Joensuu, Finland, August 20 26, 2006

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1 Sesson Number: Parallel Sesson 4A Sesson Ttle: Productvty Measurement: Methodology and Internatonal Comparsons Sesson Organzer(s): Bart van Ark, Unversty of Gronngen, Netherlands Sesson Char: Bart van Ark, Unversty of Gronngen, Netherlands Paper Prepared for the 9th General Conference of The Internatonal Assocaton for Research n Income and Wealth Joensuu, Fnland, August 6, 6 Measurng Multfactor Productvty Growth Anta Wölfl, CEPII (Centre d Etudes Prospectves et d Informatons Internatonales) Dana Hajkova, Monetary Polcy and Strategy Dvson, Czech Natonal Bank, For addtonal nformaton please contact: Author Name(s) : Anta Wölfl Author Address(es) : 9, Rue Georges Ptard, 7574 Pars Cedex 5, France Author E-Mal(s) : anta.wolfl@cep.fr Author FAX(es) : +33 () Author Telephone(s) : +33 () Ths paper s posted on the followng webstes:

2 MEASURING MULTIFACTOR PRODUCTIVITY GROWTH Anta Wölfl *, Dana Hajkova **, ABSTRACT Ths paper quantfes and examnes the contrbuton of captal, labour and multfactor productvty (MFP) to GDP growth and analyses the role of measurement of captal and labour nputs for the MFP estmate, usng a comprehensve growth accountng exercse for 4 OECD countres. For most OECD countres, the strongest contrbutons to GDP growth over the past decade have come from growth n total captal nput and MFP. Ths s to some extent related to an ncreasng role of nformaton and telecommuncaton technologes n economc growth, partcularly over the - perod. The mportance of measurement ssues vares substantally wth the type of measurement ssue beng consdered. Substantal dfferences are observed between employment- and hours worked based MFP growth rates. Also the respectve weghts wth whch captal and labour enter the growth accountng equaton, and thus, the assumptons concernng the effcency of producton and competton n product markets, sgnfcantly nfluences the resultng MFP estmate. Fnally, the results suggest that polcy conclusons on the bass of dfferent emprcal studes should be made very carefully, n partcular as regards the tme perod for whch the respectve studes have been undertaken, as well as whether actual or trended tme seres are beng consdered. * ** Centre d Etudes Prospectves et d Informatons Internatonales, CEPII, Pars; e-mal: wolfl@cep.fr Monetary Polcy and Strategy Dvson, Czech Natonal Bank, Prague; e-mal: dana.hajkova@cnb.cz Acknowledgements: Ths paper was prepared n the framework of the establshment of an OECD Productvty Database n and 4, whle both authors were workng for the OECD. The results n ths paper are, therefore, partly based on data of the OECD Productvty Database of md-4, and are not necessarly dentcal to the most recent data of the OECD database (see Table A n the appendx). However, secton of the paper replcates some of the most recent measures of the OECD Productvty Database for reference. Partcular thanks for comments and deas go to Drk Plat, Paul Schreyer and Guseppe Ncolett. We would lke to thank also the partcpants of the OECD-nternal semnar on Productvty measurement n December, for ther helpful comments. The opnons presented n ths paper are the opnons of the authors and do not necessarly reflect the opnons of the OECD or ts member governments.

3 TABLE OF CONTENTS. Introducton...4. Growth n GDP and productvty emprcal results The growth accountng framework and the data Growth n GDP and ts components Growth n MFP and the role of measurement Measurng MFP n a growth accountng framework - basc concepts and methodologes...4 The general framework...4 Measurng physcal captal...6 Measurng labour nput... Measurng labour and captal shares The mpact of measurement on MFP growth a senstvty analyss... The measurement ssues analysed... Emprcal results for 8 OECD countres Concluson...33 References...34 Appendx

4 . Introducton Captal deepenng and growth n multfactor productvty (MFP) have obvously been mportant drvers of economc growth snce the s. However, assessment of the sze of ther growth contrbuton can be greatly nfluenced by measurement ssues. In ther semnal paper of 967, Jorgenson and Grlches, for nstance, found that the contrbuton of multfactor productvty to output growth declned from ntally about 47 of total output growth to about.7 after correctng for potental errors n measurng output, captal and labour nput, as well as the method of aggregaton. They concluded that If quanttes of output and nput are measured accurately, growth n total output s largely explaned by growth n total nput. In ths case, the observed growth n total factor productvty s neglgble. The present paper re-examnes the contrbuton of captal, labour and multfactor productvty to GDP growth, usng a comprehensve growth accountng exercse for several OECD countres. The man contrbuton of ths paper s to draw attenton to the mportance of the measurement of MFP. The growth accountng methodology breaks GDP growth down nto the weghted sum of growth rates of the man factor nputs, labour and captal, and the growth of MFP. Growth n MFP s measured as the so-called Solow-resdual,.e., the part of GDP growth that cannot be explaned by the growth of captal and labour nput. The paper contrasts the presented MFP measure wth those based on dfferent assumptons and examnes how to measure growth n these factor nputs and ther weghts n total costs or ncome. Ths paper bulds on the OECD Productvty Database (PDB) that makes t possble to compute more precsely the contrbutons of growth factors, ncludng the contrbuton of dfferent captal assets. The paper s structured as follows. The next secton starts wth an overvew of the composton of GDP growth over tme, and nvestgates whether GDP growth durng - was drven by compostonal changes, such as a shft from labour to captal or a shft towards ICT captal. The thrd secton examnes the effect of captal nput and labour nput measurement on the resultng MFP growth. Ths starts wth a theoretcal outlne of the man measurement ssues. The mpact of dfferent methodologes and assumptons on the resultng MFP estmate s then analysed usng a senstvty analyss smlar to that undertaken n Jorgenson and Grlches (967). The fourth secton concludes. For techncal reasons the paper uses data from December for the senstvty analyss n Secton 3. Recent results from the OECD Productvty Database are presented n Secton. For a comparson of the results, see Table A n the appendx. 4

5 . Growth n GDP and productvty emprcal results.. The growth accountng framework and the data Ths paper examnes the contrbutons of labour and captal nputs and multfactor productvty to economc growth usng the general growth accountng framework. The basc prncple of ths methodology s that growth n GDP can be broken down nto the weghted sum of growth rates of the man factor nputs, labour and captal, wth the respectve weghts beng the shares of labour remuneraton and captal ncome n total ncome or costs. 3 The part of GDP growth that cannot be explaned by the rate of growth of captal and labour, the so-called Solow resdual, s assumed to be the growth n MFP. Let Y & Y represent the growth rate of output, K & K the growth rate of captal nput, L & L the growth rate of labour nput and g growth n multfactor productvty, the general growth accountng framework can be wrtten as: Y& ( K& K ) + s ( L L) g Y = s & K L + () It s useful for the nterpretaton of the emprcal results later on to dstngush two dfferent defntons of MFP growth, or g. The classcal approach used by Solow sets growth n MFP equal to technologcal progress, n the form of a shft over tme n the technology that s underlyng the producton functon. The other approach s to thnk of MFP growth n a broader sense; n addton to pure technologcal change, t may nvolve the effect of unobserved factors, lke changes n the effcency of producton, for nstance, due to non-constant returns to scale or mperfect competton. Gven that gaugng the contrbuton of pure technologcal change would requre quantfyng the effect of the unobserved factors and would nvolve makng addtonal assumptons, the latter defnton of MFP (called apparent MFP n Schreyer, forthcomng) has been adopted n the paper. Snce, n ths case, the strct assumptons of constant returns to scale and perfectly compettve markets are not appled; total costs n the form of labour and captal remuneraton do not have to be equal to total factor ncome. As a consequence, the weghts n equaton (),.e., the shares of captal and labour, s k and s l, are the shares of captal and labour n total costs and not n total ncome, as they would be n the neoclasscal growth accountng framework. 4 The growth accountng exercse n ths paper uses the OECD Productvty Database (PDB). The methodology used n PDB wll be descrbed n more detal n the thrd secton of ths paper. There are, however, two features of the PDB that are mportant for the nterpretaton of the man patterns shown n the second part of the paper. The frst one relates to the nature of captal servces as compared wth measures of captal stock used n many other studes. The OECD Productvty Database constructs a measure of captal nput whch comes very close to the theoretcal concept of the productve captal stock nstead of a gross or wealth captal stock. It ncorporates a so-called age-effcency functon whch reflects the loss n productve capacty of a captal good over tme,.e., the rate at whch the physcal contrbuton to producton of a captal good declnes over tme. The second mportant aspect s that the OECD Productvty Database dfferentates between captal assets. Ths mples that t takes nto account the dfferences n growth rates across captal assets, enablng the analyss of the effects of captal composton on growth n GDP and MFP. In partcular, the role of nformaton and communcatons technology (ICT) for growth n GDP and MFP can be analysed thanks to 3 4 Wthn the neoclasscal growth accountng framework, total ncome s equal to total costs due to the assumptons of constant returns to scale and perfect competton n nput and product markets. For a more detaled presentaton and dscusson of these ssues, see Schreyer (forthcomng). 5

6 the dfferentaton between ICT and non-ict captal. 5 ICT-related captal assets nclude hardware, communcaton equpment and software. Non-ICT captal assets nclude transport equpment and nonresdental constructon, products of agrculture, metal products and machnery other than hardware and communcaton equpment, and other products of non-resdental gross fxed captal formaton. In order to account for rapd qualty changes of ICT-captal assets, a harmonsed hedonc prce ndex s used. 6 The results n the remanng part of secton are based on the model descrbed by equaton. 7 The change n captal nput s defned as the change n captal servces aggregated over assets and computed usng the age-effcency functon and hedonc prces. Labour nput s defned as total number of hours worked. Growth n MFP s the resdual GDP growth unexplaned by the sum of contrbutons of captal and labour,.e., ther growth rates weghted by ther respectve shares n total factor cost... Growth n GDP and ts components Fgure suggests that GDP growth n most OECD countres over the s was for a large part drven by growth n captal and MFP. In many countres, growth n captal accounted for around one thrd of GDP growth from to. A strong contrbuton of captal can n partcular be observed n the Unted States, the Unted Kngdom, Denmark, Italy, Germany and Japan, and to a lower degree n Canada. For some countres, growth n MFP s the man drver of GDP growth n the - perod. Ths s n partcular the case for Ireland, Fnland, Portugal, Australa, Sweden and France. Growth n labour nput was also mportant for a few countres over -, notably n Ireland, Canada and the Netherlands. Fgure and Fgure A n the annex ndcate that the contrbuton of captal to GDP growth s less lnked to economc cycles than the contrbuton of labour. Whle the contrbuton of labour was negatve n many OECD countres durng the frst half of the s, the contrbuton of captal was postve. Ths s even clearer when examned over a longer tme perod; n absolute terms, the contrbuton of labour has fluctuated more strongly than the contrbuton of captal for most countres whle the contrbuton of captal has stayed relatvely constant snce 98 (Fgure A). As wll be dscussed below, ths s manly due to hgher varablty n the growth rate of labour nput as compared to captal nput, and only to some degree due to changes n the relatve shares of labour and captal Snce ths paper analyses the role of ICT wthn a growth accountng framework, t offers a nonparametrc analyss of the effect of ICT on economc growth. Effects from ICT whch are not measured by the contrbuton of ICT captal assets, such as spllovers from ICT, are only ndrectly captured wthn the growth rate of MFP. For an emprcal assessment of spllovers from ICT, see, for nstance, Stroh (). For an overvew of estmatons of the captal coeffcent,.e., the elastcty of output wth regard to captal nput, see for nstance Jorgenson (). See Schreyer () for a dscusson of hedonc prce ndces. A hedonc prce ndex accounts for the changes n the qualty of a product by makng use of the relaton of the prces of dfferent varetes of a product and the amount of the characterstcs n each of the varety that have an nfluence on the prce (for a comprehensve treatment of hedonc ndexes see Trplett, 4). The hedonc prce ndex for ICT-related components s harmonzed by usng the rato of US prce ndces for ICT and non-ict related goods (see also part 3.). The reference scenaro s descrbed n more detal n secton 3. Ths s also the approach that s used n the OECD Productvty Database. 6

7 Fgure Contrbuton of captal, labour and MFP to GDP growth, - and - *, n percent Captal Contrbuton Labour Contrbuton MFP 5. n percent 3.. n.a. n.a. n.a. n.a Ireland Australa New Zealand Unted States Denmark Austra Netherlands Canada Unted Kngdom Portugal Belgum Japan Span Germany France Italy Sweden Fnland * Captal Contrbuton Labour Contrbuton MFP 5. n percent Ireland Australa Span Fnland Canada Unted States Portugal New Zealand Unted Kngdom Sweden Netherlands France Austra Belgum Denmark Italy Germany Japan Note: *) or nearest year avalable. Source : OECD Productvty Database, 6. The mportance of captal growth as a drver of GDP growth s partly due to strong nvestment n modern nformaton and communcaton technologes (Fgures and 3). 7

8 Fgure The contrbuton of growth n ICT captal assets to GDP growth - and - *, n percentage ponts Australa Unted States Sweden Denmark Unted Kngdom Canada Belgum New Zealand Japan Netherlands Fnland Span Greece Italy Portugal Ireland Austra France From to, ICT captal contrbuted on average about.5 percentage ponts to GDP growth n OECD countres (Fgure ). Very strong contrbutons of ICT captal to GDP growth can be observed n the Australa, Unted States, Canada, the Netherlands and, where ICT captal explans about one quarter of GDP growth over -. Fgure shows also that the contrbuton of ICT captal to GDP growth has strongly ncreased snce the frst half of the s. In relatve terms, the contrbuton of ICT captal to GDP growth ncreased from about 5 of total GDP growth to about durng the two perods. To some extent, growth n GDP over the and n the begnnng of the s was nfluenced by a shft n the composton of captal servces towards captal assets wth stronger growth. Ths s, for nstance, reflected n the ncreasng share of ICT captal n total captal nput (Fgure 3). Whle n the - perod, t was non-ict captal that contrbuted most to captal growth, ICT captal contrbuted to more than half of total captal growth over the - perod n ten OECD countres. Throughout the s, hardware accounted for the largest part of the contrbuton of ICT captal to growth n total captal, but software and communcatons equpment have become ncreasngly mportant. 8

9 Fgure 3 The contrbuton of growth n ICT captal to growth n total captal nput - and - *), n percentage ponts - 7. Non-ICT Hardware Communcatons Equpment Software Span Japan Canada Austra Portugal Unted States Unted Kngdom Germany France Denmark Sweden Belgum Italy Australa Netherlands Ireland New Zealand Fnland -* 7. Non-ICT Hardware Communcatons Equpment Software Ireland Portugal Canada Denmark Australa Unted Kngdom New Zealand Sweden Austra Italy Unted States Japan Netherlands France Belgum Span Germany Fnland Note: *) Or nearest year avalable. Source : OECD Productvty Database,. Fgure 4 shows that the growth rate of multfactor productvty accelerated n several countres n - as compared to the frst half of the s. Ths s the case for Australa, France, Sweden and the 9

10 Unted States, and partcularly n Fnland and Ireland, where MFP growth accelerated by more than percentage pont. In Ireland and Australa, MFP ncreased by about.5 to almost percentage ponts from the 98s to the s. The relatvely small ncrease n MFP growth over tme n the Unted States as opposed to the relatvely strong ncreases n other countres may be related to a catchng-up effect of the other countres from relatvely low levels of MFP. 5. Fgure 4: Growth n multfactor productvty, annual percentage growth - - -* 3. n percent. -. Italy Denmark Netherlands Span Japan Belgum New Zealand Austra Canada Germany Portugal Unted Kngdom France Unted States Sweden Australa Greece Fnland Ireland *) Or nearest year avalable. Source : OECD Productvty Database, 6 Fgure 4 gnores, however, that there have been strong fluctuatons n MFP growth over tme. Ths becomes clear from Fgure 5, whch presents the development n the growth rates of labour productvty, captal deepenng, and MFP snce 98, and from Fgure A, whch presents the annual average growth rates of GDP, labour, captal and MFP over tme. There are two man results from ths analyss. Frst, n most OECD countres, the growth n labour productvty, as measured by the growth of GDP per hour worked, moves almost n lne wth the growth n MFP. The vsbly negatve correlaton between captal deepenng and hours per worker clearly contrbutes to ths result. Moreover, both MFP and labour productvty show a smlar development to captal deepenng n some countres and over certan tme perods (Fgure 5). These patterns support the observaton made above that growth n OECD economes s manly drven by captal deepenng and the growth n MFP; a fndng that also holds over long tme perods. The lagged and weaker lnk between fluctuatons n captal nput and productvty may be due to two factors. The frst s the addtve nature of computed captal servces. Whle nvestment may fluctuate consderably over tme, these changes only show up as ncremental changes n the accumulated captal stock. The second reason s that possble changes n the utlsaton of captal are not reflected n the measures of captal servces.

11 Fgure 5: Movements of growth n labour productvty, captal-deepenng, and MFP, annual growth rates n percent Australa Canada Captal Deepenng MFP Labour Prod Hours/Empl Captal Deepenng MFP Labour Prod Hours/Empl Fnland France Captal Deepenng MFP Labour Prod Hours/Empl Captal Deepenng MFP Labour Prod Hours/Empl Source : OECD Productvty Database, 6

12 Fgure 5: Movements of growth n labour productvty, captal-deepenng, and MFP, annual growth rates n percent Germany Ireland Captal Deepenng MFP Labour Prod Hours/Empl Captal Deepenng MFP Labour Prod Hours/Empl Italy Japan Captal Deepenng MFP Labour Prod Hours/Empl Captal Deepenng MFP Labour Prod Hours/Empl Source : OECD Productvty Database, 6

13 Fgure 5: Movements of growth n labour productvty, captal-deepenng, and MFP, annual growth rates n percent, contnued Netherlands Span Captal Deepenng MFP Labour Prod Hours/Empl Captal Deepenng MFP Labour Prod Hours/Empl Unted Kngdom Unted States Captal Deepenng MFP Labour Prod Hours/Empl Captal Deepenng MFP Labour Prod Hours/Empl Source : OECD Productvty Database, 6 3

14 The second result from the analyss s that MFP growth shows strong fluctuatons whch are smlar to GDP growth (Fgure A). There are typcally four explanatons for the pro-cyclcal nature of MFP growth (Basu and Fernald, ; Basu et al., ). Frst, MFP measures should pck up changes n technology. Thus, f the rate of technologcal change fluctuates over tme, ths wll show up n cycles of output and productvty growth. Second, cycles n productvty growth may be related to mperfect competton and ncreasng returns to scale. Fgure 5 shows strong cyclcal behavour n nputs, notably labour nputs. Wth mperfect competton and ncreasng returns to scale, ncreases n nputs may result n productvty ncreases. Thrd, not only nvestment n nputs but also ther utlsaton may vary over the busness cycle. A cyclcally-related reallocaton of resources across uses wth dfferent margnal products (e.g., ndustres wth dfferent market power) s a fourth possble reason for the cyclcalty of aggregate MFP. 3. Growth n MFP and the role of measurement The emprcal results above confrm a strong contrbuton of captal growth and MFP growth to growth of GDP. Both the contrbuton of captal as well as the rate of growth of MFP depend, however, on the way labour and captal nputs are measured. The followng secton examnes the role of measurement for the growth rate of MFP. It starts wth an overvew of ssues of MFP measurement as derved from the theoretcal lterature. It then analyses the senstvty of measured MFP to dfferent assumptons regardng the measurement of labour and captal. 3.. Measurng MFP n a growth accountng framework - basc concepts and methodologes The man measurement ssues dscussed here are those assocated wth the computaton of captal servces and labour nput. Measurement ssues related to captal concern, n partcular, how productve captal s defned and how dfferences n the productvty of captal assets over tme or across assets are taken nto account. One major captal-related measurement ssue s also how to construct an underlyng prce ndex that can take account of rapd qualty changes n some captal assets, notably ICT. The man labour-related ssue s how to correctly measure the qualty and utlsaton of labour. Yet another set of results s obtaned when MFP s computed based on trend values of underlyng varables. These measurement ssues are descrbed n more detal below. 8 The general framework In general, (multfactor) productvty s defned as output per unt of factor nput. In order to measure multfactor productvty, Solow started from a neoclasscal producton functon Y = G F( K, L, t) (Barro, ; Hulten, ). 9 In ths formulaton, the Hcks-neutral shft parameter G t measures the shft n the producton functon at gven levels of labour and captal. Growth n multfactor productvty s then defned as the Hcks-neutral and exogenous shft of the producton functon over tme: t t t t 8 9 Ths secton provdes a rough overvew of relevant measurement ssues. It s far from comprehensve and does not treat all ssues n detal. See, for nstance, Schreyer (forthcomng) for a more detaled theoretcal and emprcal analyss of the role of exogenous versus endogenous rates of return for MFP measurement. See Grlches and Jorgenson (966), Nadr and Schankerman (98), Harper (), Jorgenson (), Stendel and Stroh () for more detaled descrptons and dscussons of growth accountng and MFP measurement. 4

15 G G Yt Y =. () F K, L ) F( K, ) t ( t t L Solow addressed the key queston of measurng G t by usng the total dfferental of the producton functon and thus a non-parametrc ndex number that does not mpose a specfc form on the producton functon. Let Y & Y represent the growth rate of output, K & K the growth rate of captal nput and L & L the growth rate of labour nput. Then, multfactor productvty growth s the part of GDP growth that cannot be explaned by the rate of growth of captal and labour as: F L ( K& L K ) ( L& L) F K g Y& K = Y. (3) Y Y In ths formulaton, F K and F L stand for the factor margnal products terms, equaton (3) becomes: F K or F L. Usng logarthmc d lny FK K d ln K FL L d ln L g =. (4) dt F dt F dt When product and factor markets are compettve and under constant returns to scale, a proft-maxmsng frm wll hre labour and nvest n captal such that nputs are pad ther margnal products. Ths means that the margnal product of captal s equal to the real user cost or rental prce per captal, F K = u / P ; and the margnal product of labour s equal to the average wage rate per employed person or per hour, F L = w / P. Let wl represent total compensaton of labour and uk total remuneraton of captal (n tme t), then the standard prmal estmate of the rate of growth of MFP follows from: wth sk d lny d ln K d ln L g = sk s L. (5) dt dt dt and s L beng the share of labour and captal n total costs or ncome. From equaton () to (5) t becomes clear that, n theory, g s equal to the growth rate of the Hcksan effcency parameter. In practce however, g s a measure of our gnorance, as Abramovtz (956, cted n Hulten ()) called t, precsely because g s a resdual. Or as Hulten () puts t: Ths gnorance covers many components, some wanted (lke the effects of techncal and organsatonal nnovaton), others unwanted (measurement error, omtted varables, aggregaton bas, model msspecfcaton). The lnk between the change n the shft parameter and the ndex number can be seen by comparng G t wth St Q Q the general formulaton of ndex number: S t : S = t ( ro K t + wlt ) ( ro K + wl ). Snce data are not contnuous over tme, but come n dscrete tme unts, the contnuous Dvsa ndex s approxmated by the Törnqust ndex. Ths means that the contnuous-tme ncome shares s k and s l are replaced by the average between-perod shares of perod t and t-. The startng values are the shares for the frst year for whch respectve data were avalable. The choce between total costs or total ncome as the reference for the nput shares depends on the assumptons underlyng the producton functon and factor and product markets. See more below on the measurement of the captal and labour shares. 5

16 Measurng physcal captal The approprate measure for captal nput wthn the growth accountng framework s the flow of productve servces that can be drawn from the cumulatve stock of past nvestments n captal assets. Flows of productve servces of an offce buldng, for nstance, are the protecton aganst ran or the comfort and storage servces that the buldng provdes to personnel durng a gven perod (Schreyer et al., ). The prce of captal servces per asset s measured as ther rental prce. If there were complete markets for captal servces, as s the case for an offce buldng, for nstance, rental prces could be drectly observed. For some assets, however, rental prces have to be mputed. The mplct rent that captal good owners pay themselves gves rse to the termnology user costs of captal. Total remuneraton for captal, or total captal ncome, s the product of the quantty of captal servces for each asset of a specfc generaton (or vntage), K t,s, and the user costs, or the prce, of captal servces that are derved from an s-year old captal good of type n year t, u t,s. 3 The growth rate of total physcal captal results then as the weghted sum of growth of servces from each asset, wth the share of captal u K ncome from each asset n total captal ncome,, as the weght: u j K j j d ln K dt N u K d ln K = (6) u K dt = j j j Measurng captal servces per asset Captal assets dffer n ther growth rates and n ther margnal productvty, and how well these dfferences are taken nto account s a determnant of the accuracy of the measured MFP growth. Theoretcally, one could dstngush between three dfferent forms of varatons n the quantty of captal servces: changes n the volume of a partcular vntage of an asset over tme (where vntage stands for a partcular model wth a partcular technology), changes n the quantty of captal servces between successve vntages of a partcular asset, and changes n the overall asset composton of productve captal stocks. 4 Wthn the OECD Productvty Database, such varatons are captured n two ways. Frst, the changes n captal servces between dfferent vntages are captured by the use of qualty-adjusted prce ndces for nvestment n the computaton of productve stocks. Second, dfferences n the productvty across assets are captured by applyng user cost weghts n order to aggregate across dfferent types of assets. It can be shown that user cost weghts, approxmate the elastcty of producton of ndvdual assets. The growth accountng lterature has emphassed the role of changes n captal qualty over tme. Technologcal progress does not fall lke manna from heaven as s assumed n the neoclasscal model of growth accountng (Greenwood and Jovanovc,, Hulten, ). New captal s better than the old 3 4 The followng descrpton of the OECD approach concentrates on measurement ssues that are relevant for the senstvty analyss below. Total payments for captal servces are expressed n current prces but for convenence t s assumed that these current prce payments can be broken down nto a prce component uk t and a quantty component K t. Emprcally, t s almost mpossble to dsentangle these three dfferent forms of qualty dfferences as ths would requre data on a level of detal that s not publcly avalable. However, the senstvty analyss below wll try to come as close as possble to an emprcal assessment of these dfferent forms of dfferences or varatons n captal qualty. 6

17 captal because of wear and tear, but also because the new captal s more productve than the old one was when t was new. As a consequence, the measured MFP growth wll overstate true MFP growth f t fals to account for the changes n the composton of factor nputs towards assets of hgher qualty (Barro, ). In order to capture changes n productvty of assets over tme, notably across dfferent generatons, Hulten () proposes to compute nvestments and the captal stock, or the servces that can be derved from the exstng captal stock, n terms of effcency unts. The captal stock n effcency unts can be dentfed as the product of the captal stock n natural unts and the average emboded techncal effcency, defned as the weghted average of the best-practce effcency levels assocated wth each past vntage of nvestment. 5 To the extent possble, the data on productve captal servces used n the OECD Productvty Database, take such changes n captal qualty nto account. The productve stock of asset at the end of perod t, St, s computed as the accumulaton of past nvestments, It s, takng nto account changes of productvty per asset over tme, as represented by the retrement functon, F s, and the age-effcencyfuncton, h s. The productve captal stock at the end of perod t- can thus be wrtten as: t = t ( hs Fs I t s ) s= S. (7) Equaton (7) starts wth the assumpton that the flow of captal servces from an s-year old asset s n proporton to the volume of nvestment of that asset s years ago. Ths assumpton s made snce typcally nether the flow of captal servces nor the length of lags between purchases of nvestment goods and ther actual use n the producton process are known. The quantty of nvestment of asset n year t, It s, s ether measured n physcal unts f a truly homogenous asset can be observed or s obtaned as the deflated value of current prce nvestment. The functon F s n equaton (7) reflects the retrement pattern, whch s needed to descrbe how assets are wthdrawn from servce. Typcally, a retrement pattern s a dstrbuton around the expected or mean servce lfe. For nstance, each truck n a fleet of dentcal vehcles of the same age has the same expected servce lfe (Schreyer et al., ). In practce, however, some of the trucks are retred before or after the expected servce lfe. For present purposes, F s s assumed to be non-negatve and decreasng n s, the age of an asset. For a new asset wth s=, F takes a value of one. The functon h s n equaton (7) reflects the age-effcency functon. The ratonale behnd ths functon s that a cost-mnmsng producer wll choose a composton of captal assets of dfferent vntages such that the relatve productvty of two dfferent vntages s just equal to ther relatve user costs. The ageeffcency functon reflects the loss n productve capacty of a captal good (of a partcular generaton) over tme or the rate at whch the physcal contrbuton of ths captal good to producton declnes over tme. For the purpose at hand, the age-effcency functon s called h s, wth non-negatve values that 5 Instead of computng the rato between the quanttes of nvestment, or of the captal stock, n natural and effcency unts, t s also possble to compare the prces of captal goods n natural and effcency unts. The nvarance property of Hulten () or Jorgenson (966) states that the total amount spent on nvestment goods s nvarant to the unts n whch the goods are measured. That s, f captal goods are measured n effcency unts, the prces of the captal goods are such that that the total amount spent n captal measured n natural unts s equal to the total amount spent n captal measured n effcency unts. 7

18 declne wth rsng age s: h s = for a new captal good (s=) and h s = for a captal good that has reached ts maxmum servce lfe. In ths general formulaton, no other assumptons are made concernng the shape of h s. Measurng captal stock or prces n effcency unts captures, however, both, the varaton n qualty of captal goods wth ncreasng age or tme of utlsaton, as well as the varaton from one generaton to another, the so-called vntage captal effect. Theoretcally, these two cases could be dsentangled. 6 Measurng user costs per asset The computaton of user costs s derved from a basc relaton n captal theory (Jorgenson, 967) whch states that the market prce of an asset equals the dscounted value of the rentals that the asset s expected to generate n the future. In the absence of complete markets, ths relaton can be re-formulated to state that the value of an asset equals the dscounted margnal revenues from usng the asset n producton n the future. If vntage prces are not observable, Hulten () shows that the user cost of captal for an s-year old asset u t, s can be expressed as the product of the purchase prce of ths asset ( q t, s ) multpled by the gross rate of return (GRR) on ths asset. The computaton of user costs n the OECD Productvty Database, follows ths dea (Schreyer et al., ). The gross rate of return s defned as the sum of the dscount rate r (or net rate of return), plus the rate of deprecaton ( ) mnus the rate of asset prce d t, s change ( ζ t,s ) plus an nteracton term of deprecaton and asset prce change year old asset at tme t are thus computed as: 7 d t, s ζ t, s. User costs of an s- u t, s = q r + d ζ + d ζ ) (8) t, s ( t, s t, s t, s t, s Qualty adjusted prce ndces Measurement problems may also occur snce t s often dffcult to separate the quantty and qualty of dfferent consumpton and nvestment goods. Ths s partcularly mportant n the case of goods or captal assets where qualty changes rapdly, such as ICT nvestment. The lterature proposes here to use qualty adjusted prce ndces (Trplett, 4). The results n the Secton of ths paper are based on a harmonsed 6 7 If we suppose that frms nvest every year n captal goods of the same characterstcs as regards ther ageeffcency profle and of the same generaton, the average emboded techncal effcency would not change, the change n the qualty of captal stock n natural and effcency unts would be dentcal. If we assume, however, that frms nvest every year n captal goods of dentcal characterstcs, but of dfferent generatons, average emboded techncal effcency would be dentcal to the changes n techncal effcency from one generaton or vntage to the other. Hulten () derves theoretcally that the man drver of change n qualty of the captal stock s the vntage captal effect,.e., the change n qualty from one generaton of captal assets to another. The results of the senstvty analyss suggest, n lne wth ths hypothess; that the vntage effect s much more mportant as a drver of qualty change than dfferent assumptons as regards the age-effcency-profle per captal asset. For more nformaton on the expected prce change and the assumptons underlyng the deprecaton, see Schreyer et al. () 8

19 hedonc prce ndex for ICT-related components, whch uses US prce ndces for ICT and non-ict related goods. 8 In contrast to other studes where the harmonsaton s acheved by the use of the exchange rate, a polynomally smoothed rato of the ICT and non-ict related prce ndex s used n the OECD Productvty Database as the relevant tool for the harmonsaton. 9 usa usa Let λ = P, ct Pnon ct be the rato of the US prce of an ICT captal asset and the prce of non-ict assets. Ths rato s assumed to be smlar across countres. Then the harmonsed hedonc prce ndex for ICT-related assets for another country, for nstance ndexed by deu for Germany, s computed as the product of the prce ndex for the non-ict-related assets from deu Germany and the smoothed rato of prce ndexes (λ) from the USA, P, P λ. ct = deu non ct Aggregaton across assets The standard one-sector Solow model of growth accountng does not take nto account that frms produce wth dfferent producton functons. Frms mght for nstance dffer n the mx of captal assets that they use for producton. And, as seen above, captal assets may themselves dffer n ther relatve productvty, not only across tme but also wthn one perod of tme and generaton. Ths dfference s, for nstance, central to the theoretcal and emprcal dscusson about above-average postve effects of ICT technology on productvty growth, as dscussed above. The senstvty analyss below wll calculate the captal composton effect,.e., we derve what would happen f dfferences n productvty across captal assets were not approprately taken nto account n the contrbuton of captal to GDP growth. Dfferences n the margnal productvty of assets are captured by the user cost per asset, whch s the approprate weght for the aggregaton across assets to calculate the volume of captal servces. If, n contrast, market prces of the assets are used for the aggregaton of the dfferent assets, an aggregate measure of the net captal stock would be constructed. Let uk = u K represent the total remuneraton of captal, measured as the sum of the values of captal servces for each ndvdual asset type, u K. The total volume change n captal servces s then the weghted average of the changes n captal servces suppled by each asset,.e. d ln K dt = u K uk ( d ln K dt). Ths mples the followng for measured MFP growth: d lny uk N u K d ln K wl d ln L N u K g = = dt C = uk dt C dt = C d ln K dt wl d ln L, (9) C dt where C = uk + wl. The effect of cross-asset dfferences n captal productvty on measured MFP growth may be substantal. 8 9 Comparng the MFP estmates based on these dfferent prce assumptons comes close to the approach proposed by Hulten () to estmate the average emboded technologcal effcency of the captal stock by the rato of prces of these captal goods n effcency and natural unts (footnote 6). See also Schreyer (, ). In Schreyer et al. (), the user costs of asset are based on an exogenous expected net rate of return. The lterature, notably Jorgenson and Grlches (967), Barro () as well as Greenwood and Jovanovc (), therefore stress the mportance of adjustng for dfferences n captal assets for the estmaton of MFP. The dfferences n growth rates among captal assets and changes of the structure of captal assets may result n based MFP estmates f they are not accounted for. The possble sze of such an effect s 9

20 Ths can be seen by comparng g wth the growth rate of MFP, g ), where dfferences n margnal productvtes across captal assets are not taken nto account. N N ) d lny uk m K d ln K wl d ln L uk u K g = = g + dt C = WK dt C dt C = uk m K WK d ln K dt (), Where m stands for the market prce of each asset and WK = N = m K s the measure of net (wealth) captal. The composton effect (net of other measurement ssues dscussed) thus reflects the dfference n the sets of weghts used for aggregaton; n contrast to ĝ, the measure g puts more weght on (and hence excludes from the measured MFP) the growth n the stock of productve assets wth shorter lves and hgh user cost, whose effect thus wll be entrely assocated wth the contrbuton of captal. Measurng labour nput Smlarly to captal nput, the overall contrbuton of labour nput to GDP growth n a growth accountng framework s computed as the product of the growth n labour nput (or servces) and the share of labour ncome n total product, s L ( d ln L dt). Labour ncome, wl, s calculated as the compensaton of workers. Data on worker s compensaton are, however, only avalable for employees, not for self-employed persons. Compensaton of self-employed persons s typcally computed by assumng that the average compensaton per self-employed person s dentcal to the average compensaton per employed person. In the reference scenaro of MFP labour nput s measured as total hours worked as opposed to total employment. The measure of total hours worked captures the use of labour better than total employment and s thus an approprate measure of labour nput wthn a growth accountng framework. As average hours worked per worker vary substantally across dfferent OECD countres, usng hours worked as a measure of labour nput does also mprove the cross-country comparablty of productvty measures. The lterature on growth accountng stresses the role of adjustng labour nput for the qualty of labour. Ths s best done by adjustng labour nput by the change n the skll composton of total employment. The ntuton behnd ths s parallel to that behnd the adjustment for dfferences n the qualty of physcal captal and states that productvty growth s nfluenced by dfferences n competences or the level of human captal of each worker. Scarpetta et al. (), for nstance, dstngush sx dfferent employment groups: three educaton levels (below upper secondary, upper secondary and tertary educaton) for each gender. As n the case of total captal servces, total change n labour servces results from the weghted sum of growth n labour servces per gender-educaton group; the weghts are based on relatve margnal productvty (proxed by relatve wages) and employment shares of each gender-educaton group. Let L be the hours worked per gender-educaton type, j, and n the total labour servces can then be expressed as: w j ther respectve relatve wage rate. The change j llustrated by Table A, whch depcts the dfferences and trends n ndvdual captal assets growth rates and ther share n total captal. ICT assets play a very sgnfcant role, both due to the very hgh growth rates of ICT captal assets and also because of the shft n shares towards these assets. The composton of labour nput s not yet adjusted n the OECD-Productvty Database, although some work s underway.

21 dl dl j w j L j = v j, where v j =. () dt j dt w L It s assumed that the rate of change n average hours worked s dentcal across educaton and gender groups. Ths mples L j = e j L, where L s a measure of total labour nput (.e. hours worked) and e j s the employment share of gender-educaton group j n total employment. The weght hence reflects the cost share of each type of labour nput n the total cost of labour. In order to separate the effect of labour composton, or labour qualty, and the effect of hours worked a measure of labour qualty, ndependent of hours worked, s constructed as: dlq de j = v j dt j dt. () Measurng labour and captal shares As ndcated above (equaton 5), the growth accountng framework can be wrtten as the weghted average of the contrbuton of growth n labour and captal. If wl represents total compensaton of labour and uk total remuneraton of captal (n tme t), the standard prmal estmate of the rate of growth of MFP follows from: d ln F g = dt d lny = dt s K d ln K dt s L d ln L dt. (3) In the classcal growth accountng framework, s k and s l are the respectve shares of each factor payment n total output. The results above do, however, allow for non-constant returns to scale and mperfect competton, and reflect, thus, a more general nterpretaton of MFP, the so-called apparent MFP. In ths case, total costs n the form of labour and captal remuneraton do not have to be equal to total factor ncome. As a consequence, the weghts n equaton () and (5),.e., the shares of captal and labour, s k and s l, are the shares of captal and labour n total costs and not n total ncome, as they would be n the neoclasscal growth accountng framework The mpact of measurement on MFP growth a senstvty analyss The followng secton presents results from a senstvty analyss whch assesses the emprcal mpact of labour- and captal-related measurement ssues on measured MFP growth. Ths s done by computng MFP growth on the bass of dfferent scenaros of measurng captal servces and labour where each of these scenaros addresses one key measurement ssue, namely: a) assessng the effect of an age-effcency profle of captal assets over tme by usng a measure of gross captal stock nstead of captal servces; b) takng account of dfferences n productve capacty across captal assets by the computaton of the composton effect of captal nput; c) assessng the mpact of qualty adjusted prce ndces, usng natonal prce ndces nstead of the harmonsed hedonc prce ndex for ICT captal assets; d) assessng the utlsaton and composton of labour nput; and e) smoothng fluctuatons n annual MFP growth measures by computng a trend seres of MFP. 3 Schreyer (forthcomng) provdes an extensve dscusson and argumentaton on how captal and labour shares could or should be computed when total costs are not equal to total ncome.

22 Ths senstvty analyss s prmarly ntended to show the potental sze of the dfference n measured MFP growth based on dfferent assumptons. It provdes an ntal pcture of the mpact of dfferent measures of captal and labour on the growth of MFP and explans to some degree why MFP estmates are dfferent n varous emprcal studes. 4 It s meant as a frst step n analysng crucal measurement ssues whch, therefore, does not touch on all possble measurement ssues. 5 Moreover, whle t s the ntenton of ths senstvty analyss to analyse partcular measurement ssues, t s not possble to totally dsentangle the measurement problems. For nstance, the computaton of the composton effect of captal nput may capture to some degree an effect related to the general age-effcency of captal assets as well as an effect due to dfferences n captal productvty between ICT- and non-ict captal. It s, therefore, not possble to calculate the total mpact of measurement as the sum of the ndvdual effects analysed. The measurement ssues analysed In what follows, dfferent approaches of measurng captal and labour nput wll be separately compared wth the reference scenaro that has been used n secton above. In ths reference scenaro, MFP s measured usng total hours worked; captal servces, based on a partcular age-effcency profle per captal asset and takng nto account dfferent captal assets; shares of captal and labour nput n total costs; harmonsed hedonc prces of ICT-captal assets; and actual tme seres. The measurement ssues that are analysed n ths senstvty analyss are: 4. Labour nput: Total hours worked versus total employment Labour composton: The measure of labour composton that s used n the senstvty analyss follows the procedure presented n secton 3. above. It s based on data on the level of educaton attanment from Scarpetta et al. (), complemented wth nformaton from the Barro and Lee () database. Data on relatve wages are from Jean and Ncolett () for Canada, Denmark, Span, France, the Unted Kngdom, Ireland, Italy, Sweden, and the Unted States, and complemented wth data from Scarpetta et al. () for Australa, Germany, Fnland, the Netherlands, and Portugal. For Japan, data by four educatonal categores are avalable that are not drectly comparable wth the other countres. However, for ths country, full nformaton on wages and employment for the years,,, can be used. 5. Captal nput: Captal servces versus a measure of gross captal stock: The measure of captal stock used n the senstvty analyss assumes a one-hoss-shay effcency functon. Ths assumes that the exstng captal assets can be used wth full effcency over the entre lfe-tme of the asset; ther productvty drops to zero after they are retred, however (see also OECD, ). Captal composton: Ths senstvty analyss compares the reference scenaro of captal servces, wth an alternatve scenaro, whch approxmates the volume of captal stock per captal asset by market prces for each captal asset. Aggregatng n each scenaro over captal assets wth dfferent 4 5 See also Schreyer (forthcomng). Among the lst of possble further measurement ssues are, for nstance, questons related to cross-country dfferences n captal tax regmes, the treatment of own-account software and prvate versus publc sector nvestment.

23 rates of change n the qualty or effcency levels and comparng the resultng MFP growth rates, reveals the contrbuton of qualty changes n captal to the MFP measure. Harmonsed versus natonal prce ndces of ICT goods 6. Cost versus ncome shares: To see how MFP estmates are nfluenced by the way the weghts of captal and labour are computed, a varant of the neoclasscal MFP estmate s computed. Ths uses the assumptons of constant returns to scale and perfect competton n the nput and output markets and computes endogenous rates of returns to captal. It departs from the smple measure of labour share s L as computed by s L =wl/py, where wl s the value of the compensaton of labour and PY s the value of gross domestc product n market prces. Assumng constant returns to scale and compettve markets, the captal share s K s equvalent to sl. Generally, ths measure would gve more weght to the captal contrbuton and MFP would thus be reduced n tmes of more buoyant development n captal nput than n labour nput Actual versus trend seres: The senstvty analyss uses the Hodrck-Prescott flter (Hodrck and Prescott, ) to cyclcally adjust the tme seres of GDP, employment, hours per person, captal servces and stock and the employment shares. Under ths method, trend values of a varable y, y trend, are defned such that they mnmze: HP( λ) ( y y trend = t t + λ t t ) [( y y ( y trend trend trend t+ t t ) y trend t )] (4) where λ s the parameter of the mportance gven to the smoothness of the trend seres as opposte to ts proxmty to actual values. The standardzed OECD smoothng procedure s used. The end-ofsample-bas s reduced by applyng the growth rates of the related seres (busness sector captal stock for total economy captal stock and servces) n the OECD Medum Term Reference Scenaro forecasts to the exstng data up to 8. 7 The estmate of trend MFP growth s then obtaned as the dfference between trend GDP growth and the sum of the contrbutons of trend growth n labour and captal nput, weghted by ther shares as defned above. Trend labour nput s defned as the product of trend seres of employment and hours per person. Labour nput s not adjusted for composton n ths case The ncrease n the weght of captal s due to the calculaton of the captal share as sk = sl, and depends on the assumpton that the rate of return s endogenously determned. Assumng exogenous rates of return, but usng the ncome and not the cost share would reduce both, captal and labour shares, as opposed to the apparent MFP measure based on exogenous rate of returns, and would assgn a stronger role to MFP growth and a smaller role to the factor nputs. OECD (b). Another possblty to measure trend MFP that was not pursued here s to apply the HP flter (3) on MFP estmates based on non-trend values. 3