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1 econsor Make Your Publicaions Visible. A Service of Wirschaf Cenre zbwleibniz-informaionszenrum Economics Kamps, Chrisophe Working Paper The Dynamic Effecs of Public Capial: VAR Evidence for OECD Counries Kiel Working Paper, No. Provided in Cooperaion wih: Kiel Insiue for he World Economy (IfW) Suggesed Ciaion: Kamps, Chrisophe () : The Dynamic Effecs of Public Capial: VAR Evidence for OECD Counries, Kiel Working Paper, No. This Version is available a: hp://hdl.handle.ne/9/7768 Sandard-Nuzungsbedingungen: Die Dokumene auf EconSor dürfen zu eigenen wissenschaflichen Zwecken und zum Privagebrauch gespeicher und kopier werden. Sie dürfen die Dokumene nich für öffenliche oder kommerzielle Zwecke vervielfäligen, öffenlich aussellen, öffenlich zugänglich machen, verreiben oder anderweiig nuzen. Sofern die Verfasser die Dokumene uner Open-Conen-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gesell haben sollen, gelen abweichend von diesen Nuzungsbedingungen die in der dor genannen Lizenz gewähren Nuzungsreche. Terms of use: Documens in EconSor may be saved and copied for your personal and scholarly purposes. You are no o copy documens for public or commercial purposes, o exhibi he documens publicly, o make hem publicly available on he inerne, or o disribue or oherwise use he documens in public. If he documens have been made available under an Open Conen Licence (especially Creaive Commons Licences), you may exercise furher usage righs as specified in he indicaed licence.

2 Kiel Insiue for World Economics Duesernbrooker Weg 5 Kiel (Germany) Kiel Working Paper No. The Dynamic Effecs of Public Capial: VAR Evidence for OECD Counries by Chrisophe Kamps Sepember The responsibiliy for he conens of he working papers ress wih he auhor, no he Insiue. Since working papers are of a preliminary naure, i may be useful o conac he auhor of a paricular working paper abou resuls or caveas before referring o, or quoing, a paper. Any commens on working papers should be sen direcly o he auhor.

3 The Dynamic Effecs of Public Capial: VAR Evidence for OECD Counries* Absrac The issue of wheher governmen capial is producive has received a grea deal of recen aenion. Ye, empirical analyses of public capial produciviy have been limied o a small sample of counries for which official capial sock esimaes are available. Building on a new daabase ha provides inernaionally comparable capial sock esimaes, his paper esimaes he dynamic effecs of public capial using he vecor auoregressive (VAR) mehodology for a large se of OECD counries. The empirical resuls sugges ha here is evidence for posiive oupu effecs of public capial in OECD counries, bu hardly any evidence for posiive employmen effecs. Keywords: Public capial; VAR model; Coinegraion; OECD counries JEL classificaion: C3; E6; H5 Chrisophe Kamps Kiel Insiue for World Economics Kiel, Germany Phone: Fax: ckamps@ifw-kiel.de Homepage: hp:// *This paper is a revised version of chaper 3 of my docoral disseraion (Kamps b). I would like o hank seminar paricipans a he annual meeing of he European Economic Associaion in Madrid and a he annual meeing of he Inernaional Insiue of Public Finance in Milan as well as Kai Carsensen, Annee Kamps and Joachim Scheide for helpful commens. All remaining shorcomings are mine.

4 Inroducion The issue of wheher governmen capial is producive has received a grea deal of recen aenion. Early empirical sudies invesigaing public capial produciviy in general followed srucural approaches such as he so-called producion funcion approach pioneered by Aschauer (989). In mos recen years, however, many researchers have esimaed vecor auoregressive (VAR) models ha place less resricions on he ineracion among he model variables. So far, hese sudies have been limied o a small number of counries because of a lack of capial sock daa. Building on a new daabase ha provides inernaionally comparable capial sock esimaes for a large se of OECD counries, his paper aemps o fill his gap, esimaing he dynamic effecs of public capial using he VAR mehodology. The VAR approach has a number of advanages over srucural approaches such as he producion funcion approach: (i) Whereas he producion funcion approach assumes a causal relaionship running from he hree inpus o oupu, he VAR approach does no impose any causal links beween he variables a priori. Raher, VAR models allow o es wheher he causal relaionship implied by he producion funcion approach is valid or wheher here are feedback effecs from oupu o he inpus. (ii) Unlike he producion funcion approach, he VAR approach allows for indirec links beween he model variables. In he producion funcion approach, he long-run oupu effec of public capial is given by he elasiciy of oupu wih respec o capial. In conras, in he VAR approach, he long-run oupu effec of a change in public capial resuls from he ineracion of he model variables. For example, i is conceivable ha public capial does no direcly affec oupu bu ha a change in public capial has an impac on oupu only indirecly via is effecs on he privae facors of producion. The VAR approach allows o capure such indirec effecs. (iii) Unlike he producion funcion approach, he VAR approach does no assume ha here is a mos one long-run (coinegraion) relaionship among he four model variables. The Johansen (988, 99) mehodology described in Secion 3 allows o explicily es for he coinegraion rank (he number of long-run relaionships) and o impose i in he esimaion of he VAR model. Esimaion of VAR models is based on a reduced form. Wihou he prior soluion of an idenificaion problem, he VAR esimaes canno be given a srucural inerpreaion and can in general no be used for policy analysis. In his paper, we consider he soluion o he idenificaion problem known as he recursive approach, ha was inroduced by Sims (98) For a review of his lieraure see Surm e al. (998).

5 and is sandard in he relaed lieraure. This approach is applied in Secion, presening empirical resuls on he dynamic effecs of public capial for OECD counries. The paper is organized as follows. Secion briefly reviews recen sudies ha have applied he VAR approach o sudy he effecs of public capial. Secion 3 describes he economeric mehodology underlying our empirical applicaion. Secion presens new empirical evidence on he dynamic effecs of public capial for OECD counries building on capial sock esimaes provided by Kamps (a). Secion 5 discusses he robusness of he empirical resuls. The las secion summarizes he main findings. A Shor Survey of he Lieraure This secion briefly reviews he empirical lieraure having applied he VAR approach o sudy he dynamic effecs of public capial. The only survey of he VAR approach so far, Surm e al. (998), raced merely four sudies. Insead, Table summarizes informaion on weny VAR sudies, winessing he increased populariy of his approach in he very recen pas. A number of ineresing findings wih respec o he objec of invesigaion and model specificaion emerge from he able: (i) Nearly half of he considered VAR sudies have invesigaed he effecs of public capial for he Unied Saes. Moreover, only wo sudies, Minik and Neumann () as well as Pereira (b), have exended he analysis o a group of OECD counries. (ii) The vas majoriy of sudies has relied on annual daa, due o he resricion ha capial sock daa are no available a higher frequency. (iii) The majoriy of sudies has considered a model in he four variables public capial, privae capial, employmen and oupu. In he remaining cases, in general eiher invesmen has been subsiued for capial or addiional variables have been included in he model. (iv) There is a wide variey of model specificaions as regards he (non-)consideraion of coinegraion. Some sudies, such as Cullison (993), specify VAR models in firs differences wihou esing for coinegraion. This way of proceeding seems dubious since i neglecs poenial long-run relaionships beween he levels. Oher sudies, such as Lighar (), specify VAR models in levels based on he resul of Sims e al. (99) ha ordinary leas squares esimaes of VAR coefficiens are consisen even if he variables are non-saionary and possibly coinegraed. Unforunaely, he consisency of VAR coefficien esimaes does no carry over o esimaes of impulse response funcions as discussed in he nex secion. Finally, some sudies, such as Pereira (), es for coinegraion using he Engle-Granger (987)

6 3 approach, hus neglecing he possibiliy ha here may be more han one coinegraion relaionship in higher-dimensional sysems. The las column of Table repors he main conclusions of he considered sudies regarding he long-run oupu effecs of public capial. As can be seen in he majoriy of sudies he long-run response of oupu o a shock o public capial is posiive. In general, he effecs are considerably smaller han hose repored in he lieraure applying he producion funcion approach (see, e.g., Pereira ()). However, almos all of hese sudies fail o provide any measure of he uncerainy surrounding he impulse response esimaes so ha i is impossible o judge he saisical significance of he resuls. For hose sudies for which such measures are provided, he long-run oupu effec is in general insignifican. Anoher imporan resul emerging from his lieraure is ha many sudies find evidence for reverse causaion, i.e., feedback from oupu o public capial and vice versa (see, e.g., Baina (998)). This suggess ha i is indeed imporan o rea public capial as endogenous variable. Our sudy can be viewed as boh a reassessmen of and an addiion o he exising empirical lieraure: (i) We reassess he empirical lieraure by carefully addressing he imporan issue of coinegraion and by providing confidence inervals measuring he uncerainy surrounding he poin esimaes of he impulses responses. (ii) We add o he empirical lieraure by presening resuls for a large sample of OECD counries for many of which here is no VAR evidence so far. 3 3 Economeric Mehodology The Unresriced VAR Model A p-h order vecor auoregressive model, denoed VAR(p), can be expressed as X = A X + A X + K + Ap X p + ΦD + ε, () Some of he sudies lised in Table do no perform a policy analysis. In hese cases, he las column of he able has an n.a. (no available) enry. 3 Noe ha he wo sudies ha come closes o ours in scope, Minik and Neumann () and Pereira (b), boh use public invesmen as model variable whereas we use public capial. This secion builds on he assumpion of a known lag order p. In he empirical applicaion, he opimal lag order is explicily esed for.

7 where X [ x,, x ] ' is a se of variables colleced in a ( k ) vecor, A j denoes a K k k k marix of auoregressive coefficiens for j =,, K, p, and Φ denoes a k d marix of coefficiens on deerminisic erms colleced in he d vecor D. The vecor ε [ ε,, ε ]' is a k-dimensional whie noise process, i.e., E [ ε ] =, E [ ε ε ' ] = Ω E K [ ε ' ] = s k ε for s, wih Ω a ( k k ) symmeric posiive definie marix., and Esimaion of he unresriced VAR model is paricularly easy. Condiioning on he firs p observaions ( denoed X, X, K X ) X, p+ p+, and basing esimaion on he sample, X, K X T, he k equaions of he VAR can be esimaed separaely by ordinary leas squares (OLS). Under general condiions, he OLS esimaor of A [ A,, ] is consisen and asympoically normally disribued. Remarkably, his resul no only holds in he case of saionary variables, bu also in he case in which some variables are inegraed and possibly coinegraed (Sims e al. (99)). Based on his resul many researchers have ignored nonsaionariy issues and esimaed unresriced VAR models in levels. A drawback of his approach is ha, while he auoregressive coefficiens in Equaion () are esimaed consisenly, his may no be rue for oher quaniies derived from hese esimaes. In paricular, Phillips (998) showed ha impulse responses and forecas error variance decomposiions based on he esimaion of unresriced VAR models are inconsisen a long horizons in he presence of non-saionary variables. In conras, vecor error correcion models (VECMs) produce consisen esimaes of impulse responses and of forecas error variance decomposiions if he number of coinegraion relaions is esimaed consisenly. As impulse response analysis is one of he main ools for policy analysis based on VAR models, a careful invesigaion of he coinegraion properies of he VAR sysem is warraned. The Coinegraed VAR Model The saring poin of he coinegraion analysis is ha any VAR(p) model () can always be wrien in equivalen VECM form K A p X = ΠX + Γ X + Γ X + K + Γp X p+ + ΦD + ε, () where p A i i= Π I + coefficiens, respecively. p and Γ j Ai ( j =,, K, p ) denoe ( k k ) marices of i= j+

8 5 Three ineresing cases can be disinguished: (i) If he coinegraion rank r =, hen rank( Π ) = and he variables colleced in X are no coinegraed. In his case, here are k independen sochasic rends in he sysem and i is appropriae o esimae he VAR model in firs differences, dropping X as regressor in Equaion (). (ii) A he oher exreme, if r = k, hen rank( Π ) = k and each variable in X aken individually mus be saionary. Or, in oher words, he number of sochasic rends, given by k r, is equal o zero. In his case, he sysem can be esimaed by applying OLS eiher o he unresriced VAR in levels (Equaion ()) or o is equivalen represenaion given by (). (iii) In he inermediae case, < r < k, he variables in X are driven by < k r < k common sochasic rends and rank( Π ) = r < k. In his case, esimaing he sysem given by () by OLS is no appropriae since cross-equaion resricions have o be imposed on he marix Π. Insead, he maximum likelihood approach developed by Johansen (988, 99) can be applied in order o esimae he space spanned by he coinegraing vecors. An addiional asse of Johansen s approach is ha i enables us o es for he number of coinegraing relaions, which in many applicaions is unknown a priori. The specificaion of he deerminisic erms D in Equaion () plays an imporan role in he analysis because he asympoic disribuions of he es saisics used for he deerminaion of he number of coinegraing vecors depends on he assumpions made on hese erms (see Johansen (995: 56 57)). Johansen (995) disinguishes five alernaive models, corresponding o alernaive ses of resricions on he deerminisic erms. In he following, we concenrae on he model which seems o be he mos relevan for our problem: he consan is lef unresriced and he rend is resriced o he coinegraing space. 5 This specificaion eliminaes he poenial for quadraic rends in X, while allowing for linear rends in X and for rend-saionary coinegraing relaions. The laer may be jusified on he grounds ha he coinegraing space migh conain a producion funcion as one coinegraing vecor (see, e.g., Surm and De Haan (995)). The Srucural VAR Model The previous wo sub-secions have described how he VAR model can be esimaed for alernaive assumpions on he coinegraing rank. As hese models are reduced-form models, 5 Pesaran and Smih (998: 83) argue ha he case analyzed here is one of wo cases paricularly relevan in pracice, he oher one being ha of a resriced consan and no linear rend.

9 6 lile can be learned abou he underlying economic srucure unless idenifying resricions are imposed. This sub-secion shows how o give VAR models a srucural inerpreaion and, in paricular, shows how o derive impulse response funcions from he reduced-form parameer esimaes. Impulse responses give an insigh ino he reacion of key macroeconomic variables o an unexpeced change in one variable (here, e.g., public capial). The subsequen analysis is based on he unresriced VAR model given by Equaion (). This model can serve in he srucural analysis irrespecive of wheher he variables in X are non-saionary or no. 6 Pre-muliplying Equaion () by he ( k k ) marix A gives he srucural form * * * X = A X + A X + K + Ap X p + AΦD Be, (3) A + where * Ai for i =, K, p, and Be = A ε describes he relaion beween he Ai A srucural disurbances e and he reduced-form disurbances ε. In he following, i is assumed ha he srucural disurbances e are whie noise and uncorrelaed wih each oher, i.e. he variance-covariance marix of he srucural disurbances, denoed Σ, is diagonal. The marix A describes he conemporaneous relaion among he variables colleced in he vecor X. Wihou resricions on he parameers A A*, i and B, model (3) is no idenified. In he empirical lieraure, a large number of alernaive idenificaion procedures have been applied. In he empirical applicaion we use he recursive approach originally proposed by Sims (98) ha resrics B o a k-dimensional ideniy marix and A o a lower riangular marix. ha The soluion o he idenificaion problem given by he recursive VAR approach implies Ω = PP', where / Σ P A and A is lower riangular. This, in urn, implies ha P is a lower riangular marix wih he sandard deviaions of he srucural disurbances on is principal diagonal. Moreover, i can be shown ha P is he (unique) Cholesky facor of he symmeric posiive definie marix Ω (Hamilon (99: 9-9)). Noe, however, ha while P is unique for a given ordering of he variables in X, here are k! possible orderings in oal. Hence, i is imporan o check how sensiive he dynamic properies of he model are o alernaive orderings of he variables.

10 7 Once he idenificaion problem has been solved, he model dynamics can be analyzed by impulse response funcions. Le Θ n for n =,, denoe he marix holding he impulse responses a horizon n. Then he row i, column k elemen of Θ n gives he response of variable i o an one-sandard-deviaion increase in he kh variable, n periods ago. As he impulse responses are random variables i is useful o provide confidence inervals in order o measure he uncerainy surrounding he esimaed impulse responses. In he empirical applicaion, we repor confidence inervals based on he boosrap mehodology. The simple boosrap algorihm can be summarized as follows:. Esimae he parameers of he model () by he appropriae mehod. * *,, T. Generae boosrap residuals ε K ε by randomly drawing wih replacemen from he se of esimaed residuals ˆ ε, K, ˆ ε. T 3. Condiion on he pre-sample values ( X p+,..., X ) = ( X p+,..., X ) and consruc boosrap ime series X ˆ * X recursively using Equaion (), ˆ * K + ΦD + ε, =, K, T. * * * ˆ = A X + + Ap X p. Re-esimae he parameers A, K, A p, µ and µ from he generaed daa and calculae * * he impulse response funcions Θˆ *, n =,,, K n. 5. Repea seps a large number of imes (in he empirical applicaion: ) and calculae he α and elemens of α percenile inerval endpoins of he disribuion of he individual Θˆ * n, n =,,, K. In he empirical applicaion, we se α =. 6 and accordingly repor 68% confidence inervals. 7 6 While in he esimaion of he VAR parameers i is crucial o disinguish he hree cases analyzed in he previous secion, he analysis can proceed based on he represenaion () once he esimaion sage has been compleed. All ha is necessary is o map he parameers Π and Γi from he VECM () o he A i marices. 7 In he empirical VAR lieraure, ypically eiher 68% or 95% confidence inervals are repored. Sims (987: 3) argues agains he use of 95% confidence inervals in VAR sudies on he grounds ha here is no scienific jusificaion for esing hypoheses a he 5 % significance level in every applicaion. He suggess o rea he saisical significance of impulse responses derived from VAR coefficien esimaes differenly from ha of coefficien esimaes in sandard economeric models. I is inheren in VAR models ha mos of he parameer esimaes are insignificanly differen from zero when esed a he 5% level, and his ranslaes ino relaively large confidence inervals for impulse responses. Sill, esimaes from unconsrained VAR models are widely hough o provide a useful daa summary. Agains his background, Sims and Zha (999: 8) recommend he use of 68% confidence inervals for esimaed impulse responses. In he empirical applicaion,

11 8 Empirical Resuls This secion presens empirical evidence on he dynamic effecs of public capial for OECD counries based on VAR models. Secion. deals wih model selecion and deerminaion of coinegraion rank. Secion. presens he resuls of an impulse response analysis based on a se of benchmark idenifying assumpions.. Model Specificaion and Esimaion Daa The counries considered in his paper are he same as hose considered in Kamps (a). 8 Wih a few excepions, he sample periods cover he years For each counry, we G specify a four-variable VAR model including he public ne capial sock, K, he privae ne P capial sock, K, he number of employed persons, N, and real GDP, Y. Expressing all variables in naural logarihms muliplied by and denoing he ransformed variables by lower-case leers, he vecor of endogenous variables X can be expressed as X k, k, n, y ]'. The evidence repored in Kamps (a: 7) suggess ha he [ variables are inegraed of order one. VAR Order Selecion The exposiion of he VAR mehodology in Secion 3 was based on he implici assumpion of a known lag order p. In empirical applicaions, however, he lag order is ypically unknown. In he economeric lieraure, a number of selecion crieria have been proposed ha can be used o deermine he opimal lag order. The selecion crieria considered here are (i) we follow his advice, ye we refrain from drawing srong conclusions abou he saisical significance of he esimaed impulse responses. 8 Ausralia, Ausria, Belgium, Canada, Denmark, Finland, France, Germany, Greece, Iceland, Ireland, Ialy, Japan, he Neherlands, New Zealand, Norway, Porugal, Spain, Sweden, Swizerland, Unied Kingdom and he Unied Saes 9 Ausria 965 ; France 965 ; Greece 96 ; Iceland 967 ; Neherlands 969 ; New Zealand 96 ; Spain 96. Real GDP and employmen are drawn from he OECD Analyical Daabase, Version June. The capial sock esimaes are aken from Kamps (a) and available a hp:// Muliplying he variables in logarihms by faciliaes he inerpreaion of he esimaed impulse responses. In his case, he impulse responses give he percenage change in he level of he respecive variable.

12 9 he Akaike (97) informaion crierion (AIC), (ii) he Schwarz (978) informaion crierion (SC), and (iii) he Hannan and Quinn (979) informaion crierion (HQ). The firs hree columns of Table give he opimal lag order seleced by he hree crieria for each of he OECD counries considered. Whereas he AIC selecs a lag order of for mos counries, he HQ and SC crieria selec a lag order of in mos cases. Given he small sample size, we are ineresed in a parsimonious specificaion of he model. Thus, we choose he lag order seleced by he SC crierion in general. Ye, we also perform specificaion ess ha check wheher for he lag lengh seleced by he SC crierion he residuals are free from firs-order auocorrelaion, homoscedasic and normally disribued. Since he race es for coinegraion is robus o deviaions from he normaliy assumpion (see Cheung and Lai (993: 3)) and since he asympoic properies of he VAR parameer esimaors do no depend on he normaliy assumpion (see Lükepohl (99: 359)), we do no dismiss he specificaion chosen by he SC crierion if he normaliy es indicaes ha he residuals are non-normal. However, if he auocorrelaion es indicaes ha he residuals are auocorrelaed, we increase he lag order compared o he one seleced by he SC crierion unil he auocorrelaion es does no rejec he null hypohesis anymore. The las hree columns of Table show he resuls of he hree specificaion ess for he chosen lag order for each of he OECD counries considered. The resuls show ha a he 5% significance level here are no signs of residual auocorrelaion and in general no signs of heeroscedasic residuals. 3 The following seps of he empirical analysis are, hus, based on he lag orders displayed in he middle column of Table. Deerminaion of Coinegraion Rank Neoclassical growh heory suggess ha along he balanced growh pah (seady sae) he socalled grea raios are consan, i.e., variables such as oupu, capial, consumpion and invesmen grow a he same consan rae. King e al. (99) firs invesigaed he In he case of Denmark, a dummy variable (se o in 973, - in 97 and oherwise) was included because wihou he dummy variable he null hypohesis of no serial correlaion had o be rejeced a he 5% significance level for all lag orders beween and. In he case of Germany, a dummy variable (se o in 99 and oherwise) was included in order o accoun for he level shif in he variables due o German Reunificaion. 3 Excepions are Ireland and Ialy for which he heeroscedasiciy es saisic is significan a he 5% level. In boh cases, increasing he lag lengh o, as suggesed by he AIC, worsened he performance of he model wih respec o residual auocorrelaion. As auocorrelaion is more derimenal han heeroscedasiciy, we choose he shorer lag lengh in boh cases.

13 coinegraion implicaions of neoclassical growh heory. They showed ha he consancy of he grea raios implies ha if he individual variables are non-saionary hey mus be driven by a single common sochasic rend. Translaed o our problem his implies ha he public capial o oupu raio and he privae capial o oupu raio are poenial coinegraing relaions. In addiion, a hird poenial coinegraing relaion migh be given by a producion funcion of he ype considered, e.g., by Aschauer (989). Ye, his criically hinges on he naure of echnology. If echnology is modeled as a rend-saionary process (see, e.g., Surm and De Haan (995)), hen he producion funcion could be a coinegraing relaion. However, if echnology is a non-saionary process (see, e.g., Crowder and Himarios (997)) hen he producion funcion will no describe a saionary relaion beween he variables ~ colleced in he vecor X [ k, k, n, y, ]'. To sum up, based on economic heory we expec o find a mos hree coinegraing relaions. We es for he number of coinegraing relaions using Johansen s (988, 99) race es. 5 The esing sequence can be expressed as follows (Lükepohl ()): H ( r ) : rank( Π ) = r versus H ( r ) : rank(π) = k, r =,, K, 3. () The esing sequence sars wih he null hypohesis ha he coinegraion rank is zero. If his hypohesis canno be rejeced, hen he esing sequence erminaes and a VAR model in firs differences is he appropriae model. A he oher exreme, if all null hypoheses have o be rejeced, hen he variables can be regarded as (rend-)saionary in levels. Table 3 displays he es resuls for each of he counries considered here. The resuls show ha for a large majoriy of counries he number of coinegraing relaions is eiher wo or hree. For he remaining counries, he coinegraion rank is lower; for wo counries, New Zealand and Porugal, i is even zero. As a consequence, for hese wo counries we esimae a VAR model for he variables in firs differences. For he oher counries, we esimae a VECM imposing he appropriae rank resricion. This, of course, raises he quesion of where he sochasic rends in he daa come from. Technology is widely viewed o be he prime candidae for a sochasic rend. 5 We use he criical values abulaed by MacKinnon e al. (999). These criical values are also used in he case of Denmark and Germany. The empirical models for hese wo counries include dummy variables. I is well known ha dummy variables may affec he asympoic disribuion of he race es saisic. This is paricularly rue for sep dummies ha give rise o broken linear rends in he levels of he variables. The dummy variables considered here, insead, are asympoically negligible.

14 . Impulse Response Analysis This secion analyzes he dynamic properies of he esimaed VAR models for he OECD counries considered in his sudy wih he help of impulse response funcions. As was discussed in Secion 3, here is a need o idenify VAR models in order o be able o give he impulse response funcions a srucural inerpreaion. In his secion, we idenify he VAR models for he individual counries by assuming ha he relaion beween he reduced-form disurbances ε and he srucural disurbances e akes he following form: a a a 3 a a 3 a 3 k ε k ε n ε y ε G P = k e k e n e y e G P, (5) There are six unknown parameers in Equaion (5) as well as four unknown parameers in he diagonal covariance marix of he srucural disurbances, Σ. Since here are en disinc elemens in he covariance marix of he reduced-form residuals, Ωˆ, he model is jus idenified. This se of idenifying assumpions is an example for he recursive approach originally proposed by Sims (98); i has been widely applied in relaed lieraure (see Secion ). As he ordering of variables in he recursive approach may affec he resuls, he robusness of he resuls o alernaive orderings of he variables is explored in Secion 5. The paricular ordering of variables resuling from he benchmark idenificaion scheme has he following implicaions: (i) Public capial does no reac conemporaneously o shocks o he oher variables in he sysem, (ii) privae capial does no reac conemporaneously o shocks o employmen and real GDP, bu is affeced conemporaneously by shocks o public capial, (iii) employmen does no reac conemporaneously o shocks o real GDP, bu is affeced conemporaneously by shocks o boh privae and public capial, and, (iv) real GDP is affeced conemporaneously by shocks o all oher variables in he sysem. Noe ha afer he iniial period he variables in he sysem are allowed o inerac freely, i.e., for example, shocks o real GDP can affec public capial in all periods afer he one in which he shock occurs. The assumpions on he conemporaneous relaions beween he variables can be jusified as follows: Movemens in governmen spending, unlike movemens in axes, are largely

15 unrelaed o he business cycle. In paricular, governmen spending on capial iems involves large decision and implemenaion lags. Therefore, i seems sensible o assume ha public capial is no affeced conemporaneously by shocks originaing in he privae secor. In a similar vein, privae capial is largely unrelaed o he business cycle. 6 Employmen, while being srongly pro-cyclical, in general lags he business cycle. 7 Thus, i seems appropriae o assume ha employmen is unaffeced conemporaneously by oupu shocks. Ordering oupu las can be jusified by, e.g., a producion funcion which shows ha he hree inpus affec oupu conemporaneously. The Dynamic Effecs of Public Capial Figure shows he effecs of a shock o public capial for he OECD counries considered here for a horizon of 5 years. Each subplo in he figure displays a poin esimae of he impulse responses as well as a 68% confidence inerval compued wih he boosrap procedure described in Secion 3. The shocks o public capial have size one sandard deviaion for each counry. While his precludes a quaniaive comparison of he effecs across counries, shocks of such size have he aracive feaure ha hey can be viewed as represenaive for ypical shocks ha occurred during he sample period in he individual counries. A quaniaive comparison of he long-run effecs across counries is given a he end of his secion. The subplos in Figure show ha in general he oupu effec of a shock o public capial is posiive. For mos counries, he oupu response is posiive a all ploed horizons up o he endpoin of 5 years. The figure also reveals ha he impulse responses are esimaed quie imprecisely, as winessed by large confidence inervals for some counries. Judged by he 68% confidence inervals, he oupu responses are saisically significan in abou half of all cases. Apar from he general paern described above, wo oher ineresing paerns can be observed. Firs, here are a few counries for which he oupu response is negaive a all ploed horizons (Ireland, Japan, Porugal). Second, here are some counries for which he shor-run oupu response is negaive, while he medium-run response is posiive (Canada, Iceland, Norway, Spain, Unied Kingdom). 6 See, e.g., King and Rebelo (999: 938) for evidence for he Unied Saes. 7 See, e.g., Sock and Wason (999: ) for evidence for he Unied Saes. Noe, however, ha heir resuls are compued for quarerly daa. I is, hus, unclear wheher he finding ha employmen lags oupu also applies on an annual basis. We follow he lieraure and order employmen before oupu in he srucural VAR model.

16 3 Given hese resul paerns, i is ineresing o invesigae wheher hey can be raced back o he responses of he oher hree variables. If a neoclassical producion funcion was a valid descripion of he relaion beween he four endogenous variables, hen he impulse responses of public capial, privae capial and employmen aken ogeher should enable us o explain he observed paerns of oupu responses. As regards he impulse responses of public capial o a shock o public capial no ploed here 8, he poin esimaes of he responses are posiive for all counries. For he majoriy of counries, he poin esimaes are posiive for all horizons, and, judged by he 68% confidence inervals, he responses are saisically significan in mos cases. Thus, he responses of public capial are consisen wih he general paern observed for he oupu responses. As regards he wo oher paerns of he oupu responses, in mos cases hey can no be explained by he paern of he public capial responses alone. In paricular, negaive oupu responses as observed for some counries are no easily reconciled wih posiive public capial responses unless public capial is conceived o have a negaive marginal produciviy. Among hose counries wih a negaive oupu response, his is only conceivable in he case of Japan. As shown in Kamps (a), Japan exhibis by far he larges public capial o oupu raio among he OECD counries in our sample. I is, hus, conceivable ha he public capial o oupu raio in Japan is beyond is opimal level so ha addiional public capial has a negaive effec on oupu. While his migh be an explanaion for he negaive oupu response in he case of Japan, i is implausible for he oher counries exhibiing negaive oupu responses. In paricular, Porugal exhibis he lowes public capial sock per head among he OECD counries in our sample (see Table 3 in Kamps (a)). Agains his background, i is hardly imaginable ha he marginal produciviy of public capial is negaive in Porugal. Anoher possible explanaion is ha public capial crowds ou privae capial and employmen. The impulse responses of privae capial o a shock o public capial no ploed here 9 show ha in he vas majoriy of counries privae capial and public capial are complemens in he medium run. Ineresingly, however, in almos half of he counries privae capial and public capial are subsiues in he shor run. Among hese counries are Canada and Spain, wo of hose counries for which a negaive shor-run bu a posiive medium-run oupu response was observed. Thus, for hese wo counries he responses of 8 The figure holding he responses of public capial o shocks o public capial is available upon reques. 9 The figure holding he responses of privae capial o shocks o public capial is available upon reques. This is rue for Porugal, implying ha crowding ou of privae capial does no seem o be he reason for he negaive oupu response observed for his counry.

17 privae capial may explain he paern of he oupu responses. The general equilibrium analysis performed by Baxer and King (993) suggess he following explanaion for he sign swich of he privae capial responses: There are wo opposing forces deermining he response of privae capial. One of hese forces is he resource cos associaed wih financing an addiional uni of public capial. This cos reduces he resources available o he privae secor and all oher hings being equal induces a fall in privae invesmen. The oher force is he posiive effec of an increase in public capial on he marginal produciviy of privae capial, all oher hings being equal inducing a rise in privae invesmen. If public capial accumulaes gradually, hen he firs force will dominae he second in he shor run, whereas in he medium o long run he second force will dominae. As regards he impulse responses of employmen o a shock o public capial no ploed here, hey do no show a general paern. For roughly one hird of he counries he responses are negaive implying ha employmen and public capial are subsiues, while for he oher counries he responses are eiher posiive implying ha employmen and public capial are complemens or no significanly differen from zero, judged by he 68% confidence inerval. The lack of clear-cu resuls for employmen is deplorable also from a heoreical perspecive because he responses of employmen can be very useful in order o es compeing heoreical models. For example, radiional Keynesian models predic ha employmen will rise in response o an increase in governmen spending, which is a esable hypohesis. Issues are more complicaed when i comes o neoclassical models such as he general equilibrium model such as he one considered by Baxer and King (993). The policy experimens performed wih his model sugges a possible explanaion for he inconclusive evidence on he employmen response. An increase in public capial exers wo opposing wealh effecs and depending on he way addiional public capial is financed possibly also a subsiuion effec. For example, if public capial is financed by non-disorionary axes and is only mildly producive, hen employmen will rise in response o a shock o public The figure holding he responses of employmen o shocks o public capial is available upon reques. The employmen responses of Porugal are no significanly differen from zero, implying ha he employmen responses like he public and privae capial responses canno raionalize he negaive oupu response observed for his counry. Noe ha Porugal is one of only wo counries for which boh he Engle-Granger es and he Johansen es fail o rejec he null hypohesis of no coinegraion. Possibly, he empirical model is misspecified even hough he specificaion ess repored in Table sugges oherwise. Alernaively, daa qualiy migh be an issue in he case of Porugal. For example, whereas he real GDP series for Porugal conained in he OECD Analyical Daabase sars in 96, he Poruguese saisics office INE and Eurosa currenly publish GDP daa according o ESA 995 saring only in 987 and 995, respecively. As we do no know he underlying cause for he puzzling resuls of he impulse response analysis, we choose o rea Porugal as an oulier in he following.

18 5 capial. However, if public capial is financed by disorionary axes and is only mildly producive, hen employmen will fall in response o such a shock. The empirical model is silen on hese issues because i does no include any governmen revenue variables. The reason is, of course, ha including all variables in he VAR model ha are ineresing in his respec (non-disorionary axes, disorionary axes, governmen deb and governmen consumpion) would quickly exhaus he available degrees of freedom. Table displays summary informaion abou he long-run effecs of public capial for he OECD counries in our sample. The able displays long-run elasiciies of privae capial, employmen and real GDP wih respec o public capial, respecively. These long-run elasiciies are special in ha hey capure he dynamic feedback beween he four variables in he sysem. 3 Therefore, hey can be viewed as he empirical counerpar of he general equilibrium effecs ypically considered in heoreical models. The long-run elasiciies considered here are concepually differen from he elasiciies of a producion funcion. Whereas for a producion funcion, e.g., he elasiciy of oupu wih respec o public capial gives he percenage change in oupu per exogenous one-percen change in public capial holding fixed he privae inpus and excluding feedback effecs, e.g., from oupu o public capial, he long-run elasiciies wih respec o public capial repored here accoun for he dynamic ineracion beween he variables in he sysem. The resuls repored in Table show ha for mos counries he long-run elasiciy of oupu wih respec o public capial is posiive, giving suppor o he hypohesis ha public capial is producive. 5 Judged by he 68% confidence inervals, his long-run elasiciy is saisically significan in he majoriy of counries. In mos of hese counries, he long-run elasiciy is smaller han, i.e., a one-percen long-run increase in public capial is associaed wih a less han proporional increase in oupu. The long-run elasiciy of privae capial wih respec o public capial is posiive for mos counries, indicaing ha privae capial and public capial are complemens in he long run. As is he case for oupu, his elasiciy again judged by he 3 See, e.g., Pereira (b) for anoher sudy using his concep. Baxer and King (993: 33)), e.g., make a similar disincion in heir quaniaive analysis of a dynamic general equilibrium model. 5 There are wo excepions o his general finding: Japan and Porugal. As was menioned above, he esimae for Porugal is difficul o raionalize, herefore we rea i as oulier. As regards Japan, he long-run elasiciy aken on is own seems o sugges a very srong negaive oupu effec of public capial. However, none of he hree elasiciies repored for Japan is saisically significan judged by he 68% confidence inerval. Moreover, he long-run response of public capial o a shock o public capial is almos zero. While he long-run responses of he oher hree variables are also close o zero, hey are larger in absolue value han he long-run response of public capial. This ranslaes ino misleadingly large long-run elasiciies of privae capial, employmen and oupu, respecively. I is more likely ha he rue long-run elasiciies are zero in he case of Japan.

19 6 68% confidence inervals is saisically significan and smaller han in he majoriy of counries. As already noed in he inerpreaion of he impulse responses, he resuls for employmen are less conclusive. In all counries excep four, he long-run elasiciy of employmen wih respec o public capial is no saisically significan. In hose counries in which i is significan, his elasiciy is eiher posiive or negaive. Taken ogeher, he resuls for employmen seem o sugges ha public capial and employmen are neiher complemens nor subsiues in he long run, bu raher ha hey are unrelaed in he long run. To sum up, an increase in public capial in OECD counries on average can be expeced o lead o an increase in oupu in he long run, bu here is lile evidence ha i is he appropriae policy measure if he aim is o increase employmen in he long run. Is There Evidence for Reverse Causaion? In Kamps (a), esimaion of a producion funcion was based on he assumpion ha public capial, privae capial and employmen are exogenous wih respec o oupu. This implied ha feedback from oupu o he inpus was excluded by assumpion. The VAR model, insead, allows for such feedback by reaing all variables as endogenous. Wheher i is imporan o do so in an empirical applicaion, can be clarified wih he help of a causaliy analysis. While i is possible o formally es for causaliy in he sense of Granger (969), he impulse response analysis can also be regarded as a ype of causaliy analysis (Lükepohl )). 6 In our conex, i is mos ineresing o invesigae wheher here is feedback from oupu o public capial, i.e., wheher he impulse responses of public capial o an oupu shock are significanly differen from zero a some poin in he response horizon. Figure depics he impulse responses of public capial o a shock o real GDP. Noe ha our idenifying assumpions resric he impac response of public capial o be zero. The impulse responses show ha in he vas majoriy of counries public capial increases afer a posiive oupu shock. In mos cases, hese responses are saisically significan, judged by he 68% confidence inervals. These resuls sugges ha i is indeed imporan o rea public capial as endogenous variable in empirical invesigaions. 7 The general resul ha public 6 The mehodology for esing Granger causaliy in higher dimensional sysems is developed in Dufour and Renaul (998). These auhors show ha impulse responses do no summarize all informaion abou causal links in higher dimensional sysems (Dufour and Renaul (998: 3)). Impulse responses no significanly differen from zero are no sufficien o rule ou causaliy. Ye, if he impulse responses are significanly differen from zero, hen his is a clear indicaion of causaliy. As is shown below, his is he case for he vas majoriy of counries in our sample. 7 The same is rue for privae capial and employmen which boh also show responses o an oupu shock significanly differen from zero. Deailed resuls are available upon reques.

20 7 capial posiively reacs o oupu shocks has a sraighforward inerpreaion: An unanicipaed increase in oupu will in general enail an increase in governmen revenue so ha he resources available for public invesmen increase. Likewise, an unanicipaed decline in oupu will lead o a deerioraion of public finances. The hisorical record suggess ha governmens in OECD counries in he 97s and 98s ended o reac o high budge deficis ha arose a a ime when rend growh in oupu declined by cuing public invesmen (see De Haan e al. (996: 7)). 5 Sensiiviy Analysis: Alernaive Idenificaion Assumpions As was menioned in Secion 3, he resuls of he impulse response analysis may be sensiive o he ordering of variables in he recursive VAR approach. In he benchmark VAR model analyzed in Secion, he variables were ordered as follows: [ X k, k, n, y ]'. All in all, here are! = possible orderings of he variables. As an analysis of all possible orderings would be exremely arduous in he presen conex, we consider a single alernaive ordering ha places public capial las in he lis of variables: X [ k P, n, y, k G ]'. This implies ha public capial is affeced conemporaneously by shocks o all oher variables, bu ha he oher variables are unaffeced conemporaneously by shocks o public capial. This can be regarded as an exreme deparure from he benchmark case in which public capial was unaffeced conemporaneously by shocks o privae capial, employmen and oupu. While he benchmark ordering of variables seems more plausible given he decision and implemenaion lags involved in fiscal policy, i would be reassuring if he resuls obained for his alernaive ordering were similar o hose obained in he benchmark case. Figure 3 displays he impulse responses of GDP o a shock o public capial for his alernaive ordering of variables. The figure shows ha, wih a few excepions, he resuls are qualiaively very similar o hose obained for he benchmark ordering of variables (see Figure ). The main excepions are Finland and New Zealand for which he impulse responses swich signs. Quaniaively, he impulse responses are in general somewha smaller in absolue value han in he benchmark case. All in all, Figure 3 suggess ha he oupu effecs of public capial which are he focus of ineres are no very sensiive o alernaive orderings of he model variables.

21 8 6 Conclusion This paper has provided new evidence on he dynamic effecs of public capial in OECD counries based on he VAR mehodology. In conras o he producion funcion approach rouinely applied in he lieraure, his mehodology reas all variables as endogenous and, hus, allows for feedback effecs from oupu o he hree inpu variables. Moreover, applicaion of he Johansen (988,99) mehod has shown ha i is imporan o accoun for he possibiliy of muliple coinegraing vecors among he model variables. The main resuls of he analysis can be summarized as follows: (i) For he majoriy of counries in our sample, shocks o public capial end o have significan posiive oupu effecs. (ii) In conras o he resuls documened in he lieraure for he producion funcion approach, here is lile evidence for supernormal reurns o public capial. The resuls presened in his paper sugges ha one reason for he exremely high reurns o public capial obained for some counries for he producion funcion approach migh be ha he laer approach ignores feedback effecs from oupu o public capial. (iii) For he vas majoriy of counries in our sample, public capial and privae capial are long-run complemens. As regards he shor-run relaion beween hese variables, wo groups of counries can be disinguished: a firs group for which public capial and privae capial are shor-run subsiues, i.e., privae capial declines in response o a shock o public capial, and, a second group for which public capial and privae capial are shor-run complemens. (iv) For he vas majoriy of counries, he long-run response of employmen o a shock o public capial is saisically insignifican. In oher words, here is lile evidence for he hypohesis ha employmen can be fosered by addiional public capial.

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