www.elsevier.es/cesjef
Cuadernos
de
economía
ARTICLE
Speed
of
economic
convergence
and
EU
public
policy
夽
M.
Jesús
Delgado
Rodríguez
a,b,∗,
Sonia
de
Lucas
Santos
c,daDepartamentodeEconomíaAplicadaII,P.◦Artilleross/n,28670Madrid,Spain
bUniversidadReyJuanCarlos,Spain
cDepartamentodeEconomíaAplicada(UdiEstadística),CiudadUniversitariadeCantoblanco,28049Madrid,Spain
dUniversidadAutónomadeMadrid,Spain
Received21December2016;accepted12January2017 Availableonline11March2017
JEL
CLASSIFICATION
E13; O41; H54
KEYWORDS
Speedof convergence; Growthmodel; Publicpolicies
Abstract TheaimofthispaperistoestimatethepotentialeffectsofEU-15publicpolicies on economic convergence.In particular, anempirical proposal ispresented tocompare, in
terms ofconvergencespeed, the resultsreached inthe EU withthe policies implemented
withthoseobtainedunderalternativepoliciesduringthe1980---2010period.On thebasisof thisapproach,twotypesofscenarioswerederived,dependingonwhetherthechangesinthe policy instrumentsareconsideredinallthe EU-15countriesorineachofthem separately. ResultsshowthatitwouldhavebeenpossibletoobtainbetterresultsfortheEUconvergence withhigherratesofinfrastructureandeducation investment,which providesupportforthe coordinationofthesepoliciesbetweenthemembercountries.
© 2017 Asociaci´on Cuadernos de Econom´ıa. Published by Elsevier Espa˜na, S.L.U. All rights reserved.
CÓDIGOSJEL
E13; O41; H54
PALABRASCLAVE
Velocidad convergencia;
VelocidaddeconvergenciaypolíticaspúblicasenlaUE
Resumen Elobjetivodeestetrabajoesestimarlosefectospotencialesdelaspolíticas públi-cassobrelaconvergenciaeconómica.Enparticular,presentamosunapropuestaempíricapara comparar,entérminosdevelocidad deconvergencia,losresultadosobtenidos enlaUEcon laspolíticasimplementadasconlosresultados quesepodríanhaberalcanzadoconpolíticas públicasalternativasduranteelperiodo 1980-2010.Sobrela basedeesteesquema, deriva-mosdostiposdeescenariodependiendosiloscambiosenlosinstrumentosdepolíticapública
se producen en todos los países europeos o sólo en alguno de ellos de forma separada.
夽 FinancialsupportbytheInstituteforFiscalStudiesisgratefullyacknowledged.
∗Correspondingauthor.
E-mailaddress:mariajesus.delgado@urjc.es(M.J.DelgadoRodríguez).
http://dx.doi.org/10.1016/j.cesjef.2017.01.001
Modelosde crecimiento; Políticaspúblicas
Losresultadosmuestranquehubierasidoposibleobtenermejoresresultadosentérminosde convergenciaeconómicaenlaUEsisehubieranaumentadolosratiosdeinversiónen infraestruc-turayeducación,locualrespaldalacoordinacióndeestaspolíticasenlospaísesmiembros. © 2017Asociaci´onCuadernosde Econom´ıa. Publicadopor ElsevierEspa˜na, S.L.U.Todoslos derechosreservados.
1.
Introduction
Literature on economic growth has devoted considerable effort to analyze the speed of convergence towards the stationary state. An extensive and influential number of researchpapers demonstratethe existence of conditional convergence;thatis, the tendency ofthe mostbackward economiestosystematicallygrowatafasterratethanmore developedeconomies,oncetheconditioningfactorsofthis processarecontrolledfor(Mankiwetal.,1992;Barroand Sala-I-Martín,1995).Thisisdeterminedbyitsownstructural characteristics,amongwhichtechnology,publicpoliciesand populationgrowthrateareincluded.Oneofthereasonsfor theimportanceof this analysisis itscapacitytoevaluate the role played by these conditioning factors --- primarily publicpolicyinstruments---withtheobjectiveof establish-ingwhetherpartoftheobservedconvergence(ifany)can beattributedtotheseinstruments.
InthecontextoftheEuropeanUnion,developmentand cohesionpolicieshavereceivedgreaterattentionsincethe beginning of the 1980s and, according to the European Commission, they have positively contributed to income convergence in the EU. However, structural policies in Europehaveoftenbeenquestionedarguingthattheymainly serveredistributional purposes,buttheyhavelittleeffect onfostering economic growth andconvergence at theEU level.Thus,despitethelargebodyofempiricalliterature, thedebateconcerningthecapacityoftheEuropeanpolicies to influence convergence remains open. Why have pub-lic policiessofar had sucha limitedimpact oneconomic convergence? Could it have been possible to accelerate theprocessof European convergenceimplementing alter-nativepublicpolicies?Therearemultiplefactorsthatmight explainwhy,despitetheincreaseoffundsavailablesincethe eighties,thereislittleornoevidenceofgreatereconomic convergenceacrosscountriesin theEU. Amongthe possi-bleexplanations,somehighlightthat,despitetheincrease in the volume of development funds,the funds available arestilltooscarcetohaveanysignificantimpactongrowth rates (Rodriguez-Pose and Fratesi, 2004; Varga and Veld, 2011; Reggi and Scicchitano, 2014). This paper seeks to makeacontributiontothisdebateofferingausefulproposal tovaluehowtheconvergenceprocessmighthaveresulted underalternativepublicpolicieswhichdifferintherateof publicinvestment.Specifically,inthisstudywepay atten-tiontotheeffectonthespeedofconvergenceofanincrease intherateofinvestmentininfrastructureandinhuman cap-italendowmentssincedevelopmentandcohesionpoliciesin theEUsupportinvestmentsinbothareas.
Building ona standard neoclassical growthframework, the study uses a programming routine with Matlab for estimating convergence applying fixed effects models to
develop a proposal in which the convergence regressions arerepeatedwithdifferentpublicpolicies.Thispaper dif-fers frommuchof themainstream convergenceliterature focusedonthecomparisonofresultsobtainedusing differ-entestimationtechniques, groupsofcountriesor periods. The primary focus here willbe onthe comparison of the speed ofconvergenceobserved witha widerangeof sim-ulatedresults,whichwillmakeitpossibletoestablishifa more favourable outcome would have been possible. The programming routine is applied in this study to a panel datasetoftheEU-15memberstatesduringthe1980---2010 period.Twotypesofscenariosarederived:thefirstscenario makesitpossibletoestimatethespeedofconvergencein theEU-15arisingfromincreasesintherateofinvestment in all the countries at the same time; and a second sce-nariowherewe estimatethespeedof convergencein the EU-15resultingfromincreasesintherateofinvestmentin eachoneatdifferenttimes.Inthisway,anattemptwillbe madetomeasurenotonlythecapacityofalternative pub-licpoliciestoinfluencetheEuropeanconvergence,butalso the roletheymayplayin each countrytowardsachieving convergenceintheEU-15.
Thispaperisorganizedasfollows.Section2outlinesthe derivation of the growth model employed and describes the estimation technique and the empirical framework. Section 3 presents the data and results. The last section providesthemainconclusionsofthisstudyandfuturelines ofresearch.
2.
Methodology
2.1. Derivationofthegrowthmodel
We rely in our analysis on the most common measure of convergence inthe literature,i.e., theregression of GDP growthover a longperiodof timeagainstinitial GDP lev-els and a set of explanatory variables in a cross section of countries (Barro and Sala-I-Martín, 1995). Our specifi-cation followsthe approachof Mankiwetal. (1992),who derivedtheconvergenceequationwhenpubliccapitaland human capital wereincluded. The pointof departureis a Cobb-Douglasproductionfunctionwithconstantreturns per-formance.Theproductionfunctionis:
Yt=K ˇ
t(AtLt)1−ˇ, (1)
where Yt represents aggregate production; Kt, physical
capital;Lt,employmentandA,thelevelofexogenous
tech-nologyandlaboureffectiveness.So,AtLtcanbeinterpreted
empiricallysolvethecorrespondingconvergenceequation.
AtandLtgrowexogenouslyatratesgandn,respectively.On
theotherhand,itisassumedthataconstantshareofincome
Sis savedandinvestedandthatthisrateofinvestmentis givenexogenously.Theincreaseofthestockofcapitalcan bedefinedas:
˙
Kt=SK ˇ t(AtLt)
1−ˇ
−ıKt, (2)
whereadotabovethevariabledenotesdifferentiationwith regardtotimeandıistherateofdepreciation.
Defining yt as income per effective labour unit, yt= (Yt/AtLt),andktascapitalpereffectivelabourunits,kt= Kt/AtLt,wecanobtainthemovementequationsforthe pro-ductionfactor:
˙
kt=Skˇt−(n+g+ı)kt. (3) Inthesteadystate(indicatedby*),thecapitalper effec-tivelabourunitk∗t isconstant.Thus,for ˙kt=0,
k∗=
S
(ı+n+g)
1/(1−ˇ)
. (4)
Eq. (4) allows us to analyze the factors affecting the steadystatesolutionandthedifferentstationarystatesin theeconomiesunderstudy.Capitalpereffectivelabourunit inthesteadystatedependspositivelyontherateofcapital investment,whiletherateofdepreciation,andthegrowth ratesofpopulationandtechnologicalprogress,havea neg-ativeinfluence.
Incomepereffectivelabourunitis,by(1),yt=(kt)ˇ. Tak-inglogarithms,differentiating,andsubstitutingyit=Yit/Lit using(3),
dlnyt dt =ˇ
dlnkt dt =ˇ[Se
−(1−ˇ)lnkt−(n+g+ı)]. (5)
Log-linearizingaroundthesteadystate,
dlnyt
dt =ˇ[(ˇ−1)(n+g+ı)(lnkt−lnk
∗)], (6)
where the approximation around the steady state is carried out as follows. From the function f(lnkt)= [Se−(1−ˇ)lnkt−(n+g+ı)], thefirst orderTaylor expansion aroundlnk∗ is given byf(lnkt)∼=f(lnk∗)+f(lnk∗)(lnkt− lnk∗),wheref(lnk∗)=0andf(lnk∗)=−(1−ˇ)(n+g+ı). Denoting thespeed ofconvergencetowardsthesteady stateby=(1−ˇ)(n+g+ı)makesitpossibleto reformu-lateEq.(6)asfollows:
dlnyt
dt =−ˇ[lnkt−lnk
∗]=−[lny
t−lny∗]. (7) ThedifferentialEq.(7)implies:
lnyt=e−tlny0+(1−e−t)lny∗, (8)
where lny0 is the logarithm of the income per effective labourunitatthebeginningoftheperiod.Subtractinglny0 frombothsidesoftheequalityanddividingbytgivesthe averagerateofincomegrowth:
lnyt−lny0
t =
(1−e−t) t lny
∗−(1−e−t)
t lny0. (9)
Using yt=(kt) ˇ
and (4) to replace the logarithm of incomepereffectivelabourunitinsteadystategives:
lnyt−lny0
t =
(1−e−t) t
ˇlnS−ˇln(n+g+ı) 1−ˇ
−(1−e−t)
t lny0. (10)
Productionfunction(1)canbeeasilygeneralized.Mankiw etal.(1992)addhumancapitaltophysicalcapitalintheir augmentedSolowmodel,whileBajo-Rubio(2000)considers
mprivateinputsand2publicinputs(publicinputs,however, enterintheproductionfunctioninaspecialway).Let(1)be generalizedtoaproductionfunctionwhereinvestment(S) isdisaggregatedintoinvestmentinprivatephysicalcapital (Sk),humancapital(Sh),andpubliccapital(Sg):
Yt=Ktˇ1H ˇ2 t G
ˇ3
t (AtLt)1−ˇ1−ˇ2−ˇ3, (11)
Adapting the results in Bajo-Rubio (2000),Eq. (12), to oursetupleadstothefollowingconvergenceequation,that generalizestheresultsin(10):
lnyt−lny0
t =
(1−e−t) t
ˇ1lnSk+ˇ2lnSh+ˇ3lnSg−(ˇ1+ˇ2+ˇ3)ln(n+g+ı) (1−ˇ1−ˇ2−ˇ3)
− (1−e−t)
t lny0. (12)
Sinceincomeper capita(Yt/Lt)=ytAt,Eq.(12)canbe rewritten in terms of the growth of income per capita, insteadofincomepereffectivelabourunits:
ln(Y/L)t−ln(Y/L)0
t =
(1−e−t) t
ˇ1lnSk+ˇ2lnSh+ˇ3lnSg−(ˇ1+ˇ2+ˇ3)ln(n+g+ı)
(1−ˇ1−ˇ2−ˇ3) −
(1−e−t)
t (ln(Y/L)0−lnA0)+g.
(13)
Intheempiricalapproachtotheconvergenceequation we take t=1, insteadof considering a singleperiod asin thederivationofthegrowthmodel,totakeintoaccountall theyearsandusepaneldatatechniques.Furthermore,itis assumedthattheinitiallevelA0reflectsnotonlytechnology butalsoendowmentsofresources,theclimate,institutions, etc.,whichcandifferamongcountries,leadingusto con-siderlnAt=a++ut, where ais a constantcommon to allcountries,isacountryfixedeffect,andutisani.i.d.
residualterm.So theterm allows ustoconsidering the unobservableheterogeneitiesand thedifferencesin tech-nology.
2.2. Estimationofthegrowthmodel
0 20 40 60 80 100 –0.085
–0.08 –0.075 –0.07 –0.065 –0.06
(1) Parameter associated beta–convergence in EU
% variation of public investment rate in infrastructures
Beta-convergence parameter
0 20 40 60 80 100 –8
–7.5 –7 –6.5
(3) Significance test
% variation of public investment rate in infrastructures
t–stat beta-convergence
parameter
0 20 40 60 80 100 0
0.05 0.1 0.15 0.2 0.25 0.3 0.35
(2) Parameter of public investment rate in infrastructure in EU
% variation of public investment rate in infrastructure
Parameter of public
investment rate in infrastructure
0 20 40 60 80 100 1.5
2 2.5 3 3.5 4 4.5 5
(4) Significance test
% variation of public investment rate in infrastructure
t-stat parameter of public investment rate in infr.
Figure1 Scenarioa:Responseofbeta-convergencetosimulatedchangesintherateofpublicinvestmentininfrastructureinthe EU-15(andt-statistics).Scenariob.Responseofbetaconvergencetosimulatedchangesininfrastructureinvestmentinmember states(andt-statistics).
fortheestimationofthemodelonthebasisofa program-mingroutinewithMATLAB.1Becauseeachestimationcanbe
consideredasasimulatedsituation,wedevelopinthis anal-ysisapathofsimulatedresultstocomparewiththeresults observedintheperiod1980---2010.
Toestimatetheconvergenceequation,thefixedeffects model provides the basis, where it is assumed that each explanatoryvariablehasasinglecoefficient;thatis,ithas thesameeffectonthedependentvariable,whileeach indi-vidualvariablehasadifferentconstantwhichrepresentsthe individualeffect.Formally,themodeltobeestimatedisthe following:
ln
yi,t yi,t−1
=+bln(yi,t−1)+˛ln(xi,t)+ıi+ui,t, (14)
where yit=Yit/Lit is the annual GDP per effective labour unitofcountryi=1,...,Ninyeart=1,...,T;xi,tisa
vec-torofk×1explanatoryvariables;iistheindividualeffect;
andui,tisadisturbanceterm.Inthiscase,theconceptof
conditionedconvergenceisanalyzedbyintroducing hetero-geneityinthemodelbymeansoftheintroductionoffixed effectsand theeffectof other variables,xi,t,that
repre-sents the specific steady state of each country, assuming that thefixed effects i are correlatedwith them. When
thebeta-convergenceparameter(b)isnegative,thepoorest
1Intheestimationofthemodelweusedtheroutineprogramming
inMatlabavailableinhttp://www.spatial-econometrics.com/.The
programminginMatlabforthesimulationsinthisworkare
avail-ableonrequest.Inouranalysisweareimplicitlyassumingthatit
ispossibletochangeonevariablewithoutaffectingtheothersto
facilitatetheinterpretationoftheresults.
economiesgrowfasterthanthericher,sothereis conver-genceinincomepercapita.
The within-estimator is calculated in deviations with respect to the mean using Ordinary Least Squares (OLS), making it possible to consistently estimate the parame-ters of the model associated with beta-convergence and with the explanatory variables, since its consistency will not depend onthe specification of fixed effects i which
havebeeneliminatedwiththetransformation.2This
estima-tionalsoprovidesaframeworktocontrastbeta-convergence without violating proposition 6 in Bernard and Durlauf (1996), although it is affectedby measurement error and bynonstationarity.3
The main interest of our proposal is to offer a pro-gramming routine that facilitates the generation of the alternative values for the exogenous variables of interest (inthisstudythemvariablesofpublicpolicy)andthe sub-sequentestimationoftheconvergenceequation.Estimation ofEq.(14)willberepeatedHtimes,dependingontherange ofvariationselectedfortherateofpublicinvestment.The public investment rates usedareexpressed asa percent-age of GDP, which facilitates the generation of different policiesbyvaryingtheweightofpublicinvestmentinGDP. Thesevariations(j)canbeestablishedwithabsolute
flex-ibilityandtheywilldepend,first,onthestepincrease(inc) introduced ineach estimation.Inourstudy,wehave con-sidered applyinga stepincrease of 5% thataugments the same value in each newestimation, untilit rises a
maxi-2SeeBaltagi(2008:15)formoredetails.
3SeeWooldridge(2002:chapters10and12).Inthiscase,anError
(1) Parameter associated beta convergence in the EU
(3) Significance test parameter associated beta convergence in the EU
0 20 40 60 80 100
–0.068 –0.066 –0.064
Austria
Beta convergence
0 20 40 60 80 100
–0.066 –0.064 –0.062 –0.06
Germany
Beta convergence
0 20 40 60 80 100
–0.068 –0.066 –0.064
Belgium
Beta convergence
0 20 40 60 80 100
–0.068 –0.066 –0.064 –0.062
Spain
Beta convergence
0 20 40 60 80 100
–0.066 –0.064 –0.062
Finland
Beta convergence
0 20 40 60 80 100
–0.068 –0.066 –0.064 –0.062
France
Beta convergence
0 20 40 60 80 100
–0.064 –0.063 –0.062
Greece
Beta convergence
0 20 40 60 80 100
–0.066 –0.064 –0.062 –0.06
Ireland
Beta convergence
0 20 40 60 80 100
–0.068 –0.066 –0.064
Italy
Beta convergence
0 20 40 60 80 100
–0.064 –0.062 –0.06
Luxembourg
Beta convergence
0 20 40 60 80 100
–0.066 –0.064 –0.062 –0.06
Netherlands
Beta convergence
0 20 40 60 80 100
–0.0645 –0.064 –0.0635 –0.063
Portugal
Beta convergence
0 20 40 60 80 100
–0.068 –0.066 –0.064 –0.062
Denmark
% variation of public investment rate in infrastructures
Beta convergence
0 20 40 60 80 100
–0.068 –0.066 –0.064
United kingdom
% variation of public investment rate in infrastructures
Beta convergence
0 20 40 60 80 100
–0.066 –0.064 –0.062 –0.06
Sweden
% variation of public investment rate in infrastructures
Beta convergence
0 20 40 60 80 100
–6.5 –6.4 –6.3 –6.2
Austria
T-stat bconverg.
0 20 40 60 80 100
–6.4 –6.2 –6 –5.8
Germany
T–stat bconverg.
0 20 40 60 80 100
–7 –6.5 –6
Belgium
T-stat bconverg.
0 20 40 60 80 100
–6.4 –6.2 –6 –5.8
Spain
T-stat bconverg.
0 20 40 60 80 100
–7 –6.5 –6
Finland
T-stat bconverg.
0 20 40 60 80 100
–6.5 –6 –5.5
France
T-stat bconverg.
0 20 40 60 80 100
–6.2 –6 –5.8 –5.6
Greece
T-stat bconverg.
0 20 40 60 80 100
–6.5 –6 –5.5
Ireland
T-stat bconverg.
0 20 40 60 80 100
–7 –6.5 –6
Italy
T-stat bconverg.
0 20 40 60 80 100
–6.5 –6 –5.5
Luxembourg
T-stat bconverg.
0 20 40 60 80 100
–6.2 –6.1 –6 –5.9
Netherlands
T-stat bconverg.
0 20 40 60 80 100
–6.2 –6.1 –6 –5.9
Portugal
T-stat bconverg.
0 20 40 60 80 100
–6.5 –6 –5.5
Denmark
% variation of public investment rate in infrastructures
T-stat bconverg.
0 20 40 60 80 100
–7 –6.5 –6
United kingdom
% variation of public investment rate in infrastructures
T-stat bconverg.
0 20 40 60 80 100
–6.4 –6.2 –6 –5.8
Sweden
% variation of public investment rate in infrastructures
T-stat bconverg.
Figure1 (continued)
mumof100%inthelastone.Thatis,wewillhaveobtained
Hestimatesofbeta-convergence:
H= Rangeofvariation
inc =
100%
5% =20 (15)
Oncetherangeofvariationshasbeendecided,asecond aspecttobeconsideredishowitwillbeintroducedtoensure thatwearenotincorporatingonlyachangeoforigininthe variableofinterest.Withthisaim,wedecidedtointroduce
thestepincrease(inc)graduallyineachestimation.Tothis end, we have divided it by the number of years studied, obtainingthecumulativeincrease(cinc)thatwewillapply everyyear, untiltheproposed stepincreaseis reached in thelastone.Inourcase,thecincthatappliesis:
cinc= 5%
(2) Parameter of public investment rate in infrastructure in the EU
(3) Significance test parameter associated public investment rate in infrastructure
0 20 40 60 80 100
1.7 1.8 1.9 2
Austria
T-stat P.Infra.
0 20 40 60 80 100
1 1.5 2 2.5
Germany
T-stat P.Infra.
0 20 40 60 80 100
1 1.5 2
Belgium
T-stat P.Infra.
0 20 40 60 80 100
1 1.5 2 2.5
Spain
T-stat P.Infra.
0 20 40 60 80 100
1.8 2 2.2
Finland
T-stat P.Infra.
0 20 40 60 80 100
1.4 1.6 1.8 2
France
T-stat P.Infra.
0 20 40 60 80 100
1.5 2 2.5
Greece
T-stat P.Infra.
0 20 40 60 80 100
1.5 2 2.5
Ireland
T-stat P.Infra.
0 20 40 60 80 100
1.4 1.6 1.8 2
Italy
T-stat P.Infra.
0 20 40 60 80 100
2.6 2.8 3
Luxembourg
T-stat P.Infra.
0 20 40 60 80 100
1 1.5 2
Netherlands
T-stat P.Infra.
0 20 40 60 80 100
1.5 2 2.5
Portugal
T-stat P.Infra.
0 20 40 60 80 100
1.4 1.6 1.8 2
Denmark
% variation of public investment rate in infrastructures
T-stat P.Infra.
0 20 40 60 80 100
1.7 1.8 1.9 2
United kingdom
% variation of public investment rate in infrastructures
T-stat P.Infra.
0 20 40 60 80 100
2 2.05 2.1
Sweden
% variation of public investment rate in infrastructures
T-stat P.Infra.
0 20 40 60 80 100
0.012 0.013 0.014 0.015
Austria
P.Infra.
0 20 40 60 80 100
0.005 0.01 0.015 0.02
Germany
P.Infra.
0 20 40 60 80 100
0.008 0.01 0.012
Belgium
P.Infra.
0 20 40 60 80 100
0.005 0.01 0.015
Spain
P.Infra.
0 20 40 60 80 100
0.012 0.013 0.014 0.015
Finland
P.Infra.
0 20 40 60 80 100
0.008 0.01 0.012 0.014
France
P.Infra.
0 20 40 60 80 100
0.01 0.012 0.014 0.016
Greece
P.Infra.
0 20 40 60 80 100
0.013 0.0135 0.014 0.0145
Ireland
P.Infra.
0 20 40 60 80 100
0.01 0.012 0.014
Italy
P.Infra.
0 20 40 60 80 100
0.018 0.0182 0.0184 0.0186
Luxembourg
P.Infra.
0 20 40 60 80 100
0.008 0.01 0.012 0.014
Netherlands
P.Infra.
0 20 40 60 80 100
0.0115 0.012 0.0125 0.013
Portugal
P.Infra.
0 20 40 60 80 100
0.008 0.01 0.012 0.014
Denmark
% variation of public investment rate in infrastructures
P.Infra.
0 20 40 60 80 100
0.011 0.012 0.013 0.014
United kingdom
% variation of public investment rate in infrastructures
P.Infra.
0 20 40 60 80 100
0.012 0.013 0.014 0.015
Sweden
% variation of public investment rate in infrastructures
P.Infra.
Figure1 (continued)
Westartfromaminimumof0%foryear1,augmenting 0.23%everyyearuptothecorrespondingincreaseof5%in yeart(inouranalysist is22).Thesevariationsgenerated withMatlabareplacedincolumns(Hcolumns)toobtainthe alternativepoliciesusedin theestimations.Every column
shows the evolution of the variationsthrough theperiod, whichwillbeusedtogeneratenextcolumnofvariationsby incorporatingtheincreaseselected.
Scenarioa:Generatingvariationsinallthecountries:
(Xt)TxS= ⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣
1,1=0 2,1=1,1+inc=5% ... H,1=H−1,1+inc=95%
1,2=1,1+cinc=0,23% 2,2=1,2+inc=5,23% ... H,2=H−1,2+inc=95,23% ..
. ... . .. ...
1,T =1,T−1+cinc=4,77% 2,T =1,T+inc=9,77% ··· H,T=H−1,T+inc≈100% ⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦
;(17)
Orvectorially:
j(Xt)=[1,t(Xt),2,t(Xt),...,H,t(Xt)] (18)
Scenariob:Generatingvariationsineachcountry sepa-rately:
i(x i,t)TxH=
⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣
i
1,1=0
i 2,1=
i
1,T ···
i H,1=
i H−1,T
i 1,2=
i
1,1+cinc i 2,2=
i
1,1+cinc ... i H,2=
i
H,1+cinc ..
. ... . .. ...
i 1,T =
i
1,T−1+cinc i 2,T =
i
2,T−1+cinc ··· i
H,T≈100% ⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦
;(19)
Orvectoriallyas:
i
j(xi,t)=[i1,t(xi,t),2,ti (xi,t),...,iH,t(xi,t)] (20) Estimationsofthemodelparameters(14)andthevectors of(17)and(19)withthevariationswillbeusedtoevaluate publicpoliciesusingthespeedofconvergenceascriterion forthisanalysis.Theresultsarepresentedingraphicalform, where the graphs plot onthe x-axisthe variations of the vectors (18) or (20) and on the y-axis the corresponding estimatesfortheEU-15convergenceparameterorfor the parameter associated with the public policy variable and their correspondingt-statistics.In this analysiswe obtain a path of simulated values for the speed of convergence that is compared with the observed result for the EU-15 convergenceprocessovertheperiod1980---2010.
Inthisstudy,theeffectofintroducingtheincreaseinthe exogenousvariableofinterestinallofthecountriescanbe evaluatedwiththefollowingmodel:
ln
yi,t yi,t−1
−ˆ˛ln(xli,t=/m)=+ˇln(yi,t−1)+ln(xmi,t+j)
+ıi+ui,t, (21)
where j,t is a column vector, corresponding to col-umn j which incorporates the cumulative increases for
t=1,...,T forthevariableofinterestxm
i,tofeachcountry and assuming the rest of k---m variables remain constant. Inthisway,j=1,...,Hestimationsofthemodel(21)are carriedout,resultingindifferentvaluesoftheparameter ofbeta-convergence.
The effectofthechangesontheexogenousvariableof interestforaspecificcountrycanbeevaluatedestimating themodel:
ln
yi,t yi,t−1
−ˆ˛ln(xli,t=/m)=+ˇln(yi,t−1)+ln(xmi,t+ i j)
+ıi+ui,t, (22) where: i
j,t is a column vector, corresponding to column
j which incorporates the cumulative increases for t=
1,...,Tforthevariableofinterestxm
i,tofcountryiand main-tainingceterisparibustherestofk---mvariables.Inthisway,
j=1,...,H estimations ofmodel (22)will becarriedout forthei=1,...,Ncountries,resultingindifferentresults ofthebeta-convergence.
3.
Data
and
results
Theestimationoftheconvergenceequationwascarriedout usingapaneldatafortheEU-15memberstatesduringthe period1980---2010. Table 1 presents the variables used in theestimationoftheconvergenceequation.Data concern-ingthe seriesof employment, population, gross domestic productandgrossinvestment wastakenfromWorldBank DataIndicators(http:data.worldbank.org/indicator).They havebeen expressed inPPPinternational US$ inthe year 2000usinginformationfromEurostat:http://epp.eurostat. ec.europa.eu/portal/page/portal/statistics/themes. Data on public education expenditure is taken from OECD
Table1 Informationvariablesemployed.
yit GDPpereffectivelabourunit(PPP
internationalUS$year2000)
Sk,it PrivateinvestmentasapercentageofGDP
Sg,it PublicinvestmentasapercentageofGDP
Sh,it Publicinvestmentineducationasapercentage ofGDP
g Rateofexogenoustechnicalchangeconstant
andequalto0.02a
it Rateofpopulationgrowthbyworker’sage
ı Rateofcapitaldepreciationconstantand equalto0.03a
a Asisstandardinthegrowthliterature,wetakeg+ıtobe
equalto0.05forallcountriesandyears(see,e.g.Mankiwetal.,
Table2 Estimation ofconvergenceequation.Dependent variable:ln(yit/yit−1).
Independentvariables Datapanelmodel
withfixedeffects
ln(yit−1) −0.061(−2.29)**
lnSk−ln(n+g+ı) 0.031(1.90)* lnSg−ln(n+g+ı) 0.002(0.51) lnSh−ln(n+g+ı) −0.016(−1.15)
Speedofconvergence 0.056
TestFIndividualeffects F(14,446)=3.79
Hausmantest 2(4)=13.63
WaldFtest F(4,446)=3.96
Thet-ratiosshowninparentheses().
* Significantparameterat90%.
**Significantparameterat95%.
EducationataGlanceandexpressedinthesametermsas therestofvariables.
Inthissectionweseektocomparetheresultobtainedin termsofconvergencespeedintheEU-15withthepolicies implementedduring1980---2010withresultsthatcouldhave beingobtainedincreasingthe rateof investmentin infra-structureandeducationofthatperiod.Wehaveproceeded intwosteps:first,werunthepaneldataregressiontoobtain theresultsoftheconvergenceequation(Table2).
Second, the structural parameters from the previous regression are used to estimate the convergence equa-tionwith the generated public policies,obtaining a path of values for the speed of convergence, for the param-eter associated with the public policy variable and their correspondingt-statistics.Thus,this analysis willmake it possibletoestablishifitwouldhavebeenpossibletoobtain morefavourableoutcomesintermsofspeedofconvergence thantheresultsobservedfor thisperiod.Moreover,the t-statisticsalso allow usto determine whatchanges in the implementedpolicies(ifany)generatesignificantimpacts ontheconvergenceprocess.
The convergence equation, according to expression (14), is estimated by applyingthe model of fixed effects proposed above. In Table 2 we present the results from the regression. The results show that in the sample the relationshipbetweentheinitialGDPperworkerandgrowth ofper workerGDP is negativeandhighly significant. This representsconvergenceacrosstheEUmemberstatesinthe sampleduringtheperiod1980---2010.
The estimations carried out also make it possible to obtainsomeresultsastotheinfluenceofthepublicpolicies developed in the European economies during this period: public provision of infrastructure and education. For the periodanalyzed,aninsignificantinfluenceofpublic invest-ment and education on the growth rate of the European countriesisderivedfromtheestimationcarriedout.These resultsareconsistentwiththefindingsofmanyresearchers (BartkowskaaandRiedl,2012;AlvarezandBarbero,2016). Buttheoverallvaluationofthestudiesismixed.Ageneral viewontheimpactofpublicinvestmentongrowthhasbeen wellrecognizedsincetheseminalworkofAschauer(1989, 1990) who focuses on infrastructure investment. Recent surveyssummarizingthecurrentstate oftheliteratureon
infrastructureandgrowthcanbefoundinRompandDeHaan (2007) or Irmen and Kuehnel (2009) which show that the relationship between infrastructure and convergence still remainanunresolvedpuzzle.Ontheotherhand,education investmentareofinterestintheworkofBlankenau(2005) andBlankenauetal.(2007)whofindapositiverelationship between public education expenditure and growth for developed countries.BenhabibandSpiegel(1994) provide an overview on the impact of human capital on growth. KruegerandLindahl(2001)orVandenbussche etal.(2006) present amoreskepticalviewontheimpactofeducation policyforindustrializedcountries.Inthispaper,wesupport themoreskepticalviewonbothpublicpoliciesandclaimed that expenditure in infrastructure and education in the EU-15doesnotsufficetocountertheimbalancesgenerated bymarketforcesandeconomicintegrationandthatiswhat explainstheresultsobtained.TheWaldteststatisticsshow that the explanatory variables introduced in the analysis are conjointly significant. Table 2 also includes an F-test which confirms jointsignificance of individual effects for eachcountry.
Usingthefixed-effectscoefficientsintheestimationof the convergence equation, we introduce increasesin the two economic policy instruments: infrastructure (Fig. 1) and education investments (Fig. 2) and derive two types of scenarios for them to examine how the EU speed of convergencerespondstoincreasesintherateofinvestment of allthe countries(scenario a)or in each of them sepa-rately(scenario b). The resultsobtained arepresented in graphicalformandthescenariosshowtheresponseofthe betaconvergenceparameter(1)andoftheeconomicpolicy instrumentparameter(2)andtheirt-statistics(3)and(4), while theother factorsremainconstantandaretherefore notpresented.
accountother factorsthatcancondition theircapacityto influence growth(this is thecase ofprivate capital) and, therefore,greaterincreasesinpublicinvestmentcouldnot achievetheexpectedresults.Furthermore,itisfoundthat agreaterjointinvestmenteffortwouldhavehadapositive effectonthespeedofconvergenceintheEU-15,reinforcing theimportanceofthecoordinationofthesedevelopments andcohesionpoliciesbetweenthememberstates.
Fig. 1 (scenario b) displays the second scenario which focusesonthepath oftheEU-15speedof convergencein responsetoincreasesinthepublicinvestmentrateof infra-structureintheEuropeaneconomiesseparately(weobtain then 15graphs for each parameter).In thiscase, we find scarcelyany responseofthe speedof convergencetothe increasesintherateofinvestmentininfrastructureofthe memberstates (itsvaluesrangein thiscase from0.06 to 0.067). We only observe a slight decline in the speed of convergenceatthebeginningoftheseriesinsomecountries and,fromthat result,theincreasesin therateof invest-mentofinfrastructurewillnothaveresponseintherateof convergence.Thisresultsuggeststhatthereisnodeficitof infrastructureintheEuropeancountries,aresultwhichis inaccordancewithotherworksontheseeconomies(Kamps, 2005).Investmentininfrastructurehasbeenoneofthemain prioritiesinthedevelopmentandcohesionpoliciesintheEU inrecent decades,whichhasmadeitpossible toincrease the level of these endowments in all the countries. As a resultthereisnocountrythathascapacitytoinfluence sep-aratelytherate ofconvergence inthe EU-15.In thecase oftheparameterofpublicinvestmentininfrastructureand itst-statistics (graphs 2 and 4), resultsconfirm again the positive and significant impact of this variableon the EU convergence.
In theanalysis ofthe potentialimpacts ofincreasesin therateofinvestmentineducationinalltheEUcountries
(Fig.2,scenarioa),thesimulatedvaluesobtainedforthe speedof convergenceand its t-statistics show that there wascapacitytofavourconvergenceinthisperiod.Therise intheconvergencerateissmaller thaninthecase ofthe rate in infrastructure (the speed of convergence reaches themaximum value of 0.07) which indicates that despite ageneralimprovementineducationperformanceintheEU, progressinconvergenceisslow.Wealsofindalimittothe capacityofpublicexpenditureoneducationtoencourage convergence, although the change in the track record is less pronouncedthan in the rate of infrastructure, main-tainingahigherlevelofspeedofconvergence.Inthiscase again,resultssupporttheideathatwhileresponsibilityfor educationin Europe lieswiththe member states,the EU hasanimportantroleincontributingtothedevelopmentof educationbyencouragingcooperationandpolicy coordina-tionbetweenthecountries.Anotherimportantresultisthat increasesin therateofexpenditureineducationallowus toobtainevidenceofthepositiveandsignificantimpactof thispolicyinstrumentonconvergence,whichsupportsthe importanceofincreasingthefundsdedicatedtoeducation sothattheyhavesignificantimpactongrowthrates(graphs 2and4).
Fig.2(scenariob)shows theevolutionoftheEUspeed ofconvergencewhen therate ofinvestment in education risesineachof thememberstatesseparately. Theresults demonstrateagainthatincreasesinthisrateineachoneof thecountriesstudiedseparatelyhavelesscapacityto influ-encepositivelytheconvergenceintheEU.Theresponseof theparameterisscarce(valuesrangebetween0.0601and 0.064).InthecaseofNetherlandsandLuxembourg,results showthatif thesecountriesincrease theirrateof expen-diturein education, the speed of convergence in the EU decreases.Thesearecountriescharacterizedby maintain-ingthehighestinvestmentratesineducationintheEU,so
0 20 40 60 80 100 –0.075
–0.07 –0.065 –0.06 –0.055 –0.05
(1) Parameter associated beta convergence in EU
% of variation of public investment rate in education
Beta-convergence parameter
0 20 40 60 80 100 –7
–6.5 –6 –5.5 –5 –4.5 –4
(3) Significance test
% of variation of public investment rate in education
t-stat parameter
of beta-convergence
0 20 40 60 80 100 –0.05
0 0.05 0.1 0.15 0.2 0.25 0.3
(2) Parameter associeted public investment rate in education in EU
% of variation of public investment rate in education
Parameter of public
investment rate in education
0 20 40 60 80 100 –1
0 1 2 3 4
(4) Significance test
% of variation of public investment rate in education
t-stat parameter of public
investment rate in education
(1) Parameter associated beta convergence in the EU
0 20 40 60 80 100 –0.063 –0.062 –0.061 –0.06 Austria Beta convergence
0 20 40 60 80 100 –0.0628 –0.0627 –0.0626 –0.0625 Germany Beta convergence
0 20 40 60 80 100 –0.0625 –0.062 –0.0615 –0.061 Belgium Beta convergence
0 20 40 60 80 100 –0.063 –0.0625 –0.062 –0.0615 Spain Beta convergence
0 20 40 60 80 100 –0.064
–0.062 –0.06
Finland
Beta convergence
0 20 40 60 80 100 –0.063
–0.062 –0.061
France
Beta convergence
0 20 40 60 80 100 –0.064
–0.062 –0.06
Greece
Beta convergence
0 20 40 60 80 100 –0.061 –0.0605 –0.06 –0.0595 Ireland Beta convergence
0 20 40 60 80 100 –0.063 –0.062 –0.061 –0.06 Italy Beta convergence
0 20 40 60 80 100 –0.0615
–0.061 –0.0605
Luxembourg
Beta convergence
0 20 40 60 80 100 –0.0634 –0.0633 –0.0632 –0.0631 Netherlands Beta convergence
0 20 40 60 80 100 –0.066 –0.064 –0.062 –0.06 Portugal Beta convergence
0 20 40 60 80 100 –0.063
–0.0625 –0.062 –0.0615
Denmark
% variation of public investment in education
Beta convergence
0 20 40 60 80 100 –0.063
–0.062 –0.061
United kingdom
% variation of public investment in education
Beta convergence
0 20 40 60 80 100 –0.064
–0.062 –0.06
Sweden
% variation of public investment in education
Beta convergence
(4) Significance test parameter associated beta convergence in the EU
0 20 40 60 80 100 –6.3 –6.2 –6.1 Austria T -s tat bc on verg.
0 20 40 60 80 100 –6.28 –6.26 –6.24 Germany T-st at bc on verg.
0 20 40 60 80 100 –6.26 –6.24 –6.22 –6.2 Belgium T-st at bc on verg.
0 20 40 60 80 100 –6.3
–6.2 –6.1
Spain
T-stat bconverg.
0 20 40 60 80 100 –6.4 –6.3 –6.2 –6.1 Finland T-st at bc on verg.
0 20 40 60 80 100 –6.28 –6.26 –6.24 –6.22 France T-st at bc on verg.
0 20 40 60 80 100 –6.4 –6.3 –6.2 –6.1 Greece T-st at bconverg.
0 20 40 60 80 100 –6.1 –6 –5.9 Ireland T-st at bconverg.
0 20 40 60 80 100 –6.3 –6.2 –6.1 Italy T-st at bc on verg.
0 20 40 60 80 100 –6.14
–6.12 –6.1
Luxembourg
T-stat bconverg.
0 20 40 60 80 100 –6.36 –6.34 –6.32 –6.3 Netherlands T-stat bconverg.
0 20 40 60 80 100 –6.4 –6.3 –6.2 –6.1 Portugal T-stat bconverg.
0 20 40 60 80 100 –6.28
–6.26 –6.24 –6.22
Denmark
% variation of public investment in education
T-st
at
bc
on
verg.
0 20 40 60 80 100 –6.3
–6.2 –6.1
United kingdom
% variation of public investment in education
T-sta
t
bc
on
verg.
0 20 40 60 80 100 –6.4
–6.3 –6.2 –6.1
Sweden
% variation of public investment in education
T-st
at
bc
on
verg.
Figure2 (continued)
thatincreasesinrateswouldlimittheabilitytoincreasethe speedofconvergence.Anywaythechangeintheparameter ofconvergence inthese casesis soreducedthat it isnot possibletodrawrelevantconclusionsfromtheseresults.In theanalysisoftheeffectoftherateofinvestmentin edu-cationonconvergence(graphs2and4),wefindageneral positiveimpactreinforcingtheideathathigherinvestment ratescanobtainpositiveimpactofthisvariable.
(2) Parameter associated public investment rate in education
0 20 40 60 80 100 0.012 0.013 0.014 0.015 Austria P.Education
0 20 40 60 80 100 0.005 0.01 0.015 0.02 Germany P.Education
0 20 40 60 80 100 0.008
0.01 0.012
Belgium
P.Education
0 20 40 60 80 100 0.005
0.01 0.015
Spain
P.Education
0 20 40 60 80 100 0.012 0.013 0.014 0.015 Finland P.Education
0 20 40 60 80 100 0.008 0.01 0.012 0.014 France P.Education
0 20 40 60 80 100 0.01 0.012 0.014 0.016 Greece P.Education
0 20 40 60 80 100 0.013 0.0135 0.014 0.0145 Ireland P.Education
0 20 40 60 80 100 0.01
0.012 0.014
Italy
P.Education
0 20 40 60 80 100 0.018 0.0182 0.0184 0.0186 Luxembourg P.Education
0 20 40 60 80 100 0.008 0.01 0.012 0.014 Netherlands P.Education
0 20 40 60 80 100 0.0115 0.012 0.0125 0.013 Portugal P.Education
0 20 40 60 80 100 0.008
0.01 0.012 0.014
Denmark
% variation of public investment in education
P.Education
0 20 40 60 80 100 0.011
0.012 0.013 0.014
United kingdom
% variation of public investment in education
P.Education
0 20 40 60 80 100 0.012
0.013 0.014 0.015
Sweden
% variation of public investment in education
P.Education
(5) Significance test parameter associated public investment rate in education
0 20 40 60 80 100 1.7 1.8 1.9 2 Austria T-stat P.Educ.
0 20 40 60 80 100 1 1.5 2 2.5 Germany T-stat P.Educ.
0 20 40 60 80 100 1
1.5 2
Belgium
T-stat P.Educ.
0 20 40 60 80 100 1 1.5 2 2.5 Spain T-sta t P.Educ.
0 20 40 60 80 100 1.8 2 2.2 Finland T-sta t P.Educ.
0 20 40 60 80 100 1.4 1.6 1.8 2 France T-sta t P.Educ.
0 20 40 60 80 100 1.5 2 2.5 Greece T-sta t P.Educ.
0 20 40 60 80 100 1.5 2 2.5 Ireland T-sta t P.Educ.
0 20 40 60 80 100 1.4 1.6 1.8 2 Italy T-sta t P.Educ.
0 20 40 60 80 100 2.6 2.8 3 Luxembourg T-sta t P.Educ.
0 20 40 60 80 100 1 1.5 2 Netherlands T-stat P.E du c.
0 20 40 60 80 100 1.5 2 2.5 Portugal T-stat P.E du c.
0 20 40 60 80 100 1.4
1.6 1.8 2
Denmark
% variation of public investment in education
T-sta
t
P.Educ.
0 20 40 60 80 100 1.7
1.8 1.9 2
United kingdom
% variation of public investment in education
T-sta
t
P.Educ.
0 20 40 60 80 100 2
2.05 2.1
Sweden
% variation of public investment in education
T-stat P.Educ.
Figure2 (continued)
impactonindividualconvergenceislowerbecauseits pro-visiondependsonnationalgovernments,whichencourages thedesirabilityofcoordinatingtheseEuropeanpolicies.
4.
Conclusions
OuranalysisisfocusedontheimpactontheEU-15 conver-genceofincreasesintherateofinvestmentininfrastructure
Fromapolicyanalysispointofview,theseresultsprovide supportforpoliciesthatdedicateeffortstoimprove infra-structure and human capital in the European economies astheyhave still capacityto contributepositively tothe processofconvergenceintheEU-15.Anotherpolicy impli-cationthatcanbedrawnfromthisanalysisoftheEuropean countries is the importance of the coordination of these developmentsandcohesion policiesbetween the member states.Likewise,thedecisionaboutthequantitiesof infra-structure and education tobe allocated in each member state should bemade in function of an evaluation of the effectofthemarketfailureandthereforeitshouldleadto amoreefficientallocationofresources.
References
Alvarez,I.,Barbero,J.,2016.Thepublicsectorandconvergence
withspatialinterdependence:empiricalevidencefromSpain. AppliedEconomics48,2238---2252.
Aschauer,D.A.,1989.Ispublicexpenditureproductive?Journalof
MonetaryEconomics23,117---200.
Aschauer,D.A.,1990.Whyisinfrastructureimportant?In:Munnell,
A.H.(Ed.),Is There aShortfall inPublic CapitalInvestment? FederalReserveBankofBoston,MA,Boston,MA,pp.21---68.
Bajo-Rubio,O.,2000.AfurthergeneralizationoftheSolowmodel:
theroleofthepublicsector.EconomicsLetters68,79---84.
Baltagi,B.,2008.EconometricAnalysisofPanelData.JohnWiley&
Sons.
Barossi,M., Gonc¸alez, R., Diniz, E., 2005. The empirics of the
Solowgrowth model: long-termevidence. Journalof Applied Economics24,31---51.
Barro,R.J.,Sala-I-Martín,X.,1995.EconomicGrowth.McGraw-Hill.
Bartkowskaa,M.,Riedl, A.,2012. Regional convergenceclubs in
Europe:identificationandconditioningfactors.Economic Mod-elling29,22---31.
Benhabib, J., Spiegel, M., 1994. The role of human capital in
economicdevelopment,evidencefromaggregatecross-country data.JournalofMonetaryEconomics34,143---173.
Bernard,A.B.,Durlauf,S.N.,1996.Interpretingtestsofthe
conver-gencehypothesis.JournalofEconometrics71,161---173.
Blankenau, W.F., 2005. Public schooling, college subsidies and
growth. Journal of Economic Dynamics and Control 29, 487---507.
Blankenau, W.F., Simpson, N.B., Tomljanovich, M., 2007. Public
educationexpenditures, taxation andgrowth:linking data to theory.AmericanEconomicReview,PapersandProceedings97, 383---397.
Irmen, A., Kuehnel, J., 2009. Productive government
expendi-ture and economic growth. Journalof Economic Surveys 34, 692---733.
Kamps,C.,2005.Thedynamiceffectsofpubliccapital:VAR
evi-dence for 22 OECD countries. International Tax and Public Finance12,533---538.
Krueger,A.B.,Lindahl,M.,2001.Educationforgrowth:whyandfor
whom?JournalofEconomicLiterature39,1101---1136.
Mankiw,N.G.,Romer,D.,Weil, D.N.,1992. Acontributiontothe
empiricsofeconomicgrowth.QuarterlyJournalofEconomics 107,407---437.
Monfort,M.,Cuestas,J.C.,Ordo˜nez,J.,2013.Realconvergencein
Europe.EconomicModelling33,689---694.
Ott,I.,Soretz,S.,2011.Publicpoliciesandconvergence.Journal
ofEconomicDynamics&Control35,1435---1450.
Reggi,L.,Scicchitano,S.,2014.AreEUregionaldigitalstrategies
evidence-based?Ananalysisoftheallocationof2007---13 struc-turalfunds.TelecommunicationsPolicy38(5---6),530---538.
Rodriguez-Pose,A.,Fratesi,U.,2004.Betweendevelopmentand
socialpolicies:theimpactofEuropeanstructuralfundsin objec-tive1,regions.RegionalStudies38,97---113.
Romp,W.,DeHaan,J.,2007.Publiccapitalandeconomicgrowth.
PerspektivenderWirtschaftspolitik8(SpecialIssue),6---52.
Vandenbussche,J.,Aghion,P.,Meghir,C.,2006.Growth,distanceto
frontierandcompositionofhumancapital.JournalofEconomic Growth11,97---127.
Varga,J.,VeldFin‘t.,2011.Cohesionpolicyspendinginthenew
memberstatesoftheEUinanandogenousgrowthmodel. East-ernEuropeanEconomics49,29---54.
Wooldridge,J.M.,2002.EconometricAnalysisofCross-Sectionand
