45th CONGRESS OF THE EUROPEAN REGIONAL SCIENCE ASSOCIATION August 2005, Vrije Universiteit Amsterdam

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1 45th CONGRESS OF THE EUROPEAN REGIONAL SCIENCE ASSOCIATION August 2005, Vrje Unverstet Amsterdam Aggregate Productvty Effects of Road Investment A Reassessment for Western Europe Andreas Kopp OECD/ECMT Transport Research Centre 2, rue André Pascal Pars FRANCE Ph Andreas.Kopp@oecd.org ABSTRACT Knowledge about the productvty effects of nfrastructure would allow more nformed decsons to be taken on the overall budget allocatons for nfrastructure nvestment n general and transport nfrastructure n partcular. Ths paper analyses the macroeconomc productvty effects of road nvestment n 13 western European countres. It revews the prevous attempts to measure the macroeconomc effects of nfrastructure nvestment whch often suffer from an unresolved endogenety problem. The producton theory framework used explctly ncludes the modelng of natonal transport ntenstes and the fact that transport servces depend on prvate captal nvestment and government nvestment n roads. The endogenety bas s addressed by ntroducng an estmaton breakdown whch combnes natonal productvty effects wth overall productvty effects for the country group as a whole, to make resduals of the estmaton orthogonal to the explanatory varables. Productvty s measured by the Toernqust productvty ndex. The productvty effects depend on the sgn of the rato of vehcle stock to the road stock elastcty of producton. The fxed-effects panel data analyss shows that transport nfrastructure has a postve effect on macroeconomc productvty. The varance of road nfrastructure nvestment n the panel explans, however, only a small part of the macroeconomc productvty development. Keywords: Road nvestment; macroeconomc productvty; panel data analyss. 1

2 1. INTRODUCTION Transport nfrastructure nvestment and road nfrastructure nvestment n partcular are seen, by a major part of the general publc and by many poltcal decsonmakers, as a central nstrument to promote regonal or natonal economc growth. Large-scale nvestment n the road network formed part of long-term growth polces n the US under the Dwght D. Esenhower System of Interstate and Defence Hghways, whch was launched n 1956 and led to over mles of hghways by 1980 (Federal Hghway Admnstraton, 1976). In 1998, the Transportaton Equty Act was sgned, assgnng US$203 bllon to mprove the natonal hghway nfrastructure. Of ths amount, US$176 bllon were allocated for hghway constructon (cf. Chandra and Thompson, 2000). The European Councl of October 2003 called on Member States to...promote nvestment n networks and knowledge. It hghlghted the mportance of speedng up the roll-out of European transport, energy and electronc communcatons networks and of ncreasng nvestment n human captal. These are crucal steps to boost growth, better ntegrate an enlarged Europe and mprove the productvty and compettveness of European busnesses on global markets (Commsson of the European Communtes, 2003). The Communty budget contrbutes 700 mllon euros annually to fund up to 10 per cent of Trans-European Network (TEN) projects. The Structural Funds are foreseen to provde 29.2 bllon euros for transport nfrastructure, Coheson fund resources can moblse up to 1.5 bllon euros per year for nfrastructure nvestment. Furthermore, the Commsson s consderng settng up an nnovatve Guarantee Instrument to facltate prvate sector fundng n PPPs for TEN transport projects. The European Investment Bank supports the Growth Intatve wth a 50 bllon euro TEN Investment Faclty to be allocated to TEN s prorty projects. In addton, the EIB renforces ts fnancng capacty under the Structured Fnance Faclty whch, nter ala, supports the TEN projects. On the natonal level, transport nfrastructure nvestment s consdered to be of equal mportance to ncrease economc growth. The strong role assgned to transport nfrastructure nvestment as a vehcle for economc growth appears to be worth crtcal examnaton for at least two reasons: 2

3 There s no strong growth theory foundaton for the hypothess that an ncrease n transport nfrastructure nvestment would lead to an mmedate and lastng ncrease n growth rates of economc actvty. Rather, accordng to the exogenous growth theory, an ncrease n the nvestment rate (whch does not necessarly result from an ncrease n transport nfrastructure nvestment) leads to an ncrease n the ncome level (Barro and Sala--Martn, 1995). Some varants of endogenous growth theory do provde a lnk between transport nfrastructure nvestment and growth rates. The lnk s establshed by the effects of transport nfrastructure nvestment on urban form and the sze dstrbuton of ctes, and the resultng agglomeraton economes (Lucas, 1988; Black and Henderson, 1999; Lucas, 2001; Lucas and Ross-Hansberg, 2002). However, the lnks from transport nfrastructure nvestment to economc growth are less drect than clamed n publc debates, and related arguments are rarely used n polcy dscussons. There s no clear, emprcal evdence that transport nfrastructure nvestment leads to hgher growth or even to a hgher level of ncome. Some authors nterpret the strong correlaton between publc captal and macroeconomc productvty, whch was found for the Unted States of Amerca, as evdence that nfrastructure generally provdes valuable servces to the prvate sector and that, n partcular, the slowdown n US publc nvestment after the early 1970s explans a substantal proporton of the concomtant productvty slowdown 1. Other authors have argued that publc captal s endogenous, n that hgher publc nvestment s due to the publc sector response to an ncreased demand for nfrastructure servces resultng from hgher aggregate ncome 2. Sectoral and regonal dsaggregaton have led to smaller, postve but more robust effects (see the revew n Cohen and Morrson Paul, 2004). A number of studes have looked nto ssues whch complcate the estmaton of publc nfrastructure nvestment effects, such as the exstence of spatal spllovers from publc nfrastructure nvestment n geographcally lnked areas and the temporal dependence of estmated nfrastructure effects. Kelejan and Robnson (1997) allowed for spatal lags of dependent and ndependent varables along wth spatal correlaton of the error terms. Holtz-Eakn and Schwartz (1995) consder nterstate spllovers n a producton model based on long lags to accommodate long-run adjustment, and Boarnet (1998) measured cross-county spllovers usng a Cobb-Douglas producton 3

4 functon approach. Among the studes whch addressed the more specfc queston of whether road nfrastructure nvestment ncreased productvty, Carlno and Voth (1992) found that the productvty of US states was hgher the greater the densty of hghways. Holtz-Eakn and Schwartz (1995) could not confrm the strong postve productvty effects of transport nfrastructure on the state level. Holtz-Eakn and Lovely (1996) succeeded n relatng output growth to the postve effect transport nfrastructure nvestment had on the number of frms n the manufacturng ndustry, wthout observng a drect effect on manufacturng productvty. Wthn the producton functon approach, Cannng (1999) and Cannng and Bennathan (n.d.) have used a dfferent method to solve the problem of the endogenety of publc captal. It s based on the non-statonarty of the data for output per worker and captal stock per worker. Ths means that the producton functon may represent a long-run, contegratng relatonshp. They use ths fact to apply the panel data co-ntegraton methods of Kao and Chang (2000). Usng ths method, and the assumpton that producton functons are dentcal for all countres, whle the relatonshp between nvestment and ncome vares across countres, allows each country n the sample to have ts own short-run nvestment dynamcs, to gve consstent estmates of the parameters of the producton functon whch are robust to reverse causalty. Ths paper s related to the study of Fernald (1999). He tred to gve an answer to the queston of how changes n road stock affected the relatve productvty performance of US ndustres from 1953 to Hs argument s based on the hypothess that f roads contrbute to ndustres productvty, ndustres whch use roads ntensvely should beneft more from ther expanson. Gven the complementarty between vehcle use and road use, and the lack of drect measures for ndustral road use, vehcle use s employed as a drect measure of road ntensty. The basc result of Fernald s study s that changes n road growth are assocated wth larger changes n productvty growth n ndustres whch are relatvely vehcle-ntensve. Ths fndng supports the hypothess that ndustres wth more than average vehcles benefted more than proportonately from road buldng. Ths result, n 4

5 turn, suggests that the correlaton between aggregate productvty and nfrastructure reflects causaton from changes n road stock to changes n productvty. If roads dd not contrbute to aggregate productvty at the margn, but governments just bult more roads as aggregate ncome rose, one would not expect any partcular relatonshp between an ndustry s vehcle ntensty and ts relatve productvty performance when road growth changes. The results do not, however, support the dea that publc nvestment offers a contnung route to ncreasng ncome. The US ndustry data are consstent wth the vew that the massve roadbuldng of the 1950s and 60s offered a one-off boost to the level of productvty, rather than an nstrument to contnung rapd growth n productvty. In ths paper a smlar approach s taken. We dstngush the western European countres by ther transport ntensty, as well as ther use of labour and captal. The next secton sets out the conceptual framework for the emprcal analyss. Secton three explans some data and econometrc ssues, and the results of the emprcal analyss are presented n secton four. In secton fve we make some concludng remarks. 2. THE MODEL In ths secton we develop the background of the estmaton equaton. We formalze the noton that countres whch have relatvely transport-ntensve ndustres beneft more than countres wth a relatvely low transport ntensty from an ncrease n road nfrastructure nvestment. We consder a set of n countres. The growth accountng wth road nfrastructure starts out from natonal producton functons. For each country, the producton of gross output Q, depends on non-transport captal stock K, employment L and transport servces T. Output also depends on the economy s technologcal level U, whch s assumed to progress n a Hcks-neutral way. Transport servces depend on the servces of road stock G as well as the natonal stock of transport equpment V. Omttng tme subscrpts, we have the followng natonal producton functons: 5

6 ( K, H, L, T[ G V ]) Q U F, = (1) for = 1,,n. Equaton (1) represents the gross producton functon of the representatve frm usng the prmary nputs, captal K, labour L and transport servces T, as the only ntermedate nput. The transport servces are produced usng road servces G and the servces of the vehcle stock V. The frms do not choose nput G but the number of vehcles, whch s V. Takng logarthms of (1) and formng the total dfferental, we obtan: dq Q dq Q du 1 = + L. U F ( F dk + F dl + F T dv F T dg) K T V + T G, or (2) du F K dk FL L dl FV V dv FG G dg = + K + + U F K F L F V +. (3) F G F j denotes the dervatve of the producton functon wth respect to nput j, whle the F J coeffcents J ndcate producton elastctes,.e. the percentage ncrease of gross output F f the nput J s ncreased by one per cent. Frms do not take nput decsons wth respect to road servces. However, nput decsons wth respect to vehcles are not ndependent of the road servces provded by the exstng road captal stock. The output elastcty wth respect to road servces can be expressed relatve to the elastcty wth respect to vehcles: FG G F GG F V F V = = F F V V φ (4) F VV F F F The parameter φ equals the rato of output elastctes of roads and vehcles. The producton elastcty of vehcles measures the transport elastcty of the natonal economy. Hence the parameter lnks the observed transport ntensty of the economy to the ndrect nput road use. We expect φ to be postve,.e. we expect economes whch are relatvely transport-ntensve to be relatvely road-ntensve. Due to the separablty assumpton mplct n (1), φ also equals the rato of the elastctes wth respect to G and V n producng 6

7 transport: T G G φ = (5) TV V The formal dervaton of the estmaton equaton and the nterpretaton of results are now greatly smplfed by assumng that the φ are dentcal for all countres, that s, we assume that the functon for transport servces T has the form of a Cobb-Douglas functon. Assumng that the manufacturng ndustres of all countres are prce-takers n factor markets, cost mnmzaton mples that the producton elastctes can be nterpreted as factor shares and the shares of ntermedate goods n the value of gross producton. Denotng the share of factor j n gross output of country by: j J F J F s j = =, (6) J F F addng country subscrpt ; we can then rewrte (3) by: dq Q du dk dl dv = + sk + sl + sv + φ sv. (7) U K L V G dg To express the productvty ncrease as the Solow resdual,.e. as the ncrease n value added mnus the contrbutons of the prvate factors of producton, we have to take account of the followng dentty: dq Q = dy Y si di 1 I (8) 1 s I ( s ) I where Y denotes value added, I real ntermedate goods and s I the share of nomnal nputs of ntermedate goods I n the value of gross output 3. We then have, as the expresson for the Solow resdual: dρ = ρ dy Y s K dk K s L dl sv L dv V (9) 7

8 wth s = s (1/(1 s )) denotng the share of factor j n value added. Gven (7) we have for country : j j I dρ ρ = φs V dg G du + U (10) In other words, the observed growth n productvty s the sum of the technology shock n terms of value added and the percentage ncrease n producton whch s due to the relatve ncrease n road servces. The road servces enjoyed by country do not only depend on the road nvestment n country but also on: the road servces and road nvestment on the tradng partners terrtory, dependng on trade ntenstes and the transport ntenstes of the blateral goods trade 4 ; congeston n the ndvdual countres, whch determnes the level of road servces provded by natonal road stocks. To account for blateral trade, the road servce consumed by country s defned as ts own and the tradng partners road stock multpled wth the share of domestc consumpton and the share of blateral exports n the value added of country : dg G = dg g + N J = 1 e j Y dg j g j, for j = 1,..., N (11) Road servces do not only depend on the stock of road captal but also on collectve road use or, more specfcally, on congeston. To account for congeston, the natonal road servce supply g s defned as the real road stock value dvded by the number of vehcles regstered n country. By measurng congeston n ths way we mplctly assume that car usage does not change much over tme or, n partcular, that t does not go down. By dvdng road stock by the number of vehcles we adopt the assumpton of Barro and Sala-- Martn (1995) and Mankw (1992). Wth ths specfcaton, any ndvdual producer takes road use by others as gven. 8

9 Wth (10) as the estmaton equaton, there s stll the problem of endogenety. If reverse causalty and publc nvestment depended on aggregate ncome rather than the other way around, then country productvty shocks would affect road growth. To address the endogenety problem, we consder the followng regresson breakdown: du U du = U + ε (12) wth U denotng the overall shock of the group of countres. The resduals ε of equaton (12) are, by constructon, orthogonal to the natonal productvty shocks and hence to the changes n natonal government expendture on transport nfrastructure. The Solow resdual for the country group as a whole s defned as: d ρ = φs ρ V dg G + d U U (13) where G denotes the overall growth of road servces,.e. the rato of real road stock to the number of vehcles and s s the share of vehcle cost n nomnal value added. V Both Solow resduals, for the country group and the ndvdual countres, are computed as Törnqust ndces of value added growth. That s, the dscrete changes n productvty are expressed as: ln ( ρt ) ln( ρt 1) = ln( Yt ) ln( Yt 1 ) 1/ 2( skt skt 1) ln( Kt ) ln( Kt 1) 1/ 2( slt slt 1) ( ln( Lt ) ln( Lt 1 )) 1/ 2( s s )( ln( V ) ln( V )) Vt Vt 1 t t 1 ( ) (14) To derve the estmaton equaton and substtutng for the overall productvty shock, we have: du U = d ρ φs ρ V dg G + ε (15) The expresson for the natonal growth rate of productvty s then: 9

10 dρ ρ = φs V dg G d ρ dg + φs + ε (16) V ρ G and we have: dρ d ρ = φs ρ ρ V dg G dg g dg φs ε φ sv s s + = + ε (17) V G V G where s g denotes the share of road servces of country n total road servces of the country group. The left-hand sde of (17), the dfference between the natonal growth n productvty and the productvty growth of the country group, s postve f country has a hgher productvty ncrease than average. The share of G n G,.e. s g, s hgher, the hgher the road stock of country relatve to the road stock of the country group and/or the hgher the trade ntensty of country. If road nfrastructure nvestment s productve, we would expect countres wth an above-average road stock and an above-average vehcle ntensty to beneft more than average from nvestment n road stock. Therefore, we would expect φ to be postve. Recall that φ equals the rato of output elastctes of roads and vehcles, lnkng observed decsons on nvestment n vehcles to unobserved road use. A postve φ then captures the dea that vehcle-ntensve countres are, or should also be, more road-ntensve. 3. DATA AND ECONOMETRIC ISSUES The emprcal analyss ncludes western European countres for whch data on all the varables nvolved are avalable. The largest gaps n the data were found for transport nfrastructure nvestment, and for the real value of vehcle stock. The countres n the sample are Austra, Belgum, Fnland, France, Germany, Italy, the Netherlands, Norway, Portugal, Span, Sweden and the Unted Kngdom. 10

11 A major part of the data used were taken from the OECD s STAN (Structural Analyss) database (OECD, 2004e). Ths holds for gross producton fgures, for value added, gross captal stock fgures and the data on labour compensaton. The employment fgures n terms of hours worked have been taken from the OECD Productvty database (OECD, 2004d). The changes n vehcle stock were computed from the STAN fgures on the producton of motor vehcles, tralers and sem-tralers, subtractng exports and addng mports. The vehcle stock fgures were calculated by applyng the permanent nventory method and usng the deprecaton rate of per cent proposed by Joergensen and Yun (1991). The long-term nterest rate reported n the OECD Outlook (OECD, 2004c) s used as the requred rate of return on captal. Lackng nformaton on the relevant taxes and subsdes, the user cost of captal s approxmated by the sum of the dscount rate and the requred rate on return to captal. The total cost of vehcle captal dvded by nomnal value added gves the share of the vehcle captal cost n value added whch s used to compute the Törnqust ndex of productvty growth. Nomnal fgures have been deflated usng the deflator for prvate captal nvestment provded by the OECD Economc Outlook (OECD, 2004c). Very few ECMT member countres provde data on transport nfrastructure stocks. The road stock fgures are computed by applyng the permanent nventory method to the ECMT data (ECMT, 2004b) on transport nfrastructure nvestment. Followng Boskn et al. (1991), t s assumed that roads deprecate geometrcally at a rate of 1.98 per cent per year. Constant natonal currency values for road stock are calculated by usng the deflator for government nvestment, reported n the OECD Economc Outlook (OECD, 2004c). As mentoned above, the varable "road servces" takes account of nternatonal trade relatons and congeston. Blateral trade coeffcents are based on the blateral trade data provded by the STAN Blateral Trade Data Base (OECD, 2004a, 2004b)5. Congeston s depcted by dvdng the constant currency value of road stock by the number of vehcles. The data on the number of vehcles are collected n the ECMT Statstcal Report on Road Accdents (ECMT, 2004a). Wherever absolute natonal currency values have had to be added up or compared, they have been made commensurable by usng the PPP converson factors of the OECD Economc Outlook (OECD, 2004c). 11

12 4. RESULTS For all the countres n the sample, the Toernqust ndex of productvty ncreased durng the perod from 1975 to 2000 (see Fgure 1), Portugal, Fnland and Sweden havng the greatest overall ncrease of total factor productvty. The ncrease n the ndex was hghly volatle, but decreased on average over the whole perod, as can be seen from Fgure 2. The transport nfrastructure nvestment data show that the absolute numbers for transport nfrastructure nvestment, and road nfrastructure n partcular, are hghly volatle. They do, however, show a contnuous ncrease n road stock whch s, however, unable to keep pace wth GDP growth. That s, the share of transport nfrastructure nvestment n GDP s secularly decreasng for the western European countres. For road stock, ths mples contnuous growth, as shown by Fgure 3, but at substantally decreasng rates (see Fgure 4). 12

13 Fgure 1: Toernqust ndex of real productvty Year 13 Austra Belgum Denmark Fnland France Germany Italy Netherlands Norway Portugal Span Sweden Unted Kngdom Index 1975 = 100

14 Fgure 2: TFP growth Year 14 Austra Belgum Denmark Fnland France Germany Italy Netherlands Norway Portugal Span Sweden Unted Kngdom growth of average TFP Log. (growth of average TFP) Per Cent

15 Fgure3: Road stock n 1975 nternatonal dollars Year 15 Austra Belgum Fnland France Germany Italy Netherlands Norway Portugal Span Sweden Swtzerland Unted Kngdom Mll nt. Dollars

16 Fgure 4: Growth rates of captal stock Year 16 Austra Belgum Fnland France Germany Italy Netherlands Norway Portugal Span Sweden Swtzerland Unted Kngdom Per cent

17 We estmate the relatonshp between the growth of road servces and the change n the Toernqust ndex by usng a fxed-effects model. That s, we allow for country-specfc, unobserved characterstcs nfluencng the relatonshp between road nfrastructure nvestment and macroeconomc productvty effects, whch are assumed to be constant over tme. Estmatng the dfference between natonal productvty growth and productvty growth as a functon of the product of natonal vehcle ntensty and natonal road servces, and the product of overall vehcle ntensty and overall road servces, we obtan the results gven n Table 1. Number of obs. = 300 Table 1. Fxed effects regresson 1, Independent varables for natonal and nternatonal road stock dfftfp Coeffcent Standard Error t P > t 95 p.c. Confdence Interval prod prod constant R-sq: wthn = between = overall = F test that all u = 0 : F(11,286) = Prob > F = The table shows dfftfp as the ndependent varable, and prod1 and prod2 as the explanatory varables, the estmaton coeffcents of the latter, the t values, the P values and the 95 per cent confdence nterval. The table shows that the estmaton coeffcents have the expected sgns,.e. φ s postve, as the coeffcent of the product of the natonal vehcle share and the natonal road servces s postve, and negatve for the product of the overall vehcle share and the overall road stock. An ncrease n natonal road servces by nvestment n natonal road nfrastructure mproves, ceters parbus, natonal productvty growth relatve to the productvty growth of the country group. All coeffcents are hghly sgnfcant and the F-test shows desred results. However, as can be seen from the reported coeffcents, the share n the varaton of productvty growth explaned by road nvestment s very low. 17

18 Estmatng the dfference n productvty growth on the natonal and country group levels as a functon of the dfference between the products of vehcle shares and road servces on the natonal and nternatonal levels, does not change, as can be seen from Table 2, affect the fundamental results. φ, the rato of producton elastctes of road stock and vehcle stock, remans postve. The sgnfcance of the estmaton coeffcent s, however, slghtly decreased and the regresson coeffcents are even worse than n the frst model. Table 2. Fxed effects regresson 2, Dfference between vehcle share weghted natonal and nternatonal road stock Number of obs. = 300 dfftfp Coeffcent Standard Error t P > t 95 p.c. Confdence Interval dffprod constant R-sq: wthn = between = overall = F test that all u = 0 : F(11,287) = Prob > F = The thrd estmaton model adds a tme dummy to estmaton model 2. Ths mproves the performance of the estmate n that the statstcal sgnfcance of the estmated φ s mproved and the regresson coeffcents are ncreased. The low coeffcent for the tme varable suggests that there s no problem of spurous correlaton, due to the ndependent and dependent varables followng the same tme trend. 18

19 Table 3. Fxed effects regresson 3, Dfference of vehcle share weghted natonal and nternatonal road stock and year dummy Number of obs. = 300 dfftfp Coeffcent Standard Error t P > t 95 p.c. Confdence Interval dffprod year constant R-sq: wthn = between = overall = F test that all u = 0 : F(11,286) = Prob > F = CONCLUDING REMARKS Ths paper has argued that nvestment n road nfrastructure ndeed has postve macroeconomc productvty effects. The results of the paper do not, however, justfy a general concluson that natonal road nfrastructure nvestment levels should be ncreased. The rate of return mpled by the above analyss does not seem to be hgh (for many countres around 5 per cent) 6. A relatvely low rate of return mght not necessarly be due to too hgh a level of nvestment but could be due to a msallocaton at the local level. As demand for transport servces s hghly unequally dstrbuted over space and even over tme, local road nfrastructure nvestment projects mght have hgh expected rates of return, even f the overall mpled rate of return s low. The greater ncome that can be acheved wth the gven resources may be assocated wth greater external costs, n partcular n the form of envronmental damage. On the other hand, the underprovson of transport nfrastructure servces leads to external costs n the form of tme costs, whch are not reflected n the natonal accounts data used here. Whle t s certanly true that GDP s an mperfect welfare measure, further research s requred to 19

20 dentfy how the mpact of transport nfrastructure on ncome dffers from the mpact on welfare. An analyss such as the above can, however, gve a broad ndcaton as to an approprate level of nfrastructure nvestment, at least based on the hypothetcal assumpton that the assgnment of nvestment resources to ndvdual projects s ratonal. To lnk the above macroeconomc analyss to plannng tools to allocate regonal nfrastructure resources and cost-beneft analyss at the project level s a matter of future research. NOTES 1. Aschauer (1989, 1990) started the dscusson on the productvty effects of publc nvestment. Hs fndng of large postve productvty effects beng caused by publc nvestment has been confrmed by Munnel (1990, 1992), Nadr and Manuneas (1994), Kocherlakota and Y (1996a), Morrson and Schwartz (1996b) as well as Duggal et al. (1999a). 2. See, for example, Aaron (1990), Hulten and Schwab (1991), Holtz-Eakn (1994) as well as Sturm and de Haan (1995). 3. On measurng the productvty ncrease by the Solow resdual, see Hall (1990) and the dscusson n Basu and Fernald (1997). 4. On the mplcatons of nternatonal trade for the ncentves to nvest n transport nfrastructure, cf. Bougheas et al. (2003). 5. Road nvestments mght have an mpact on the trade coeffcents. Gven the resultng concern about the potental endogenety of the weghts, the average values for the sample perod are used. In ths we follow an approach proposed by Case et al. They provde the argument that, when usng average values over several years for the weghts, the weghts and the explanatory values are orthogonal. Thus the ntroducton of the weghts does not lead to a correlaton of the ndependent varables and the resduals. 6. It s calculated by multplyng the share of vehcle captal costs n value added by the rato of value added to the value of road stock, and multplyng ths product by φ. 20

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