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Barriers to innovation and subsidy e¤ectiveness
¤
XuliaGonzálezy,JordiJaumandreuzandConsueloPazóx
Thisversion: June2001
Abstract
Thispaperexploresthee¤ectsofR&Dcommercialsubsidiesbymeansofamodelof
…rms’decisionsaboutperformingR&Dwhensomegovernmentsupportcanbeexpected.
Toestimate the parameters of interest we use an unbalanced panel sample of 1,800
performingandnon-performingSpanishmanufacturing…rms. Forthenon-performing
…rms,wecomputethetrigger subsidies requiredtoinduceR&Dspending(ameasure
of market failure). Amongtheperforming …rms, we can detectthe ones thatwould
cease to perform R&D if subsidies were eliminated. We alsoexplore the change in
theprivately…nanced R&De¤ortof theperforming…rms. Resultssupporttheclaim
thatmarketfailuresarerealandsubsidiesstimulateR&Dactivities,butalsoshowthat
actualsubsidiesgoto…rmsthatwouldhaveperformedR&Dotherwise.
Keywords: R&D,innovation,subsidies,thresholds,Tobitmodel
JELClassi…cation:O32,L11,C24
¤
Wearegratefulforthecommentsandsuggestionsmadeby IsabelBusom,Lars-HendrickRöller,Peter
Zemsky,andtheaudiencesatthe2ndCEPRConferenceonAppliedIndustrialOrganizationheldinLisbon
andatUniversidadCarlosIIIdeMadrid. Weacknowledge…nancialsupportfromCICYT,projectsSEC2000-
0268andSEC1999-1236-C02-01,andfromXuntadeGaliciaPGIDT00PXI30005PN.
y
Dpto. EconomíaAplicada.FacultadedeEconómicas.UniversidadedeVigo. AsLagoasMarcosendes/n,
36310Vigo. Spain.E-mail: xgzlez@uvigo.es
z
Dpto. deEconomía. UniversidadCarlosIIIdeMadrid. c/Madrid126,28903Getafe(Madrid). Spain.
E-mail: jordij@eco.uc3m.es
x
Dpto. FundamentosdaAnáliseEconómica. FacultadedeEconómicas.UniversidadedeVigo. AsLagoas
Marcosendes/n,36310Vigo. Spain. E-mail: cpazo@uvigo.es
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1. Introduction
Publicsectorsofallindustrializedcountriesspendconsiderableamountsofmoneyinsup-
portingcommercial R&Dofmanufacturing…rms. Firms apply for subsidiesforresearch,
and agencies choose theresearchtobefunded. Theeconomic justi…cation of these pro-
gramsliesinthepresumablefailureofthemarkettoprovideincentivesto…rmstoallocate
enoughresourcestoinnovativeactivities(Arrow(1962),Nelson(1959)). Positiveexternali-
tiesa¤ectingother…rmsandconsumersinduceadivergencebetweenthesocialandprivate
returnsofsuchactivities.
Despite the spread of these subsidies, the evidence of their e¤ects on …rms’ behavior
remainsrelativelymodestandcontroversial(see,forexample,thesurveyonrecentmicroe-
conometric evidence by Klette, MoenandGriliches (2000)
1
). Researchers are currently
tryingtodetermine whether subsidies stimulateR&D, inthe sense that…rms undertake
projectsthatotherwisewouldnothavebeencarriedout,andalsoifthepublicfundscrowd
outthecompany-…nancedR&Dexpenditure. Theanswersarefar fromunanimous, often
depending on the methodology employed. For instance, a recent …rm-level econometric
study by Wallsten (2000) using asampleofUS …rms claims that, controlling for grants
endogeneity,noe¤orte¤ectisdetectedandcrowdingoutispresent. Onthecontrary, the
workbyLach(2000)withpaneldataonIsraeli…rms…ndsapositivelong-runelasticityof
company-…nancedR&Dexpenditureswithrespecttosubsidies
2
.
Thispaperisaimedatexploringthee¤ectsofR&Dcommercialsubsidiesbyfocussingon
themodellingof…rms’decisionswhensomegovernmentsupportcanbeexpected: whether
ornottoperformR&Dprojects,andtheassociatedlevelofR&De¤ort(R&Dexpenditure
oversales). It triestoshedlightonthe questionsofinterestby constructinganexplicit
1
Ortherelated works byHall andVan Reenen (2000),on …scalincentives, andDavid,Halland Toole
(2000)onpublic/privateR&D.
2
Someevidenceon the“additionality”ofsubsidies is alsofound byToivanenand Niininen(2000)with
Finnish …rmdata, while Busom(2000) …nds some crowdingout witha small sample of f Spanish publicly
granted…rms. ParisiandSembenelli(2001)haverecentlyestimatedhighlyelasticresponsesofR&Dexpen-
dituresofItalian…rmstothecostoffunds.
1
theoretical frameworktoexplainwhyandhowthe…rms’ investments canturnouttobe
inhibited, and employing a sample of highly heterogeneous …rms to identify the model
parameters(asamplethatinparticularincludesbothR&Dperformers,subsidisedornot,
andnon-performers).
From the estimation of the model we derive pro…tability thresholds and gaps for the
expenditure on innovative activities for every …rm. For non-performing …rms, the gap
betweentheirunobservedoptimalR&Dspendingandthepro…tabilitythresholdisameasure
ofthemarketfailure. Forthese…rms,wecomputethetriggersubsidiesrequiredtoinduce
R&Dspending. Amongtheperforming…rms,wecandetectthosethatwouldcrossbackthe
pro…tabilitythresholdandceasetoperformR&Difsubsidieswereeliminated. Inaddition,
wecanassesssubsidye¢ciencyforalltheperforming…rmsbyexploringthechangesinthe
privately…nancedR&De¤ortobtainedasane¤ectofthegrant.
Resultsclaimthatmarketfailuresarerealandthatsubsidiescanplayaroleinstimulating
R&Dactivities,butalsothatactualsubsidiesinfactgoto…rmsthatwouldhaveperformed
innovative activities had they not received the subsidy. However, subsidies increase the
privatefundsinvestedonR&Dbythese…rms.
To model …rms’ decisions we consider each …rm a competitor in prices in a product
di¤erentiatedindustry,whichcanshiftthedemandforitsproductbyenhancingproduct
quality through R&Dexpenditures. Demand characteristics, technological opportunities
andset-upcostsofR&Dprojectsinteracttodetermineapro…tabilitythresholdofspending.
Belowthisthreshold,R&Dcostsarenotcompletelyrecoveredinthemarketbymeansof
thesales increment. Firms canthen…ndit more pro…table not toundertakeinnovative
activities,butthisdecisioncanbemodi…edifexpectedsubsidiesreducesthecostofR&D.
The same framework explains how performig …rms take into consideration the expected
grantstodeterminethesizeoftheR&Dplannedexpenditures.
ThisframeworknaturallyleadstoaTobittypemodellingofthecensoredvariableoptimal
e¤ort,whichisthewayemployedtoestimatethemodelparameters. Beforethis,unobserv-
able expected subsidies are estimated from data on ex-post observed grants. Subsidies
arepresumablygrantedbyagenciesaccordingtothecontemporarye¤ortandperformance
2
of …rms, andhence are endogeneous. This two-step procedure also allows us to obtain
estimatesthatarerobustwithrespecttothepossiblebiasesderivedfromthisendogeneity.
Toestimatethemodel weuseanunbalancedpanelofmorethan1,800Spanishmanu-
facturing…rmsobservedduringtheperiod1990-97. Thedatacomefromarandomsample
drawnbyindustriesandsizestrata, andhenceresultscanbeclaimedtobevalidfor the
wholeindustry. Duringtheperiod,Spanishcentralandregionalgovernments,aswellasthe
EuropeanUnion,maintainedseveralcommercialR&Dsubsidyprogramswhichaccounted
forinnovations’ primary source of support. Firmsample behavioris, however, heteroge-
neous. Almost20%ofthe…rms withmorethan200workersandabout70%ofthe…rms
underthissize donotreporttoperformformal R&D. Andonly afractionofperforming
…rms,increasingwith…rmsize,obtainssubsidies.
The rest of the paper is organizedas follows. Sectiontwosummarises the theoretical
framework. Sectionthreepresentstheeconometricmodelandexplainshowitcanbeusedto
measurethedi¤erentsubsidye¤ects. Sectionfourdescribesthedatasetandthemainfacts
aboutsubsidies. Section…vereports theeconometricresultsandsectionsixdiscussesthe
impliedsubsidye¤ects. Sectionsevenconcludes. Appendix1isdevotedtosomeeconometric
detailsandAppendix2todescribingtheemployedsampleandvariables.
2. R&Dwithset-upcosts
ThissectioncharacterisestheR&Ddecisionsof…rmsandrelatesthemtosubsidies
3
.
Firmicompetesinpricesinagivenproductdi¤erentiatedindustry, facinganegatively
slopeddemand. Demand,however,canbeshiftedbyenhancingthequalityoftheproduct.
Wewillwritedemandaseq
i
(p
i
;p
¡i
;s
i
),wherep
i
standsfortheownprice,p
¡i
forthevector
ofpricesoftherivals,ands
i
forthelevel ofquality, andwewillsuppose@eq
i
=@s
i
>0and
@eq
2
i
=@s
2
i
·0. Inwhatfollows,wewillassumethatpricecompetitioncanbetakenasstable
over time andsubsumedin therelevant own-price demandelasticity, andhence we will
writeeq
i
(p
i
;p
¡i
;s
i
)=q
i
(p
i
;s
i
). Wewillrelaxthisassumptionintheempiricalexerciseby
3
ThemodelfollowsGonzalezandJaumandreu(1998).
3
consideringthepossibilityofeventualchangesincompetition. Wealsomomentarilydrop
thesubscriptiforsimplicity.
QualitycanbeimprovedbyincurringR&Dexpenditures,denotedhenceforthbyx,ac-
cordingtosometechnologicalrules. Inparticular,tosurpassthecurrentindustrystandard
quality s(0); …rmi must incur some set-up costs that we will denote by F. Beyond F,
R&Dexpendituresa¤ectqualityaccordingtothe“productionfunction”s =s(x), where
@s=@x > 0 and @
2
s=@x
2
·0: Set-up costs usually stem from the indivisibility of some
resources.
A…rmcanapplytohaveitsR&Dexpendituressubsidizedwithpublicfundsbyamone-
taryfraction½. Butthe…rmmusttakeitsdecisionsex-ante(atthetimeofsettingitsR&D
plans)andweassumethattheyarebasedonthe…rm’sexpectationaboutthesubsidythat
will be obtained, ½
e
. Ontheother hand, public subsidies canbeassociatedto ahigher
levelofexpendituree¢ciency,sincetheyoftengiveaccesstootherfacilitiesoradvantages
(e.g. access to public laboratories and researchers). By the same token, they could be
hypotheticallylinkedtolessexpendituree¢ciency,forexamplebecausetheyeaseliquidity
constraintsandhencediscipline. Accordingly, wewillparametrizetheexpectedcostofa
unitofe¢cientR&Das(1¡½
e
)
¯
,where¯isameasureofsubsidye¢ciency
4
.
Supposenowthatproductionmarginalcostisc. Tosettheproductpriceanddecidethe
pertinenceandlevelofR&Dexpenditures,the…rmmustsolvetheproblem
max
p;x
(p¡c)q(p;s)¡(1¡½
e
)
¯
x
[1]
subjectto
s=
8
<
:
s(0) ifx<F
s(x) otherwise
whichturns out to be a problem with anon-convex constraint. The equilibrium of the
…rmwillbecharacterizedbythepair(p
e
;x
e
)suchthat(p
e
;x
e
)=maxf¦(p
¤
;x
¤
);¦(p
¤¤
;0)g,
wherep
¤
andp
¤¤
maydivergeand(p
¤
;x
¤
)istheinteriorsolution. Thatis,the…rmwillchoose
4
If¯=1theobtainedpublicfundsleaveunchangedthee¢ciencyofthecompany-…nancedfunds.
4
whether or not perform R&D activities according to an incremental pro…t-expenditures
comparisoncondition.
Assumethat…rmscaninanycaseobtainanon-negativepro…tperformingR&D,thatis,
¦(p
¤
;x
¤
)¸0. Then,optimalnon-zeroe¤ortofbothperformingandnon-performing…rms
canbesummarizedintheuniqueexpression
E
¤
´
x
¤
p¤q¤
=(
s
q
@q
@s
x
s
@s
@x
)=(¡
p
q
@q
@p
(1¡½
e
)
¯
)
[2]
whichresultsfromrearrangingtheFOCinteriorconditionsof[1],andisaDorfman-Steiner
type of condition (Dorfman andSteiner (1954)). Non-performing…rms, however, would
onlychoosethis(localmaximum)allocationiftheyhadn’tamorepro…tablealternative.
Formula[2]showsthatoptimale¤ortincreaseswiththeelasticityofdemandwithrespect
toR&Dexpenditure, whichcanbeconceptually decomposedintheelasticityofdemand
withrespecttoquality (demandconditions) andthe elasticityofquality withrespect to
R&Dexpenditure(technologicalopportunities);withthedegreeofmarketpower(thein-
verseofthepriceelasticity),andwiththeexpectedsubsidy. Thise¤ortwillonlybeobserved
inpracticewhenit surpasses athresholde¤ort
Ejointly determinedby the factorsthat
in‡uencetheaboveelasticities,includingthevalueoftheset-upcosts
5
.
Eissimplythelevel
ofR&De¤ortatwhichthe…rmwouldbeindi¤erenttoperformingR&Dornotintheab-
senceofsubsidies(the…rmwouldobtainthesamepro…t). Hence(expected)subsidieshave
twodi¤erente¤ects. Ontheonehand,theycaninducesome…rmstoperformR&D.Onthe
other,theyenhanceR&Dexpendituresof…rmsthatwouldperforminnovativeactivitiesin
anycase.
Underlying[2], wecanassume thestandardaccount of determinants of innovativeac-
tivities(see, for example, Cohen (1995) or CohenandLevin(1989)). Whenit comes to
specifyingtheequationsandinterpretingthevariablee¤ects,itisimportanttokeepinmind
howweexpecttheseelasticitiestoevolveacrossequilibriums. Letusbrie‡ysummarisethe
5
Givenourassumptions,e¤ortisexpectedtoincreasemonotonicallywiththeR&Dexpenditures.
5
partial e¤ectsexpectedaccordingtothemodel
6
. Market powervariablesareexpectedto
be associatedwith higher e¤orts but probably witha small or null e¤ectonthresholds.
Variablesrepresenting ahighsensitivityofsales to R&Dexpendituremust induce lower
thresholds and higher e¤orts. Variables measuring set-up costs are expected to increase
e¤ort(throughelasticities)andthresholds.
3. Barriers toR&Dandsubsidye¤ects
Inthissectionweshowhowtheparametersofthepreviousmodelcanbeestimatedwith
aTobittypeeconometricmodel,andwepresenttheestimationprocedure. Thenwede…ne
themeasuresofthee¤ectsofsubsidies.
3.1Econometricmodel
Takelogsin[2]andletzstandforthevectorof“reduced-form”variablesthatdetermine
the value of the(log of) elasticities. Wehavethe following semi-structural econometric
relationship
7
e
¤
=¡¯ln(1¡½
e
)+z¯
1
+u
1
[3]
wheree
¤
=lnE
¤
andu
1
isarandomdisturbance.
Accordingtoourtheoreticalframework,e
¤
isacensoredvariable. Hence,toconsistently
estimatetheparameters, we musttakeintoaccount its observabilityrule. Letus specify
thisruleas
6
These e¤ects can be obtained byperformingsome comparative statics exercises. Ausefulparticular
modeltoperformsuchexercisesisobtainedbyassumingq(p;s(x))=q
0
(p)(1+"ln
x
F
)andusingk=F=pq
0
(p)
asameasureofset-upcosts.
7
It can be called d semistructural because e the expected subsidies enter r the e¤ort equation in the way
they appear in the e …rst order condition, but elasticities -or their associated variables: price e or margins,
shares,etc...-areendogeneousvariables oftheunderlyingmodelthat wereplacebyasetof reducedform
determinants(i.e. theotherexplanatoryvariables).
6
e=
8
<
:
e
¤
ife
¤
>
e
0
otherwise
[4]
with
e=z¯
2
+u
2
[5]
whereerepresentsobservede¤ortandtheequationfor
especi…esthethresholdsincluding
arandomdisturbancetermu
2
. Thresholdscanbepresumedtobeafunctionofthesame
variablesthatdetermineelasticities,butthee¤ectsofthesevariableson
egivetheheightof
the“barriers”tothepro…tabilityofR&D.Wewilltake…rmsascompetinginheterogeneous
environmentsandhencehavingidiosyncraticthresholds.
Equations[3], [4]and[5] de…neaTobittypemodel,inwhichoptimal e¤orte
¤
istaken
as apartiallyobservablevariable, only observedwhenitstochasticallysurpassesthe…rm
pro…tabilitythreshold
e
8
.
3.2Estimationprocedure
Estimationofthemodel…rstrequiressolvingtheproblemoftheunobservabilityofthe
expectationvariable½
e
. Infact, onlyex-post grantedsubsidies areobservable. Then,we
willfollowa twostepprocedure, …rst estimatingtheconditional expectationofsubsidies
andthensubstitutingtheestimatedvaluesfortheunobservableexpectations.
Letuswriteanddecomposetheexpectedsubsidyasfollows
½
e
=E(½jy)=P(½>0jy)E(½j½>0;y)
[6]
whereP(½>0jy)standsfortheprobabilityofthegrant, E(½j½>0;y)fortheexpected
valueofthesubsidyconditionalonitsgranting,andyforthevectorofotherconditioning
variables. Todeal withthehighnon-linearity oftheexpectedsubsidies, wewill estimate
thesetwoconditionalexpectationfunctions,using…rmobservablecharacteristicsascompo-
nentsofy,andwewillusethe…ttedvaluestoestimate½
e
. WewillestimateP(½>0jy)by
8
Econometricmodels of censoredvariables with stochasticthresholds datebacktoGronau(1973)and
Nelson(1977).
7
meansofaprobitmodelandwewillemploythebestlinearpredictorE(ln½j½>0;y)=y°
toconstructanestimateofE(½j½>0;y)
9
,
10
.
Subsidiesarepresumablygrantedbyagenciesaccordingtothecontemporarye¤ortand
performanceof …rms, andhence areendogeneous (theirvaluesarelikely tobecorrelated
with the random term u
1
) . The two-step procedure used to obtain ½
e
will also allow
us to consistently estimate the parameters of thee¤ort equationin the presence ofthis
endogeneity. Itsu¢cestoadequatelyselectthevariablesy. Theregressorsusedtoestimate
[6]mustbevalidinstrumentsfor½(thatis,exogeneousorpredeterminedvariables).
Substituting
b
½
e
for½
e
inthee¤ortequation,wewillestimatethewholemodelbymax-
imumlikelihood. Themodel turns outtobe atype2generalizedTobitaccordingtothe
classi…cationinAmeniya(1985), wherealternativeidenti…cationconditionsare discussed
(seealsoMaddala(1983)). Oneoftheseconditionsistheavailabilityofatleastonevariable
thatenterstheequationforthecensoredvariablebutcanbeexcludedontheoreticalgrounds
ofthethresholds equation. This conditionarises naturallyinourmodel, whereexpected
subsidiescanbesafelyexcludedfromthedeterminantsofthresholds
11
. Inpractice,wewill
alsoexcludeothervariablesonstatisticalgrounds. TechnicaldetailsontheMLestimation
procedurearegiveninAppendix1.
3.3Measuringpro…tabilitygapsandsubsidye¤ects
Givenparameter estimatesofthismodel, oneisreadytocomputeindividual threshold
estimatesandtousethemtoassessthee¤ectsofsubsidieswhenthe…rmisconfrontedwith
barrierstoR&D.
Let us …rst de…nepro…tabilitygaps. We de…nepro…tabilitygaps as the di¤erencebe-
9
Wewillassumethatv=E(ln½j½>0;y)¡y°isN(0;¾
2
). ThenE(½j½>0;y)=exp(y°+
1
2
¾
2
).
10
The econometric procedure that we follow in this s case openly di¤ers from the one employed d in the
estimation of thee¤ort equation. This s is because here we aresimply interested in the estimation of the
conditionalexpectationofobservedgrantedsubsidies,andnotintheexpectationofa(theoreticallyde…ned)
latentvariableliketheoptimale¤orte
¤
. Inaddition,“two-part”estimationsofexpressionslike[6]perform
verywellinprediction(see,forexample,LeungandYu(1997)).
11
Thishappensbecausee¤ortthresholdsforpro…tabletechnologicalactivitiesarede…nedintermsofthe
totalexpenditureneeded,independentlyofitscomposition.
8
tween the optimal e¤ort in the absence of subsidy andthethresholde¤ort. Ifnegative,
they give theR&Dexpenditure(interms of%ofsales) bywhichthe…rmfalls short to
undertakepro…tableinnovativeactivities. Ifpositive, theygivetheR&Dexpenditure(in
termsof%ofsales)thatthe…rmwouldmake,intheabsenceofsubsidies,inadditiontothe
minimumpro…tableamount. Noticethatthetwoe¤ortsthatdeterminepro…tabilitygaps
areunobservablebutthatourmodelmeasuresthenon-stochasticcomponentsrespectively
byexp(z
b
¯
1
)andexp(z
b
¯
2
)
12
.
With pro…tability gaps measured, we can evaluate the (actual and potential) roles of
subsidiesintheperformanceofinnovativeactivities. Letus…rstfocusontriggersubsidies.
Wede…nethesesubsidiesasthevalueofthe½
e
’sthatwouldinducenon-performing…rmsto
undertakeinnovativeactivities(by…llingtheirnegativepro…tabilitygaps). Thesesubsidies
canbeestimatedasthevaluesof½
e
thatsolvetheequations¡
b
¯ln(1¡½
e
)+z(
b
¯
1
¡
b
¯
2
)=0
for…rmswithe=0(non-performing…rms)and¡
b
¯ln(1¡
b
½e)+z(
b
¯
1
¡
b
¯
2
)<0(correctly
predicted).
Let us then evaluate the role of a subsidy withdrawal. Some …rms are likely to be
performinginnovativeactivitiesbecausethesupporte¤ectoftheexpectedsubsidy…llsin
thenegativepro…tability gapthatwouldexist initsabsence. Wetakethese…rmsas the
oneswithe>0(performing…rms)andforwhich¡
b
¯ln(1¡b½
e
)+z(
b
¯
1
¡
b
¯
2
)>0(correctly
predicted)butwithz(
b
¯
1
¡
b
¯
2
)<0(negativepro…tabilitygap).
Allthisreferstotheabilityofsubsidiestoinduce…rms(potentiallyore¤ectively)toinvest
inR&D. But, accordingtothemodel, howdosubsidieschangethe expenditure of…rms
that perform innovative activities? Firstly notice that R&Dexpenditures are expanded
inthemodel to incrementsales and, therefore, therateof changeine¤ort constitutes a
lower boundfortherateofincreaseinexpenditure
13
. Secondly, changes ine¤ortdepend
12
Pro…tabilitygaps can becomputed in anumber of ways. Below w weuse the di¤erences between the
non-stochasticcomponentsofthee¤ortandthresholdequations,whichgiveanintuitivemeasureofthegaps
explainedbysystematicfactors.
13
Total R&Dexpenditure may be written as the e product of e¤ort by sales x = Epq. The e change in
expendituremaybeconceptuallydecomposed inthesumof twochanges: thechangeduetosales andthe
changeine¤ort. Anassessmentofthesalese¤ectofsubsidieswouldonlybepossiblewithamorecomplete
9
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