o scale. This is an imporan assumpion since i implies ha he value of oupus should equal he value of inpus in equilibrium. In our empirical work, we use an ex pos rae of reurn in our user coss of capial, which forces he value of inpus o equal he value of oupus for each period. The funcion g is known as he GDP funcion or he naional produc funcion in he inernaional rade lieraure; see Kohli (1978) (1991),

5 4 Given a vecor of oupu prices P and a vecor of available primary inpus x, define he period business secor GDP funcion, g (P,x), as follows: 7 (1) g (P,x) max y {P y : (y,x) S }. Thus business secor GDP depends on (which represens he period echnology se S ), on he vecor of oupu prices P ha he business secor faces and on x, he vecor of primary inpus ha is available o he marke secor. If P is he period oupu price vecor and x is he vecor of inpus used by he business secor during period and if he GDP funcion is differeniable wih respec o he componens of P a he poin P, x, hen he period vecor of business secor oupus y will be equal o he vecor of firs order parial derivaives of g (P,x ) wih respec o he componens of P: 8 (2) y = P g (P,x ). If he GDP funcion is differeniable wih respec o he componens of x a he poin P,x, hen he period vecor of inpu prices W will be equal o he vecor of firs order parial derivaives of g (P,x ) wih respec o he componens of x: 9 (3) W = x g (P,x ). The consan reurns o scale assumpion on he echnology ses S implies ha he value of oupus will equal he value of inpus in period : (4) g (P,x ) = P y = W x. The above maerial will be useful in wha follows bu of course, our focus is no on GDP; insead our focus is on he income generaed by he business secor or more precisely, on he real income generaed by he business secor. However, since business secor GDP is disribued o he facors of producion used by he business secor, nominal business secor GDP will be equal o nominal business secor income. An approximae welfare measure ha can be associaed wih business secor producion is he real income generaed by he business secor in period,, which is defined as he number of consumpion bundles ha he nominal income could purchase in period : (5) W x /P C = w x = p y = g (p,x ) Woodland (1982) and Feensra (2004; 76). I was inroduced ino he economics lieraure by Samuelson (1953). 7 The funcion g (P,x) will be linearly homogeneous and convex in he componens of P and linearly homogeneous and concave in he componens of x; see Diewer (1974; 136). Noaion: P y M m=1 P m y m. 8 These relaionships are due o Hoelling (1932; 594). Noe ha P g (P,x ) [ g (P,x )/ P 1,..., g (P,x )/ P M ]. 9 These relaionships are due o Samuelson (1953) and Diewer (1974; 140).

6 5 where P C > 0 is he period consumpion expendiures deflaor and he business secor period real oupu price p and real inpu price w vecors are defined as he corresponding nominal price vecors deflaed by he consumpion expendiures price index: 10 (6) p P /P C ; w W /P C ; The firs and las equaliy in (5) imply ha he period real income generaed by he business secor,, is equal o he period GDP funcion, evaluaed a he period real oupu price vecor p and he period inpu vecor x, g (p,x ). Thus he growh in real income over ime generaed by he business secor can be explained by hree main facors: (Technical Progress or Toal Facor Produciviy growh), growh in real oupu prices and he growh of primary inpus. Formal definiions for hese hree growh facors will be given below. Using he linear homogeneiy properies of he GDP funcions g (P,x) in P and x separaely, i can be shown ha he following counerpars o he relaions (2) and (3) hold using he deflaed prices p and w: (7) y = p g (p,x ) ; (8) w = x g (p,x ). ; Define a family of period produciviy growh facors or echnical progress shif facors (p,x,): 11 (9) (p,x,) g (p,x)/g 1 (p,x). Thus (p,x,) measures he proporional change in he real income produced by he business secor a he reference real oupu prices p and reference inpu quaniies used by he business secor x where he numeraor in (9) uses he period echnology and he denominaor in (9) uses he period 1 echnology. Thus each choice of reference vecors p and x will generae a possibly differen measure of he shif in echnology going from period 1 o period. I is naural o choose special reference vecors for he measure of echnical progress defined by (9): a Laspeyres ype measure L ha chooses he period 1 reference vecors 10 Our approach is similar o he approach advocaed by Kohli (2004; 92), excep he essenially deflaes nominal GDP by he domesic expendiures deflaor raher han jus he domesic (household) expendiures deflaor; i.e., he deflaes by he deflaor for C+G+I, whereas we sugges deflaing by he deflaor for C. Anoher difference in his approach compared o he presen approach is ha we resric our analysis o he marke secor GDP, whereas Kohli deflaes all of GDP. Our reamen of he balance of rade surplus or defici is also differen. [Deal wih his earlier] 11 This measure of echnical progress is due o Diewer and Morrison (1986; 662). A special case of i was defined earlier by Diewer (1983; 1063).

7 6 p 1 and x 1 and a Paasche ype measure P ha chooses he period reference vecors p and x : 12 (10) L (p 1,x 1,) = g (p 1,x 1 )/g 1 (p 1,x 1 ) ; (11) P (p,x,) = g (p,x )/g 1 (p,x ). Since boh measures of echnical progress are equally valid, i is naural o average hem o obain an overall measure of echnical change. If we wan o rea he wo measures in a symmeric manner and we wan he measure o saisfy he ime reversal propery from index number heory 13 (so ha he esimae going backwards is equal o he reciprocal of he esimae going forwards), hen he geomeric mean will be he bes simple average o ake. 14 Thus we define he geomeric mean of (10) and (11) as follows: 15 (12) [ L P ] 1/2 ; A his poin, i is no clear how we will obain empirical esimaes for he heoreical produciviy growh indexes defined by (10)-(12); his problem will be addressed shorly. We urn now o he problem of defining heoreical indexes for he effecs on real income generaed by he business secor due o changes in real oupu prices. Define a family of period s real oupu price growh facors (p 1,p,x,s): 16 (13) (p 1,p,x,s) g s (p,x)/g s (p 1,x). Thus (p 1,p,x,s) measures he proporional change in he real income produced by he business secor ha is induced by he change in real oupu prices going from period 1 o, using he echnology ha is available during period s and using he reference inpu quaniies x. Each choice of he reference echnology s and he reference inpu vecor x will generae a possibly differen measure of he effec on real income of a change in real oupu prices going from period 1 o period. Again, i is naural o choose special reference vecors for he measures defined by (13): a Laspeyres ype measure L ha chooses he period 1 reference echnology and reference inpu vecor x 1 and a Paasche ype measure P ha chooses he period reference echnology and reference inpu vecor x : 12 Saler (1960; 30-31) defined similar Laspeyres and Paasche measures of echnical change using cos funcions insead of GDP funcions. 13 See Fisher (1922; 64). 14 See he discussion in Diewer (1997) on choosing he bes symmeric average of Laspeyres and Paasche indexes ha will lead o he saisfacion of he ime reversal es by he resuling average index. 15 The heoreical produciviy change indexes defined by (10)-(12) were firs defined by Diewer and Morrison (1986; ) in he nominal GDP conex. 16 This measure of real oupu price change was essenially defined by Fisher and Shell (1972; 56-58), Samuelson and Swamy (1974; ), Archibald (1977; 60-61), Diewer (1980; ) (1983; 1055) and Balk (1998; 83-89).

8 7 (14) L (p 1,p,x 1, 1) = g 1 (p,x 1 )/g 1 (p 1,x 1 ) ; (15) P (p 1,p,x,) = g (p,x )/g (p 1,x ). Since boh measures of real oupu price change are equally valid, i is naural o average hem o obain an overall measure of he effecs on real income of he change in real oupu prices: 17 (16) [ L P ] 1/2. Finally, we look a he problem of defining heoreical indexes for he effecs on real income due o changes in inpu quaniies. Define a family of period real inpu quaniy growh facors (x 1,x,p,s): 18 (17) (x 1,x,p,s) g s (p,x )/g s (p,x 1 ). Thus (x 1,x,p,s) measures he proporional change in he real income produced by he business secor ha is induced by he change in inpu quaniies used by he business secor going from period 1 o, using he echnology ha is available during period s and using he reference real oupu prices p. Each choice of he reference echnology s and he reference real oupu price vecor p will generae a possibly differen measure of he effec on real income of a change in inpu quaniies going from period 1 o period. As usual, i is naural o choose special reference vecors for he measures defined by (17): a Laspeyres ype measure L ha chooses he period 1 reference echnology and reference real oupu price vecor p 1 and a Paasche ype measure P ha chooses he period reference echnology and reference real oupu price vecor p : (18) L (x 1,x,p 1, 1) = g 1 (p 1,x )/g 1 (p 1,x 1 ) ; (19) P (x 1,x,p,) = g (p,x )/g (p,x 1 ). Since boh measures of real inpu growh are equally valid, i is naural o average hem o obain an overall measure of he effecs of inpu growh on real income: 19 (20) [ L P ] 1/2. Recall ha business secor real income for period was defined by (5) as equal o nominal period facor paymens W x deflaed by he household consumpion price deflaor P C. I is convenien o define as he period chain rae of growh facor for real income: 17 The indexes defined by (13)-(16) were defined by Diewer and Morrison (1986; 664) in he nominal GDP funcion conex. 18 This ype of index was defined as a rue index of value added by Sao (1976; 438) and as a real inpu index by Diewer (1980; 456). 19 The heoreical indexes defined by (17)-(20) were defined in Diewer and Morrison (1986; 665) in he nominal GDP conex.

9 8 (21) / The Translog GDP Funcion and Exac Index Numbers We now follow he example of Diewer and Morrison (1986; 663) and assume ha he log of he period (deflaed) GDP funcion, g (p,x), has he following ranslog funcional form: 20 (22) lng (p,x) a 0 + m=1 M a m lnp m + (1/2) m=1 M k=1 M a mk lnp m lnp k + n=1 N b n lnx n + (1/2) n=1 N j=1 N b nj lnx n lnx j + m=1 M n=1 M c mn lnp m lnx n. Noe ha he coefficiens for he quadraic erms are assumed o be consan over ime. The coefficiens of he above ranslog funcional form mus saisfy cerain resricions in order for g o saisfy he appropriae regulariy condiions ha were lised earlier. 21 Diewer and Morrison (1986; 663) showed ha 22 if g 1 and g are defined by (22) above and here is compeiive profi maximizing behavior on he par of all marke secor producers for all periods, hen (23) = ; = 1,2,... where,, and are defined above by (21), (12), (16) and (20) respecively. In addiion, Diewer and Morrison (1986; ) showed ha, and could be calculaed using empirically observable price and quaniy daa for periods 1 and as follows: (24) ln = m=1 M (1/2)[(p m 1 y m 1 /p 1 y 1 ) + (p m y m /p y )] ln(p m /p m 1 ) = ln P T (p 1,p,y 1,y ); (25) ln = n=1 N (1/2)[(w n 1 x n 1 /w 1 x 1 ) + (w n x n /w x )] ln(x n /x n 1 ) = ln Q T (w 1,w,x 1,x ); (26) = / where P T (p 1,p,y 1,y ) is he Törnqvis (1936) oupu price index and Q T (w 1,w,x 1,x ) is he Törnqvis inpu quaniy index. Equaions (23) are in raes of growh. I is possible o obain counerpars o hese equaions in a levels form as follows. Thus we can express he level of real income generaed by he business secor in period in erms of an index of he echnology level or 20 This funcional form was firs suggesed by Diewer (1974; 139) as a generalizaion of he ranslog funcional form inroduced by Chrisensen, Jorgenson and Lau (1971). Diewer (1974; 139) indicaed ha his funcional form was flexible. 21 These resricions may be found in Diewer (1974; 139). 22 Diewer and Morrison esablished heir proof using he nominal GDP funcion g (P,x). However, i is easy o rework heir proof using he deflaed GDP funcion g (p,x) using he fac ha g (p,x) = g (P/P C,x) = g (P,x)/P C using he linear homogeneiy propery of g (P,x) in P.

10 9 of Toal Facor Produciviy in period T, of he level of real oupu prices in period A, and of he level of primary inpu quaniies in period, B. 23 Thus we use he growh facors, and as follows o define he levels T, A and B : (27) T 0 1 ; T T 1 ; = 1,2,... ; (28) A 0 1 ; A A 1 ; = 1,2,... ; (29) B 0 1 ; B B 1 ; = 1,2,.... Using he above definiions and he exac equaions (26), we can esablish he following exac relaionship for he level of real income generaed by he business secor in period,, and he period levels for echnology, real oupu prices and inpu quaniies: (30) / 0 = T A B ; = 1,2,.... For some purposes, i is convenien o decompose he aggregae period conribuion facor due o changes in all deflaed oupu prices ino separae effecs for each change in each oupu price. Similarly, i can someimes be useful o decompose he aggregae period conribuion facor due o changes in all marke secor primary inpu quaniies ino separae effecs for each change in each inpu quaniy. We firs model he effecs of a change in a single (deflaed) oupu price, say p m, going from period 1 o. Counerpars o he heoreical Laspeyres and Paasche ype price indexes defined by (14) and (15) above for changes in all (deflaed) oupu prices are he following Laspeyres ype measure Lm ha chooses he period 1 reference echnology and holds consan oher oupu prices a heir period 1 levels and holds inpus consan a heir period 1 levels x 1 and a Paasche ype measure Pm ha chooses he period reference echnology and reference inpu vecor x and holds consan oher oupu prices a heir period levels: (31) Lm g 1 (p 1 1,...,p 1 m 1,p m,p 1 m+1,..., p 1 M,x 1 )/g 1 (p 1,x 1 ); m = 1,...,M; (32) Pm g (p,x )/g (p 1,...,p m 1,p 1 m,p m+1,..., p M,x ) ; m = 1,...,M. Since boh measures of real oupu price change are equally valid, i is naural o average hem o obain an overall measure of he effecs on real income of he change in he real price of oupu m: 24 (33) m [ Lm Pm ] 1/2 ; m = 1,...,M. 23 This ype of levels presenaion of he daa is quie insrucive when presened in graphical form. I was suggesed by Kohli (1990) and used exensively by him; see Kohli (2003) (2004) and Fox and Kohli (1998). 24 The indexes defined by (31)-(33) were defined by Diewer and Morrison (1986; 666) in he nominal GDP funcion conex.

11 10 Under he assumpion ha he deflaed GDP funcions g (p,x) have he ranslog funcional forms as defined by (22) in he previous secion, he argumens of Diewer and Morrison (1986; 666) can be adaped o give us he following resul: (34) ln m = (1/2)[(p m 1 y m 1 /p 1 y 1 ) + (p m y m /p y )] ln(p m /p m 1 ) ; m = 1,...,M. Noe ha ln m is equal o he mh erm in he summaion of he erms on he righ hand side of (24). This observaion means ha we have he following exac decomposiion of he period aggregae real oupu price conribuion facor ino a produc of separae price conribuion facors; i.e., we have under presen assumpions: (35) = M. The above decomposiion is useful for analyzing how real changes in he price of expors (i.e., a change in he price of expors relaive o he price of domesic consumpion) and in he price of impors impac on he real income generaed by he marke secor. In he empirical illusraion which follows laer, we le M equal hree. The hree ne oupus are: Domesic sales (C+I+G); Expors (X) and Impors (M). Since commodiies 1 and 2 are oupus, y 1 and y 2 will be posiive bu since commodiy 3 is an inpu ino he marke secor, y 3 will be negaive. Hence an increase in he real price of expors will increase real income bu an increase in he real price of impors will decrease he real income generaed by he marke secor, as is eviden by looking a he conribuion erms defined by (34) for m = 2 (where y m > 0) and for m = 3 (where y m < 0). As menioned above, i is also useful o have a decomposiion of he aggregae conribuion of inpu growh o he growh of real income ino separae conribuions for each imporan class of primary inpu ha is used by he marke secor. We now model he effecs of a change in a single inpu quaniy, say x n, going from period 1 o. Counerpars o he heoreical Laspeyres and Paasche ype quaniy indexes defined by (18) and (19) above for changes in inpu n are he following Laspeyres ype measure Ln ha chooses he period 1 reference echnology and holds consan oher inpu quaniies a heir period 1 levels and holds real oupu prices a heir period 1 levels p 1 and a Paasche ype measure Pn ha chooses he period reference echnology and reference real oupu price vecor p and holds consan oher inpu quaniies a heir period levels: (36) Ln g 1 (p 1,x 1 1,...,x 1 n 1,x n,x 1 n+1,..., x 1 N )/g 1 (p 1,x 1 ) ; n = 1,...,N; (37) Pn g (p,x )/g (p,x 1,...,x n 1,x 1 n,x n+1,..., p N ) ; n = 1,...,N.

12 11 Since boh measures of inpu change are equally valid, as usual, we average hem o obain an overall measure of he effecs on real income of he change in he quaniy of inpu n: 25 (38) n [ Pn Pn ] 1/2 ; n = 1,...,N. Under he assumpion ha he deflaed GDP funcions g (p,x) have he ranslog funcional forms as defined by (22) in he previous secion, he argumens of Diewer and Morrison (1986; 667) can be adaped o give us he following resul: (39) ln n = (1/2)[(w n 1 x n 1 /w 1 x 1 ) + (w n x n /w x )] ln(x n /x n 1 ); n = 1,...,N. Noe ha ln n is equal o he nh erm in he summaion of he erms on he righ hand side of (25). This observaion means ha we have he following exac decomposiion of he period aggregae inpu growh conribuion facor ino a produc of separae inpu quaniy conribuion facors; i.e., we have under presen assumpions: (40) = N. 4. Oupu and Inpu Aggregaes and Convenional Produciviy Growh for he U.S. In Diewer (2013), an annual daa base for an Exended Business Secor (EBS) was developed for he U.S. economy for he years The oupu concep for his EBS was defined o be he GDP of he enire economy in year (a producer prices) less he gross value of housing services less general governmen value added. I is obvious ha he general governmen secor does no engage in compeiive profi maximizing behavior so i is naural o exclude his secor from he business secor. I is also naural o exclude he services of Owner Occupied Housing (OOH) since hese services are impued and are no based on profi maximizing behavior. However, he EBS concep also excluded he services of rened housing. The reason for his exclusion is ha accurae informaion on he sock of renal housing and he value of he land ha he renal sock sis on is no available so i was decided o exclude all residenial housing services from he business secor concep. Diewer (2013) liss price and quaniy index daa for he following ne oupus of he ECB: C (personal consumpion less housing services), I (invesmen), G (deliveries of goods and services o he general governmen secor by he EBS), 8 classes of expors of goods, 9 classes of impors of goods, expors of services and impors of services. The source for hese series was he Bureau of Economic Analysis (2012) (BEA). Diewer also consruced a price and quaniy series for aggregae labor inpu L ino he Exended Business Secor based on BEA informaion and informaion from he Bureau of Labor Saisics (2012) Produciviy Program. Informaion from he BEA (2012) was used o consruc series for 27 ypes of reproducible capial and invenory socks used by he 25 The indexes defined by (36)-(38) were defined by Diewer and Morrison (1986; 667) in he nominal GDP funcion conex.

13 12 Exended Business Secor. Finally, informaion from he USDA (2012a) (2012b) and from he Board of Governors of he Federal Reserve (2012) was used o consruc esimaes for he price and quaniy of agriculural and non-agriculural land used by he ECB. Thus in oal, asse socks used by he EBS for 29 differen asse classes were consruced. Denoe he price indexes for consumpion, invesmen and ne deliveries of he EBS o he general governmen secor as P C, P I and P G and denoe he corresponding quaniy indexes as Q C, Q I and Q G. Define P D, he year price of domesic EBS producion, as he chained Törnqvis price index of P C, P I and P G. P D is lised in Table 1 below and he corresponding implici Törnqvis quaniy index Q D is lised in Table 2 below. Define P X as he chained expor Törnqvis price index of he 9 expor price series lised in Diewer (2013), P X1,...,P X9. This aggregae expor price series is lised in Table 1 below and he corresponding implici Törnqvis quaniy index Q X is lised in Table 2 below. Similarly, define P M as he chained Törnqvis impor price index of he 10 impor price series (adjused for ariffs) lised in Diewer (2013), P M1,...,P M10. This aggregae impor price series is lised in Table 1 below and he corresponding implici Törnqvis quaniy indexes Q M is lised in Table2 below. We define an EBS aggregae oupu price index for year, P Y, as a chained Törnqvis price index of he price indexes P D, P X, P M wih quaniy weighs Q D, Q X, Q M. Denoe he corresponding implici Törnqvis oupu index as Q Y. The series P Y and Q Y are lised in Tables 1 and 2. Noe ha all price series have been normalized o equal uniy in Thus he corresponding quaniy unis are in billions of consan 1987 dollars. 26 Table 1: Price Indexes for EBS Oupu and Inpu Aggregaes and TFP Year P C P D P X P M P L P K P KW P Y P Z TFP Noe also ha he producer price of he consumpion aggregae, P C, is also lised in Table 1. This is he price index ha will be used o deflae nominal prices ino real prices.

14 GAG The las rows of Tables 1 and 2 lis he Geomeric Average Growh (GAG) rae for each of he series in he corresponding column. Table 2: Quaniy Indexes for EBS Oupu and Inpu Aggregaes and Real Capial Oupu Raios Year Q C Q D Q X Q M Q L Q K Q KW Q Y Q Z Q KW /Q Y GAG We urn our aenion o aggregae inpu series. Tables 1 and 2 above lis Diewer s esimaes for he price and quaniy of EBS labour services, P L and Q L. Denoe P KW as he beginning of he year chained Törnqvis price index of he 29 EBS capial socks lised in Diewer (2013) and Q KW as he corresponding implici quaniy index. These indexes are also lised in Tables 1 and 2 respecively. The las column of Table 2 also liss he real capial oupu raios for he Exended Business Secor, Q KW /Q Y, for he years I can be seen ha he capial oupu raio declined from 2.37 in 1987 o 1.88 in 2011, an average rae of decline of abou 1% per year. I is necessary o explain how user coss of capial were consruced. Before doing his, i is useful o lis various approximae ax raes ha Diewer (2013) developed; see Table 3

15 14 below. The various axes are defined as follows: C is he year consumpion ax; MG is he year ariff rae on impors of goods; L is he year ax rae on labor (income axes plus social securiy conribuions); P is he year propery ax rae on srucures and business and agriculural land, 27 K is he (sock) rae of business income axaion as a fracion of beginning of year asse value and BI is he rae of business income axaion as a fracion of ne operaing surplus in year. The las column of Table 3 also liss r, he balancing afer ax Inernal Rae of Reurn in year, which will be explained more fully below. The las row in Table 3 liss he arihmeic average of he various raes in each column. Table 3: Tax Raes on Oupus and Inpus for he US Economy and he Balancing Afer Tax Rae of Reurn on Asses r : Year Average C MG L P Using he asse specific propery ax raes Pn, he (sock) general business ax raes K, he depreciaion raes n for n = 1-29 ha are lised in Diewer (2013) along wih he corresponding asse prices and quaniies, P Kn and Q Kn, user coss U n for he 29 asse classes can be defined as follows: 28 K BI r 27 In equaions (41) and (42) below, Pn 0 if asse n is no a srucure or a land asse and Pn P is asse n is a srucure or land asse. 28 For addiional maerial on user coss and many hisorical references, see Jorgenson (1963) (1989) (2012), Hall and Jorgenson (1967), Chrisensen and Jorgenson (1969), Harper, Bernd and Wood (1980), Diewer (1980) (2005a), Schreyer (2001) (2009), Gu (2012) and Diewer (2012).

16 15 (41) U n [r + K + Pn + n ]P Kn ; n = 1,...,29 ; = 1987,...,2011 where r is suiable real afer ax cos of capial ha applies o he enire exended business secor in year. We follow naional income accouning convenions and define r o be he balancing real rae of reurn; i.e., i is he rae of reurn ha is consisen wih he year value of business secor ne oupu being equal o he value of primary inpus used by he business secor in year, where he user coss defined by (41) are used as prices for he beginning of he year capial inpus. Thus r can be deermined as he soluion o he following linear in r equaion for = 1961,...,2011: (42) P C Q C + P I Q I + P G Q G + P X Q X P M Q M = P L Q L + n=1 29 [r + K + Pn + n ]P Kn Q Kn ; = 1987,...,2011 where he various price and quaniy series were defined above. The resuling series of balancing real raes of reurn are lised in Table 3 above. I should be noed ha r can be inerpreed as a real ineres rae; i.e., i is he income earned by he business secor in year relaive o he saring capial sock, valued a he average invesmen prices for he period. This explains why we have no included a capial gains erm in he user cos formulae defined by (41). 29 Denoe P K as he year capial services price index, which is he implici chained Törnqvis price index of he 29 user coss U n wih he capial socks Q Kn as he corresponding quaniies and le Q K be he corresponding direc chained Törnqvis capial services quaniy index. 30 The aggregae price and quaniy indexes for capial services, P K and Q K, are lised in Tables 1 and 2. From he las row in Table 2, i can be seen ha he Geomeric Average Growh (GAG) rae of capial services over he sample period was 2.66% per year, abou 0.88 percenage poins per year bigger han he corresponding rae of growh of he EBS capial sock, which grew a 1.78% per year. The higher rae of growh of capial services is explained by he fac ha machinery and equipmen capial sock componens end o grow more rapidly han srucures componens bu he higher depreciaion raes for M&E inpus leads o a higher user cos weigh for M&E inpus and relaively lower user cos weighs for srucures as compared o he corresponding sock weighs. Thus overall capial services grew more rapidly han he corresponding aggregae capial sock due o his differenial weighing effec. Once he labour and capial aggregaes have been consruced, we can consruc a direc Törnqvis quaniy inpu aggregae of Q L and Q K which we denoe by Q Z, which is lised in Table 2. The corresponding implici aggregae inpu price index, P Z, is lised in Table 1. The produciviy level in year of he U.S. Exended Business Secor, TFP, is defined as he aggregae year oupu, Q Y divided by aggregae year inpu, Q Z : We have essenially absorbed he capial gains (or losses) erm ino r. 30 Noe ha oupu componens of GDP were aggregaed using direc chained Törnqvis price indexes whereas inpu componens of GDP are aggregaed using direc chained Törnqvis quaniy indexes. The reason for his change is due o our desire o apply equaions (24) and (25) laer in he paper. 31 This is also known as Mulifacor Produciviy or Toal Facor Produciviy; see he BLS (1983) or Schreyer (2001).

17 16 (43) TFP Q Y /Q Z ; = 1987,..., Produciviy growh for year,, is defined as he produciviy level in year divided by he previous year s produciviy level: (44) TFP /TFP 1 ; = 1988,..., The las column of Table 1 above liss he produciviy levels, TFP, for he EBS for he years The Geomeric Average Growh rae for TFP over his period was 1.157% per year, which is quie saisfacory for an advanced counry. 32 I can be seen ha TFP for he EBS fell for only 3 years: 1991, 2008 and I is possible o compare our TFP esimaes for our EBS wih he Bureau of Labor Saisics (2012) Mulifacor Produciviy (MFP) esimaes for he U.S. Privae Secor; 33 see Char 1 below. Our TFP growh in he EBS averaged 1.157% per year, somewha higher han BLS MFP growh in he Privae Secor which averaged 0.962% per year, a rae ha is abou 20% lower. Deermining he exac causes of he differences is a ask for fuure research. 34 Char 1: TFP and MFP for he U.S. Economy: TFP MFP 32 The arihmeic average of he TFP growh raes for he enire period was 1.16% per year. For he period, he arihmeic average of he TFP growh raes was 1.19% per year and for he period, he arihmeic average of he TFP growh raes was 1.14% per year. 33 See he BLS (2012) or Table 32 in Diewer (2013) for he MFP series. 34 The mos likely sources of he differences are: (i) differen scopes, in paricular our exclusion of rened housing services (included in he BLS Privae secor) and inclusion of he governmen enerprise secor (excluded in he BLS Privae Secor) ; (ii) some uni value ype aggregaion bias in he aggregaion of capial in he op down mehod (see he discussion in Jorgenson (2012; 12), Jorgenson and Schreyer (2012), Gu (2012) and Diewer (2012) on his source of bias); (iii) differing land series and (iv) differen user cos formulae.

18 17 Produciviy growh is no necessarily he enire sory behind he growh in living sandards: if he price of U.S. expors increases more rapidly han he price of U.S. impors, hen he real income generaed by he business secor should increase. This erms of rade effec is no aken ino accoun in he above produciviy compuaions. Thus in he following secion, we implemen he ranslog real income mehodology explained in secions 2 and 3 above and his approach will enable us o assess he conribuion o U.S. living sandards of changes in he U.S. erms of rade. 5. Explaining Real Income Growh Generaed by he Exended Business Secor: he Gross Oupu Approach The basic mehodology used in his secion was explained in secions 2 and 3 above bu can be summarized as follows. The business secor faces exogenous domesic and inernaional prices for he ne oupus i produces: domesic oupus, expors and (minus) impors. The business secor also uilizes inpus of labour and capial in order o produce is oupus. The value of oupus produced by he business secor less he value of impors used (value added) mus evenually flow back o he labour and capial primary inpus ha were used o produce value added. This is he (gross) income generaed by he business secor. We divide his gross income in year by he price of consumpion in year, P C, in order o urn his nominal income ino real income equivalens ; 35 his real income is he number of consumpion bundles ha could be purchased by he owners of he labour and capial inpus ha were used in year by he U.S. Exended Business Secor. Divide each of he prices P D, P X, P M, P L and P K by he price of consumpion, P C, in order o form he corresponding real oupu and inpu prices facing he business secor in each year. There are six quaniaive facors ha can be used o explain he real income generaed by he business secor in year : The price of domesic producion P D (an aggregae of C+I+G) relaive o he price of consumpion in year, P C ; The price of expors relaive o he price of consumpion in year, P X /P C ; The price of impors relaive o he price of consumpion in year, P M /P C ; The quaniy of labour used by he business secor in year, Q L ; The quaniy of capial used by he business secor in year, Q K and The level of echnology of he business secor in year. The formal model explained earlier, based on he work of Diewer and Morrison (1986), allows us o decompose he growh of real income from year 1 o, / 1, ino muliplicaive year o year conribuion facors D, X, M, L, K and ha describe he effecs of changes in he six explanaory variables lised above going from year 1 o. Our ranslog model leads o he following equaion which decomposes he year o year 35 Formally, P Y Q Y /P C = P Z Q Z /P C. Thus can be defined for each year using he informaion in Tables 1 and 2.

19 18 growh in real income generaed by he business secor, / 1, ino a produc of six year o year explanaory conribuion facors: (45) / 1 = D X M L K ; = 1988, 1963,...,2011. Thus if D is greaer han one, his means ha he domesic price of oupu grew faser han he price of consumpion going from year 1 o and D measures he conribuion of rising real domesic oupu prices o he growh in real income. Similarly, if X is greaer han one, his means ha U.S. expor prices grew faser han he price of consumpion going from year 1 o and X measures he conribuion of rising real expor prices o he growh in real income generaed by he EBS. However, if if M is greaer han one, his means ha U.S. impor prices did no increase as quickly as he price of consumpion going from year 1 o and M measures he conribuion of falling real impor prices o he growh in real income generaed by he business secor. If L is greaer han one, hen business secor labour inpu increased going from year 1 o and L measures he conribuion of he increase in labour inpu o he growh in real income generaed by he EBS. Similarly, if K is greaer han one, hen business secor (gross) capial services inpu increased going from year 1 o and K measures he conribuion of he increase in capial inpu o he growh in real income generaed by he EBS. Finally, if is greaer han one, hen he efficiency of he EBS increased from year 1 o and measures he conribuion of he efficiency increase o he growh in real income generaed by he U.S. business secor. These year o year conribuion facors are lised in Table 4 along wih he (arihmeic) averages of hese conribuion facors in he las hree rows of he Table. 36 The las column in Table 4 gives he produc of he real expor and real impor price conribuion facors, XM, defined as XM X M. Roughly speaking, XM is a erms of rade conribuion facor; i gives he conribuion o real income growh of he combined effecs of real changes in he inernaional prices facing he U.S. business secor. 37 Table 4: Exended Business Secor Annual Growh in Real Income and Annual Conribuion Facors Year / 1 D X M L K XM The hird row from he boom gives he arihmeic average over he years and he remaining rows give he averages over he years and Noe ha he conribuion facors are one plus he growh raes. 37 Ulrich Kohli has poined ou ha his is a sligh abuse of erminology. Sricly speaking, he erms of rade is he price of expors over he price of impors and hence involves only wo prices. Our definiion of XM involves hree prices: he price of expors, he price of impors and he price of domesic consumpion. Our erms of rade conribuion facor is he rae of change counerpar o Kohli s (2006; 50) (2007) rading gains facor.

20 Ave Ave Ave Viewing Table 4, i can be seen ha over he enire sample period, he real income generaed by he Exended Business Secor grew a 2.46% per year. However, he average raes of growh were very differen during he 12 years prior o 2000 and he 12 years subsequen o During he pre 2000 period, real income grew a a 3.28% per year rae and only a a 1.63% rae in he pos 2000 period. During he pre 2000 period, he posiive average growh facors were: labor growh (+1.65% per year), TFP growh (+1.19% per year), capial services growh (+0.85% per year) and falls in real impor prices (+0.42% per year). The negaive growh facors for he pre 2000 period were: falls in real domesic prices 38 ( 0.52% per year) and falls in real expor prices ( 0.34% per year). During he pos 2000 period, he posiive average growh facors were: TFP growh (+1.14% per year), capial services growh (+0.71% per year) and a iny increase in real expor prices (+0.01% per year). The negaive growh facors for he pos 2000 period were: increases in real impor prices 39 ( 0.15% per year), falls in real domesic prices 40 ( 0.04% per year) and decreases in labor inpu ( 0.04% per year). Thus TFP growh and growh in capial services inpu were major posiive conribuors o real income growh in boh periods bu labor inpu growh changed from being a major posiive conribuor o a small negaive conribuor and changes in real expor and impor prices changed from a small posiive conribuor (+0.08% per year) in he pre 2000 period o a larger negaive conribuor ( 0.14% per year) in he pos 2000 period. The annual change informaion in Table 4 can be convered ino levels using equaions (30), (35) and (40) in secion 3 above. Thus le T, A D, A X, A M, B L, B K and A XM be he cumulaed producs of he annual link facors, D, X, M, L, K and XM 38 This fall in real domesic prices was caused by invesmen prices ha increased much more slowly han consumpion prices. 39 The price of energy impors increased dramaically during his period. 40 This fall in real domesic prices was caused by invesmen prices ha increased much more slowly han consumpion prices.