EU KLEMS WORKING PAPER SERIES Product

Transcription

1 Capial Aggregaion and Growh Accouning: A Sensiiviy Analysis Working paper nr. 25 Abdul Azeez Erumban EU KLEMS WORKING PAPER SERIES Produc

2 Capial Aggregaion and Growh Accouning: A Sensiiviy Analysis Working paper nr. 25 Abdul Azeez Erumban EU KLEMS Projec Produciviy in he European Union: A Comparaive Indusry Approach June 2008 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".

3 Capial Aggregaion and Growh Accouning: A Sensiiviy Analysis Abdul Azeez Erumban June, 2008 Absrac Wih he increasing imporance of invesmen in Informaion Technology, mehods for measuring he conribuion of capial o growh have re-assumed cenre-sage in recen growh accouning lieraure. The imporance of using capial service growh raes raher han capial sock growh raes has long been advocaed, and has become mainsream pracice. However, he choice for a paricular rae of reurn in he derivaion of capial service prices is no sraighforward and has barely been researched. Using four alernaive renal price models based on boh exernal and inernal raes of reurn models his paper quanifies he differences in mulifacor produciviy growh raes (MFPG) under differen model assumpions. The differences in MFPG are also examined in erms of he inclusion of axes and subsidies in he calculaion of renal prices. Empirical analysis, carried ou for four EU counries and he US in 26 indusries during shows ha he use of capial sock overesimaes MFPG in mos indusries. Incorporaion of axes seems o have only modes effec. The magniude of divergence generaed by alernaive renal price models-paricularly beween inernal models- is quie low. The difference is seen o be relaively high beween exernal rae of reurn models and inernal rae of reurn models. Groningen Growh and Developmen Cenre, Faculy of Economics, Universiy of Groningen, Pos Bus 800, 9700 AV Groningen, The Neherlands, a.a.erumban@rug.nl The auhor is graeful o Bar van Ark, Marcel Timmer, Rober Inklaar, Gerard Kuper and Theo Eicher for commens and suggesions on he paper. The usual disclaimer applies

4 1. Inroducion The measuremen of capial and is conribuion o economic growh has been an imporan issue of aenion in economics for long ime. Wih he increasing imporance of invesmen in Informaion and Communicaion Technologies (ICT), mehods for measuring he conribuion of capial o aggregae growh have reassumed cenre-sage in growh accouning lieraure (Jorgenson, 2001; van Ark e al., 2008; Jorgenson and Vu, 2005; Inklaar e al, 2008). Dividing he oal capial ino ICT capial and non-ict capial, sudies have aemped o delineae he conribuion of hese wo componens o oal growh using he growh accouning framework. 1 One major issue in he quanificaion of capial s conribuion o economic growh using his framework is relaed wih he measuremen of capial inpu. Though many sudies sill use aggregae capial sock as a measure of capial inpu (e.g. Jones and Olken, 2005; Caselli, 2004), i has long been advocaed ha he flow of capial services, raher han he capial sock, is appropriae for producion and produciviy analysis (Jorgenson, 1963; Jorgenson and Griliches, 1967; Hall and Jorgenson, 1967). The challenge in measuring capial services for growh accouning is associaed wih he implici naure of he capial services; he quaniy of capial services is no usually direcly observable (Harper e al., 1989). Therefore, he empirical researcher has o rely on heoreical yardsicks o approximae he capial services. Following he heoreical argumens of Jorgenson (1963), Hall and Jorgenson (1967), and Jorgenson and Griliches (1967) capial services are usually derived using he esimaed capial sock for he individual asses and he relevan user cos or renal price of capial, assuming ha flows are in proporion o he socks a individual asse level. However, here are differen ways of measuring renal price of capial and hereby of obaining capial service growh raes. The selecion of any paricular measure may significanly influence he calculaed growh raes of capial and is conribuions o oupu growh. The aim of his paper is o examine wheher he use of differen renal price models in capial service aggregaion produce significanly differen capial services growhs. Harper e al. (1989) have conduced a sudy by uilizing five alernaive renal price models o evaluae he capial aggregaion for he US manufacuring indusries over he period Their resuls show significan differences beween various models. While Harper e al. (1989) limis heir sudy o he US manufacuring secor only, we do his exercise across 26 indusry groups (see Table 3) in four EU counries along wih he US, over a more recen ime period, Furhermore, we specifically examine he effec of alernaive capial aggregaion procedures on he measured mulifacor produciviy growh (MFPG). This is imporan because he choice of a paricular rae of reurn will have consequences on he measured MFPG as i will affec he cos share of capial and hereby he growh rae of capial services (see discussion in nex secion). An aemp is also made o empirically undersand he impac of including ax in he renal price equaion on he growh raes of capial and hereby MFPG. I has been argued ha ax plays a major role in alering invesmen behaviour (e.g. Hall and Jorgenson, 1967). However, mos sudies in he conex of he EU have considered pre-ax renal prices in order o arrive a capial service growh raes. Therefore, axaion has o be incorporaed in he measuremen of capial service prices (see secion 3.1 for a deailed discussion). 1 There are also sudies ha ried o examine he US-EU produciviy gap in erms of differences in ICT use, by classifying indusries according o heir ICT inensiy. See for insance van Ark e al (2003) and Daveri (2004). 2

5 The paper is organized ino seven secions. In Secion 2 we presen a brief discussion on he analyical lieraure concerning growh accouning and capial aggregaion. In Secion 3 we discuss renal price formulaion and he measuremen of is componens. Secion 4 discusses he daa used in he empirical analysis. Empirical resuls are discussed in Secion 5, and finally Secion 6 concludes he paper. 2. Growh Accouning and Capial Aggregaion Assuming a compeiive marke and consan reurns o scale (CRS), he sandard growh accouning equaion wih value-added as oupu (Y) and labour (L) and capial (K) as inpus can be wrien as 2 : Δ lny = Δ ln A + aδ ln L + (1 a ) Δ ln K (1) where he subscrip sands for ime, and A denoes he echnical progress, ofen called as he mulifacor produciviy (MFP). 3 a is he share of labour in he value-added averaged over he wo ime periods, and -1 (i.e. a ( ) / = a + a 1 2 ), and Δ denoes he change in he relevan variable over he previous year. Equaion (1) clearly shows ha oupu growh is measured as a weighed sum of growh of labour and capial flows, where he weighs are he shares of each inpu in he value added. This implies ha in order o implemen equaion (1) i is essenial o calculae he growh rae of aggregae inpus and oupu. 4 Ideally, one should be able o derive he growh in aggregae inpus as he cos share weighed sum of growh of inpus (Jorgenson e al., 1987). In he case of labour such weighs may be derived from he wage raes. The absence of an observable service price, however, makes i difficul o direcly measure aggregae capial service growh raes. Capial sock consiss of differen ypes of heerogeneous asses wih specific capial service levels. Therefore, his heerogeneiy has o be aken ino accoun while aggregaing capial services across various asse ypes. Assuming a sric proporionaliy beween capial services and capial socks a he level of individual asses 5, Jorgenson (1963) and Jorgenson and Griliches (1967) have developed aggregae capial service measures ha ake ino accoun he heerogeneiy of asses. In accordance wih heir aggregaion procedure, he growh rae of aggregae capial services may be measured as n sr s Δ ln K = γ Δ ln (2) i= 1, K i, i n s, i, K i, i= 1 s where γ i, = ( γ i, + γ i, 1 ) / 2 and γ i = ci, K / i c, 2 For a deailed discussion on growh accouning, see, among ohers, Jorgenson and Griliches (1967), Barro (1999) and Hulen (2000). 3 Inklaar e al (2008) provides a useful summary of he concep of MFP (see Box 1, Inklaar e al 2008). 4 See OECD (2001 a and b)-he so-called capial and produciviy manuals- and EUKLEMS (2007) for discussions on he measuremen of oupu and inpu for produciviy analysis. 5 Noe ha even hough one would assume proporionaliy beween capial sock and capial service a individual asse level, he facor of proporionaliy would vary across asse ypes and over ime depending upon he marginal produciviy of each asse ype. A he aggregae level, he capial services should ake accoun of he differences in he service delivered by differen asse ypes. 3

6 where K sr is he aggregae capial services in year, n is he number of asses, K s i, is he capial sock of asse i in year, c i, is he renal price of asse i in year, and γ i, is he share of i h asse in oal capial compensaion in year. γ i effecively incorporaes he qualiaive differences in he conribuion of various asse ypes, as he capial composiion changes. I is eviden from (2) ha he wo imporan componens of he capial service measure are capial sock (K s ) and he service prices (renal price) of capial (c). Hence, hough he relevan measure of capial inpu in he produciviy analysis is he flow of capial services, i is essenial o have consisen measures of capial sock in produciviy analyses in order o pracically esimae capial service flows. The usual pracice of measuring capial sock is based on a perpeual invenory mehod, i.e. s s K i, = ( 1 i ) K i, 1 + I i, δ (3) where δ i is he rae of depreciaion for he i h capial asse and I i, is he real invesmen in asse i insalled in he beginning of period. Using (2) and (3) he change in aggregae capial service growh raes may be measured as a weighed sum of he growh raes of asse specific capial socks, wih he weighs being he relaive compensaion share of each asse. 6 The remaining ask, herefore, is o consruc appropriae measures of capial service prices for each asse ype (c i, ) - renal prices or user cos of capial-, in order o derive he relaive compensaion shares. 3. Measuremen of Renal Prices (c) As in he case of he wage rae for labour, he renal price for capial represens he uni cos of using a capial good for a specified period of ime (Jorgenson and Yun, 1991). If here is an acive renal marke for capial asses i would have been possible o obain he capial service prices direcly as he renal price of using a capial asse, from which one can calculae he capial service flow. However, he renal prices of he capial service are unobservable, as capial services are delivered by capial goods over he course of heir lifeime o heir owners, wihou any recorded marke ransacion. Therefore, i is essenial for he researcher o impue he implici renal price ha he owners of capial asses pay hemselves as users, which is herefore ofen called as he user cos of capial (Harper e al., 1989; Balk, 2007). While impuing renal prices one has o ake ino accoun ha capial goods deliver heir service (o heir owner) over he lengh of several years. Hall and Jorgenson (1967) have developed a mehodology wihin he boundaries of neoclassical heory. In his framework he renal price of capial is impued from he relaionship beween he price of a new asse and he discouned value of all fuure services derived from ha asse (also see Chrisensen and Jorgenson, 1969; Jorgenson 1967). In he absence of corporae axes, hey derive his relaionship as, 6 The economic raionale of using he renal share weighs o aggregae capial services is ha he invesors expec o ge more services in shor ime from an asse whose price is relaively high (or service life is relaively small). As one of he referees have poined ou, one could also accoun for he asse heerogeneiy while calculaing he conribuion of capial o oupu growh, by enering each ype of capial as a separae argumen in he producion funcion. This, however, will no be an appropriae soluion in growh accouning, as i requires imposing he facor shares. Also noe ha he growh rae of aggregae capial sock may be calculaed ln (K s /K s -1) where K s = K s i,. Such growh rae may differ significanly from he calculaed share weighed growh rae using (2), as he laer accouns for he asse heerogeneiy. The difference beween hese wo is ofen considered as a measure of capial qualiy or composiion effec. 4

7 I r + s P ( s) = e ( δ )( ) c( ) s d where P I is he price of capial asses, r is he discoun rae (or rae of reurn) and s and are respecively he ime of acquisiion of capial goods and he ime a which heir services are supplied. Differeniaing wih respec o ime Chrisensen and Jorgenson (1969) have provided a discree ime derivaion of his equaion: 7 (4) I I I c i, = r Pi, 1 + δ i Pi, Pi, (5) where P I is he expeced capial gain erm, i.e. he expeced gain or loss from holding an asse over ime. In he above formulaion, Chrisensen and Jorgenson (1969) assumes he capial gain o be perfecly anicipaed (so ha all expecaions are realized), i.e. he difference beween curren and I I I previous period invesmen prices P = ( P P 1 ). 3.1 The Role of Taxes The above derivaion of renal prices, based on he assumed correspondence beween asse prices and service prices absracs from any ype of axes. I is imporan o noe here ha he asse price - service price correspondence depends on he ax srucure for propery income generaed by he asse. This is because axes are assumed o play a major role in alering invesmen behaviour, he premise being ha enrepreneurs in pursui of gain will be more araced o purchasing capial goods if prices are low (Hall and Jorgenson, 1967). For insance, invesmen decisions of firms can be highly responsive o corporae ax reforms as i may affec he reurn o invesmen (see Cummins e al, 1996). Therefore, he derivaion of renal prices of capial, which assumes correspondence wih asse prices, should accoun for he impac of axes. In his regard, he effec of corporae axes on he cos of capial has been subjeced o discussion in he lieraure (see for insance, Hall and Jorgenson, 1967). 8 In line wih Hall and Jorgenson (1967) and Harper e al. (1989), incorporaing ax facors equaion (5) can be rewrien for i h asse as: 9 I I I c i, = Ti, r Pi, 1 + i Pi, Pi, + bi, δ (6) where b i is he effecive rae of propery axes (nominal valued axes assessed on he real sock of capial, see Harper e al, 1989), T i is he marginal rae of effecive axaion on capial income in asse i in period, defined as (see Jorgenson and Yun 1991): 7 We avoid he deails of his derivaion. Ineresed readers may refer o Chrisensen and Jorgenson (1969). 8 Hall and Jorgenson (1967) examine he effec of ax policy on he cos of capial and conclude ha ax policy highly influences levels and iming of invesmen expendiures. They also noe he crucial role of ax policy in changing he composiion of invesmen; liberalizaion of depreciaion rules has caused a shif away from equipmen in he US, while he invesmen ax credi and depreciaion guidelines have caused a shif owards equipmen. 9 See Jorgenson and Sulliven (1981) for a deailed discussion on he derivaion of he ax incorporaed renal price formula. 5

8 T i = 1 u z i, k i,, (7) 1 u where u is he sauory corporae income ax in year, z i is he presen value of depreciaion deducion for ax purpose on a uni invesmen on asse i over he lifeime of he invesmen and k i is he effecive rae of invesmen ax credi. 10 The user cos formulaion in equaion (6) is assumed o be equivalen o he marginal produc of capial (under perfec compeiion). I reflecs he shadow price of capial (Jorgenson, 1963) in ha i can be considered as he marke price of an asse if rened o a user (in he presence of a well developed renal marke). 3.2 The componens of Renal prices Equaion (6) shows ha he general formulaion of renal price comprises he nominal rae of reurn, he nominal cos of depreciaion, corporae axaion and he nominal gain from holding he asse for each accouning period, i.e. capial gain. The empirical par of his paper is concerned wih he measuremen of (6) and herefore he major componens of renal prices. The measuremen of hese componens may be accomplished in differen ways. In wha follows, we discuss he alernaive ways of measuring hese componens followed in he presen Paper Depreciaion (δ) Depreciaion measures he loss of he marke value of a capial asse over ime. Is imporance in renal prices sems from he fac ha he invesor expecs o ge more services in a shor ime from an asse wih relaively shorer service life. Therefore, while calculaing capial service growh raes, higher weigh should be aribued o asses ha are rapidly depreciaing. For insance, if invesmen in ICT capial, which is a shor-living asse, is growing faser han ha in non-ict capial, he composiion of capial sock will change in favour of ICT asses. Naurally, since he lifeime of he ICT equipmen is shorer i will have a high depreciaion rae compared o non-ict capial. Consequenly, from (6) i is eviden ha he renal price of ICT equipmen, ceeris paribus, will be higher han ha of non-ict capial so ha he growh rae of ICT equipmen in oal capial services ges a higher weigh han ha of non-ict capial. In oher words, a uni worh of invesmen in ICT capial has higher service flow han a uni worh invesmen in non-ict capial. The issues associaed wih he measuremen of he depreciaion are well-discussed in he economic lieraure (see Hulen and Wykoff, 1981 and oher papers in Hulen, 1981). 11 Depreciaion raes may vary over ime and across counries and indusries. However, considering he compuaional simpliciy and he empirical suppor provided by Hulen and Wykoff (1981) he general pracice in empirical lieraure is o assume a consan geomeric depreciaion rae. We do no delve much ino his issue in his Paper. Raher, we op o follow general pracice. We assume a geomeric depreciaion paern. Therefore, we concenrae below on he oher wo componens- he rae of reurn and he capial gain. 10 Invesmen ax credi is a credi agains ax liabiliies in proporion o invesmen expendiure (Jorgenson and Yun 1991) aimed o encourage invesmen. I is equivalen o subsidies or invesmen grans aimed o offse ax liabiliy. 11 Also see Diewer (2001) who provides a discussion on he disincion beween ime-series and cross-secion depreciaions. Time-series depreciaion capures he effec of changes in asse prices beween wo ime periods and he effec of changes in he age of he asse. Thus i includes boh he effec of depreciaion as well as inflaion. 6

9 3.2.2 Raes of Reurn (r) The rae of reurn may be considered o represen he annual reurn on an invesmen as a percenage of he oal amoun of money invesed, or as he opporuniy cos of holding an asse (OECD, 2001a). I may be measured eiher as an exernal (also called exogenous or ex ane) rae of reurn or an inernal (also called endogenous or ex pos) rae of reurn. 12 In he exernal approach he rae of reurn is represened by some exogenous rae such as ineres raes on governmen bonds. In he inernal approach, on he oher hand, raes of reurn are derived as residual, given he value of capial compensaion, depreciaion and capial gains. Clearly here is a problem of choice beween exernal and inernal measures of raes of reurn in he produciviy analysis, and consequenly his issue has been widely discussed in he lieraure (Bernd and Fuss, 1986; Harper e al, 1989; Diewer, 2001; Hulen, 1990). Though here is no consensus on he maer, Bernd (1990) has shown ha he inernal raes which reflec realized marginal producs are heoreically more consisen for produciviy analysis. The poin here is ha in growh accouning one is ineresed o undersand he realized conribuion of capial raher han he expeced conribuions (Bernd and Fuss, 1986; Oulon, 2007). The implied assumpion here is ha he abiliy of inernal reurn o approximae he realized marginal produc is higher han ha of exernal rae of reurn (Bernd, 1990). Recenly, his posiion has been quesioned (see Schreyer e al, 2003). Schreyer e al (2003) argues ha he inernal measures need no be necessarily he correc measures of realized marginal produciviy if for insance he capial is rened by a producer a a given pre-agreed renal price o be paid a he end of he period. A recen sudy by Oulon (2007) proposes an hybrid approach, where he rae of reurn in capial services are derived using exernal rae of reurn bu he capial weighs in growh accouning are derived using inernal (i.e. share of gross operaing surplus in value added) assumpions. He concludes ha he inernal rae is a beer measure o use in a growh accouning exercise from a heoreical perspecive, as suggesed by Bernd (1990). Table 1: Inernal Vs. Exernal Rae of Reurn Definiion Raionale The-ory Advan ages Inernal (ex pos) Residual, given he values of capial compensaion, depreciaion and capial gains. Equaliy of propery income and he curren value of capial services Consisen wih neoclassical heory, and hence he neoclassical growh accouning framework Assumes ha sum of renal paymens for all asses equal o oal propery compensaion (M) ha can be derived from value added Exernal (ex ane) Derived from some exogenous informaion, such as financial marke informaion. Prior o making an invesmen decision, firms will have some idea of he required rae of reurn in deciding how much o inves which need no be equal o he realized (or ex pos) rae (Oulon, 2007). No neoclassical assumpions Do no impose he condiion ha he gross operaing surplus is exhaused by facor paymens. 12 See Table 1 for a snapsho of hese wo approaches. Also see EUKLEMS (2007) and OECD (2001a) for a discussion of hese alernaives. 7

10 as a residual afer labour compensaion, which implies (i) if an asse is excluded rae of reurn will be overesimaed (e.g inangibles)13 (ii)rae of reurn will be overesimaed if appropriae adjusmen is no made for labour compensaion for self-employed, which is par of he mixed income componen of operaing surplus. (iii)neoclassical CRS and perfec compeiion assumpions-in pariy wih growh accouning assumpions. Since he rae is derived as a residual from naional accouns, here is no choice problem Independen of he number of asses, and herefore do no have he problem of over esimaion caused by he exclusion of cerain asses or he presence of labour compensaion for self-employed Relaxes perfec compeiion and CRS assumpions. Choice of an appropriae rae is required. Since here is no consensus on which rae should be used, he choice is lef o he empirical researcher. Hence i is imperaive o know how sensiive he final growh raes of capial and MFPG are o such empirical choices. We use boh hese measures in our empirical analysis in order o examine he sensiiviy of MFPG and capial services o hese choices. In wha follows we explain he procedure adoped in his paper o derive he raes of reurn under hese wo assumpions. The Inernal Rae of Reurn (IR): The inernal rae of reurn is defined as a residual obained afer adjusing capial compensaion for depreciaion and capial gain. This approach, advocaed by Hall and Jorgenson (1967), esimaes he inernal rae of reurn wih he help of an accouning ideniy ha assumes ha he sum of renal paymens o all asses is equal o he oal capial compensaion, i.e. M = n i= 1 c K s i, i, (8) where M is he oal ren received from he various asses in each ime period (or he propery income in ime ), which can be empirically measured as: M = P Y w L (9) y y where P is he value added price, w is he wage rae and L is he labour inpu. The oal capial income or propery compensaion is hus calculaed as he nominal value added minus labour compensaion, assuming a compeiive marke and CRS. 14 I consiss of pre-ax profis, capial consumpion allowances, ne ineres, ransfer paymens, business subsidies, indirec axes and he porion of firms income aribuable o capial. Therefore, he inernal rae of reurn may be measured as a residual afer adjusing M for measures of depreciaion, capial gain and axes. Following Chrisensen and Jorgenson (1969), he inernal rae of reurn can be measured as: 13 However, i is noed by Baldwin e al (2005) ha if he growh rae of omied asse is he same as he average growh of included asses, here will be no bias in inernal rae due o asse omission. 14 Noe ha he sum of labour and capial compensaion equals gross value added a facor cos under all he ypical neo classical assumpions concerning a producion funcion (Bernd and Hesse, 1986). 8

11 IR n I M δ i, T i, Pi, i = 1 = n i = 1 K P s i, I i, 1 T T i, i, K P s i, I i, K s i, + b where IR is he inernal rae of reurn, which is assumed o be consan across all asses in an indusry, bu varies across indusries. As is clear from equaions (9) and (10) one advanage of using an inernal rae is ha he surplus is aken direcly from naional accouns from which he required daa for produciviy analysis is also derived. Thus i ensures full consisency beween income and producion. We measure he IR using equaion (10). The Exernal Rae of Reurn (ER): The inernal approach discussed above is heoreically consisen under he assumpions of CRS, compeiive markes, zero profis and an expeced rae of reurn which equals he ex-pos, realized rae of reurn. A number of sudies have suggesed an exernal or ex ane rae of reurn insead of his inernal rae of reurn ha should overcome some of he limiaions of he laer (Diewer, 1980, Diewer, 2001; Schreyer e al, 2003, Schreyer, 2004; Balk, 2007). In he exernal approach he rae of reurn is aken from some exogenous informaion, such as financial marke informaion. For insance, he rae of reurn could be considered as an exernal rae of ineres if a loan is aken (OECD, 2001a). The raionale here is ha prior o making an invesmen decision, firms will have some idea of he required rae of reurn in deciding how much o inves (Oulon, 2007). This expeced rae need no be equal o he realized (or inernal) rae. The choice of an exernal rae helps o relax he sric neoclassical assumpions of CRS and perfec compeiion, as i does no impose he condiion ha he gross operaing surplus is exhaused by facor paymens (see e.g. Balk, 2007). 15 Balk (2007) argues ha he inernal rae of reurn measure is more prone o measuremen error, as i closes he gap beween he inpu and oupu side of he producion uni, by assuming a zero profi. He provides an approach where he value added is assumed o be he sum of capial and labour coss and profis, hus waiving he neo-classical zero profi and marginal cos pricing assumpions. However, he choice of an appropriae exernal rae is problemaic as here is no well-defined guidelines on which rae should be used. Diewer (1980) has suggesed a wide range of differen raes. Diewer (2001) has suggesed a 4 per cen rae of reurn for OECD counries, under he assumpion ha producers face a real ineres rae of around 4 per cen. He suggess ha his rae is consisen wih long-run economy-wide observed real rae of reurn for OECD counries ha ranges 3 o 5 per cen. 16 In he presen sudy, we use his 4 per cen consan exernal rae of reurn (hereafer CER). i, K s i, (10) 15 The profis in exernal measure can be above he normal profi. Therefore, he difference beween ex pos gross operaing surplus and ex ane capial services may be considered as indicaion of monopoly profis, or presence of economies of scale (Baldwin e al 2005; Schreyer e al, 2004; Schreyer, 2004). The premise is ha he gross operaing surplus could be a sum of capial compensaion and a measure of monopoly power. The laer could arise due o he presence of mark-up over marginal cos, or due o Schumpeerian enrepreneurial incenives or increasing reurns o scale, all of which are assumed o be nonexisen in ex pos rae, under sric neoclassical assumpions (see Schreyer e al. 2004). I could also be due o measuremen error caused by he omission of cerain facors (See Box 1; also see Diewer, 2001; Balk, 2007). 16 Also see Oulon (2007) who makes a similar assumpion. 9

12 3.2.3 Capial Gain The hird componen of renal prices is he capial gain componen. I measures he change in value of an asse ha corresponds o a rise or fall in he price of ha asse, independen of he effecs of ageing. I measures he difference in he price of new capial asses in wo periods, and is herefore independen of ageing. A posiive capial gain reduces he user cos of holding he asse, and is herefore subraced, while a negaive gain (or a loss) increases he user cos and herefore mus be added. Despie is crucial role in he renal price specificaion, here is more han one way by which he capial gain can be incorporaed in he measuremen of renal prices. We include capial gain in our measures of raes of reurn and renal prices using hree alernaive models. 1-Perfecly anicipaed capial gain: As shown in equaion (5) one way of incorporaing capial gain ino he measuremen of renal prices is o assume a perfecly anicipaed capial gain (Chrisensen and Jorgenson, 1969; Jorgenson and Yun, 1991; Harper e al, 1989). Boh in (5) and in (10) he expeced capial gain is represened by annual realized capial gain, ha is ha is he I I I difference beween curren and las year prices i.e. Pi, = ( Pi, Pi, 1 ). Following Harper e al (1989), we call his rae of reurn model as inernal nominal rae of reurn (INR) model. 2-Zero capial gain: A second possibiliy is o drop his erm from he user cos and rae of reurn equaion. This implies ha he producers expec curren prices o prevail in he following period, so ha he expecaions are saic (Woodland, 1975). This rae of reurn measure, which does no include capial gain erm, is called he inernal own rae of reurn (IOR). Afer comparing his approach wih he perfecly anicipaed capial gain approach, Jorgenson and Sieber (1968) have shown a relaive preference for he laer. However, we measure rae of reurn wihou capial gain since our objecive is o undersand he sensiiviy of measured MFPG o alernaive model assumpions. 3-Smoohed capial gain: While he role of capial gain and is inclusion in he renal prices is widely acknowledged, he use of annual capial gain and perfec anicipaion assumpions are subjec o criicism (Denison, 1969; Diewer, 1980). Denison (1969) argued ha long-erm averages of capial gain would be more appropriae as capial gains are highly volaile. The use of a long-erm average capial gain erm migh help o reduce he volailiy in renal prices. In accordance wih Harper e al. (1989), we use a smoohed capial gain series by employing a hree-year moving average. These smoohed capial gain measures are hen subsiued for he perfecly anicipaed capial gain erm in (10), hus providing a hird inernal rae of reurn model which we call he INR wih smoohed capial gain (INRS). Noe ha in all he models we assume ha he nominal rae of reurn is he same for all asses wihin an indusry, while he consan exernal rae of reurn is he same for all asses and indusries. Also, he 4 per cen exernal rae of reurn is assumed o be a real rae of reurn (ne of capial gains), and herefore will be used in he renal price models ha do no incorporae capial gain (i.e. equaion 6 excluding capial gain). All he hree inernal raes of reurns are esimaed wih and wihou ax, hus providing 6 measures of rae of inernal rae of reurn. Thus ulimaely we have 8 differen renal price models and corresponding capial service and produciviy growh raes. Table 2 liss hese 8 renal price models. 10

13 Table 2: Alernaive Renal Price Models Model Abbreviaion Rae of Reurn Capial Gain Tax 1 CER Consan Exernal No No 2 CERTX Consan Exernal No Yes 3 INR Inernal Nominal Annual No 4 INRS Inernal Nominal Smoohed No 5 INRTX Inernal Nominal Annual Yes 6 INRSTX Inernal Nominal Smoohed Yes 7 IOR Inernal Own No No 8 IORTX Inernal Own No Yes 4. Daa and Variables The daa used in his sudy are based primarily on O'Mahony and van Ark (2003), and is updaes available hrough Groningen Growh and Developmen Cenre (GGDC) websie. 17 The sudy is conduced for four EU counries- Neherlands, France, Germany and UK- and he US using annual daa for he period for 26 indusry groups lised in Table 3. The empirical implemenaion in his paper consiss of he measuremen of he MFPG, using alernaive measures of capial service growh raes. Hence he major variables ha ener ino our analysis are facor inpus (labour and capial) and oupu. For he oupu daa, he curren price gross value added obained from naional accouns saisics is deflaed using value added deflaors wih base Labour inpu is measured as he produc of oal hours worked and a measure of labour composiion. In order o calculae MFPG, we also needed he share of labour and capial in he value added (see equaion 1). The labour share is calculaed as labour compensaion divided by value added, boh in curren prices and he former adjused for income of self employed labours. Assuming perfec compeiion and CRS, he capial share is derived as a residual, i.e. value added minus labour compensaion as a percenage of oal value added. 18 Capial sock is esimaed using he perpeual invenory mehod for six asse ypes, using equaion (3). The asses considered for his purpose are non-it machinery, non-residenial srucures, ranspor equipmen, IT equipmen, communicaion equipmen and sofware. The aggregae capial sock is arrived a by summing capial socks across hese six asses. And he aggregae capial service growh raes are derived using equaion (2) applying alernaive renal prices calculaed using differen raes of reurn models lised in Table 2. For his we required daa on depreciaion raes and asse prices. A geomeric rae of depreciaion is assumed. These raes are based on Fraumeni (1997) and Jorgenson and Siroh (2000) and are indusry-specific. 19 Invesmen price deflaors wih base year 1995 are used o represen he asse prices. 17 For a deailed discussion on he daa see Inklaar e al (2005). 18 I may be noed here ha if one use an ex ane measure in deriving oupu share of capial, i will produce an oupu elasiciy of capial which is differen from he one we use. However, in our empirical analysis, hough we employ alernaive raes of reurns (ex pos and ex ane), following he recen heoreical conjecure (see Oulon, 2007), he oupu share of capial is measured by ex pos in all cases. 19 See Inklaar e al (2005). 11

14 Table 3: Indusries and ISIC Codes Number Indusry ISIC rev3 code 1 Agriculure, foresry and fishing Mining and quarrying Food producs Texiles, clohing and leaher Wood producs 20 6 Paper, prining and publishing Peroleum and coal producs 23 8 Chemical producs 24 9 Rubber and plasics Non-mealic mineral producs Meal producs Machinery Elecrical and elecronic equipmen & insrumens Transpor equipmen Furniure and miscellaneous manufacuring Elecriciy, gas and waer Consrucion Wholesale rade Reail rade Hoels and resaurans Transpor & sorage Communicaions Financial inermediaion Business services Social and personal services Non-marke services Apar from he inpu, he oupu and he price daa, we also require ax daa in order o derive raes of reurn and renal prices. As noed by Jorgenson and Yun (1991), he appropriae ax rae o analyze he impac of ax incenives for invesmen is corporae income ax. Following Harper e al. (1989) we use he effecive marginal rae of corporae ax, since we wan o calculae he renal price. The marginal rae of effecive axaion mirrors he incenive o inves. We measure he marginal rae of axaion by equaion (7), using he daa on sauory ax raes on corporae income and he presen discouned value of depreciaion allowances provided by Devereux, e al (2002). 20 The sauory ax raes in he counries in our sample have shown a declining endency over ime, paricularly during he recen years (also see Sørensen, 2007). The depreciaion allowances in Devereux, e al (2002) are available for wo ypes of asses, i.e. plan & machinery and indusrial buildings. We have calculaed he 20 This daa is available from Insiue of Fiscal Sudies websie hp:// /inernaionalaxdaa.zip. A deailed descripion of he sources, definiion and consrucion of hese daa is provided in Devereux, e al (2002), and Devereux, and Griffih (2003). Noe ha Giannini and Maggiulli (2002) have esimaed effecive ax raes for EU counries. We, however, op o use he IFS daa as i provides ime series for he enire period of analysis. The sauory ax raes in Giannini and Maggiulli (2002) for he counries in our sample are comparable wih he IFS raes. For insance, in 1999 he sauory ax raes in IFS daabase are respecively 35, 40, 52 and 30 per cens for Neherlands, France, Germany and he UK, which are approximaely he same in Giannini and Maggiulli (2002) also, as eviden from heir Figure 4. 12

15 effecive ax rae (T i ) using hese wo raes, in such a way ha he rae for indusrial buildings has been applied for non residenial srucures in our invesmen daa, and he depreciaion allowances for plan and machinery are used for all oher asses including sofware ha comes under he caegory of machinery. Since we had no informaion on invesmen ax credi, i is assumed o be zero in our calculaions. The value added in our daa consiss of operaing surplus, compensaion o employees, and he axes on producion. Therefore, while deriving he inernal rae of reurn as a residual of capial compensaion (measured as value added minus labour compensaion), we also need o subrac hese n axes (see equaion 10). The calculaion of indirec axes ( [ b K i i ]) is made direcly from he Naional Accouns of seleced counries. The daa on axes on producion 21 was gahered from he Source OECD Naional Accouns Daabase under componens of value added. These values are divided over calculaed aggregae capial sock in order o arrive a he ax rae (b i ). However, hese raes are no available for individual asses. Therefore, a common rae is derived by dividing, across all asses, oal ax values by oal capial sock, and his rae is applied o all asses. Noe ha in our empirical implemenaion, we have also measured raes of reurn and renal prices wihou his measure of indirec ax, as his daa includes axes no only on capial bu also on employees compensaion. However, since he resuls are found o remain he same, hey are no repored. i = 1 5. Empirical Resuls We have measured he raes of reurn and he renal prices using he four model assumpions, wih and wihou corporae axes (see Table 2). Thus we have 8 differen measures of renal prices, raes of reurns and he corresponding capial service and MFP growh raes. In his secion we discuss he sensiiviy of esimaed MFPG o hese 8 alernaive model assumpions. 5.1 Negaive Renal Prices Since he inernal raes of reurns are measured as a residual, a pracical problem arises when capial income in naional accouns (gross operaing surplus measured by M in equaion 9) becomes negaive. 22 This may resul in negaive raes of reurn. 23 In such cases, he measured renal prices using inernal rae of reurn may also become negaive. Negaive renal prices can also arise even if he rae of reurn is posiive, when here are large capial gains in he user cos formula. Such negaive renal prices are heoreically inconsisen, as he heoreical assumpion underlying he derivaion of growh accouning framework requires inpu prices o be posiive (Bernd and Fuss, 1986). Therefore, he evens of negaive renal prices in a paricular model may be considered as crieria for choosing a 21 These daa consis of axes payable on goods and services when hey are produced, delivered, sold, ransferred or oherwise disposed of by heir producers plus axes and duies on impors ha become payable when goods ener economic erriory by crossing froniers or when services are delivered o residen unis by non-residen unis. They also include oher axes on producion, consising mainly of axes on he ownership or use of land, building or oher asses used in producion, or on he labour employed or on compensaion paid o employees. 22 In cases where here are high amoun of ne subsidies, or losses, value added may become less han labour compensaion resuling in negaive propery compensaion. 23 Barbara Fraumeni commened ha he problem of negaive rae of reurn may be handled by aggregaing indusry groups of similar characerisics. However, while we looked a he paern of negaive appearances we found ha hey are in indusries no of near characerisics. 13

16 paricular model of rae of reurn. The models ha make a large number of negaive renals may be leas preferred. Table 4: Percenage of Negaive Values in Renal Prices Model NLD FRA GER UK US Average INR INRTAX INRS INRSTAX IOR IORTAX Noe: All numbers are in percenages Table 4 provides he percenage of negaive values ha appeared for each model of renal prices. The able shows ha he larges numbers of negaive values appeared in he models ha incorporae capial gain and ax (INRTX). Ou of 3900 renal prices (26 indusries 6 asse ypes 25 years), on average 1.6 percen of negaive values are observed, wih a maximum of 2.5 per cen in Germany and a minimum of 0.8 per cen in he Neherlands. 24 Similar o wha we observe, Harper e al (1989) also found larges negaive renal prices in INR, followed by INRS and IOR models. In general, Germany and UK have winessed he larges number of negaive renal prices while he lowes is found in he US. The indusries ha have produced negaive renal prices in all counries are mining and quarrying, exiles, wood and wood producs, peroleum and coal producs, elecrical and elecronic equipmens and ranspor equipmens (Appendix Table 1). The asse ha has produced negaive renal prices in inernal models in all he counries is non-residenial srucures. As noed by Bonde and Sørensen (2006) his may largely be due o he swing in he invesmen prices causing high capial gain componen in his asse ype. This is suppored by he observaion ha among he hree inernal models IOR has produced he leas number of negaive renal prices, suggesing ha he inclusion of capial gain causes he negaive renal prices. Overall, i is hard o argue ha one model is beer han he oher in erms of he presence of negaive renal prices, as he difference in he number of negaive renal prices produced by hese alernaive models are quie small. Though he IOR model seems o produce relaively less number of negaive values, he difference beween IOR and oher models in erms of he number of negaive renal prices is quie small. In all he cases, on average only less han 2 per cen of negaive values are observed. 24 Surprisingly, in he case of consan raes of reurn models, Germany has shown a posiive number of negaive values in he ax incorporaed model. A deailed look a he daa reveals ha his is in he indusry mining and quarrying, during he years This may be aribued o he high subsidies given o his indusry during his period. If we look a he axes on producion in German mining indusry during his period, i is as high as (- ) 102 per cen of real value added in These axes have shown a declining rend in laer years, hough hey declined only o (-) 68 per cen in

17 5.2 Effec of Alernaive Rae of Reurn Models: Aggregae Resuls We have calculaed he renal share weighed capial service growh raes using (2) for all 26 indusry groups in each counry separaely, over he period using alernaive renal prices. The resuling capial service growh raes along wih capial sock growh raes for he aggregae economy are ploed in Figure I is quie clear ha he capial services grow faser han capial sock in mos years, hus leaving a gap beween he levels of hese wo. This is due o he shif in he composiion of capial; increasing share of shor living asses will resul in acceleraed capial service growh, hence, following Harper e al (1989), we call i a composiion effec. I can be also seen from he Figure ha he capial service growh raes produced by differen models end o differ, hough no very significanly. While he difference is more prominen beween inernal and exernal models, paricularly wih hose which do no include capial gain, i is rivial beween inernal models, in general. In he UK and France, he capial services derived using CER models end o grow a a slower pace compared o he inernal models. This is more visible in he UK, which is in conformiy wih Oulon (2007) 26. The inclusion of ax in he calculaion of raes of reurn and renal price makes he sory no very differen. I caused very lile difference in he calculaed growh raes. The capial service growh raes are plugged ino equaion (1) in order o calculae he MFP growh. A comparison of he MFPG obained from differen models will help us undersand how sensiive he measured MFP growh is o hese differen capial aggregaion procedures. The effec of alernae aggregaion procedure on aggregae economy MFPG is depiced in Figures 2a o 2d. 27 The Figures depic he difference in average MFPG for he enire period, along wih wo sub periods, and under various assumpions. 25 The oal economy capial and MFP growh raes are derived as simple average across indusries. One could also derive he aggregae MFPG as a weighed average of individual indusry growh raes. However, since our ineres is o undersand he sensiiviy of hese growh raes o alernae model specificaions he former approach is appropriae. 26 See Oulon (2007, Figure 2, pp. 311). 27 The oal economy capial and MFP growh raes are derived as simple average across indusries. One could also derive he aggregae MFPG as a weighed average of individual indusry growh raes. However, since our ineres is o undersand he sensiiviy of hese growh raes o alernae model specificaions he former approach is more sensible. 15

18 Figure 1: Growh of Capial (under various assumpions) and Labour Inpus, used in TFPG Calculaion, NETHERLANDS FRANCE GERMANY Labor inpu growh raes UK US NLD FRA GER UK US K K_CER K_CERTX K_INR K_INRTX K_INRS K_INRSTX K_IOR K_IORTX Noes: K is he capial sock and K_* are he capial services using * rae of reurn and he suffix TX indicaes he presence of ax variable in rae of reurn. Labour inpu is he produc of hours worked and labour composiion (ofen considered as a measure of labour qualiy). 16

19 Figure 2: The Effec of Alernaive Capial Aggregaion on MFPG (in %) Figure 2a: The Capial Composiion Effec on MFPG NLD FRA GER UK US NLD FRA GER UK US NLD FRA GER UK US INR INRS IOR CER INR INRS IOR CER INR INRS IOR CER Noe: MFPG using capial services - MFPG using capial sock. Figure 2b: The Tax Effec on MFPG NLD FRA GER UK US NLD FRA GER UK US NLD FRA GER UK US INR INRS IOR CER INR INRS IOR CER INR INRS IOR CER Noe: MFPG using capial services wihou ax minus MFPG wih ax. Figure 2c: The Rae of Reurn Effec on MFPG (Inernal vs. Exernal) NLD FRA GER UK US NLD FRA GER UK US NLD FRA GER UK US INR INRS IOR INR INRS IOR INR INRS IOR Noe: MFPG using inernal models minus MFPG wih exernal models. Figure 2d: The Rae of Reurn Effec on MFPG (Inernal vs. Inernal) NLD FRA GER UK US NLD FRA GER UK US NLD FRA GER UK US INR INRS INR IOR INRS IOR INR INRS INR IOR INRS IOR INR INRS INR IOR INRS IOR Noe: Difference in MFPG using alernaive inernal models as menioned in legend. All are un-weighed averages across 26 indusries 17

20 In Figure 2a he average composiion effecs on MFPG measured as he difference beween he MFPG measured using he growh rae of capial service and capial sock are depiced. I may be noed ha he larger composiion effec could occur due o he shif owards equipmen invesmen, paricularly ha of shor-living equipmens. Similarly, he decline in he relaive price of an asse (for insance he decline in he price of equipmen such as IT equipmen relaive o srucures) would make he relaive magniude of capial gain erm ha is subraced from he renal price equaion smaller aribuing i a larger weigh in capial services (see Harper e al, 1989). Boh hese facors would cause a larger capial service growh rae, and lower MFPG. In mos counries he capial composiion effec on MFPG is negaive indicaing ha capial sock ends o overesimae he MFPG. Excepions o his phenomenon are Germany and he UK, paricularly during he second period, In general he effec is seen o be larger in he exogenous rae of reurn model and leas in IOR models. Such large difference beween capial service growh rae and capial sock growh rae in he case of exogenous rae of reurn is observed by Oulon (2007) in he case of UK. Our resuls are comparable o Harper e al (1989) for he Unied Saes, in erms of ranking of differen models and signs of he effec, excep for he CER model where he signs are differen. The second panel in he figure depics he difference in measured MFPG when corporae axes are included in renal price models. I is clear from he Figure 2b ha he inclusion of ax variable has shown generally very meagre effecs on MFPG. The differences are quie marginal and ypically lower han 0.05 percenages. US is he only counry where here is some difference observed when ax is incorporaed hroughou he period, bu only in he consan exernal rae of reurn model. We conclude ha he incorporaion of axes in he calculaion of renal prices migh be heoreically appealing, bu empirically no very relevan. To compare alernaive models of renal prices, i can be seen ha here are modes differences beween exernal and inernal models (Figure 2c). The exernal models end o produce lower MFPG compared o he inernal models. This is rue in all he counries excep in he UK, bu only in models ha incorporae capial gain. The effec is seen o be relaively larger in he US, paricularly during , followed by he Neherlands and France. Noably he difference is larger when capial gains are excluded from inernal models (i.e. IOR models). Thus he exernal models end o be closer o inernal models when capial gains are incorporaed in he laer. Beween he differen inernal models here seems o exis no significan difference in mos counries. Neverheless, he inclusion of capial gain erm in he inernal models does make some differences a leas in some counries (Figure 2d). For insance, in he US and in he UK, he difference beween models wih capial gain and wihou capial gain amouns up o more han (0.15) percenage poins during In boh hese counries, he difference beween INR wih annual capial gain and INR wih smoohed capial gain is also relaively more, hough he magniude is sill rivial. This may sugges ha difference in INR and IOR in hese counries may be due o he swing in he invesmen prices ha would affec he capial gain erm. IOR model has generally shown a endency o produce larger MFPG compared o he INR models. 18