The Sensitivity of Capital Services Measurement: Measure all assets and the cost of capital

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1 The Sensiiviy of Capial Services Measuremen: Measure all asses and he cos of capial Rober Inklaar Groningen Growh and Developmen Cenre, Universiy of Groningen May 2008 Absrac The measuremen of capial inpus is sill a conenious issue: many choices have o be made ha have poenially large effecs on he resuling capial inpu series, some enailing differing assumpions abou firm behaviour. This paper compares a large number of mehodological choices and heir impac on US capial services growh a he indusry and aggregae level. The resuls show ha measuring all asses, in paricular inangible asses, and he choice for he rae of reurn maer subsanially, while oher choices are less imporan. I also argue ha for pragmaic reasons, an exernal rae of reurn is preferable because i is a ransparen and robus choice. This paper is wrien as par of he EU KLEMS projec on Growh and Produciviy in he European Union. This projec is funded by he European Commission, Research Direcorae General as par of he 6h Framework Programme, Prioriy 8, Policy Suppor and Anicipaing Scienific and Technological Needs.

2 Inroducion A new building, piece of machinery or sofware package will be used in producion for a considerable period of ime. For how long ends o differ, where buildings have service lives measured in decades, machinery has a producive life of around en o weny years and sofware needs o be replaced afer hree o five years. The key challenge in measuring capial as a producion facor is how o accoun for hese differences across asses and ge an accurae measure of he overall service flow from hese capial asses. In his paper, I es he sensiiviy of capial inpu measures o he mehodological choices ha are made. 1 As he concep of capial services will likely be recognized in he upcoming revision of he Sysem of Naional Accouns (SNA), an analysis of he imporance of various mehodological choices will be useful for saisical agencies seeking o inroduce capial services measures in heir Naional Accouns. I show ha he choice for he rae of reurn is paricularly imporan. 2 A furher imporan issue I deal wih is which asses o measure and include. In curren inernaional comparisons, such as he EU KLEMS daabase, 3 only fixed reproducible asses can be included. However, land and invenories are also par of he producive capial sock and including hem maers subsanially. 4 Inangible invesmen is anoher imporan caegory. In he new SNA, he recommendaion will likely be made o capialize research and developmen spending and much of sofware spending is already recognized as an invesmen. Using he daa and classificaion of Corrado, Hulen and Sichel (2006), I show ha including inangible is also of firs-order imporance. My approach in his paper is mainly pragmaic. I is obviously imporan o use capial inpu measures ha are informed by economic heory, bu as i urns ou, some refinemens ha are imporan from a heoreical perspecive urn ou o have only a limied impac on he growh of capial inpu. Of key imporance is accouning for he heerogeneiy of asses. A dollar or euro worh of buildings will yield subsanially lower producive services han a compuer because he user cos of capial is lower. Jorgenson and Griliches (1967) were among he firs o argue his poin and i remains as imporan as i was back hen. However, he specificaion of he user cos is as conenious as ever. In brief, he user cos consiss of a required rae of reurn on capial, he depreciaion rae, an asse revaluaion erm and an adjusmen for he ax reamen of capial asses. 5 In his paper, I do no discuss he esimaion of he depreciaion rae or he sensiiviy o differen depreciaion rae esimaes. 6 However, he oher componens of he user cos are deal wih in deail. The enire sensiiviy analysis is based on daa for he Unied Saes. The main reason is ha some daa are no available for oher counries. In paricular, here is US daa on all he necessary ax parameers and capial socks for land, invenories and inangibles. 7 Mos if no all of hese daa are lacking for oher counries. This also highlighs an imporan secondary aim of his paper. The main goal is o evaluae he sensiiviy of capial inpu measures o he assumpions used, bu he resuls can 1 The focus is on producive socks of capial used in producion, no wealh socks; see Schreyer (2008) for more discussion on his disincion. 2 This discussion is complemenary o ha of Oulon (2007) based on daa for he UK. 3 See 4 See e.g. Diewer (2008). 5 See Hall and Jorgenson (1967). 6 For more discussion on ha opic, see he Schreyer (2008) manual on capial measuremen. 7 The basic invesmen daa are from he BEA; axes, land and invenories are from he BLS and invesmen in inangible asses is from Corrado, Hulen and Sichel (2006). 2

3 inform wheher i is useful for oher counries o develop measures for some conceps ha hey currenly do no measure. In relying on US daa, his exercise is comparable o ha of Harper e al. (1989) bu he range of mehodological choices considered is larger. An inernaional comparison, such as Erumban (2008), is also very insighful bu would resric he range of mehodological choices. The resuls show he imporance of including inangible asses and he choice for he rae of reurn. The inclusion of land and invenories and ax parameers are comparaively somewha less imporan, bu may sill meri furher sudy and daa collecion. The specificaion chosen for he asse revaluaion erm and he reamen of negaive user coss are of secondary imporance. Choosing he rae of reurn is paricularly conenious. On heoreical grounds, one should use an ex-pos or inernal measure of he rae of reurn, as was argued by Bernd and Fuss (1986). However, his ends o cause problems in pracice, some of which may be relaed o he assumpions underlying he heoreical framework. The hybrid soluion proposed by Oulon (2007) does no solve many of hese problems and ends lead o subsanially higher growh raes han eiher he ex-ane or ex-pos approach. Using an ex-ane or exernal measure of he rae of reurn avoids hese issues and is hus preferred from a pragmaic poin of view. 8 Concepual framework To frame he discussion, I firs discuss he basic approach o capial measuremen. 9 Given invesmen (a consan prices) I in indusry i, asse k a ime, and geomeric depreciaion rae, he capial sock A can be esimaed using he perpeual invenory mehod as follows: A, = 1 δ A + I,. (1) i k, ( k ) i, k, 1 i, k We are ineresed in he service flow from each of he asses raher han he value of asses accumulaed and he value of sock A is in general no a good indicaor of he conribuion of A o overall capial services. For example, buildings make up he larges par of he oal sock by value, bu he long service life of a building implies a long flow of services from hese buildings. To capure he marginal produc of a capial asse, a user cos of capial is esimaed, following Hall and Jorgenson (1967). This requires assuming ha firms are price akers in he marke for capial asses and hence, marginal coss equal he marginal produc of capial. The basic user cos formula of Hall and Jorgenson (1967) is: u 1 ITC τ Z k, k, i, k, = Ri, + δ k vi, k, + τ Tk, Ri, + δ k vi, k, 1 τ + τ, P P (2) ( ) ( ) wih ITC he invesmen ax credi rae he corporae ax rae, Z he presen value of depreciaion allowances, R he rae of reurn on capial, v he asse revaluaion erm and P he propery ax rae. How he rae of reurn and asse revaluaion erm are implemened in pracice will be discussed below. Given he user cos, capial compensaion C, or he income sream associaed wih he asse, can be calculaed as: I (3) C i, k, = ri, k, Ai, k, ui, k, pi, k, Ai, k, 8 Noe ha his is also he choice made by Saisics Neherlands in heir produciviy accouns, mosly in order o make he fewes number of heoreical assumpions, see Balk (2008). 9 See oher sudies for he formal derivaions of wha follows, e.g. Oulon (2007), Harper, Bernd and Wood (1989) or Bernd and Fuss (1986). 3

4 where r is he renal price of he capial asse and p I he invesmen price. Capial services K can be calculaed as a Törnqvis aggregae of individual capial socks, using capial compensaion as weighs. The wo-period capial compensaion shares are given by: (4) c i, k, 1 = 2 C C k i, k, 1 i, k, 1 + k C i, k, C i, k, so ha he growh in capial services can be calculaed as: (5) K & i = ci k A&,,, i, k,, k, where a do over a variable denoes percenage growh. The key issue is how o implemen equaion (2) in pracice. Jorgenson and associaes (see e.g. Jorgenson e al. 2005) assume perfec foresigh and perfec compeiion in heir approach o measuring capial inpu. In ha case, v is he acual price change of he invesmen good during ha period, so ha (2) can be rewrien as: u i k = T Ri + k p&,,, i, k, δ + τ I P (6) ( ) Furhermore, he assumpion of perfec compeiion implies ha he sum of capial income equals residual income, i.e. indusry oupu minus inermediae purchases and labor compensaion. Denoing residual income by CAP, R can be solved from he following equaion: I I P I (7) CAP i, = Ci, k, = T ( Ri, + δ k p& i k ) + p,, τ i, k, Ai, k, k ( ) k R I is referred o as he inernal rae of reurn. This approach has he advanage of a consisen sysem of accouns as all oupu is aribued o facor income. In a more recen conribuion, Oulon (2007) asks which rae of reurn o use in a more general seing wih uncerainy. In such a seing, firs used by Bernd and Fuss (1986), firms firs choose heir capial invesmens and when uncerainy abou inpu prices, demand and echnology is resolved in he nex period, hey choose heir oher inpus. As a resul, he inernal rae of reurn ha is observed ex pos gives he appropriae measure of he marginal produc of capial and in general, he ex ane and ex pos cos of capial will differ. Furhermore, he ex pos rae of reurn will in general differ across asses. Oulon proposes a hybrid approach where he uses an ex ane rae of reurn o esimae aggregae capial services growh according o equaions (3)-(5) and hen use he ex pos rae o esimae he conribuion of capial o oupu growh. Anoher source of many pracical problems wih ex pos user coss is he asse revaluaion erm. Asse prices end o flucuae subsanially from year o year and in pracice, rapidly rising asse prices are he main reason for negaive user cos esimaes. Again, from a heoreical perspecive, an ex pos user cos based on an inernal rae of reurn and realized asse price changes is he correc measure of he marginal produc of capial (under he assumpion discussed above, see Oulon, 2007). Following his line of reasoning hough would eiher mean acceping negaive marginal producs or making adhoc adjusmens. There is no heoreical reason for rejecing negaive marginal producs bu again, from a pracical vanage poin i seems hard o accep ha in cerain years a building would conribue negaively o oupu, while in mos years he conribuion would be posiive A furher pracical problem is ha he of-used Törnqvis index requires posiive weighs o aggregae across asses and hence, posiive user coss. 4

5 As menioned above, a heoreically consisen ex pos rae of reurn will in general differ across asses, making an empirical implemenaion impossible (Oulon, 2007). The nex bes hing for hose who wan o say as close as possible o he heoreical framework would be o use he inernal rae of reurn based on equaion (7) in combinaion wih acual annual asse price changes. However, his means ha in case of, say, a negaive user cos, an alernaive inerpreaion migh be ha he rae of reurn on ha asse is much higher han he inernal rae of reurn. Trying o avoid he pracical problems discussed above by resoring o an ex ane rae and anoher specificaion for he asse revaluaion erm leads o he problem ha here are innumerable ad-hoc soluions o choose from. One of he main pracical drawbacks of relying on ex pos reurns is ha he conribuion of capial o growh is highly influenced by any measuremen errors in oupu (a curren prices) and labour compensaion. Basu e al. (2008) have shown ha a leas in finance, curren oupu measuremen is by no means wihou error and esimaing he labour compensaion of self-employed is also nooriously uncerain. Regarding he ex ane rae of reurn, here is some guidance from he lieraure. Gilchris and Zakrajsek (2007) use corporae bond daa o consruc firm-specific user coss of capial and find a srong relaionship beween his user cos and firm invesmen. This implies ha a rae of reurn based on financial marke daa ha akes ino accoun he risk associaed wih invesmen of firms is a good ex ane cos measure. In he Bernd/Fuss-Oulon models, his cos measure drives invesmen so on average (i.e. in he absence of shocks), he cos measure should be he same as he ex pos reurn on capial. Harper e al. (1989) use he yield on corporae bonds wih a Baa raing as heir ex ane measure. Here I use he (risk-free) 10-year Treasury rae plus he risk premium for commercial and indusrial loans of US commercial banks based on he Basu, e al. (2008). The main advanage is ha his measure is relevan for a larger se of risk profiles of firms. However, he resuls ha follow are very similar if he 10-year Treasury rae had been used wihou risk adjusmen. There is less guidance when i comes o specifying he asse revaluaion erm should one wan o depar from using curren asse price changes. From an ex ane poin of view, wha maers is he expeced asse price change, bu his expecaion will depend on he (unknown) informaion se of he firm. Gilchris and Zakrajsek (2007) use a five-year moving average, bu heir empirical resuls do no imply ha his is he appropriae specificaion. 11 A wide range of alernaives have been used, such as he average price change across asses or ARMA models (Oulon, 2007). 12 Given his siuaion, i seems mos sensible o compare a number of alernaives and evaluae heir impac on capial services growh and he occurrence of negaive user coss. If hese negaive user coss do occur, i is desirable from an index number perspecive o make ad-hoc adjusmens. Again, a number of plausible alernaives can be formulaed and heir impac can be esed. Daa For he empirical analysis ha follows, I use daa for he Unied Saes as his allows for he wides range of scenarios o be examined. The core daa consiss of invesmen a curren and consan prices in 47 asses for each of 30 indusries in he EU KLEMS daabase for he period These 11 Their analysis basically explains differences in invesmen across firms, so he specificaion of he expeced asse price change (which is invarian across firms) canno be validaed from his exercise. 12 Using he average price change across asses is equivalen o using a consan real rae of reurn as advocaed by Diewer (2004), see Harper e al. (1989). Also see Harper e al. (1989) for a more exensive review of he lieraure on he specificaion of he asse revaluaion erm. 5

6 daa are mosly based on he deailed fixed asse ables published by he BEA on 46 non-residenial fixed asses. We supplemen hese daa wih informaion on invesmen by he governmen and invesmen in residenial buildings. 13 We hen classify hese invesmen series o he EU KLEMS indusries. 14 I have chosen o use he se of EU KLEMS indusries as his is he mos relevan for inernaional comparisons. The analysis iself focuses on he period as all he complemenary daa are available for his period. The daa on invesmen in fixed reproducible asses (henceforh referred o as BEA asses) is supplemened by daa on residual income CAP from he EU KLEMS daabase. In he BEA GDP by Indusry Accouns, no disincion is made beween ne axes on producs and ne axes on producion. Therefore, his CAP measure does no conform o he heoreically preferable basic prices concep, which would include ne axes on producion bu exclude ne axes on producs. Our source for he ax parameers (see equaion (2)) is he BLS. These daa cover he period and we assume consan ax parameers for he period. The BLS also provide daa on socks of land and invenories. Here, we were able o combine he daa for he period wih daa based on he old SIC87 indusrial classificaion for he period. The BLS in urn uses daa on invenories from he BEA and Census as heir source. Daa on land capial socks is subjec o more assumpions. A sudy for counies in Ohio from 2001 provides informaion abou he value of land relaive o he value of srucures by indusry and his land-srucures raio is used for he enire period. Land prices are se equal o he average price of srucures (see BLS, 1997, 2007). I would obviously be preferable o have more curren informaion abou he imporance of land in producion, bu he discussion in Jorgenson, Ho and Siroh (2005, p. 166) suggess his is problemaic. For he final se of capial daa, I use newly available esimaes of invesmen in inangible asses from Corrado, Hulen and Sichel (2006). This adds daa on invesmen in compuerized informaion, scienific R&D, non-scienific R&D, brand equiy and firm-specific resources. Currenly, hese daa are only available for he privae US economy, bu for he comparison of aggregae capial services growh, his is already quie useful. In addiion o capial daa, income are needed o esimae inernal raes of reurn (CAP from equaion (7)). Here I use he daa as published in he EU KLEMS daabase. 15 This has he advanage of consisency across counries, parly because he same indusry classificaion is used as in Europe bu also because he price conceps are more comparable. CAP is calculaed by subracing labour compensaion from value added. Value added as given by he BEA in he GDP by Indusry accouns includes ne axes on producs and producion. 16 However, from a producion-heory poin of view, ne axes on producs, such as sales axes in he US, should be excluded. Ne axes on producion, mainly propery axes in he US, should be included however. A breakdown beween 13 The BEA daa on governmen invesmen are only available for a number of ypes of buildings and overall equipmen and sofware. To disinguish beween differen ypes of equipmen and sofware, daa on governmen invesmen from he 1997 Use able is used in combinaion wih he 1997 Capial Flow Table o bridge invesmen in commodiies o invesmen in BEA capial asses. This asse disribuion is held consan over he sample period, in par because older Use ables did no coun sofware expendiure as a capial invesmen. 14 Some EU KLEMS indusries, such as moor vehicle rade and repair (NACE 50) are no available in his daase. We spli up indusries using daa on value added, assuming consan asse shares and assuming consan value added shares before So in his example, we esimae invesmen for moor vehicle rade and repair by spliing up wholesale rade, reail rade and oher services (which includes moor vehicle repairs). 15 See 16 Even hough he ax variable in he BEA daase is referred o as Taxes on producion and impors, less subsidies, bu see e.g. Guo and Planing (2007). 6

7 hese wo ypes of axes is only available a he aggregae level. A he indusry level, hese wo ypes of axes are disinguished by assuming ha all subsidies are subsidies on producion and ha an indusry pays axes on producion in proporion wih he indusry s share in he capial sock of srucures. Taxes on producs are hen calculaed as a residual. 17 Labour compensaion of employees is also direcly available from he BEA daase bu an impuaion needs o be made for he labour compensaion of self-employed workers. Here I use he assumpion ha a self-employed worker earns he same average wage as an employee in each indusry. Refinemens o his have been made, for example by aking he characerisics (age, sex, educaion) of self-employed workers ino accoun or by separaely esimaing capial income and using capial and labour income esimaes o divide up non-corporae income. 18 Resuls In analyzing hese daa, I follow a boom-up approach. I firs analyze he raes of reurn and asse prices, before urning o he implicaions of hese differences for indusry-level capial growh and aggregae capial growh. Finally, I look a he conribuion of capial o oupu growh a he indusry and aggregae level and he sensiiviy o he assumpions made in capial aggregaion. Raes of reurn Figure 1 plos he aggregae inernal rae of reurn for all indusries and all marke indusries in he US for he period. 19 This inernal rae is based on he sandard se of fixed, reproducible asses, excluding land, invenories and inangible asses. For reference, an esimae of he risk-adjused cos of capial is also ploed. As discussed before, his cos of capial consiss of a 10-year Treasury bond and he risk premium associaed wih bank loans o business from Basu e al. (2008). 20 The figure shows ha boh he level and paern over ime of he inernal raes of reurn is differ considerably from he cos of capial. While he average cos of capial is only 9 percen over his period, he inernal rae across all indusries is 12 percen and for marke indusries i is 13 percen. The ime paern is also differen, wih for example rising inernal raes afer 2000, bu a declining cos of capial. The oal indusries series is no he bes basis for comparison as par of capial income used in calculaion is based on impued reurns o governmen aciviies and residenial buildings. For marke indusries, he correlaion beween he inernal rae and he cos of capial is only However, he inernal rae of reurn in Figure 1 suffers from a leas one drawback, namely he se of asses ha is covered. Table 1 shows he effec of expanding he asse se, firs wih land and 17 This procedure has as a risk ha in some indusries, he esimae of axes on producion are so high ha axes on producs would be negaive. This problem is more widespread if value added shares are used insead of he indusry share in he srucures capial sock. To avoid negaive axes and ensure ha boh ypes of axes add up o he correc aggregae, an iniial esimae of axes on producion is made, which is equal o he amoun based on he share in srucures capial or equal o oal indusry axes. Nex, a RAS procedure is used o ensure indusry axes add up o he correc aggregae. 18 The firs mehod is applied in Jorgenson e al. (2005), he second by he BLS (1997). 19 Marke indusries excludes governmen, healh and educaion because much of heir oupu is no direcly observed in he marke, which means an inernal rae esimae is mosly based on he rae ha he saisical office impued for his indusry. The real esae indusry is also excluded because he impued renal value of owner-occupied housing makes up mos of he oupu of his indusry. 20 The governmen bond is he consan mauriy series from he Federal Reserve ineres rae saisics. The risk premium is based on he yield spread of commercial paper of Treasury bills, adjused o reflec he higher average riskiness of he average bank loan over commercial paper. 7

8 invenories and hen wih inangibles. Including land and invenories leads o a subsanial decline in he inernal rae. This is o be expeced as he capial sock increases, while capial income says he same. The effec of adding inangible invesmen is smaller because i involves reclassifying expendiure on cerain services as invesmen, so capial income also rises. The overall resul of adding hese asses is o decrease he gap beween he inernal rae and he cos of capial o less han a percenage poin and he correlaion also increases considerably. This suggess ha he aggregae inernal rae of reurn is reasonably comparable o he cos of capial, bu only once all asses are measured. The indusry deail in his daase provides a furher ground for esing he economic relevance of an inernal rae of reurn. Since inangible invesmen daa is no ye available a he indusry level, he inernal raes are calculaed based on all reproducible fixed asses, land and invenories. I urns ou ha in almos wo-hirds of he 26 marke indusries, he inernal rae of reurn has a posiive correlaion wih he cos of capial and he average correlaion is Figure 2 shows he average inernal rae for each indusry over he enire period. The firs observaion is ha here is considerable heerogeneiy beween indusries. For example, he ranspor indusry shows an average inernal rae of only 3 percen and he finance indusry a rae of almos 18 percen. 21 Also, in mos indusries, he average inernal rae is acually lower han he average cos of capial. This is no jus caused by he early 1980s, when mos indusries had an rae of reurn lower han he cos of capial, bu occurs in many oher years as well. Figure 2 also shows informaion on he relaive risk of an indusry, based on he sandard deviaion of real oupu growh. The informaion in he figure already shows lile posiive relaionship, wih some indusries wih highly variable oupu growh, like ranspor equipmen, showing low reurns and firms wih sable oupu (food and obacco) showing high reurns. The correlaion beween he wo series is only Alernaive explanaions for he paern of inernal rae are no immediaely convincing eiher. A lack of compeiion could also lead o higher inernal raes, bu a comparison of concenraion raios and inernal raes shows no posiive correlaion eiher. 22 Of course, hese are jus one indicaor of risk and one of compeiion, bu i does raise he quesion wha can explain he large differences in raes of reurn across indusries. Aside from hese broader concerns abou wha he inernal rae of reurn measures and reflecs, a more pragmaic concern is ha for many counries, daa on he sock of land and invenories is no easily available. Even in he US, he daa on he sock of land is subjec o more assumpions and esimaions han oher ypes of capial. However, inernal raes based on an incomplee se of asses are oo high compared o he cos of capial (Table 1). The relaionship over ime beween he cos of capial and indusry-level inernal raes also becomes weaker once land and invenories are omied. 23 The broader significance of hese concerns for capial measuremen will be discussed below. 21 The inernal rae of reurn for finance is oversaed however. Much of he oupu of banks is esimaed and as Basu e al. (2008) show, curren saisical mehods oversae bank oupu considerably. Their esimaes of bank oupu imply an inernal rae of reurn much closer o ha of he marke economy. 22 For he concenraion raio he revenue share of he four larges firms in 2002, as given in he Economic Census, is used. 23 In 23 of 26 indusries, he correlaion is lower. 8

9 Asse prices Apar from he rae of reurn R in equaion (2), he asse revaluaion erm v also needs o be implemened. In he Jorgensonian framework discussed above he acual asse price changes are used, bu his poses problems similar o he use of an inernal rae of reurn. Under uncerainy, acual asse price changes will have boh a random and sysemaic componen. Over long periods of ime, invesmen prices of equipmen end o decline relaive o oher prices (e.g. Greenwood, Hercowiz and Krussel, 1997), bu shor-run flucuaions can disor his expeced paern. In a pracical sense, his problems becomes mos visible if he prices of srucures rise rapidly. Since heir depreciaion raes are low, he user cos of capial can acually urn negaive. In pracice, his is a relaively rare problem: in he US daase lile over one percen of he user coss are negaive, regardless of wheher an inernal or an exernal rae of reurn is used. The need for some ype of adjusmen is also discussed in Jorgenson e al. (2005, p. 169), who smooh heir asse inflaion raes in periods wih negaive user coss. This asymmeric procedure, where an adjusmen is only made if he resuls are wrong, is no very appealing. In comparison, Gilchris and Zakrajsek (2007) use fiveyear average asse inflaion raes in all years. In he Oulon (2007) model, he correc asse price o measure capial s marginal produc is he curren price change, bu his only holds if he righ (asse-specific) rae of reurn is used and for asses wih rapidly rising prices, he rae of reurn may well be lower. This argues for dampening some of he swings in asse prices while preserving he broader rends, such as he rapid price decline of compuers. Figure 3 illusraes his paern for all fixed reproducible asses by ploing he average price change over he period and he iner-quarile range o indicae he variabiliy. Compuer prices are in clearly separae class wih hreequarers of all price declines beween 12 and 21 percen per year. The prices of mos oher asses rise on average, wih mos buildings showing larger price increases han equipmen. Price swings can also be subsanial, in paricular for some ypes of srucures. This suggess using some ype of moving average is likely o do jusice o he differing rends, while smoohing ou some of he exreme swings. How he specificaion of he revaluaion erm influences capial services growh will be discussed below. Indusry capial growh The discussion above suggess a series of opions in calculaing capial services a he indusry level: The rae of reurn: an inernal rae or he cos of capial The coverage of asses: only reproducible asses, or also land and invenories Tax parameers: include hese or no Revaluaion erm: curren prices or a moving average 24 The coverage of asses is imporan because in inernaional seings, land and invenories are no available. Similarly, informaion on he reamen of capial in he ax sysem is no readily available 24 How o deal wih negaive user cos is anoher, bu quaniaively minor issue. Even using curren asse prices, only 1.3 percen of user coss are negaive. Seing hose o zero, replacing hem by he average user cos across asses or using he year-average asse price change o recalculae user coss has a negligible effec on capial services growh. 9

10 for mos counries eiher. The specificaion of he rae of reurn and he asse revaluaion erm are mosly imporan o see evaluae he imporance of he mehodological debae on hese issues. Wih four differen parameers and wo opions per parameer, here are 16 differen opions for 26 differen indusries and 29 years. To make he analysis manageable, I focus on he average growh in capial services across all years. For increased insigh, I will compare he average growh beween each of he wo opions for each parameer, holding he oher parameers consan. Of he 16 opions, half include ax parameers and half exclude hem, so he average growh beween hese wo ses can be compared. Table 2 shows he resuls of his comparison. The firs row shows an average growh in capial services across all indusries and opions of 3.65 percen per year. The choice beween an inernal rae of reurn and he cos of capial is mos imporan, wih average absolue difference in growh beween he wo of 0.52 percenage poins. In mos indusries, using he cos of capial leads o higher average growh. This is because he cos of capial is lower on average, which means he share in capial compensaion of shor-lived ICT asses is greaer and hese asses have shown faser growh over he period. The difference is larges in ICT inensive indusries like finance and business services. Wheher land and invenories are included is somewha less imporan on average, wih an average absolue difference of 0.32 percenage poins. The differences are also more concenraed in a few indusries. The difference is larges in finance, where including land and invenories subracs 1.3 percenage poins from average growh, followed by agriculure where i adds 1.2 percenage poins. In oher indusries, like hoels and resaurans, he effec is negligible. Taking he ax sysem ino accoun is already a minor issue, wih an average impac of 0.11 percenage poins. The effec is larges in finance and in business services, mosly because capial services growh is highes in hese indusries. The specificaion of he revaluaion erm maers even less for average growh. The difference beween using he curren asse price change and a five-year moving average is only 0.07 percenage poins. I also does no subsanially smooh he resuling capial growh series: he average sandard deviaion of capial growh is 2.62 percen and he difference beween curren asse prices and a fiveyear moving is only 0.10 percenage poins on average. In conras, he choice beween an inernal rae of reurn and he cos of capial leads o an average absolue difference in he sandard deviaion of 0.36 percenage poins. Finally, i is useful o examine he effec of using an inernal rae of reurn wih an incomplee se of asses compared o a more complee se. As Table 1 showed, omiing land and invenories leads o an oversaemen of he inernal rae, so he difference in capial services growh beween he inernal rae and he cos of capial should be larger if land and invenories are omied. This is indeed he case, bu i is quaniaively less imporan. The difference in capial growh beween an inernal rae and he cos of capial is 0.47 percenage poins if land and invenories are included and 0.58 if hey are omied. Aggregae capial growh In addiion o he aggregaion opions a he indusry level, here is also Oulon s (2007) proposal o consider for esimaing aggregae capial services growh. He proposes a hybrid beween using an inernal and exernal rae of reurn, where he exernal rae (i.e. he cos of capial) is used o aggregae across asses and inernal raes are used o aggregae across indusries. Furhermore, a he marke economy level, inangible asses can also be included. Table 3 shows he average growh raes for each of he parameers, averaging over he resuls based on he oher parameers as in Table 2. This 10

11 able shows how he main findings from he indusry-level also show up a he aggregae. The specificaion of he revaluaion erm maers very lile: average growh is 4.75 percen eiher way. Including ax parameers decreases capial growh by 0.19 percenage poins, a bigger effec han for mos indusries, bu modes given overall growh. Again, he se of asses and he rae of reurn maer mos. The wides asse boundary, including boh land and invenories and inangibles, shows he slowes average growh of only 4.53 percen. This is half a percenage poin lower han if hose asses were excluded. The growh based on he inernal rae and he cos of capial seem surprisingly close compared o he differences shown in Table 2. Moreover, growh based on an inernal rae is acually higher han based on he cos of capial, even hough he reverse ended o be he case a he indusry level. The reason for his is ha indusries like finance and business services migh have lower growh raes using an inernal rae of reurn, bu heir growh is sill considerably higher han he average. Furhermore, heir high inernal raes of reurn (cf. Figure 2) imply ha he share of he indusry in oal residual income CAP is much higher han ha based on he cos of capial. These wo effecs parly cancel ou, bu he increase in he indusry capial share ouweighs he decrease in indusry growh. This also explains why he hybrid opion leads o higher aggregae growh han boh alernaives: i combines high indusry growh wih a higher share of high-growh indusries. In addiion o he period averages, i can be useful o compare he growh paern over ime for a number of alernaives. As he specificaion of he revaluaion erm maers very lile, I use curren asse prices since his is he mos sraighforward in pracice. Similarly, I omi ax parameers. Figure 4 compares aggregae growh calculaed using differen raes of reurn based on he se of fixed reproducible asses. Firs of all, he hybrid opion shows higher growh in almos every year han he oher wo opion. Furhermore, even hough he average growh based on inernal raes and he cos of capial is very similar, differences are larger in some periods han ohers. In paricular, during he ICT invesmen boom in he lae-1990s, aggregae growh was around a percenage poin higher based on he cos of capial han on inernal raes, while i was a percenage poin lower in he lae-1980s. The comparison is similar for he se of asses including land and invenories. Figure 5 compares growh based on he hree differen se of asses from Table 3 and shows ha he main differences are in he lae-1990s. 25 If land and invenories are included, growh is abou half a percenage poin lower while also including inangible asses, lowers growh by abou wo percenage poins in oal. Afer 2000 hough, growh wih inangibles are included is percenage poins higher. In summary, he choice for he rae of reurn and he se of asses ha is covered maers subsanially a he indusry level and he aggregae level. Moreover, he differences are no consan over ime. The conribuion of capial o growh The analysis from he previous secions has esablished he quaniaive imporance for capial services growh of differen approaches o capial aggregaion across asses and indusries. As hese daa are ofen used in growh accouning, i is useful o place he resuls in a broader conex. In growh accouning, he conribuion of capial is esimaed as he share of capial in oal coss ime he growh of capial. Under perfec compeiion, oal coss equal oal oupu, bu as long as reurns o scale are consan, he more general expression holds (Hall, 1990). 25 Figure 5 is based on he exernal rae of reurn. The comparison is very similar for he oher opions for he rae of reurn. 11

12 The firs issue is how he conribuion of capial o growh varies depending on he se of asses ha is covered. The combinaion of an inernal rae of reurn and an incomplee se of asses is likely o be paricularly problemaic as he underlying assumpion is ha all residual income CAP can be aribued o he income from he se of asses ha is covered. The second issue is how capial compensaion esimaed using he cos of capial compares o value added. Since in his approach capial compensaion does no add up o residual income CAP, here will be economic profis or losses and i should be informaive o evaluae is size and paern over ime. Table 4 shows he resuls for he conribuion of capial o marke economy growh of value added. The op panel of he able shows he conribuion of capial o oupu growh, he middle panel shows he share of capial in oal coss and he boom panel shows he growh of capial services. 26 Curren asse prices are used for he revaluaion erm hroughou. The firs column shows ha when using inernal raes of reurn and excluding ax parameers, growh of capial has conribued 1.48 percenage poins o oupu growh if only fixed reproducible asses are covered. This conribuion drops o 1.41 if land and invenories are included and rises o 1.67 if inangibles are included as well. The conribuions are almos idenical if ax parameers are included. The paern is also similar for he hybrid case, excep ha he conribuions are higher because of a higher growh in capial services. In boh cases, including land and invenories decreases he conribuion because growh of hose asses is slower han average while he amoun of capial income is unchanged a 31 percen of value added (since oal coss equal oupu in boh cases). Including inangibles adds around 11 percen o GDP, leading o a capial share ha is 7 percenage poins higher, so even hough capial growh including inangibles is lower (cf. Table 3), he conribuion of capial o oupu growh is higher. Using he cos of capial in calculaing user coss leads o a monoonically increasing conribuion of capial if more asses are covered, since capial compensaion increases wih each addiion. However, he conribuion o oupu growh is always lower han in he oher wo rae of reurn opions. The reasons for his vary, bu for he case when only fixed reproducible asses included, he lower capial share is he main reason compared o he inernal rae of reurn. Adding more asses and including ax parameers decrease he gap unil he poin where, in erms of he average conribuion, using inernal raes or he cos of capial maers lile. Unlike for he oher opions, including ax parameers is an imporan facor, mosly because i increases he capial share. The resuls also illusrae he bias in esimaing he capial conribuion by using an incomplee se of asses in combinaion wih inernal raes of reurn. While he cos of capial conribuions show ha fixed reproducible asses conribue a mos 1.21 percenage poins o oupu growh, he inernal rae esimaes imply a conribuion of abou 1.5 percenage poins. The differences in conribuion are also vary sable over ime wih he conribuion based on he cos capial he lowes and he hybrid he highes wih he inernal rae as an inermediae version. Figure 6 shows a more revealing picure, comparing he capial share based on residual income CAP o he capial shares implied by using he cos of capial o esimae capial compensaion, all wihou aking inangible asses ino accoun. The residual income share is fairly consan over his period, varying beween 30 and 34 percen of oupu, while capial compensaion is much more variable. The figure shows he difference beween hese wo conceps for four cases, namely including and 26 Noe ha for he inernal rae and hybrid opions, he average annual growh in capial services ime he average capial share is almos equal o he average annual conribuion. The difference is more noiceable for he cos of capial because, as discussed below, he capial share is more variable. 12

13 excluding land and invenories and including and excluding ax parameers. The basic paern is similar in hese four series bu he differences in he level is considerable. In mos years, he difference is posiive, implying ha residual income is larger han capial compensaion, bu in he mid-1980s, capial coss were so high ha capial compensaion was larger han residual income. The mos comprehensive capial compensaion measure, including land and invenories and ax parameers is higher han residual income for 13 of he years covered, implying subsanial economic losses. Figure 7 shows ha also including inangibles leads o a very similar picure, excep ha underlying residual income increases from around 35 o 41 percen of oupu. A he indusry level, he difference beween residual income and capial compensaion closely mirrors he paern of inernal raes of reurn from Figure 2. This is of course no surprise since an inernal rae in excess of he cos of capial signifies ha residual income is higher han he compensaion required for he capial sock. The number of indusries wih higher capial compensaion han residual income on average over he enire period varies subsanially beween he differen alernaives. If ax parameers and land and invenories are excluded, only he ranspor and sorage indusry has higher capial compensaion han residual income bu if boh are included capial compensaion is higher in 14 of 26 indusries. As was he case for he inernal rae of reurn, here do no seem o be sraighforward explanaions wha can explain he wide dispariy, boh over ime and across indusries. In all likelihood, measures of risk and compeiion facor ino he equaion. Measuremen errors also canno be ignored. Since CAP is calculaed as residual income, any measuremen problems in oupu or labour compensaion end up here. The esimaion of self-employed labour compensaion is a paricularly imporan source of uncerainy here. Daa on invesmen and capial income are also no colleced from he same sources and since capial services are no (ye) par of he Naional Accouns, any discrepancies beween sources is no aken ino accoun in he reconciliaion process by saisical offices. These measuremen issues sugges ha cauion is needed, in paricular in inerpreing indusry-level resuls bu also a he aggregae level. Despie hese healh warnings, a number of observaions sand ou from he analysis of capial conribuions o oupu growh. Firs, he combinaion of inernal raes of reurn and an incomplee se of asses can lead o misleading resuls as i implies oo large a conribuion of fixed reproducible asses. Using he cos of capial is less hazardous in his respec, bu necessiaes a careful consideraion of he ax sysem o avoid underesimaing he share of capial in oal coss. Finally, he hybrid soluion proposed by Oulon (2007) implies much higher capial conribuions o oupu growh han any of he oher mehods. Conclusions Measuring capial is hard. Economic heory is a useful guide for par of he way bu as illusraed by Oulon (2007), sooner or laer choices have o be made on pragmaic grounds. The aim of his paper has been o illuminae he impac of hese choices o focus aenion and hopefully research on he mos pressing issues. Some issues have no been deal wih here: ime series for invesmen by indusry and asses in boh curren and consan prices have been aken as given. I have also no discussed depreciaion raes and o wha exen we should rely on hem. For hese and oher issues relaed o capial measuremen, see he OECD Manual (Schreyer, 2008). This paper has aken indusry capial socks by asse as given and asked how hese should be aggregaed o ge an informaive measure of producive capial inpu ino producion. 13

14 Cenral in his aggregaion problem is he user cos of capial, which consiss of a rae of reurn, depreciaion rae, revaluaion erm and ax parameers. For each of hese componens differen choices and assumpions can be jusified and I compare how hese choices impac he resuls. I urns ou ha many of he choices maer only lile. For example, insead of using he curren asse price change for he revaluaion erm, moving averages can be specified bu his maers lile. Wha is imporan is ha asse-specific price changes should be aken ino accoun as in paricular, compuer prices have fallen very rapidly and his is par of he user cos of capial. The choice for he rae of reurn is more consequenial. Esimaes of he inernal rae of reurn are no easy o reconcile wih economic fundamenals such as he relaive risk of indusries or he cos of capial in financial markes. This suggess broader measuremen problems are imporan: he inernal rae of reurn will only be an economically useful concep if capial income is measured in a fully correc fashion and all relevan capial asses are correcly accouned for. Neiher of hese is likely in pracice. Oulon s (2007) hybrid approach does no solve his issue and hence, I would favour Balk s (2008) argumen for an exernal rae of reurn. This means capial cos does no fully exhaus revenue and he size of capial coss will vary depending on wheher ax parameers are included and which asses are covered. A he aggregae level, on average over ime, capial cos is comparable in size o residual income once axes are accouned for and land and invenories are covered. No accouning for eiher of hese will undersae he conribuion of capial inpu growh o oupu growh. Finally, mos inangible asses are no ye considered par of he sandard se of capial asses and here are many concepual issues. For example, he quesion how and how much knowledge (in he form of R&D) depreciaes is sill no answered in a saisfacory fashion. However, using he same assumpions as Corrado e al. (2006) shows ha including inangible asses is very imporan as well. 14

15 References Balk, B.M. (2008), Measuring Produciviy Change wihou Neoclassical Assumpions: A Concepual Analysis mimeo. Basu, S., R. Inklaar and J.C. Wang (2008), The Value of Risk: Measuring he Service Oupu of U.S. Commercial Banks mimeo. Bernd, Erns R. and Melvin A. Fuss (1986), Produciviy Measuremen wih Adjusmens for Variaions in Capaciy Uilizaions and Oher Forms of Temporary Equilibrium Journal of Economerics, 33(1), pp BLS (1997), BLS Handbook of Mehods, BLS Bullein 2490, US Deparmen of Labor: Washingon D.C. BLS (2007) Technical Informaion Abou he BLS Mulifacor Produciviy Measures, US Deparmen of Labor: Washingon D.C. Corrado, C.A., C.R. Hulen and D.E. Sichel (2006), Inangible Capial and Economic Growh NBER Working Paper, no Diewer, W.E. (2004), Issues in he Measuremen of Capial Services, Depreciaion, Asse Price Changes and Ineres Raes UBC Discussion Paper Diewer, W.E (2008), Wha is o be done for beer produciviy measuremen Inernaional Produciviy Monior 16, pp Erumban, A.A. (2008), Renal Prices, Raes of Reurn, Capial Aggregaion and Produciviy: Evidence from EU and US forhcoming in CESifo Economic Sudies. Gilchris, S. and E. Zakrajsek (2007), Invesmen and he cos of capial: New evidence from he corporae bond marke NBER Working Paper, no Greenwood, J., Z. Hercowiz and P. Krussel (1997), Long-Run Implicaion of Invesmen- Specific Technological Change American Economic Review, 87(3) pp Guo, J. and M.A. Planing (2007), Inegraing U.S. Inpu-Oupu Tables wih SNA: Valuaions and Exensions paper presened a he 16h Inernaional Inpu-Oupu Conference in Isanbul, Turkey, July Hall, R.E. and D.W. Jorgenson (1967), Tax Policy and Invesmen Behavior American Economic Review, 57(3) pp Hall, Rober E. (1990), Invariance Properies of Solow s Produciviy Residual In Peer A. Diamond (ed.) Growh/Produciviy/Employmen: Essays o Celebrae Bob Solow s Birhday, MIT Press: Cambridge. Harper, M.J., E.R. Bernd and D.O. Wood (1989), Raes of Reurn and Capial Aggregaion Using Alernaive Renal Prices in Jorgenson and Landau (eds.) Technology and Capial Formaion, pp , MIT Press: Cambridge. Jorgenson, D.W. and Z. Griliches (1967), The Explanaion of Produciviy Change Review of Economic Sudies, 34(3) pp Jorgenson, D.W., M.S. Ho, and K.J. Siroh (2005), Informaion Technology and he American Growh Resurgence, Cambridge, The MIT Press. Oulon, N. (2007), Ex pos versus ex ane measures of he user cos of capial Review of Income and Wealh, 53(2) pp Schreyer, P. (2008), OECD Manual Measuring Capial, draf version, OECD: Paris 15

16 Tables and Figures 25% Figure 1, Inernal rae of reurn for oal US indusries and yield on US governmen bonds, % 15% 10% 5% 0% Indusry code Inernal rae of reurn, oal indusries Inernal rae of reurn, marke indusries Risk-adjused ex-ane cos Transpor Agriculure Misc mfg Communicaions Elecric/elecroni Consrucion Transpor eq Mining Social/personal Reail rade Uiliies Hoels/resaurans Meal prods Moor rade Wholesale rade Oil Machinery Texiles/clohing Non-meallic Wood Paper/prining/pu Food/obacco Rubber/plasics Business ser Chemicals Finance Figure 2, average inernal rae of reurn and oupu variabiliy in US indusries, Risk-adjused cos of capial 0% 2% 4% 6% 8% 10% 12% 14% 16% 18% 20% Average inernal rae of reurn Sandard deviaion of oupu growh 16

17 Figure 3, Asse price changes , average and iner-quarile range Compuers and peripheral eq. Sofware Communicaions Phoocopy and relaed equipmen Office and accouning equipmen Railroads Communicaion buildings Medical eq. and insrumens Oher agriculural machinery Household furniure Railroad equipmen Auos Educaional buildings Elecric ransmission & disribuion Ships and boas Mining and oilfield machinery Household appliances Inernal Combusion engines Oher elecrical equipmen Nonmedical insrumens Oher equipmen Service indusry machinery Seam engines Elecric buildings Hospials and special care Consrucion racors Ligh rucks (incl. uiliy vehicles) Fabricaed meal producs General indusrial equipmen Oher furniure Mealworking machinery Oher buildings Oher rucks, buses and railers Oher consrucion machinery Special indusrial machinery Aircraf Farm racors Manufacuring buildings Oher buildings Farms Commercial buildings Residenial buildings Mining buildings Religious buildings Oher power buildings Office, including medical buildings Peroleum and naural gas buildings -25% -20% -15% -10% -5% 0% 5% 10% 15% 10% Figure 4, US marke economy capial services growh: differen raes of reurn, % 8% 7% 6% 5% 4% 3% 2% 1% 0% Inernal rae Cos of capial Hybrid

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