New Estimates of Government Net Capital Stocks for 22 OECD Countries

Transcription

1 WP//7 New Esimaes of Governmen Ne Capial Socks for OECD Counries 9 Chrisophe Kamps

2 Inernaional Moneary Fund WP//7 IMF Working Paper Fiscal Affairs Deparmen New Esimaes of Governmen Ne Capial Socks for OECD Counries 9 Prepared by Chrisophe Kamps Auhorized for disribuion by Richard Hemming April Absrac This Working Paper should no be repored as represening he views of he IMF. The views expressed in his Working Paper are hose of he auhor(s) and do no necessarily represen hose of he IMF or IMF policy. Working Papers describe research in progress by he auhor(s) and are published o elici commens and o furher debae. The issue of wheher governmen capial is producive has received a grea deal of recen aenion. Ye empirical analyses of public capial produciviy have generally been limied o he official capial sock esimaes available in a small sample of counries. Alernaively, many researchers have invesigaed he oupu effecs of public invesmen recognizing ha invesmen may be a poor proxy for he corresponding capial sock. This paper aemps o overcome he daa shorage by providing inernaionally comparable capial sock esimaes for Organizaion for Economic Cooperaion and Developmen (OECD) counries. JEL Classificaion Numbers: C8, E, E, H Keywords: Capial sock, public capial, perpeual invenory mehod, OECD counries Auhor s Address: kamps@ifw.uni-kiel.de Kiel Insiue for World Economics, Kiel, Germany. Tel.: , Fax: The firs draf of his paper was wrien while I was a summer inern in he Fiscal Affairs Deparmen of he Inernaional Moneary Fund. I hank he saff of he Fiscal Policy and Surveillance Division for heir hospialiy and cooperaion. I am especially indebed o Teresa Daba n for many helpful and clarifying discussions. I hank counry desk economiss for providing me wih informaion on naional daa sources. I would finally like o hank seminar paricipans in he annual conference of he Royal Economic Sociey, in he annual conference of he Inernaional Insiue of Public Finance and a he Universiy of Groningen, as well as Alfred Boss, Kai Carsensen, Joerg Doepke, Joachim Scheide, Jan-Egber Surm, Marcel Timmer, and Bar van Ark for helpful commens.

3 - - Conens Page I. Inroducion... II. Daa... III. Mehodology... IV. Capial Sock Esimaes for OECD Counries 9... V. Robusness of he Public Capial Sock Esimaes... VI. Evidence for he Producion Funcion Approach... A. Esimaes of Public Capial Produciviy for Alernaive Capial Measures... 8 B. Esimaes of Public Capial Produciviy for OECD Counries... 9 VII. Conclusion... References... Tables. Coverage of Governmen Gross Fixed Capial Formaion Governmen Ne Capial Sock in OECD Counries Governmen Ne Capial Sock per Head in OECD Counries Elasiciies of Oupu wih Respec o Public Capial for he Unied Saes and Canada for Alernaive Capial Sock Measures.... Elasiciies of Oupu wih Respec o Public Capial for OECD Counries for Capial Sock Esimaes from Differen Sources... Figures. Real Governmen Gross Fixed Capial Formaion in OECD Counries Implici Scrapping Raes for he Unied Saes Real Governmen Ne Capial Sock in OECD Counries Governmen Ne Capial Socks for Alernaive Esimaion Assumpions... Appendices Naional Daa Sources...

4 - - I. INTRODUCTION The issue of wheher governmen capial is producive has received a grea deal of recen aenion. In his seminal conribuions, Aschauer (989a,b) found large posiive oupu effecs of governmen capial in he Unied Saes. His resuls furher suggesed ha governmen capial was even more producive han privae capial. However, he large body of empirical lieraure ha developed afer Aschauer s early sudies challenged hese resuls. This lieraure surveyed, for example, in Gramlich (99), Surm, de Haan, and Kuper (998), and Seiz () concludes ha alhough here is evidence for posiive oupu effecs of governmen capial, he magniude of hese effecs is in general much smaller han Aschauer repored. The lack of public capial sock daa for a large number of Organizaion for Economic Cooperaion and Developmen (OECD) member counries has forced mos empirical sudies o focus on he Unied Saes. Few sudies have invesigaed he produciviy of governmen capial for oher OECD counries: examples are Ford and Pore (99), as well as Evans and Karras (99). Boh groups of auhors drew heir daa from earlier volumes of OECD (997) ha assembled capial sock series for counries over he period 97 99, provided direcly by he naional auhoriies. However, hese daa were no inernaionally comparable because esimaion mehods differed widely across counries. This was one of he reasons why he OECD suspended he publicaion of capial sock series afer 997 and cofounded he Canberra Group on Capial Sock Saisics whose aciviies resuled in he publicaion of a manual on he measuremen of capial (OECD, a). Thus far, only a few counries have adjused heir esimaion mehods; inernaionally comparable capial sock daa are sill no available. In spie of hese consrains, he analysis of public capial produciviy has coninued o be an acive area of research. Mos recen sudies use an approach based on vecor auoregressive (VAR) models (for example, Minik and Neumann, ; and Voss, ) ha unlike he earlier producion funcion and cos funcion approaches do no impose causal links among he variables under invesigaion. The main disadvanage of his approach is ha i generally requires large daa samples for convenional lag lenghs. For his reason, mos researchers employing he VAR approach have used daa on public invesmen insead of daa on he public capial sock. This choice has been dicaed no only by he lack of capial sock daa for a large number of counries, bu also by he fac ha public invesmen daa are usually available each quarer, whereas public capial sock daa are available only every year. One drawback of his choice is he implici assumpion ha he effecs of public invesmen are independen of he level of he corresponding capial sock. Economic heory suggess ha his assumpion is dubious. According o he law of diminishing reurns, an incremen o he public capial sock (ha is, public invesmen correced for fixed capial consumpion) would have a small/large oupu effec if he capial sock in he previous period were large/small. There is indeed evidence for a fas decline in he marginal produciviy of public capial (Demeriades and Mamuneas,, p. 7). Surm, de Haan, and Kuper (998, p. 8) draw aenion o he problem ha mos auhors employ daa in heir analysis which are generally chosen on he ground of heir availabiliy, wihou analyzing wheher heir conclusions are sensiive no only o he concep of he public capial sock (narrow versus broad definiion), bu also o he way he capial sock has been consruced.

5 - - This paper provides inernaionally comparable annual capial sock esimaes for OECD counries for he period 9, calculaed using he perpeual invenory mehod based on a geomeric depreciaion paern. Capial sock daa are esimaed for hree caegories of invesmen: () privae nonresidenial gross fixed capial formaion, () privae residenial gross fixed capial formaion, and () governmen gross fixed capial formaion. A sensiiviy analysis explores he robusness of he capial sock esimaes by varying he main esimaion assumpions for wo reference counries, he Unied Saes and Canada, for which public capial sock esimaes from official sources are available. The resuls of his sensiiviy analysis sugges ha he benchmark capial sock esimaes are robus. Finally, he paper repors and compares esimaion resuls for he producion funcion approach, using hree alernaive measures of he public capial sock: () auhor s own esimaes; () esimaes from naional auhoriies; and () esimaes from OECD (997). The regression resuls confirm previous resuls in he lieraure based on he producion funcion approach and show ha he elasiciy of oupu wih respec o public capial is posiive and saisically significan, bu quie large for mos counries. According o esimaes based on a simple panel daa model, he elasiciy of oupu wih respec o public capial is on average. in OECD counries. The remainder of his paper is organized as follows: Secion II describes he invesmen daa used in he esimaion of capial socks; Secion III describes he esimaion mehodology; Secion IV presens he esimaion resuls; Secion V explores he robusness of he capial sock esimaes by varying he main esimaion assumpions; Secion VI esimaes elasiciies of oupu wih respec o public capial according o he producion funcion approach for alernaive capial sock measures; and Secion VII concludes. II. DATA The basic ingredien for he esimaion of capial socks is hisorical daa on gross invesmen. These daa are aken from he June version of he OECD Analyical Daabase. The esimaion is carried ou for he following OECD counries: Ausralia, Ausria, Belgium, Canada, Denmark, Finland, France, Germany, Greece, Iceland, Ireland, Ialy, Japan, he Neherlands, New Zealand, Norway, Porugal, Spain, Sweden, Swizerland, he Unied Kingdom, and he Unied Saes. The series rerieved from his daabase expressed in consan prices and in naional currencies are (OECD code in parenheses) he oal gross fixed capial formaion (ITV), oal privae gross fixed capial formaion (IPV), privae nonresidenial gross fixed capial formaion (IBV), privae residenial gross fixed capial formaion (IHV) and governmen gross fixed capial formaion (IGV). The capial sock esimaes are available upon reques o he auhor. This daabase includes no only invesmen daa bu also a large se of oher macroeconomic variables. In addiion o invesmen, real gross domesic produc (GDPV) and employmen (ET) are also rerieved from he OECD Analyical Daabase. Mos of hese daa are available online a hp:// For mos of hese counries he daa are available for he period 9. The following OECD counries are no included in he analysis because long invesmen series are no available: he Czech Republic, Hungary, he Republic of Korea, Luxembourg, Mexico, Poland, he Slovak Republic, and Turkey.

6 - - This paper uses public invesmen daa from he OECD Analyical Daabase because apar from providing long-ime series for a large panel of counries, he daa are caegorized by insiuional secor and are more comparable inernaionally han daa from naional sources. Table gives deails abou he insiuional coverage of he public invesmen series. This informaion is imporan because he definiion of he public secor underlying he invesmen series varies no only across sources for a given counry, bu also across counries for a given source. Three definiions regarding he coverage of public invesmen are used by he counries under invesigaion: () public invesmen of he general governmen; () public invesmen of he nonfinancial public secor (general governmen plus nonfinancial public enerprises (NFPEs)); and () invesmen carried ou by economic unis engaged in aciviies labeled Public adminisraion and defense services, compulsory social securiy services (narrow definiion) and Public adminisraion, educaional services, and healh care and social assisance (broad definiion) according o he Inernaional Sandard Indusrial Classificaion (ISIC). Whereas he firs wo definiions caegorize by insiuional secor, he laer wo definiions caegorize by ype of economic aciviy. The ISIC caegory Public adminisraion, educaional services, and healh care and social assisance comes close o he definiion of he nonfinancial public secor, bu i also includes privae spending on educaion, which may, for insance, be imporan in some counries such as Canada. Figure displays he evoluion of he public invesmen GDP raio for he earlier-menioned counries over he period 9. The subplos of Figure for he individual counries show he public invesmen GDP raio for he daa from he OECD Analyical Daabase as well as if available for daa from naional sources 7 and from OECD (997). The public invesmen GDP raio has in general declined over he sample period. In some counries such as Ausria or Ireland, he decline has been paricularly pronounced. Noable excepions o he general paern include Greece, Porugal, and Spain where public invesmen GDP raios have increased considerably since accession o he European Communiy in he 98s. A comparison of he daa from differen sources reveals ha he raios calculaed for daa from OECD Analyical Daabase coincide wih daa from naional sources, excep for Belgium, Canada, Ialy, Japan, and Spain. The differences in he daa from hese wo sources and hose from he OECD (997) are quie large in mos of he cases, parly reflecing ha OECD (997) daa are based on he 98 Sysem of Naional Accouns, while he oher wo sources rely on he 99 Sysem of Naional Accouns. 8 To a cerain exen, he difference is also due o daa revisions since he publicaion of OECD (997). However, he mos imporan reason for he discrepancy in he daa from alernaive sources seems o be differen coverage of public invesmen. In OECD (997), public eniies are referred o as Producers of governmen services. This caegory in mos cases corresponds o he definiion of public aciviies underlying he invesmen series from naional sources. An imporan difference, however, is ha capial socks in OECD (997) were based on classificaions of public aciviies according o he 98 Sysem of Naional Accouns whereas recen naional daa are based on classificaions according o he 99 Sysem of Naional Accouns. 7 See Appendix for a descripion of daa from naional sources. 8 For deails on he 99 Sysem of Naional Accouns see European Commission and ohers (99).

7 - - III. METHODOLOGY The mehodology applied here in he esimaion of capial sock daa draws in large par on OECD (a) and on he U.S. Bureau of Economic Analysis (999). The esimaion exercise is comparable o ha performed by Jacob, Sharma, and Grabowski (997), who esimae capial socks by indusrial aciviy according o he ISIC. Here, however, he aim is o obain esimaes by insiuional secor wih a special focus on he public secor raher han by indusrial aciviy. Oher precursors of he presen sudy include Bernd and Hansson (99), who esimae he public capial sock for Sweden; Surm and de Haan (99), who esimae he public capial sock for he Neherlands; as well as Boskin, Robinson, and Huber (987), Holz-Eakin (99), and Munnell (99), who esimae he capial sock for local and sae governmens in he Unied Saes. This paper employs he same esimaion approach as hose sudies: he perpeual invenory mehod. The ne capial sock is esimaed for he hree subcaegories of gross invesmen available from he OECD Analyical Daabase: () privae nonresidenial gross fixed capial formaion; () privae residenial gross fixed capial formaion; and () governmen gross fixed capial formaion. 9 The basic idea of he perpeual invenory mehod is ha he ne capial sock a he beginning of he following period, K +, can be expressed as a funcion of he ne capial sock a he beginning of he curren period, K, of gross invesmen in he curren period, I, and of depreciaion in he curren period, D : K + = K + I D. () If one furher assumes geomeric depreciaion (ha is, he capial sock depreciaes a a consan rae,δ ) hen he capial accumulaion equaion can be rewrien as ( ) K I K + = δ +. () The mehod is called perpeual because all asses are forever par of he invenory of capial socks. Of course, he quaniy of services provided by an asse declines as i ages, bu i never reaches zero. This can be seen by repeaedly subsiuing equaion () for he capial sock a he beginning of period : = i= ( ) i K+ δ I i. () 9 All series are expressed in he consan prices of 99. For hose counries wih a differen base year (Ausralia 999/; Canada, 997; Iceland, 99; Norway, 997; Swizerland, 99; and he Unied Saes, 99) he series were rebased o 99. The erms depreciaion and consumpion of fixed capial are used inerchangeably in his paper. This is common in economic lieraure. Noe, however, ha depreciaion as used here differs considerably from is use in company accouns where i is calculaed on he basis of hisoric coss raher han marke prices.

8 - 7 - This expression shows ha he capial sock a he beginning of period + is a weighed sum of pas invesmen where he weighs are a decreasing funcion of he disance beween he curren period and he invesmen period. In pracice, an infinie number of pas invesmen flows is no available so ha equaion () is replaced by he following expression: K + ( ) K + ( δ ) = δ I i, () i= i where K is he iniial capial sock a he beginning of period. According o equaion (), he applicaion of he perpeual invenory mehod requires he following inpus. Firs, a ime series on gross invesmen flows is needed. The esimaions in his paper rely on invesmen daa from he OECD Analyical Daabase described in Secion II. Second, he esimaions necessiae an iniial capial sock, in our case he capial sock a he beginning of 9. Third, an assumpion on he size and he ime profile of he depreciaion has o be made. Finally, a depreciaion mehod has o be chosen. This sudy relies on geomeric depreciaion. There is no official informaion on he magniude of he iniial capial sock for any counry excep he Unied Saes. This paper follows an approach similar o ha applied by Jacob, Sharma, and Grabowski (997, p. 7) in order o esimae he iniial capial sock. For ha purpose, an arificial invesmen series for he period 8 99 is consruced for each counry by assuming ha invesmen increased by percen a year during his period, finally reaching is observed level in 9. The raionale for his assumpion is ha oal gross invesmen in he OECD counries under consideraion grew by percen a year on average during he period 9. I is, of course, highly improbable ha invesmen in he earlier period grew a he same rae as during he period 9, and ha invesmen growh was he same for all counries. However, as hisorical informaion especially on public invesmen is no available for mos of he counries under consideraion, his sudy ops for an equal reamen of all counries. The resuls of a sensiiviy analysis repored in Secion V sugges ha he assumpion on he iniial capial sock does no affec he dynamics of he resuling capial sock series o a large exen. Also, he imporance of he iniial capial sock on he level of he capial sock series fades over ime. Is conribuion o he level of he capial sock a he end of he sample is less han percen for he average OECD counry. An excepion o his general rule applies in he case of he Unied Saes. The Bureau of Economic Analysis (BEA) provides invesmen series saring in 9. This informaion is used by chaining he OECD daa which are available for 9 wih he BEA growh raes for 9. Maddison (99) esimaes gross capial socks for six OECD counries based on invesmen series ha in some cases sar in he 9 h cenury. However, he acknowledges ha he assembly of he invesmen series is a major problem because hisorical series for differen periods have o be linked and because hese series rely on differen weighing bases. Also, here are generally breaks in he hisorical invesmen series. Ye, mos imporan for our purpose is ha hisorical series on invesmen in general do no include a measure of governmen invesmen bu only measures of privae invesmen. An excepion relaes o he influenial works of Feinsein (for example, 97), who provides invesmen series for he public secor in he Unied Kingdom saring in 8. Ye, he definiion of he public secor in his sudies differs considerably from ha underlying he OECD series.

9 - 8 - This assumpion implies ha invesmen and he capial sock grew smoohly over he period 8 9, a simplificaion ha needs o be jusified, especially since some counries in he sample experienced severe damage during World War II. The quesion arises wheher he effecs of war damage on he capial sock were persisen enough o affec our esimae of he iniial capial sock a he beginning of 9. There are a leas wo reasons why war damage migh have had lile effec by 9. Firs, he counries ha experienced he larges war damage grew much faser afer World War II han he counries ha suffered lile or no war damage. Thus, real GDP in counries subjec o severe war damage migh well have reurned o is longrun rend by 9. Second, he srong rise in GDP afer World War II in hese counries was accompanied by fas increases in invesmen and in he capial sock. As a consequence, he capial sock migh also have reurned o is long-run rend by 9. 7 All in all, here are hins ha he effecs of war damage on he capial sock in counries ha were mos severely affeced had disappeared by 9, he saring year for our capial sock esimaes. The srong growh performance in he quarer cenury following World War II, ofen referred o as growh miracle, was disribued unevenly among OECD counries. As Broadberry (988) saes, he counries mos hi by war damage like Japan and Germany grew much faser han counries ha were hardly affeced by war damage, such as he Unied Kingdom and he Unied Saes. The evidence presened in Maddison (98, p. ) and Eichengreen and Rischl (998, p. ) furher suggess ha by 9 real GDP in OECD counries was close o he level implied by is long-run growh pah. Moreover, he analysis in Eichengreen and Rischl (998, p. 8) shows ha he srong growh performance in Germany was no impaired by a lack of capial due o war damage. Based In his esimaion of nonresidenial capial socks for six OECD counries, Maddison (99, pp. 8 9) assumed ha he loss in capial sock caused by war damage amouned o percen in he Unied Kingdom, 8 percen in France, percen in he Neherlands, percen in Germany, and.7 percen in Japan. These figures are subjec o a large margin of uncerainy, hough, and he war damage o producive capaciies may well have been lower han assumed by Maddison. For example, Rischl (, p. ) repors ha he indusrial capial sock in Germany in 9 exceeded prewar levels by one-hird. This capial sock was ofen composed of mulipurpose machinery and hus available for civil producion. Likewise, Eichengreen and Rischl (998, p. 8) and Giersch, Paqué, and Schmieding (99, p. 7) noe ha war damage o he capial sock in Germany was quie limied. Maddison (987, p. ) repors ha beween 9 and 97 real GDP grew by 9. percen a year on average in Japan and by.9 percen in Germany, whereas he average annual growh rae was only. percen for he Unied Kingdom and.7 percen for he Unied Saes. For example, long-run growh in real GDP was remarkably sable in Wes Germany despie he disrupions caused by World War II. Calculaions based on hisorical GDP figures drawn from Rischl and Spoerer (997) reveal ha real GDP grew by.9 percen a year on average beween 98 and 9 and by. percen beween 9 and 99. Of course, real GDP did no grow smoohly in he firs subperiod. Real GDP in 9 was lower han in 98 by roughly percen. Ye, real GDP growh over he period 9 o 9 was exremely srong, averaging almos percen a year. Maddison (987, p. 7) repors ha beween 9 and 97, he privae capial sock on average grew in Japan by 9. percen a year and in Germany by 7. percen. Calculaions based on Luezel (977, p. ) show ha he oal ne capial sock in Germany grew by 7.9 percen a year on average beween 9 and 9. Calculaions based on Michell (97) show ha ne invesmen in Germany grew by 9.7 percen a year on average beween 9 and 9. 7 The fall in capial socks due o warime disrupions was less pronounced han he fall in oupu (Maddison, 98, p. ), implying ha he gap beween capial sock levels a he end of World War II and heir long-run rend was lower han was he case for oupu.

10 - 9 - on hese consideraions we choose no o correc he capial sock esimaes a he beginning of 9 for war damage. The nex assumpion in he esimaion relaes o he size and he ime profile of he depreciaion rae. In his sudy i is assumed ha he depreciaion rae is ime-varying for he public capial sock and he privae nonresidenial capial sock and consan for he privae residenial capial sock. 8 This assumpion allows aking ino accoun he empirically observed paern of aggregae depreciaion raes. 9 Figure shows he implici scrapping rae for he real governmen ne capial sock, he real privae nonresidenial ne capial sock, and he real privae residenial capial sock in he Unied Saes for he period 9. The implici scrapping rae is calculaed as he quoien of depreciaion in period and he ne capial sock a he beginning of period (daa from he U.S. Bureau of Economic Analysis): D s =. () K Figure reveals ha he implici scrapping raes differ considerably across he hree ypes of capial. The implici scrapping rae is highes for privae nonresidenial capial and lowes for privae residenial capial. Whereas he scrapping rae of privae residenial capial has remained roughly consan over he period 9, he scrapping raes of privae nonresidenial capial and of governmen capial have ended o rise over ime. The increase is especially pronounced in he case of he privae nonresidenial capial sock, is scrapping rae having risen from abou ½ percen in 9 o abou 9½ percen in. Two developmens may parly explain he rise in he scrapping rae: Firs, i may reflec an increasing weigh of asses wih relaively shor asse lives; second, i may also reflec o a cerain degree a shorening of asse lives. Boh developmens are characerisic of ICT-relaed asses ha are par of he privae nonresidenial capial sock and o a lesser exen of he governmen capial sock. A similar paern for implici scrapping raes can be observed for oher counries. For example, Canadian and Ausralian daa reveal ha implici scrapping raes of privae nonresidenial and governmen capial have also risen since he 9s. 8 This paper assumes ha he ime profile of he depreciaion raes is he same across counries. Official esimaes of capial socks for differen counries are in general based on differen assumpions abou depreciaion raes. This is appropriae insofar as counry-specific facors influence service lives. However, only a few counries have invesigaed service lives wih paricular care, among hem he Unied Saes (OECD a, p. 99). Therefore, i seems preferable o assume idenical depreciaion raes across counries for he purpose of inernaional comparisons. Such a sandardized approach is also adoped by Maddison (99) and O Mahony (99). 9 Naional auhoriies usually esimae he conribuion of invesmen o he ne capial sock for a large number of individual asses (U.S. Bureau of Economic Analysis, 999). For mos of hese asses, naional auhoriies assume consan depreciaion raes excep for asses relaed o informaion and communicaion echnology (ICT). A he same ime, hey assume differen depreciaion raes for differen ypes of asses. As he relaive imporance of differen asses changes wih ime, so does he average depreciaion rae. The laer will increase over ime if asses wih relaively shor asse lives gain in imporance. This paper ries o capure his phenomenon by assuming a imevarying aggregae depreciaion rae.

11 - - Based on his evidence, his paper makes he following assumpions abou he ime profile of he depreciaion raes: For he period 8 o 9, he depreciaion rae is assumed o be ½ percen for governmen asses, ¼ percen for privae nonresidenial asses, and ½ percen for residenial asses. For he period 9, i is assumed gradually o increase from ½ percen o percen for governmen asses and from ¼ percen o 8½ percen for privae nonresidenial asses, and i is assumed o be a consan ½ percen for privae residenial asses (see Figure ). Equaion () formalizes he ime profile of he depreciaion raes: where in. + j j j δ max δ = δ min for all = 9, 9,...,, () j δ min j δ min is he depreciaion rae of asse ype j in 9 and j δ max is is depreciaion rae Finally, he real ne capial sock a he beginning of period + for invesmen caegory j can be expressed (see also Bureau of Economic Analysis, 999, p. M-) as K j + = i= 8 k = i+ j δ ( δ k ) j i I j i j δ + I j j j j j ( ) K δ + I = δ for all = 8,8,.... (7) Noe ha he capial sock a he beginning of he iniial period, K 8, is se equal o zero. Equaion (7) differs from equaion () in wo respecs in order o increase he realism of he esimaes. Firs, as discussed earlier, he equaion incorporaes ime-varying depreciaion raes. Second, new invesmen is assumed o be placed in service a midyear insead of a he end of he year as implied by equaion (). Invesmen ypically occurs hroughou he year, no only a he end of he year. Equaion (7), in conjuncion wih he assumpions abou he depreciaion paerns, serves o esimae ne capial socks for governmen asses, privae nonresidenial and privae residenial asses. An aracive feaure of he approach followed in his sudy is ha he esimaed public ne capial sock is equivalen o he so-called producive capial sock (OECD (b, p. ). The laer capial sock is he appropriae measure of capial inpu for produciviy analyses because i Figure shows ha he implici scrapping rae calculaed for BEA daa sharply acceleraed afer 99. To some exen, his probably reflecs he growing imporance of ICT asses characerized by asse lives ha are much shorer han hose of oher asses. Because he imporance of he ICT secor is considerably lower in mos oher indusrial counries han in he Unied Saes (OECD, c), we chose a flaer depreciaion profile for he years 99 o han ha implici in U.S. daa.

12 - - reflecs he flows of services provided by capial more appropriaely han eiher he ne or he gross capial sock. Only for a homogenous asse and geomeric depreciaion does he disincion beween he producive capial sock and he ne capial sock vanish. For lack of disaggregaed daa, he presen sudy reas public invesmen as a homogenous asse. To sum up, he applicaion of he perpeual invenory mehod requires hree imporan assumpions. Firs, an iniial capial sock has o be consruced, here for he beginning of 9. This sudy uses arificial invesmen series for he period 8 99 as an inpu for he esimaion of he iniial capial sock. Second, an assumpion on he level and he ime profile of he depreciaion rae has o be made. This paper assumes ha he depreciaion rae is ime-varying and differen across he hree ypes of invesmen considered, bu he same for all counries. Third, a depreciaion mehod has o be chosen. This sudy relies on geomeric depreciaion. Secion V analyzes in deail he imporance of each of hese assumpions for he resuling capial sock esimaes. IV. CAPITAL STOCK ESTIMATES FOR OECD COUNTRIES 9 Figure displays he evoluion of he raio of he public ne capial sock and GDP, boh a 99 prices, for he OECD counries over he period 9. The graphs for he individual counries plo no only he auhor s own esimaes of he public capial sock, bu also where available esimaes from naional auhoriies and from OECD (997). For seven counries here is no benchmark agains which he auhor s own esimaes could be assessed. The same holds for Greece, in view of he very low capial sock esimae (repored by OECD, 997) ha is due o a narrow definiion of public invesmen. For hose counries where alernaive esimaes are available, he general picure is ha in mos cases he dynamics of he auhor s own esimaes resemble hose of he alernaive esimaes. In some cases, he level of he public capial GDP raios is also similar, bu in general here are significan differences. This, in par, reflecs he fac ha he iniial level of he auhor s own esimaes depends on he arificial invesmen series assumed for he period Ye, he differences are also due o wo oher reasons: () for some counries he invesmen series shown in Figure differ sharply from each oher (Greece); and () here is a wide variey of mehods applied by naional auhoriies in he consrucion of capial sock esimaes. An aracive feaure of he auhor s own esimaes is ha hey rely on he same mehodology and homogenous invesmen daa across counries, a condiion ha is no saisfied for he alernaive esimaes. This is no rue for oher depreciaion mehods, such as sraigh-line or hyperbolic depreciaion. A special problem in he esimaion of capial socks relaes o German reunificaion. The OECD invesmen and GDP series cover Wes Germany only for he period 9 9, bu hey include Eas Germany from 99 on. As here is no informaion on he magniude of he Eas German capial sock a he beginning of 99, his paper assumes ha he raio of he Eas German capial sock wih respec o he Wes German capial sock equaled he raio of Eas German and Wes German GDP in 99 (8 percen). In he esimaion, he German capial sock a he beginning of 99 is hus increased by 8 percen for he hree asse ypes considered. From 99 on, his addiional capial sock depreciaes a he same rae as he oher asses. Ausria, France, Iceland, Ireland, he Neherlands, Porugal, and Swizerland.

13 - - Table displays he value of he public capial GDP raio for hree years of reference: 98, 99, and. The average raio for he OECD counries has declined by percenage poins over he period 98. Public capial as a share of GDP has declined in counries since he early 98s; i has slighly increased in four counries while i has srongly risen in Greece, Japan, Porugal, Spain, and Swizerland. I does no come as a surprise ha Greece, Porugal, and Spain figure among his group, because hese counries are known o have made subsanial effors o improve heir infrasrucure afer joining he European Communiy. Furhermore, i is well known ha during he 99s he Japanese governmen repeaedly aemped (in vain) o reinvigorae he sluggish economy wih he help of large spending programs focusing on consrucion. According o he esimaes, in Japan had by far he larges public capial GDP raio among he OECD counries considered in his sudy, while Ireland had he lowes. The large decline in he public capial GDP raio in Ireland during he 99s mirrors he srong fall of public invesmen as a share of GDP during his period. Fiz Gerald and ohers (999) sae ha he Irish governmen views he lack of infrasrucure as one of he major impedimens o growh. The las column of Table shows he conribuion of governmen invesmen in he period 9 o he governmen ne capial sock in he year. As explained in he previous secion, assumed invesmen daa for he period 8 99 are used in order o esimae he iniial capial sock a he beginning of he year 9. The conribuion of he assumed invesmen daa o he iniial capial sock is percen, bu heir influence gradually fades and is quie small a he end of he sample. The capial sock esimaes for he year are largely unaffeced by he assumpion on invesmen during he period 8 99, for which no daa from official sources are available. Invesmen from 9 onwards conribues an average 9 percen o he ne capial sock in he year, implying ha he average conribuion of he assumed invesmen daa is only 8 percen. Anoher way o compare he governmen capial sock across counries is o look a is absolue value for each person. For an inernaional comparison of real capial sock, hree condiions have o be me (OECD a, page 8). Firs, he definiion of he capial sock mus be he same. This condiion is fulfilled since for all counries he invesmen daa used in he capial sock esimaions are compiled according o he 99 Sysem of Naional Accouns. Second, he capial sock mus be expressed in he same currency and hird, he price level a which he capial sock is valued mus be he same. The second and hird condiions are no fulfilled since he capial sock esimaes are expressed in naional currency and valued a he naional price. These daa can be convered o a common currency and revalued a a common se of prices using so-called purchasing power pariies (PPPs). Unforunaely, PPPs for he public capial sock are no available. Insead, a proxy for his measure has o be used. The OECD (a) provides PPPs for The conribuion of he iniial capial sock varies beween. percen in he case of Denmark and. percen in he case of Japan. The differences in conribuions across counries are mainly due o differences in he level of public invesmen GDP raios over he sample period. For insance, he conribuion of he iniial capial sock is lowes in Japan because he public invesmen GDP raio here was he highes among he considered counries over he period 9.

14 - - GDP and for oal gross fixed capial formaion. In he following PPPs for GDP for from he OECD (b) are used in order o conver he public capial sock esimaes o U.S. dollars. Table gives he real per capia public ne capial sock expressed a PPPs for GDP in U.S. dollars for he years 98, 99, and. The average capial sock for each person for he OECD counries has increased by.9 percen over he period 98 (ha is, by. percen per year). This growh rae has been lower han ha of real GDP, implying ha he public capial GDP raio has declined on average during his period in he OECD, as shown in Table. A comparison across counries reveals ha he public capial sock per head is by far he highes in Japan, exceeding he average by more han percen in he year. As regards he ranking of he counries, he Unied Saes ranks considerably higher han in Table, bu Greece, Porugal, and Spain rank much lower. This discrepancy can be explained by he level and he change in real GDP, respecively. Oupu growh in he Unied Saes was very fas in he second half of he 99s, implying a decreasing public capial GDP raio during he 99s, even hough public capial expanded subsanially a he same ime. In he cases of Greece, Porugal, and Spain, boh public capial per head and real GDP per head remain low in inernaional comparison. However, public capial per head has increased on average much faser in hese counries han in OECD counries over he period 98, reflecing he srong effors o enhance public infrasrucures in connecion wih heir accession o he European Communiies. V. ROBUSTNESS OF THE PUBLIC CAPITAL STOCK ESTIMATES The key assumpions made in he consrucion of he public capial sock esimaes are he following: () invesmen in he period 8 o 99 is assumed o have grown by percen per year o finally reach is observed level in 9; () he depreciaion rae is ime-varying and assumed gradually o increase for all asse ypes excep residenial asses; and () depreciaion is assumed o be geomeric. This secion assesses he effec of hese hree assumpions. For ha purpose, alernaive public capial sock series are esimaed for wo reference counries, he Unied Saes and Canada, modifying in urn each of he assumpions. These alernaive esimaes are hen compared wih he benchmark esimaes and wih esimaes from official sources. The resuls of his exercise are depiced in Figure. The upper row of Figure shows public capial sock esimaes for alernaive assumpions on he iniial capial sock in 9 for he Unied Saes, as well as he official capial sock esimae from he U.S. Bureau of Economic Analysis. The benchmark public capial sock esimae relies on he public invesmen series provided by he U.S. Bureau of Economic Analysis for he period 9 and assumes ha public invesmen grew by percen in he period The figure also shows an esimae ha relies on he assumpion ha as is assumed for all oher The mos imporan qualiaive resuls repored in he following paragraph are unaffeced if PPPs for oal invesmen are used insead. Deailed resuls are available on reques. In, real GDP per head amouned o. percen of he OECD average in Greece, o 7. percen in Porugal, and o 79. percen in Spain (OECD, b, p. 9). 7 The official growh raes provided by he U.S. Bureau of Economic Analysis for he period 9 are chained wih he OECD invesmen series available for 9.

15 - - counries public invesmen in he Unied Saes grew by percen in he period In addiion, Figure shows an esimae ha differs in he way he iniial capial sock is consruced. This esimae of he iniial public capial sock is consruced direcly following a seady-sae approach (Fuene and Doménech,, p. 7). I follows from equaion () ha he growh rae of he capial sock can be expressed as K K+ K g = = δ + K I K. (8) Thus, he capial sock a he beginning of period can be calculaed as invesmen in period divided by he sum of he depreciaion rae and he growh rae of he capial sock in period : K I =. (9) δ + K g As he growh rae of he capial sock is unknown a priori, an assumpion abou is magniude is needed. Neoclassical growh heory suggess ha invesmen and capial grow a he same rae in he seady sae. Thus, he growh rae of capial can be approximaed by he growh rae of invesmen. As i is improbable ha he U.S. economy was in a seady sae in 9, he growh rae of capial is insead approximaed by he average growh rae of invesmen over he period 9. This growh rae was.7 percen in he case of governmen invesmen,. percen in he case of privae nonresidenial invesmen, and. percen in he case of privae residenial invesmen. Finally, he invesmen series is filered using a Hodrick-Presco filer in order o remove is cyclical componen. Figure (a) shows ha assuming a consan percen growh rae of public invesmen over he period 9 9 insead of using he hisorical Bureau of Economic Analysis (BEA) invesmen growh raes does no significanly affec he resuling public capial sock series. For he period of ineres, 9, he levels and he dynamics of boh series are almos indisinguishable. Pronounced differences occur over he period 9 only because he public capial sock based on BEA invesmen akes accoun of he large increase in public invesmen during World War II, whereas he alernaive esimae does no. Ye he effec of his difference is shor-lived. The figure also reveals ha alhough he level of he public capial sock esimaes is lower han he capial sock series repored by he BEA, he dynamics are very similar, as winessed by he srong comovemen of he growh raes of he public capial sock series. Furhermore, formal ess for equaliy beween he means and he variances of he auhor s own esimaes and of he BEA series fail o rejec he null hypohesis of equaliy. 8 Figure (a) also depics he auhor s own esimae of he public capial sock relying on he seady-sae approach. The ime profile of his esimae differs considerably from ha of he oher series shown in he figure. While he level of he iniial capial sock a he beginning of 9 is higher han ha of he BEA reference series, is level a he beginning of is comparable o ha of he auhor s own esimae and hus lower han ha of he BEA series. Furhermore, he dynamics of his 8 Deailed resuls are available upon reques. These ess are carried ou for he growh raes of he series because uni roo ess indicae ha he public capial sock series are inegraed o order.

16 - - esimae are significanly differen from ha of he oher series, as can be seen in he figure. This visual impression is confirmed by a formal es for equaliy beween he means and variances of he growh raes of his esimae and of he BEA series. These resuls sugges ha he benchmark assumpion on he iniial capial sock made in his paper seems o be a reasonable way o proceed. The middle row of Figure shows public capial sock esimaes for alernaive assumpions on he ime profile of he depreciaion rae and again conrass hese esimaes wih he official esimae repored by he BEA. The benchmark esimae assumes a ime-varying depreciaion rae increasing from ½ percen o percen, as explained in Secion III. Figure (b) also shows he public capial sock for a depreciaion rae ha based on implici scrapping raes for he oal capial sock gradually increases from percen o percen over he period 9. I also shows he public capial sock for a depreciaion rae ha is consan over ime and equal o he average implici scrapping rae empirically observed for he Unied Saes (½ percen for governmen asses). The figure reveals ha hese wo esimaes exhibi dynamics ha differ significanly from hose of he BEA series and of he benchmark esimae. The reason is ha he esimae assuming a consan depreciaion rae considerably overesimaes he growh of public capial in he 99s, whereas he esimae relying on a seeper ime profile of he depreciaion rae underesimaes he growh of public capial in he 97s and in he early 98s. All in all, he benchmark assumpion on he depreciaion raes based on empirically observed implici scrapping raes for he Unied Saes seems o be he mos sensible approach, given he alernaives. Finally, he lower row of Figure depics he influence of alernaive depreciaion mehods. Unlike he previous wo sensiiviy analyses, his exercise is no based on auhor s own esimaes, bu on official esimaes for Canada. 9 Saisics Canada provides public capial sock esimaes for hree alernaive depreciaion mehods sraigh-line, hyperbolic, and geomeric. Figure (c) shows ha hyperbolic and geomeric depreciaion resul in quie similar capial sock esimaes, whereas he esimae based on sraigh-line depreciaion differs considerably boh in levels and dynamics. The level of he auhor s own esimae based on geomeric depreciaion is in general lower han he Saisics Canada series based on he same depreciaion mehod, bu higher han is series based on linear depreciaion. The dynamics of he auhor s own esimaes are similar o ha of he Saisics Canada series based on geomeric depreciaion excep for he 9s. A formal es for equaliy beween he means and variances of he growh raes of hese wo series canno rejec he null hypohesis of equaliy. Thus, he benchmark esimaes seem sensible in he case of Canada also. To sum up, his secion has shown he effec of various assumpions on public capial sock esimaes. Visual inspecion and ess for equaliy beween he benchmark esimaes and reference series repored by he U.S. BEA and Saisics Canada reveal ha he benchmark esimaes of public capial seem quie plausible. The properies of he capial sock esimaes based on he various assumpions are furher explored in he nex secion, where hese esimaes are used as explanaory variables in regressions according o he so-called producion funcion approach. 9 As informaion on asse lives a he aggregae level is no available, his sudy canno provide capial sock esimaes ha are comparable across depreciaion mehods. For his reason he capial sock esimaes are based on implici scrapping raes for he Unied Saes and Canada insead. See Secion III for deails.

17 - - VI. EVIDENCE FOR THE PRODUCTION FUNCTION APPROACH This secion uses alernaive capial sock measures in order o esimae he elasiciy of oupu wih respec o public capial, applying he producion funcion approach. Secion VI.A presens regression resuls for he various capial sock esimaes for he Unied Saes and Canada, and hus supplemens he sensiiviy analysis presened in he previous secion. Secion VI.B presens regression resuls for OECD counries for capial sock esimaes from differen sources (ha is, for auhor s own benchmark esimaes, for esimaes from naional sources and for esimaes from OECD, 997). The producion funcion approach is one of hree main approaches ha have been employed in he empirical lieraure on he macroeconomic effecs of public capial. The oher approaches are he cos funcion approach and he vecor auoregressive (VAR) approach. This sudy concenraes on he producion funcion approach boh because i is he simples among he hree approaches and because i sill remains widely applied in he empirical lieraure. Even recen sudies relying on he less resricive VAR approach ofen provide addiional esimaes according o he producion funcion approach as a benchmark agains which o evaluae he VAR resuls (Lighar, ). Thus, here is ample evidence agains which he regression resuls of his sudy can be evaluaed. The saring poin of empirical applicaions relying on he producion funcion approach is an P P aggregae producion funcion of he form Y = AF( K, L), where Y is oupu, K is he privae capial sock, L is labor inpu, and A is an index represening mulifacor produciviy. This G expression is exended by including he public capial sock ( K ) so ha he aggregae P G producion funcion can be wrien as Y = AF( K, L, K ). Using he Cobb-Douglas form and aking he naural logarihm yields he regression equaion ha is ypically employed in empirical sudies relying on he producion funcion approach: y = P G a + a + α l + β k + γ k + ε, () where y is he log of GDP, l is he log of labor inpu, P k is he log of privae capial, log of public capial, and ε is a disurbance erm. As in Aschauer (989b), a consan, G k is he a, and a ime rend,, are inroduced as a proxy for mulifacor produciviy. The parameersα, β, and γ can be inerpreed as elasiciies of oupu wih respec o he facors of producion. An imporan issue raised by his specificaion is ha of poenial nonsaionariy of he variables included in he regression. A large number of alernaive uni roo ess are designed o discriminae beween nonsaionary and saionary processes (Survey in Phillips and Xiao, 998). We use he popular Dickey and Fuller (979, 98) es in order o deermine wheher he model See Surm, de Haan, and Kuper (998) for a discussion of he hree approaches, as well as for an overview of empirical sudies.

18 - 7 - variables are nonsaionary. This es is applied o a oal of variables ha are used in he individual-counry regressions repored in Secions VI.A and VI.B. The es resuls indicae ha he vas majoriy of variables is nonsaionary; only variables appear o be saionary in level. Among he variables ha are nonsaionary many seem o be inegraed of order wo raher han of order one according o he es resuls. Ye i is well known ha uni roo ess have low power o discriminae beween uni roo and near uni roo processes (Enders, 99, p. ). This problem is especially pronounced for small samples (Campbell and Perron, 99). One way o alleviae he problem is o make use of he cross-secional dimension of he daa and o apply panel uni roo ess o he variables. The resuls of wo popular panel uni roo ess sugges ha he variables are inegraed o he firs order. The individual-counry regressions are hus also based on his finding. Since he variables are nonsaionary esimaion of equaion () makes sense only if he variables are coinegraed. There are many alernaive mehods ha can be used o es for coinegraion (see he survey in Dolado, Gonzalo, and Marmol, ). In his paper he wo-sep procedure iniially proposed by Engle and Granger (987) is applied. In he firs sep, equaion () is esimaed by ordinary leas squares (OLS) and in he second sep an augmened Dickey-Fuller es is performed on he residual sequence { ˆ ε } in order o deermine wheher i has a uni roo. The null hypohesis of he es is ha he residual sequence has a uni roo or, in oher words, ha he variables are no coinegraed. Noe ha he criical values of he Engle- Granger es are larger in absolue value han hose of he sandard Dickey-Fuller es because he sequence { ˆ ε } is generaed from a regression equaion. The appropriae small-sample criical values can be derived from MacKinnon (99). If he variables are coinegraed, he OLS esimaes from regression () will be superconsisen, in he sense ha hey converge faser o heir rue values in probabiliy han in OLS regressions using saionary variables (Sock, 987). However, if he variables are no coinegraed, esimaing equaion () in levels migh give rise o a spurious-regression problem. Insead, i is appropriae o difference he variables in order o induce saionariy. In his case he regression equaion akes he form P y = a + α l + β k + γ k + υ, () where is he firs-difference operaor and υ is a disurbance erm. G Deailed resuls are available on reques. We use he so-called augmened Dickey-Fuller es ha is asympoically valid in he presence of serial correlaion in he errors, including wo addiional lags of he respecive variable. The es is firs carried ou for he variables in levels. In his case he es equaion includes a consan and a linear ime rend. If he null hypohesis of a uni roo canno be rejeced a he percen significance level, he es is also carried ou for he variables in firs differences. In his case he es equaion includes a consan. If he null hypohesis of a uni roo sill canno be rejeced, he es is also carried ou for he variables in second differences. Small-sample criical values are derived from MacKinnon (99). The power of a es is he probabiliy ha i will correcly lead o a rejecion of a false null hypohesis. We use he panel uni roo ess proposed by Levin, Lin, and Chu () and Im, Pesaran, and Shin (). Deailed resuls are available on reques.

19 - 8 - A. Esimaes of Public Capial Produciviy for Alernaive Capial Measures This secion supplemens he sensiiviy analysis and repors esimaes of he elasiciy of oupu wih respec o public capial for he Unied Saes and Canada, using he various public capial sock esimaes discussed in Secion V. Real GDP and employmen daa are aken from he OECD Analyical Daabase; public and privae capial socks are esimaes calculaed using he alernaive assumpions on he iniial capial sock and he depreciaion rae and depreciaion mehod considered in he previous secion. The privae capial sock is he sum of privae nonresidenial and privae residenial capial. The privae capial socks are esimaed using exacly he same mehod as he esimaion of governmen capial. The benchmark esimaion assumes ha he depreciaion rae increases from ¼ percen o 8½ percen for privae nonresidenial asses, alhough i is assumed o be consan for privae residenial asses (½ percen). Two alernaives are considered regarding he ime profile of he depreciaion rae. The firs alernaive assumes ha he depreciaion rae increases from. percen o. percen over he period 9 for all asses. The second alernaive assumes ha he depreciaion rae is ime-invarian and based on average implici scrapping raes for he Unied Saes is equal o. percen for privae nonresidenial capial and ½ percen for privae residenial capial. Finally, he capial socks for Canada for alernaive depreciaion mehods are official esimaes provided by Saisics Canada. Table repors esimaes of he elasiciy of oupu wih respec o public capial for he Unied Saes and Canada using he various public capial sock esimaes. Figures in bold indicae wheher he elasiciy is aken from he model in levels or firs differences, depending on he resuls of he es for coinegraion. Table shows ha he Engle-Granger es saisic is lower in absolue value han he percen criical value in all cases. The es resuls, hus, sugges ha here is no coinegraion among he variables and, by implicaion, ha he producion funcion as formalized in equaion () does no consiue a sable long-run relaionship. As a consequence, all esimaes are based on he model in firs differences. The esimaed elasiciies of oupu wih respec o public capial are all saisically significan and have he expeced (posiive) sign. The esimaes are, however, in general very high, ranging from. o.8 and hus implying wha Aschauer (99, p. 9) has called supernormal reurns o public capial. Ye, his is a common finding in he lieraure. For example, Surm and de Haan (99, p. ) repor elasiciies of oupu wih respec o public capial of.7 for he Unied Saes and.7 for a model similar o equaion (), esimaed in firs differences. Moreover, he regressions reveal anoher problem associaed wih he producion funcion approach: he difficuly of inerpreing he regression resuls as represening he inpu elasiciies of oupu. The esimaes of he coefficien on labor inpu are larger han one and he esimaes of he coefficien on privae capial are negaive in all regressions. Taken a face value, hese resuls sugges no only ha public capial is much more producive han privae capial bu also As he usual inference procedures are inappropriae in he presence of nonspherical disurbances, he -saisics repored in Tables and are based on he Newey and Wes (987) heeroskedasiciy and auocorrelaion consisen covariance esimaor. These esimaes are no repored in Table. Deailed resuls are available on reques. While he coefficien of employmen is saisically significan in all cases, he coefficien on privae capial is insignifican in mos cases.

20 - 9 - ha privae capial is no producive a all. Again, such a finding is no uncommon in he lieraure. For example, Surm and de Haan (99, p. ) repor ha heir esimaes for he Unied Saes imply a large negaive elasiciy of oupu wih respec o privae capial. There are several reasons o be cauious in inerpreing his finding: () he assumed funcional form of he producion funcion may no be an appropriae descripion of he daa, () he exogeneiy assumpions underlying he producion funcion approach may no be saisfied, and () he regressions may suffer from a mulicollineariy problem. This migh be a reason why he coefficien on privae capial is saisically insignifican in mos cases and has he unexpeced negaive sign. Mulicollineariy among he regressors is frequenly cied as a problem in he empirical lieraure esimaing producion funcions and cos funcions for individual counries (see he survey by Surm, de Haan, and Kuper, 998). One way o deal wih his problem is o exploi he cross-secional dimension of he daa and o esimae panel daa models insead of carrying ou individual-counry regressions. The panel esimae repored in he nex secion indeed suggess ha he implausible value for he elasiciy of oupu wih respec o privae capial found in he individual-counry regressions may be he resul of a mulicollineariy problem. B. Esimaes of Public Capial Produciviy for OECD Counries Table repors esimaes of he elasiciy of oupu wih respec o public capial for he OECD counries for equaion () using public capial sock esimaes from hree alernaive sources: firs, auhor s own esimaes; second, esimaes from naional sources; and hird, esimaes from OECD (997). The able reveals he main advanage of he auhor s own capial sock esimaes. Equaion () can be esimaed for counries while he alernaive sources allow for only and individual-counry regressions, respecively. The esimaes of he elasiciy of oupu wih respec o public capial are based on he model in firs differences wih one excepion (Belgium) since he augmened Engle-Granger es fails o rejec he null hypohesis of no coinegraion in all cases bu one. Mos of he coefficiens are saisically insignifican for he esimaions based on daa from oher sources. This resul is similar o ha of Ford and Pore (99), who esimaed models based on he producion funcion approach for OECD counries using capial sock daa from an earlier volume of OECD (997). In conras, mos of he coefficiens semming from esimaions based on auhor s own capial sock esimaes are saisically significan. Ye, in hose cases where he elasiciy of oupu wih respec o public capial is significan, i is again quie large. Moreover, for some counries he coefficien on privae capial no repored in he able is negaive, making i difficul o inerpre he esimaed coefficiens as parameers of a Cobb-Douglas producion funcion. The las row of Table repors he elasiciy of oupu wih respec o public capial for a panel consising of all OECD counries. This esimae is based on a regression equaion similar o equaion () where he inercep is allowed o vary across counries while he inpu elasiciies of oupu are assumed o be he same across counries (esimaion by fixed effecs). 7 The advanage Kennedy (998, p. 87) even cies he esimaion of he Cobb-Douglas producion funcion as he classical example of mulicollineariy. 7 The esimaion of a dynamic panel model and ess for panel coinegraion (for example, in Canning and Pedroni, 999) are beyond he scope of his sudy and a fruiful avenue for furher research.