GGDC PRODUCTIVITY LEVEL DATABASE:

Transcription

1 GGDC PRODUCTIVITY EVE DATABASE: INTERNATIONA COMPARISONS OF OUTPUT, INPUTS AND PRODUCTIVITY AT THE INDUSTRY EVE Robert Inklaar and Marel P. Timmer* Groningen Growth and Development Centre University of Groningen The Netherlands * Corresponding author: Marel P. Timmer, Groningen Growth and Development Centre, Faulty of Eonomis, University of Groningen, P.O. Box 800, N-9700 AV Groningen, The Netherlands, m.p.timmer@rug.nl, tel , fax Aknowledgements The researh on whih this paper is based is part of the EU EMS projet on Growth and Produtivity in the European Union. This projet was supported by the European Commission, Researh Diretorate General as part of the 6th Framework Programme, Priority 8, "Poliy Support and Antiipating Sientifi and Tehnologial Needs". In addition, finanial support from the NSF (Projet Integrating Expenditure and Prodution Estimates in International Comparisons ) is gratefully aknowledged. Many thanks to Mary O Mahony and Mari angasniemi who provided additional data for the breakdown of labour skill ategories. The paper benefitted from useful suggestions and omments from seminar partiipants at a DG ECFIN workshop, the PWT 2008 Workshop in Philadelphia, the final EU EMS onferene in Groningen and the 30th IARIW onferene in Portoroz.

2 Abstrat In this paper we introdue the GGDC Produtivity evel database. This database provides omparisons of output, inputs and produtivity at a detailed industry level for a set of thirty OECD ountries. It omplements the EU EMS growth and produtivity aounts by providing omparative levels and follows it in terms of ountry and industry overage, variable definition and basi data (O Mahony and Timmer, 2008). As suh, the level and growth aounts an be used together in omparative analyses of produtivity trends. The methodology followed is based on Jorgenson and Nishimizu (1985), but inludes a number of refinements suh as the use of setoral output and input measures that exlude intra-industry flows; the appliation of multilateral indies; use of relative output pries from the prodution side and the use of the exante approah to apital prie measurement. The paper outlines the onstrution and ontents of the database and presents some empirial results. The GGDC Produtivity evel database is publily available at 2

3 CONTENTS 1. INTRODUCTION 2. PRODUCTIVITY EVES AND THEIR USES 3. BASIC METHODOOGY 3.1 Produtivity measures abour produtivity levels Multi-fator produtivity levels evel Aounting 3.2 PPPs for output and inputs 4. IMPEMENTATION ISSUES 4.1 Ex-ante versus ex-post approahes to apital and produtivity measurement 4.2 Unit value ratios versus speified PPPs 4.3 Single versus double deflated value added 4.4 Setoral output and aggregation over industries Setoral versus gross output measures Aggregation of PPPs over industries 4.5 Bilateral versus multilateral models 4.6 Extrapolation of benhmark estimates 5. DATA 5.1 Nominal values of inputs and outputs 5.2 Relative pries of inputs and outputs Output PPPs PPPs for intermediate input PPPs for labour input PPPs for apital input PPPs for EU- and Euro-region aggregates 6. COVERAGE AND CONTENTS OF THE DATABASE 7. SOME EMPIRICA RESUTS 8. CONCUDING REMARS Referenes list Appendix 1 Comparison of Expenditure and Prodution Approah to GDP Appendix 2 Why benhmarks and time-series PPPs are not onsistent 3

4 1. INTRODUCTION This paper introdues the GGDC Produtivity evel database. This database provides omparisons of output, inputs and produtivity at a detailed industry level for a set of thirty OECD ountries. It omplements the EU EMS growth and produtivity aounts by providing omparative levels and follows it in terms of ountry and industry overage, variable definition and basi data (O Mahony and Timmer, 2008). As suh, the level and growth aounts an be used together in omparative analyses of produtivity trends Produtivity level omparisons at the aggregate eonomy level for large set of ountries are nowadays routinely being produed by various statistial organisations and in aademia. 1 The most useful analytial appliations of produtivity levels, however, are at the level of individual industries. Beause of signifiant methodologial and data-related problems omprehensive sets of industry produtivity levels have been sare. 2 There is a long tradition at the Groningen Growth and Development Centre (GGDC) and the National Institute for Eonomi and Soial Researh (NIESR) to provide industry-level produtivity omparisons for sets of ountries and industries. Reent studies inlude Inklaar, Timmer and van Ark (2006); Timmer and Ypma (2006); Inklaar, O Mahony, Robinson and Timmer (2003); O Mahony and de Boer (2002) and various other setoral studies by the GGDC. 3 The GGDC estimates for manufaturing and seleted servies industries have been published on a ontinuous basis in the bi-annual IO ey Indiators of the abour Market (IM) database. However, so far most of these studies were on omparative labour produtivity levels, rather than multi-fator produtivity. Also, they were based on a value added rather than a gross output onept. The main reason has been a lak of omparable data on inter-industry transations, labour and apital servie flows and purhasing power parities. 4 In this paper we extend the work by Inklaar and Timmer (2007) and present the GGDC Produtivity evel database. These aounts provide new multilateral omparisons of output, inputs and produtivity for 26 detailed industries overing the whole eonomy for a set of 30 OECD ountries. 1 Most notably, the OECD Produtivity database provides estimates for OECD ountries (OECD 2008) and the The Conferene Board and Groningen Growth and Development Centre, Total Eonomy Database, ( provides estimates for 125 ountries world wide. 2 These inlude studies at the Groningen Growth and Development Centre, the National Institute of Eonomi and Soial Researh, OECD (Pilat, 1996) and Jorgenson and ollaborators (Jorgenson, 1995). 3 See for an overview. 4 Jorgenson and Yip (2001) and Shreyer (2007) provide relative MFP levels at the aggregate level for G7 ountries. At the industry level, interspatial omparisons of multifator produtivity at industry level are available for only a limited number of OECD ountries. Dollar and Wolff (1993), van Ark and Pilat (1993), O Mahony (1996) and O Mahony and de Boer (2002) provide (single deflated) value added-based MFP omparisons. The seminal appliation of the gross-output MFP methodology at industry level is Conrad and Jorgenson (1985) on Germany-Japan-US. Jorgenson, Nishimizu and uroda (1987) and Jorgenson and Nomura (2007) provide omparisons of Japan and the US; and Gu, ee and Tang (2000) and Baldwin, Gu and Yan (2008) on Canada and the US. Most reently Inklaar and Timmer (2007) provide gross-output MFP omparisons of on Australia, Canada, Frane, Germany, Netherlands, U and US. 4

5 The paper is organised as follows. In Setion 2, we introdue various measures of produtivity levels, their meaning and possible uses. Setion 3 desribes the basi methodology of produtivity level omparisons. The methodology for level omparisons has been firmly based in the neo-lassial theory of prodution by Jorgenson and assoiates (Jorgenson and Nishimizu, 1985; Jorgenson, 1995). Instead of omparing output and input ombinations of one ountry at two different points in time as in growth aounting, one ompares input-output ombinations of two different ountries at a similar point of time. Hene the term level omparison is used to ontrast it with growth omparisons. Our approah inludes a range of refinements suh as the use of setoral output and input measures that exlude intra-industry flows (as advoated by Gollop 1979 for growth aounts, and applied in a level aount setting by Inklaar and Timmer, 2007); the appliation of multilateral indies (as suggested by Christensen, Cummings and Diewert, 1982); use of relative output pries from the prodution side (as developed in Timmer, Ypma and van Ark 2007) and the use of the exogenous approah to apital measurement (as advoated by Oulton, 2007). These issues are disussed in Setion 4. In Setion 5, we present our basi data soures. Basially, our level omparisons are based on deflating nominal inputs and output as given in national input-output tables by a set of relative pries (PPPs). We use a new set of relative output pries whih is speifially developed for making ross-ountry, industry-level produtivity omparisons. These are omplemented by relative pries for apital and labour inputs. Pries for apital are derived using the ex-ante (or exogenous) approah. In Setion 6, the ontents and the overage of the database are being disussed. Setion 7 provides some empirial results by way of illustration of the possible appliations of the database. Setion 8 onludes 2. PRODUCTIVITY EVES AND THEIR USES This paper is about omparisons of output, inputs and produtivity levels aross spae (ountries or regions). evel omparisons an be useful for various purposes, for example, in the light of the debate on soures of growth. In reent years there has been an intense interest in the effets of ICT on eonomi growth. Muh of this was sparked by researh showing that ICT played an important role in the aeleration in U.S. labour produtivity growth after Comparative studies tried to explain Europe s lagging behind and showed that differenes in ICT investment played a major role in the transatlanti divergene proess, and MFP growth lagged mainly in market servies. 5 The results from these growth aounting studies an be put in perspetive by linking them to the level omparisons provided in this paper. The interpretation of omparative growth patterns will depend on the initial starting position in terms of levels. For example, if growth is fastest in the ountry with the lowest initial level, this an be seen as ath-up growth in whih follower ountries onverge to more advaned ountries through imitation and spillover of tehnologies. In this framework one an study the impat of regulation, trade or R&D 5 See for an overview Jorgenson et al. (2005) and van Ark, O Mahony and Timmer (2008). 5

6 expenditures on eonomi growth. 6 In addition, omparisons of input levels an shed new light on issues suh as the relative ICT apital intensity of various eonomies. It measures the differenes in the penetration of new tehnology in the prodution proess. Relative levels of energy, materials and servies inputs an be important measures in debates on outsouring of servie ativities, international differenes in prodution strutures and energy use and redution strategies. Comparative produtivity levels require ratios of output as well as ratios of inputs between two (or more) ountries. The simplest way to obtain output ratios is to ompare physial output measures, suh as weight, volume or area. For example, when a labourer in the ement industry in ountry A produes 100 tons of ement per year on average ompared to 200 tons per labourer in ountry B, physial labour produtivity in the ement industry in ountry A is half that of ountry B. Nowadays the use of physial units of output for produtivity measurement is mostly restrited to benhmarking the effiieny of a partiular prodution proess for a speified produt or for a losely related group of produts over time. When omparing produtivity at firm or industry level, the heterogeneity of output and the large variety of produts makes the use of physial units irrelevant. Moreover it is often diffiult to exlusively alloate inputs to one single output. In servies, the use of physial units is often not at all possible. In pratie, one is more likely to have only aess to figures on the total values rather than quantities of output and inputs. For omparisons of produtivity levels aross spae, value measures need to be orreted for differenes in relative pries between ountries. This orretion an be made by using purhasing power parities (PPPs), whih speify the ratio of the prie for a good or servie, or for a bundle of goods and servies, between two ountries (see Setion 4.2). 7 The literature distinguishes many different measures and onepts of produtivity, eah of whih has its partiular meaning and use. Broadly, produtivity measures an be lassified into single-fator produtivity measures (relating a measure of output to a single measure of input) and multi-fator produtivity measures (relating a measure of output to a bundle of inputs). Another distintion is between produtivity measures that relate gross output to one or several inputs and those that use a value-added onept to apture movements of output. The hoie between the various measures depends in first instane on the fous and the purpose of the omparison. In Table 1 an overview is given of the produtivity measures used in this study and their abbreviations Table 1 Overview of the industry-level produtivity measures used in this study Value added based Setoral output based Single produtivity measures P_VASD, P_VADD P_SO Multi fator produtivity measures MFP_VASD, MFP_VADD MFP_SO 6 See e.g. Griffith et al. (2004) and Inklaar, Timmer and van Ark (2008). 7 A term purhasing power parity typially indiates relative levels of expenditure pries, but in pratie is also used for relative levels of prodution pries between ountries (see Setion 4). 6

7 Most single produtivity omparisons have foused on omparisons of value added per person employed or per hour worked. Combined with information for wages, this measure allows the omparison of unit labour ost, whih shed light on the relationship between produtivity and ompetitiveness (IO, 2001; OECD 2008). At the aggregate level, labour produtivity measures an be ombined with measures on the utilisation of the labour potential (e.g. employmentpopulation rates) to provide measures of ross-ountry differentials in per apita inome levels (Van Ark and MGukin, 1999; OECD, 2008). At industry level, gaps in labour produtivity levels indiate the sope for further ath up relative to the produtivity leaders. They apture differenes in tehnology in its broadest sense inluding differenes in apital intensity, apital quality, human apital, eonomies of sale and intangibles suh as management tehniques. One might also be interested in single produtivity measures based on other inputs than labour only. These measures provides insights from a prodution tehnology perspetive. For example, they an indiate the use of energy inputs per unit of output in an industry. One might also be interested in the use of other intermediate inputs suh as materials or servies (see e.g. Inklaar and Timmer, 2007). abour and apital inputs an be further subdivided into various groups of labour and apital so that one an ompare the use of high-skilled labour or ICT-apital aross ountries. This is illustrated in setion 6. Measures of multi-fator produtivity (MFP) provide an indiation of relative levels of the effiieny of input use between ountries. MFP levels are measured as the differene in output between ountries when differenes in all inputs have been aounted for. Based on the eonomi theory of prodution, differenes in MFP levels an be interpreted as differenes in the level of disembodied tehnology. Tehnology is defined here narrowly as level differenes in the prodution funtions of ountries. MFP does not, for example, inlude tehnology differenes that are embodied in the use of apital goods. However, this interpretation of MFP levels is only true under a stringent set of assumptions inluding an idential prodution funtion, onstant returns to sale, ompetitive markets and tehnial and alloative effiieny. Moreover, input measures must adequately reflet differenes in adjustment osts, ylial effets and input quality between ountries (see Shreyer 2001, Chapter 2, for further disussion). Finally, the interpretation from eonomi theory of MFP as a measure of tehnology is based on firms as deision-making units involved in revenue maximisation or ost minimisation. In analyses of higher level aggregates suh as industries, setors or aggregate eonomies, this interpretation only applies under very restritive aggregation onditions. Hene MFP is also alled a measure of our ignorane and differenes in MFP levels should therefore be interpreted with are. Multifator-based produtivity measures are well rooted in eonomi theory but due to their heavy data requirements muh less ommon in international omparisons of relative levels than single fator-based measures. For multi-fator produtivity omparisons, in theory, grossoutput MFP measures are to be preferred over value-added MFP measures at all levels of aggregation. As tehnologial hange often affets all inputs, and not only the primary fator inputs labour and apital, gross output-based MFP levels better reflet differenes in tehnology than value added-based ones. From the produer s perspetive there is no inherent differene in the primary inputs (labour and apital) and intermediate inputs (materials, energy and servie 7

8 inputs). Prodution deisions are made for all inputs simultaneously and substitution between all inputs an take plae, making them non-separable. Instead, value added-based MFP measures provide only an indiation of the importane of the produtivity differenes in fator inputs (apital and labour) for the eonomy as a whole. In priniple, when the value added-based measure is obtained by independent omparisons of gross output and intermediate inputs with their own PPPs (so-alled double deflation ), the data requirements for value-added and gross output-based omparisons of produtivity are the same. Therefore, single-deflated value added measures (using the PPPs for gross output to deflate value added) are often used in MFP omparisons due to lak of detailed prie and quantity data on intermediate inputs. This is disussed extensively in setion 4.3. An additional problem in deriving meaningful gross-output based MFP omparisons at the industry level onerns the need for setoral output measures, that is, output in an industry exluding the transations that our within the industry, i.e. intra-industry deliveries of intermediate produts. This is disussed in Setion 4.4. MFP and labour produtivity measures are not independent from eah other. Multifator produtivity measures an be used to explain single fator produtivity differenes. For example, differenes in labour produtivity levels an be explained by differenes in the ratio of apital to labour, and differenes in multi-fator produtivity. These, and other, links have been established with the help of the eonomi theory of prodution (see setion 3.1.3). In pratie, single and multifator produtivity measures are lose when one input aounts for a large part of the total value of inputs. For example, in some servie setors, where labour makes up the bulk of input osts, labour produtivity measures will be lose to measures of MFP. However, this is not to be expeted in all industries. The GGDC Produtivity evel database provides estimates of produtivity based on both gross output and value added. In the latter ase, estimates are based both on single- and double deflation. The full ontents of the database are desribed in Setion BASIC METHODOOGY In this setion we present our methodology for omparing levels of output, input and produtivity aross ountries. As we are trying to onstrut a onsistent set of produtivity measures for a large number of ountries and industries at the same time, various hoies have to be made not only onerning the use of partiular index number formulae, but also their atual implementation. In Setion 4 we desribe the various implementation issues. In this setion the basi methodology is laid out. Basially, our approah has two stages: at the lowest level, omparable sets of national symmetri input-output tables (SIOT) and detailed output and input PPPs are onstruted at the level of 45 sub-industries. The onstrution of this basi data and the underlying data soures are disussed in Setion 5. In this setion we desribe the seond stage whih onsists of two steps. In the first step, PPPs for output, apital, labour and intermediate inputs for 29 industries are derived 8

9 based on the data for 45 sub-industries. This is done with the prie-variant of the multilateral index number approah advoated by Caves et al. (1982), also known as CCD-method. These PPPs are used to impliitly derive quantities of all inputs (apital, labour and intermediate inputs) and output. In the seond step, produtivity omparisons are made for eah industry on the basis of input and output quantities in a bilateral Tornqvist model following Jorgenson and Nishimizu (1987). This approah is also known as primal level aounting. In this setion we first outline our basi methodology for measuring produtivity (3.1), followed by our approah to deriving PPPs for outputs and inputs (setion 3.2). 3.1 Produtivity measures The main aim of the GGDC Produtivity evel database is to provide produtivity omparisons between ountries. The aounts provide so-alled binary omparisons, that is omparisons between a ountry and a base ountry whih is the same in all omparisons. As most interest is in omparing the performane of ountries to the world produtivity and tehnology leader, it is natural to hoose the U.S. as our base ountry. Alternative bilateral omparisons with other ountries as the base an be made using the same approah by simply replaing the US by another base ountry (see Setion 4.5 for a disussion of multilateral models). In this setion we assume that all omparisons are made with the U.S abour produtivity levels The most ommonly used single produtivity measure for international omparisons of levels is labour produtivity. This is generally defined as an output measure divided by a labour input measure. The labour input measure an be the number of persons employed, employees or hours worked. The output measure an either be the volume of gross output or the volume of value added. We define the gross output-based measure of labour produtivity as follows. et Q SO be a volume measure of gross output and let H be hours worked. Then the volume measure of labour produtivity in ountry relative to the US based on gross output (P_SO) is given by: 8 P Q / H SO _ SO = (3.1) SO QUS / HUS Similarly, omparisons of value-added based labour produtivity (P_VA) are given by P Q / H VA _ VA = (3.2) VA QUS / HUS 8 For simpliity, a time index t is omitted. All pries, quantities and values refer to the same point of time. See setion 7 for spatial omparisons over time. 9

10 3.1.2 Multi-fator produtivity levels Comparisons of multi-fator produtivity aount for more than one input. The GGDC evel aounts provide estimates for value-added based MFP taking into aount both labour and apital servies, and gross-output based MFP taking into aount labour, apital and intermediate inputs. Following Jorgenson and Nishimizu (1987), we define the following translog quantity index of differene in multi fator produtivity based on gross output (MFP_SO) as follows SO II Q Q Q Q ln MFP _ SO = ln vˆ SO ln vˆ ln vˆ II ln (3.3) II QUS QUS QUS QUS with Q a quantity index of apital servies, Q a quantity index of labour servies and Q II a quantity index of intermediate input servies. vˆ is the share of apital servies in total osts averaged over the two ountries: v ˆ = v + v with v US = V and II ( V + V + V ) V is the nominal value of apital servies. vˆ and vˆ II are defined in a similar way for labour and intermediate inputs. Beause of the assumption of onstant returns to sale, the shares add to one: v ˆ ˆ ˆ + v + vii = 1. Alternatively, one an also define relative MFP measures based on value added rather than setoral output (MFP_VA). This index is defined as follows: where ln MFP _ VA Q Q Q = ln wˆ ln wˆ ln (3.4) Q Q Q VA VA US US ŵ is the share of apital servies in value added averaged over the two ountries w ˆ = w + w with w US ( V + V ) US V = and similarly for labour suh that w ˆ wˆ = 1. Although value added-based and gross-output based MFP measures reflet different onepts, there is a diret theoretial relationship between the two MFP measures. For two ountries with idential value added-gross output ratios, the differene in value-added based MFP equals the differene in gross-output MFP, multiplied by the inverse of the nominal share of value added in gross output. 9 However, value added shares are generally not the same aross ountries and an adjustment refleting the differene in the value added-gross output ratios is needed (see Baily, 1986 for the intertemporal ase). The formulas indiate that omparable volume measures of output and input for the two ountries are needed. When a single output is being ompared, physial measures, suh as numbers of ars, are possible. However, when omparisons are made at the industry or aggregate level where output is not represented by a single produt, output is given in value terms. In that ase a orretion for differenes in relative prie levels between ountries is needed. This is usually done + 9 Obviously, this relationship only exists when volume measures of value added and output are onsistent, that is, value added is double deflated, see setion

11 with a purhasing power parity (PPP) whih indiates the relative prie of output in one ountry relative to another ountry. The derivation of the PPPs is further disussed in Setion 5. Volume indies are alulated impliitly by the ratio of the nominal values and the relevant prie indies. For example, aggregate output quantity in ountry is given by SO SO V Q = (3.5) SO PPP SO SO with V the nominal value of output in ountry (that is, in national urreny) and PPP the relative prie of output in ountry ompared to the base ountry. Similarly, for value added: VA VA V Q = (3.6) VA PPP and for intermediate inputs: II II V Q = (3.7) II PPP For labour input one an use number of workers or total hours worked as a volume measure. This is typially done in labour produtivity measures suh as (3.1) and (3.2). However, for multi fator produtivity omparisons one would also like to inlude the omposition of labour in terms of various labour types with different produtivities, e.g. low- and high-skilled labour. This an be done by hoosing an appropriate PPP based on relative wages as disussed in setion 5: V Q = (3.8) PPP with V the nominal value of labour ompensation in ountry (that is, in national urreny) and PPP the relative prie of labour servies in ountry. And similarly for aggregate apital input in ountry : ~ V Q = (3.9) PPP with V ~ the nominal value of ex-ante apital ompensation in ountry and PPP the relative prie of apital servies in ountry. Note that beause of our approah to apital measurement, apital ompensation in this formula ( V ~ ) is based on ex-ante measures of rates of return and will differ from the ex-post measure of apital ompensation (3.4). More speifially, V = V ~ + V (3.10) R V used in equations (3.3) and where R V is (supra-normal) profits, see setion 4.1 for an elaborate disussion. 11

12 3.1.3 evel Aounting One of the main appliations in produtivity omparisons is the so-alled level aounting. 10 evel aounts provide a deomposition of differenes in value added per hour worked into differenes in apital per hour worked (apital intensity), in labour omposition (skill intensity) and in MFP. This deomposition is done as follows: VA H Q H Q H = ln MFP _ VA (3.11) ln wˆ ln + wˆ ln + VAUS HUS QUS HUS QUS HUS where ŵ and ŵ are defined as in equation (3.4). Similarly, one an deompose output per hour worked as follows: VA H Q H Q H Q H = ln MFP _ SO (3.12) II ln vˆ II ln + vˆ II ln + vˆ ln + VAUS HUS QUS HUS QUS HUS QUS HUS with the weights as defined in (3.3). The alulation of produtivity measures and the deomposition are defined aording to the formula s above at eah level of industry aggregation. As suh it follows the approah in the EU EMS Growth Aounts. The link between industry-level and aggregate produtivity level differenes an be of onsiderable importane if one is interested in the ontribution of individual industries to overall produtivity level differenes. The preise form of the aggregation proedure depends on the produtivity measure used. This is well-known in the ontext of growth aounting (see Shreyer, 2001 and Corrado et al., 2007 for a reent appliation). However, weighting shemes like Domar (1961) have not been extended to an open eonomy setting, yet, let alone in the ontext of multilateral level omparisons instead of growth omparisons. This is avenue for further researh. Comparisons of multi-fator produtivity an be made using the so-alled primal and dual approahes. In the primal approah relative MPF levels are based on omparisons of quantities as we do here. Alternatively, in the dual approah they are based on omparisons of pries. Usually, produtivity measures are expressed in terms of relative quantities, as this is most losely related to the notion of prodution as a physial proess in whih quantities of inputs are onverted into quantities of outputs. In theory, the two different estimates should be lose, but in pratie this is not always the ase, in partiular when prodution strutures differ onsiderably between the two ountries being ompared. We opt for the primal approah as we are interested in a full and onsistent deomposition of output quantities, rather than output pries. 3.2 PPPs for output and inputs To alulate quantities of input and output, nominal values are deflated by relative pries (PPPs) as in formula s (3.5)-(3.9). The PPPs for outputs and inputs are derived on the basis of detailed 10 evel aounting is also known as development aounting (see e.g. Caselli, 2005). We stik to the name level aounting as it most learly indiates the differene and similarity with growth aounting. 12

13 sets of output and input pries. Pries are aggregated using the multilateral translog prie indies introdued by Caves, Christensen and Diewert (1982) (CCD-index). Basially, in this methodology one reates an artifiial ountry by averaging over all ountries in the data set, and uses this onstruted ountry as a bridge when making binary omparisons between two ountries. 11 This reates so-alled transitive PPPs (see 4.6 for more) whih are base-ountry independent. For onveniene, the PPPs are normalised with U.S. as 1 in the database. et i be the omponents of output, then the multilateral output prie of ountry ( PPP SO ) is defined as follows: SO SO [ ln PPPi ln PPPi ] SO ln PPP = vˆ,, (3.13) ˆ i, 2 i, q i, q N i i 1 SO SO SO with v = [ v + Σ ( v / )] and v i, = pi, Qi, / V the share of omponent i in nominal setoral output in ountry. A bar indiates a geometri average over all ountries indexed by SO 1 SO q=1,..,n and N is the number of ountries, in this ase: ln PPP i = ln PPPi, q. N q Similarly the relative prie of apital input ( PPP ) is derived as [ ln PPPk ln PPPk ] ln PPP = vˆ k,, (3.14) k 1 ~ with vˆ k, = [ v, ( v, / N)] 2 k + Σ q k q and vk, = pk, Qk, / V the share of asset k in total ex ante nominal apital ompensation in ountry, with k the omponents of. See setion 5.1 for the measurement of apital servie pries p,. Similarly for labour: where l k [ ln PPPl ln PPPl ] ln PPP = vˆ l,, (3.15) l v, is the share of labour type l in total labour ompensation in ountry, and for intermediate goods: II II [ ln PPPm ln PPPm ] II ln PPP = vˆ m,, (3.16) m where v m, is the share of intermediate input type m in total intermediate input ompensation in ountry. The indies in (3.14)-(3.16) are referred to as the translog prie indies of apital, labour and intermediates. In the datafile whih aompanies this paper, the inputs are further subdivided into eight groups: two groups of labour (high skilled and others), two groups of apital (ICT-apital and non-ict apital), and four intermediate inputs: energy (E), materials (M) and servies (S) and 11 In pratie, this involves applying an ES proedure to a matrix of all possible binary Törnqvist indies. 13

14 imports (IMP). Aggregation aross the different inputs in eah group also follows the CCDmethodology exposed above. 12 For value added, two alternative PPPs are provided in the database: one based on the output and intermediate input PPPs (in a proedure known as double deflation) and one based on the output PPP only (single deflation). In the first ase a CCD-like approah is followed by taking a geometri mean of all possible binary Tornqvist indies for a partiular ountry. First, alulate the binary PPP for eah ountry pair (,q) as follows: VA VA [ ln PPP ln PPPq ] = 1 Y Y II [( ln PPP ln PPP ) vˆ ( ln PPP ln PPP )] II The weight ˆ v II,, q 1 vˆ II,, q q II,, q q (3.17) is the share of intermediate inputs in output, averaged over the two ountries. Next, an ES proedure is applied. The advantages and disadvantages of double deflation are disussed in more detail in setion IMPEMENTATION ISSUES Although the theory of measuring produtivity levels is relatively straightforward there is a high degree of freedom in the atual implementation of the various measures. In this setion we disuss a number of the most important hoies to be made in implementing the produtivity level methodology whih was outlined in the previous setion. For tratability, this disussion is organised on a topi-by-topi basis although some of the problems are learly intertwined. By providing alternative produtivity estimates we will show that the hoies to be made are far from trivial in an empirial sense as differenes an be rather large. The following issues will be disussed: Ex-ante versus ex-post approahes to apital and produtivity measurement. In this study we opt for the hybrid approah advoated by Oulton (2007) as outlined in setion 4.1. Unit value ratios versus speified PPPs. In this study we opt for a mix, but also provide an alternative data set of estimates based on speified pries only. Differenes are disussed in Setion This reates a small inonsisteny as CCD-aggregation is not onsistent in aggregation: the value of the index alulated in two stages does not neessarily oinide with the value of the index alulated in a single stage. For example, one an derive the total intermediate input PPP by aggregating diretly from the most detailed produt level available, or in two steps: first from produts to the groups of E, M, S and imports, and in a seond stage to total. Fortunately, the differenes are quantitatively minor as superlative index numbers are approximately onsistent in aggregation (Diewert 1978). 14

15 Single versus double deflated value added. Theoretially, double deflated measures of value added are to be preferred, but in some ases estimates an beome unstable. We provide both alternatives in our data files. Differenes are disussed in Setion 4.3. Setoral versus gross output measures. To orret for international differenes in vertial integration we opt for the setoral output approah advoated by Gollop (1979). This has also impliations for the aggregation proedures as disussed in Setion 4.4. Multilateral CCD versus bilateral Tornqvist models of produtivity. Mainly for expositional reasons and tratability, we opt for bilateral Tornqvist MFP measures. However output and input PPPs are based on CCD indies, see setion 4.5. Extrapolation over time of the 1997 benhmark estimates, see setion Ex-ante versus ex-post approahes to apital and produtivity measurement In our approah we use the so-alled hybrid approah to apital and produtivity measurement advoated by Oulton (2007). Basially, in the hybrid approah ex-ante measures are used in the alulation of apital input, but in the measurement of the ontribution of apital to output, and hene of MFP, ex-post measures are used as in equations (3.3) and (3.4). Traditionally, ex-post measures are used in both the measurement of apital and produtivity (Nishimizu and Jorgenson, 1981). It is favoured by most analysts of eonomi growth due to its strong foundation in neo-lassial theory. Also in the EU EMS growth aounts use is made of the ex-post rather than the ex-ante approah. However, the pratial and methodologial reasons to opt for the ex-ante approah are stronger in the ontext of level omparisons than in the ase of growth omparisons. Shreyer (2004) highlights the problems in measuring apital in the ex-post approah when the set of assets in the analysis is not omplete and argues in favour of the ex-ante approah. Balk (2007) argues that the ex-post approah is based on stringent assumptions of perfet foresight, onstant returns to sale and ompetitive markets whih are most likely not to hold in reality. Inklaar (2008) provides an empirial disussion of some of the alternatives to apital measurement in the ase of the US. While in an analysis of growth over time of one ountry one might argue that possible deviations from the assumptions of perfet markets and onstant returns to sale only slowly hange, this is muh harder to argue in the ase of omparisons aross ountries. Moreover, in level-omparisons one has to assume that ountries are the same in terms of their prodution funtions and only differ up to a salar, indiating their tehnology level. An important pratial disadvantage of the ex-post approah is the high volatility of the user ost of apital due to its nature as a residual measure. Growth aounts are usually made for analyses of growth during a period of say 5 or 10 years in whih these errors are smoothed. However, level omparisons are made for one benhmark year only and hene are highly sensitive to short-run flutuations in the rental pries. This auses problems espeially at a low industry and asset level as apital ompensation frequently turns out to be low or even negative for some assets in some years. In addition, the ex-post approah is more sensitive to measurement errors, for example onerning the lassifiation of investment by asset type. 15

16 Given this, we opt for a hybrid approah using the ex-ante approah to apital measurement, but the ex-post approah to MFP measurement. This means that the rate of return of apital is not measured as a residual as in the ex-post approah, but is based on an ex-ante required rate of return as an be found in finanial market data. In the ex-ante approah a differene will appear between total input osts and total output, whih an be alled (supranormal) profits, see setion 5. The alulation of the profits is outlined in Setion 5.1. The ontribution of apital to output is measured by multiplying its weight in total output (ex-ante apital ompensation plus profits) as in formula s (3.3) and (3.4). 4.2 Unit value ratios versus speified PPPs. evels of outputs and inputs between ountries an be ompared by using relative pries to express these outputs and inputs in a ommon urreny. It is well known that the use of exhange rates may be highly inaurate, sine relative pries and exhange rates may differ onsiderably. This will be partiularly a problem when omparisons are made at the level of industries or setors of the eonomy. Even in setors whih are open to international trade, and for whih it may be assumed that relative prie levels onverge to one in the long run, different degrees of monopoly power, lags in response to exhange rate movements, et., make this assumption unlikely to be fulfilled in pratie. For non-traded setors, there is in fat no reason at all to suppose prie ratios will equal the exhange rate. Finally, it is well reognised that the exhange rate is also influened by short-term apital movements whih should not be refleted in omparative volume measures of output and produtivity (Taylor and Taylor 2004). To aggregate aross ountries use should be made of so-alled Purhasing Power Parities (PPPs). A PPP is defined as the ratio of the prie of a produt or a bundle of produts between two ountries, with pries expressed in eah ountry s own urreny. The relative prie level is defined as the (average) prie of one ountry relative to the (average) prie of the other ountry, with 50 pries expressed in a ommon urreny. When ountries have different urrenies, the relative prie level is obtained as the ratio of the PPP to the urreny exhange rate. So the relative prie level of a hairut in Poland ompared to Germany is obtained by omparing the PPP of the hairut (for example, 30 Złoty in Poland to 15 euro in Germany) to the urreny exhange rate (for example, 4 Złoty to one euro). The relative prie level of Poland relative to Germany is then (30/15) / 4 = 50 per ent. When two ountries have the same urreny, for example, the euro, the relative prie level an be diretly derived from the PPP. For example, when the ex-fatory prie of a ton of flat steel of idential quality is 2,000 euro in Portugal against 2,500 euro in Germany, the Portuguese prie level is 80 per ent of that in Germany. For a long time, international omparisons of output and produtivity have been based on prie surveys from the International Comparisons Projet whih provide relative pries for a range of final demand produts aross ountries (ravis et al., 1982). Typially, PPPs for GDP were used, not only in studies of the aggregate eonomy but also at the industry level. Only a few attempts have been made to derive industry-speifi PPPs. These studies have shown that large ross- setor differenes in PPPs exist. By way of illustration, Fig 4.1 provides a omparison of the industry-speifi PPPs used in this study and the overall GDP PPP from the OECD. It shows 16

17 the ratio of PPPs for three major setors and total GDP. The biggest differenes an be found for the other goods setor (mainly agriulture and onstrution), for whih PPPs an easily be 50% or higher than the GDP PPP (e.g. for Japan). But also for manufaturing and market servies different relative pries an easily differ by more than 15% from the overall GDP PPP (see Timmer, Ypma and van Ark 2007 for more). In the past, industry studies were either based on underlying information from ICP, or based on produer prie information. Both approahes have their advantages and disadvantages and we use a mix of both in this study, following Timmer, Ypma and van Ark (2007) Figure 4.1 Ratio of setoral PPP and GDP PPP, AUS CAN CZE ESP FRA GER HUN IR JAP ND SWE U USA MexEle OtherG MSERV Note: Ratio of setoral PPP and GDP PPP for three setors. Soure: GDP PPP from OECD. Setoral PPPs from GGDC Produtivity evel database. For the derivation of industry output pries on the basis of expenditure pries a number of adjustments have to be made. First, the expenditure pries, whih are based on a purhasers prie onept, must be transformed into basi pries as industry output in the National Aounts is measured at basi pries, not purhasers pries. This ane be done by eliminating trade and transportation margins and net indiret taxes. Seond, expenditure ategories have to be mapped into industries. Jorgenson et al. (1987) were the first to do this for a US-Japan omparison. However, it is well known that this proedure has several drawbaks. First, the data to adjust PPPs from the expenditure side to a basi prie onept is often not available. Seond, PPPs from the expenditure side are not always a feasible option for all industries beause no prie data are 13 See van Ark and Timmer (2008) for an elaborate survey. 17

18 available for produts whih are typially used as intermediates rather than for final onsumption. Finally, PPPs from the expenditure side need to be adjusted for export and import pries. PPPs from the expenditure side reflet pries of final expenditure on produts, whih either have been produed domestially or have been imported. In addition, not all domestially produed goods are destined for final expenditure, as part is being used for intermediate demand or exported. Therefore expenditure pries inlude the pries of imports and exlude pries of exports, while basi pries should reflet the prie of domesti prodution, inluding exports and exluding imports. This adjustment however is extremely diffiult to make. The other alternative is to use PPPs from the prodution side, based on produer prie information. At the industry level, PPPs from the prodution approah are theoretially preferable as they refer to the orret prie onept that is required at output level. Moreover, these PPPs will naturally fit the industry-lassifiations and over all output, both final and intermediate goods. But they have one big disadvantage. PPPs from the expenditure side are derived from speified pries that are obtained from a speifi survey set up for the purpose. Prodution PPPs are mostly only available through ratios of unit values derived from (national) prodution ensuses and business statistis surveys, as basi pries for speified items at produer level are often not available. These unit value ratios have the disadvantage of introduing produt mathing problems in international omparisons. Without preise speifiation of the produts ompared, hanes are higher that differenes in produt quality will be refleted in the relative pries. 14 Also, this approah is only feasible for those industries for whih unit value information is available. In a reent study Timmer, Ypma and van Ark (2007) provide two sets of PPPs: one based on unit value ratios for 1997 from the ICOP projet at the University of Groningen and one based on speified expenditure pries side from OECD for the 1999 ICP-round, whih were adjusted for trade and transportation margins and net taxes. They argue that the hoie on whether to use PPPs from the expenditure or prodution side is an empirial one, and will differ by industry. They provide a framework to assess the strengths and weaknesses of PPPs from the expenditure side in different industries using a supply-use framework. PPPs from the expenditure side only approximate the industry level pries in ase most of the expenditure is on domestially produed goods and the industry output being produed goes mostly to domesti final expenditure and not to intermediate onsumption or exports. Ultimately, they present a mixture of PPPs from the prodution and expenditure side. The prodution PPPs are mainly based on unit value ratios and 14 Due to the produt mathing problem PPPs from the prodution side are often based on samples of produts whih are biased towards relatively homogeneous, less sophistiated goods. The underlying unit value ratios may not always be representative of the more upgraded, high-quality varities in the same industry. Another issue, linked to this, onerns the sampling error of expenditure PPPs vis-à-vis prodution PPPs. In priniple one might expet a bigger sampling error for unit value ratios ompared to speified expenditure PPPs. As more aggregate items are being mathed, produt mix problems and the quality problem may raise the sampling error of prodution PPPs. ihtenberg and Grilihes (1989) showed that in an intertemporal ontext produer prie indies in the US based on speified produt pries are superior to those based on ensus unit value ratios as prie dispersions are muh higher for the latter. 18

19 over agriulture, mining, manufaturing (exept high-teh), transport, ommuniation and trade industries. PPPs for other industries are based on speified expenditure pries. In this study we use the mix of UVRs and expenditure PPPs provided by Timmer, Ypma and van Ark (2007). As an alternative we also provide a file with results based on speified expenditure pries only. 15 Figure 4.2 shows the sensitivity of the omparisons to the hoie of PPP set. It gives the log ratio of value added using mix of PPPs (our preferred hoie) and using PPPs from expenditure side only. Figure 4.2 Sensitivity to hoie of PPPs, OR ITA JAP AUS AUT ESP FRA IR BE PRT GER U DN CAN SWE FIN ND Goods prodution Market servies Note: og ratio of value added using mix of PPPs (our preferred hoie) and using PPPs from expenditure side only. Value added is single deflated. Soure: Appendix Table 1. Figure 4.2 shows that differenes an go either way as mix PPPs are sometimes higher and sometimes lower than expenditure PPPs. For goods prodution differenes are relatively minor and often within 5%-bounds. Differenes for market servies an be muh larger though. For example, real value added in Italy, orea and Japan ompared to the U.S. is more than 15% higher when using the expenditure PPPs. A more detailed analysis at the industry level reveals that this is due to differenes for the trade and transportation setor. 16 Expenditure PPPs for these 15 This PPP set ontains only expenditure PPPs, exept for agriulture and mining for whih no expenditure PPPs exist. All output of these industries onsist of intermediate inputs, not final goods. For these industries UVR estimates are used. Similarly, for distributive trade no expenditure PPP is available (see Timmer and Ypma 2006 for an extensive disussion). The overall GDP PPP is used instead. 16 For the other market servie industires only expenditure PPPs are available and hene PPPs are tne same in the two alternative sets. 19

20 servies are extremely low in various Asian and Eastern European ountries (see Appendix Table 1). Arguably these expenditure PPPs refer to highly subsidised pries for publi transportation whih have little relevane for transport pries faing firms. 17 In ontrast, estimates of distribution PPPs based on expenditure pries appear to be too high for Nordi ountries. Appendix Table 1 further shows that the lower level of aggregation, the bigger differenes an beome. For some individual industry-by-ountry ells the two estimates diverge markedly. 4.3 Single versus double deflated value added In theory, the prie of value added should be based on the pries of output and the pries of intermediate inputs. As suh, the data requirements for a value added based MFP measure is exatly the same as for a gross output based MFP measure. However, in pratie, for reasons disussed below, one often opts to ignore the pries of intermediate inputs, and uses the PPP for gross output instead. The latter approah is alled single deflation, as opposed to double deflation in whih the pries of intermediate inputs are taken into aount as in equation (3.17). Single deflation has some important problems to it. It suffers from a so-alled terms-oftrade bias 18 and a substitution bias. Firstly, the terms-of-trade bias arises when relative pries of output and intermediate inputs differ for a partiular industry. For example, it might be the ase that while the observed gross output pries in ountry A are the same as in ountry B, the unobserved intermediate input pries are lower in A. In that ase value added in A is overestimated relative to B when using single deflation, beause the prie gain from the lower input pries is now refleted in A s volume measures of value added. Seondly, differenes in relative pries of primary fator inputs and intermediate inputs an lead to differenes in the use of intermediate inputs, leading to substitution effets. Relatively lower intermediate input pries will lead to a higher use of intermediate inputs ompared to the use of apital and labour inputs in the prodution proess. When using single deflation, this substitution effet between intermediate inputs and value added is not refleted in the relative volume measure of value added. In pratie, the terms-of-trade and the substitution biases are diffiult to disentangle. The main point here is that as long as relative intermediate input pries do not move in tandem with relative output pries aross ountries, measures of single deflated value added will be biased. The double deflation proedure does not suffer from this bias and therefore most European ountries and the US reently adopted double deflation tehniques in the ompilation of value added time series in their National Aounts. We also apply double deflation tehniques in this ross-ountry study. However, in pratie double deflation also has a number of well-known problems to it. Firstly, double deflation puts larger requirements on data, as besides PPPs for gross output, 17 Timmer et al. (2007) adjusted the expenditure PPPs for taxes and subsidies, but for transportation servies this appeared to be nearly impossible due to the hugh amounts of diret and indiret subsidies whih ould not be derived on a produt basis from published National Aount statistis. 18 Note that the onept terms of trade refers to relative pries of outputs and inputs in the domesti eonomy, and do not refer to terms of trade as used in international trade literature in whih they refer to the differenes in import and export pries. 20