mpact social innovation

economic foundationempowering people

SIMPACTPROJECTREPORTReport#D2.1

SocialInnovationSimulationModelandScenariosMehtapAKGÜÇaandMiroslavBEBLAVÝa

aCEPS

December2016

The SIMPACT project receives funding from the European Union’s Seventh FrameworkProgramme for research, technological development and demonstration under Grant

AgreementNo:613411.

AcknowledgementsWewouldliketothankJudithTerstriep,MariaKleverbeck,StevenDhondtandotherconsortiumpartnersofSIMPACTaswellasstakeholderswhohaveparticipatedinthestakeholderexperimentsfortheirvaluableinputsorcommentsalongthedevelopmentandtestingofthetheoreticalmodelling.SIMPACTSIMPACT is a research project funded under the European Commission’s 7th Framework Programme from 2014-2016andistheacronymfor«BoostingtheImpactofSIinEuropethroughEconomicUnderpinnings».Theprojectcon-sortiumconsistsoftwelveEuropeanresearchinstitutionsandisledbytheInstituteforWorkandTechnologyoftheWestphalianUniversityGelsenkircheninGermany.SuggestedCitationAkgüç, M. and M. Beblavy (2016): Social Innovation Simulation Model and Scenarios. Report D2.1 of the project«Boosting the Impact of SI in Europe through Economic Underpinnings» (SIMPACT), European Commission – 7thFrameworkProgramme,Brussels:EuropeanCommission,DGResearch&Innovation.LegalNoticeTheinformationandviewssetoutinthisreportarethesoleresponsibilityoftheauthor(s)anddonotnecessarilyre-flecttheviewsoftheEuropeanCommission.DocumentProperties

ProjectAcronym SIMPACT

ProjectTitle BoostingtheImpactofSocialInnovationinEuropethroughEconomicUnderpinnings

Coordinator InstituteforWork&TechnologyofWestphalianUniversityGelsenkirchen

DeliverableD2.1 SocialInnovationScenarios

Author(s) MehtapAkgüç,MiroslavBeblavý

DocumentIdentifier FP7-SSH.2013.1.1-1-613411-SIMPACT–D2.1

WorkPackage WP2SocialInnovationBehaviourScenarios

Date 23December2016

DisseminationLevel PU-Public

DisseminationNature R-Report

DocumentStatus Final

SIMPACT–D2.1|i

TableofContents

EXECUTIVESUMMARY 1

1 OBJECTIVESOFTHEREPORT 2

2 BACKGROUNDANDMOTIVATIONFORMODELLINGSOCIALINNOVATION 4

3 BRIEFLITERATUREREVIEW 7

4 THESIMULATIONMODEL 9

4.1 Ourapproach 9

4.2 Modelingredients 10

4.3 Functionalformsandassumptions 14

4.4 Decisionmakinginthemodel 16

4.5 Baselineanalyticalsolutionofthemodel 17

5 IMPLEMENTATIONOFTHETHEORETICALMODEL:SIMULATIONRESULTS 18

6 MODELEXTENSIONSANDSOCIALINNOVATIONSCENARIO BUILDINGBASEDONSIMULATIONRESULTS 25

6.1 ScenarioI:TheRoleofEnablingFactorsforSI 25

6.2 ScenarioII:ConsequencesofUncertaintyintheProcessofSI 27

6.3 ScenarioIII:BureaucraticBarriers,ManagerialBurdenandImplicationsforScalabilityofSI 31

6.4 SummaryofSIscenariosbasedonsimulationmodelextensions 36

7 CONCLUDINGREMARKS 37

REFERENCES 39

ii|SIMPACT–D2.1

ANNEX 41

FiguresFigure1.GoogleTrendsof"SocialInnovation"(April2016) 5Figure2.IntrinsicUtilityofSocialInnovators 12Figure3.IntrinsicUtilityandRiskAversion 19Figure4.UtilityfromOthersUsingSIandSocietalFrictions 19Figure5.LevelofSocialInnovation(baseline) 20Figure6.IncreaseinRiskAversion 21Figure7.SILevelatZeroCostScenario 22Figure8.SILevelatHighCostScenario 22Figure9.SILevelwithLowestEfficiency 23Figure10.SILevelwithModerateEfficiency 23Figure11.SILevelwithHighEfficiency 24Figure12.SILevelwithUncertainty(1) 29

Figure13.SILevelwithUncertainty(2) 30

Figure14.SILevelwithUncertaintyandHigherCosts 30

Figure15.SILevelintheBaselineCase 33Figure16.SILevelwithLowManagerial/BureaucraticBurden 34Figure17.SILevelwithHighManagerial/BureaucraticBurden 35

TablesTable1SIScenariosandSimulationResults 36

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EXECUTIVESUMMARY

Thisreportdescribesthetheoreticalmodelofsocialinnovationtoaimatgettingfurtherinsights about its economic underpinnings. The baseline model provides a set ofpredictionsbysimulatingtheanalyticalsolution.Themodelischoseninaparsimoniousmanner in order to ensure a tractable and analytical solution, which summarises thelevel of social innovation as a function of the model parameters and variables. Thevarious versions of the model with different parameter values can be interpreted asreflecting various national and regional aswell aswelfare state typologies. The socialinnovationmodelpresented in this report is initiallybasedon tools fromneoclassicaleconomics,but italsoextendsthis frameworkby incorporatingbehaviouralaspects inthe decision-making. Specifically, the report moves the baseline modelling approachforwardbyincludingfuture-basedscenariobuilding.Thesesocial innovationscenariosbringthebaselinesimulationmodelclosertothereal-lifecasesandreflectonthefuturepossibleeventstoguidepolicymaking.

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1 OBJECTIVESOFTHEREPORT

Thisreportisthefirstdeliverable(D2.1)ofSIMPACT'sWorkPackage2(WP2)SocialInnovation Behaviour Scenarios corresponding to research activities of the followingtasks(seeSIMPACT,DescriptionofWork,pp.25):

• Task2.1:SimulationModelandReferenceScenariosofSocialInnovation(SI),

• Task2.2:Small-scaleStakeholderExperiments–FromModeltoReality,

• Task2.3:SimulationIterations(threeiterationsatmonths18,27,32),

• Task2.4:SIScenarioBuilding.

Thereportdescribesanddevelopsthetheoreticalmodel toeconomicallyunderpinsocial innovation.Theinitialmodelprovidesasetofbaselineresultsbysimulatingtheanalyticalsolutionofthemodel.Themodelischoseninaparsimoniousmannerinorderto ensure a tractable and analytical solution, which summarises the level of socialinnovationasa functionof themodelparametersandvariables.Thesocial innovationmodelpresented in this report is initiallybasedon tools fromneoclassical economics,butitalsoextendsthisframeworkbyincorporatingbehaviouralaspectsinthedecision-making. Specifically, the report moves the baseline modelling approach forward byincludingfuture-basedscenariobuilding.Socialinnovationscenariosare"understoodasintermsoftheprobabilityofsocialinnovationgivencertainsetsofinteractionsbetweenindividuals inandwiththeirenvironmenttosupportsocial innovationstakeholdersincopingwithuncertainties associatedwith social innovation" (SIMPACT,DescriptionofWork, pp. 25). These social innovation scenarios bring the baseline simulationmodelclosertothereal-lifecases,despitethelimitationsinthetheoreticalframework.Overall,the social innovation scenarios reflect on the future possible events to guidepolicymaking.

Theinitialmodelandscenarioshavebeenthroughthreeiterationsovertheprojectlifespan(2014-2016).Inparticular,duringtheSIMPACTprojectprogressmeetings,eachiterationofthemodellingandsimulationexerciseisregularlyreviewedbyconsortiumpartners,which fed themodelwith the empirical evidence collected by SIMPACT andcontributed to the fine-tuning of the approach. After the internal review process, themodelling approach, simulation results and various scenarios have been regularlypresented to and tested with stakeholders during the small-scale stakeholder

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experiments,which is part of theWP2Task 2.2Small-scaleStakeholderExperiments–FromModeltoRealityandarejointlyorganisedbyTUDOandCEPS.

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2 BACKGROUNDANDMOTIVATIONFORMODELLINGSOCIALINNOVATION

Thesocietiesoftodayhavebeenfacingvariouschallenges,suchasaging,long-termunemployment, migration, gender discrimination, most of which are addressed bypublicpoliciesacrosscountries.However,forvariousreasons,thesechallengesarenotcompletelyovercomeyet.To thisend,new ideasorsolutions,broadlygatheredunderthe roof of social innovation, complementing or accompanying public policies andservices, come more and more to the forefront to address some of these socialchallenges.Despitetheconnotationofthewordinnovation,socialinnovationisactuallyquitedifferentfromastandardmarket-orientedinnovation,wherebytheformerisnotnecessarily profit-driven and is mainly a frugal solution to a social problem in anecosystemwithscarcityoffundsandabundanceofsocietalchallenges.

Bearingtheseaspectsinmind,therearevariouswaysinwhichonecandefinesocialinnovation. In the framework of SIMPACT project, social innovation refers to “novelcombinations of ideas and distinct forms of collaboration that transcend establishedinstitutionalcontextswiththeeffectofempoweringand(re)engagingvulnerablegroupseitherintheprocessoftheinnovationorasaresultofit”(Rehfeldetal.,2015;Terstriepet al., 2015). In a way, the focus is mainly on the social innovations, which targetdisadvantaged individuals that couldbe socially excludedorwhoseuseful skills couldnot have been put in effective use (e.g. labourmarketmismatch and unemployment)becauseofmarketorpublicservicefailure.

Despite the recent surge in social innovation around the world, the concept ofinnovation is not so new. In economic history, the pioneering figure advocating theimportanceofinnovationwasthewell-knowneconomistJosephSchumpeter.Basically,he identified innovationas thecriticaldimensionofeconomicchangeandargued thatthelatterrevolvesaroundinnovation,entrepreneurialactivities,andmarketpower.Hesought toprove that innovation-originatedmarketpowercouldprovidebetter resultsthan the invisible hand and price competition (Pol and Carroll, 2006). In theSchumpeterianapproach,technologicalinnovationoftencreatestemporarymonopolies,allowingabnormalprofits thatwouldsoonbecompetedawayby rivalsand imitators.These temporary monopolies were necessary to provide the incentive for firms todevelopnewproductsandprocesses.Thiswholephenomenonisalsoknownwidelyas“creativedestruction”. It ispossible toadapt someof these conceptsofmarket-driven

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innovation to social innovation, bearing in mind its social objectives (not necessarilyprofitmaximizing),thecontext,andlackofresources.

Evidencesuggeststhattherehasbeenrisingpopularityandinterestsovertheissueofsocialinnovation.OnewaytocheckthistrendistohaveasnapshotanalysisinGoogleTrendsusingthesearch“socialinnovation”.Figure1depictsthisrisingtrendsinsocialinnovationsince theearly2000s.Wesee that the compoundword “social innovation”hasbeenenteredinsearchenginesinanincreasingmannerovertime.Wealsolookattheword“innovation”usingGoogletrends,buttheresultingoutcomeismoreflat(notreportedhere).

Figure1.GoogleTrendsof"SocialInnovation"(April2016)

Another way to see the rising interest and popularity of social innovationphenomenon is givenby aquick semantic analysis.Mulganet al. (2007) report that aGooglesearchoftheword“innovation”inMarch2007threwupabout121millionwebpages, ranging from articles to toolkits, books to consultancies. On the contrary, thesearchfor“socialinnovation”generatedonly840,000pages.Againstthesenumbers,ourrecentsearchanalysisinApril2016involvingaGooglesearchoftheword“innovation”resulted in 392 million web pages while “social innovation” resulted in 32,900,000.Therefore,thereseemstobeabigprogressandrisinginterestonthesocialinnovationin the last decade, but the latter still remains far behind the former even today.Nevertheless,thisexponentialjumpintheimportanceofsocialinnovationinthegeneralinterest shows that this typeof innovation is going tobeon the social agenda for theyearstocome.

As listed by Mulgan (2006), there are thousands of examples of successful socialinnovations that have appeared in recent times, including neighbourhood nurseries,Wikipedia, Open University, holistic health care, microcredit and consumercooperatives, the fair trademovement, communitywind farms,online self-helphealthgroups and so on, to name a few. Although the success of and increasing publicawareness about such initiatives imply a generally rising interests toward social

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innovation, there still seems to be a lack of theoretical approach to systematize,streamline, and understand the onset, process, sustainability, and scalability of socialinnovation. Compared to the vast amount of academic research on technological, for-profit orbusiness-oriented innovations, there isno corresponding supplyof academicresearchonsocialinnovationoratbest,itisonlyatitsinfancy.

Tothisaim,therehasbeenasurgeamongacademicstowardmoresocialinnovationresearch,suchasSIMPACT,amongothers.Eachoftheseendeavoursaimatcontributingand advancing the social innovation research from different angles and using variousbut sometimes overlapping methodologies. SIMPACT’s approach is very specific infocusing on the economic underpinnings of social innovations in order to boost theirimpactsacrossEurope.Theprojectcoversvariousanglesofsocial innovationsrangingfromempiricalevidencecollectionwithcasestudiesandsocialinnovationbiographies,developmentoftoolstounderstandthe“businessmodel”ofsocialinnovationandtoolsto measure and possibly assess the impact of it to more theoretical approaches inconceptualizing, modelling and providing scenario-building based on simulationmethods and policy instruments. The current paper is contributing to the SIMPACTproject from the theoretical economic model building and scenario simulationperspective.

The objective and structure of this paper is to describe the theoretical model ineconomicsinordertogainfurtherinsightsasregardstothefactorsdeterminingsocialinnovation. The model is based on individual preferences and decision making andincorporates elements such as riskpreferences, intrinsic utility, bureaucratic barriers,uncertainty(intheformofshocksonthedemandside),andcostsofundertakingsocialinnovation.Withinacomparativestaticexercise,theanalyticalsolutionofthemodelisthenusedtosimulatevariousscenariosgivendifferentparametervaluesandsuggestspathways,drivers,andbarrierstothesocialinnovationprocessfromatheoreticalpointofview.Thepurposeof thisapproach is tocontribute to informeddecision-makingofpolicymakers,investorsandinnovators.

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3 BRIEFLITERATUREREVIEW

Thekeyindustriesofthe21stcenturysuchashealth,education,childcare,eldercare,whenaddedup,areexpectedtohavealargershareinGDPcomparedtoITinthefuture.Atthesametime,thesearealsothemainareaswheremanysocialchallengesarisesuchas aging, long-term care, unemployment and so on, which then create vulnerabilitieswithin and across societies. Mulgan et al. (2007) states that a contented and stableworld might have little need for innovation and that innovation becomes imperativewhenthingsgetworse,whensystemsdonotworkproperlyorwheninstitutionsreflectpastratherthancurrentproblems.

Mulgan(2006)statesthatmostof thesechallengesarebeingsomewhataddressedby public policies and services, but clearly given the recent global downturn coupledwith othermajor socio-ecological societal transitions, these policies and services alsodependalotonco-production,co-creationbytheuser,patient,learnerandsoon.Whatismore, such challenges couldbealsoaddressedby innovative solutionsendorsedbysocially driven, motivated and creative individuals. In this vein, Mulgan (2006)highlightsthat(social)change,ontheonehand,happensusuallywithbravepeoplewhoare willing to take risks and who have leadership skills to lead and convince otherindividuals in the society. On the other hand, it is also very important that theindividualswhoaretobeimpactedbythesocialchangecouldbepersuadedtoabandonand/ormodifyexistinghabits(Mulgan,2006).

Nevertheless,oneshouldnotethat to leadasocialchangethatcanconvince largergroups in thesociety forachangewould likelybe theoutcomeof theactionsofmanysocial innovators. In that case, the latter would contribute to mainstreaming andinstitutionalising new practices that facilitate social change rather than action ofindividualsocialinnovators.However,SIMPACTfocusesoninstitutionalratherthanonsocialchange.

As is reflected in SIMPACT’s understanding of social innovation, Mulgan (2006)assertsthatnewsocialideasarerarelyinherentlynewperseandthatmostofthetimetheycombineprevious ideasto formcreativecombinations. Inthatsense,exchangeofideascanstimulatefurthercreationofideasthroughexternalitiesandspillovereffects.Inthesocialcontextthatwefocuson,suchinteractionofideasisevenmoreimportant.

Pointing to the scarcity of resources and planetary challenges pushing furtherboundaries of ecological systems, Westley (2013) states that “we need innovativesolutionsthattakeintoaccountthecomplexityoftheproblemsandthenfostersolutions

8|SIMPACT–D2.1

thatpermitoursystemstolearn,adapt,andoccasionallytransformwithoutcollapsing.More important, we need to build the capacity to find such solutions over and overagain.”

The success of social innovation is influenced by the current state of play of itsecosystemandopennessof thesystemtoallowentranceof “new”actors(Terstriepetal.,2015). Inparticular,social innovationsbelongtoacomplexandcontext-dependentspecificecosystemshapedbyalreadyexistinglegal,economic,andsocialstructuresandactors.Therefore,itisnotsurprisingtoobserveresistanceagainstasociallyinnovativesolution.Thisiscloselyrelatedtothenotionofincumbentversusnewcomerclashasinthebusiness-driveninnovation.Accountingforsocialandculturalcomplexity,demandsofdifferentactorsorbyactorsandtheirenvironment,thedilemmaapproachpointstothe necessity to balance, for example, economic and social modes of efficiency orbetweencooperativeandcompetitivemodesofinteraction(Rehfeld&Terstriep,2015).It suggests, that there exists no best solution, but social innovations (or underlyingprocesses)alwaystendtoreconciletwoextremesofacontinuuminaspecificway.

As this brief literature review suggests, there is a growing interest over socialinnovationresearchfromseveralfieldsofstudy.However,tothebestofourknowledge,the theoretical model and simulation approach presented in this report is the firstexerciseofitstypeinthecontextofsocialinnovation.

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4 THESIMULATIONMODEL

4.1 Ourapproach

As mentioned in the previous sections, SIMPACT investigates the economicfoundations of social innovation in relation tomarkets, public sector, and institutionswith the intention of providing a dynamic framework for action at the level ofindividuals, organisations, andnetworks as stated inTerstriep et al. (2015). In lineofthisobjective,wepresentatheoreticalmodelinordertogetfurtherinsightsasregardsthefactorsdeterminingsocialinnovation.

In the context of this paper , a model is a set of assumptions and equationsdescribing, in general, behaviour of an actor (agent) or a set of actors (agents) undergiven circumstances. Given the theoretical approach, the analysis of social innovationviasucheconomicmodelandsimulationscouldbeconsideredasanexanteapproach,i.e.beforesocialinnovationtakesplace.

In the economics profession, researchers build models, which are—to a certainextent—simplified descriptions of reality, in order to enhance their understanding ofhowthingswork(Ouliaris,2012).Obviously,therealworldismuchmorecomplexthanwhatthemodelisabletocapture;therefore,theeconomiststendtoenrichthemodelasmuch as possible with the aim of reflecting the actual pro-cesses, behaviour, andoutcomes inreal life.However, there isaclear trade-offbetweenmodelrealism—thatusually requires complex models while complicating the computation—andparsimony—, which keeps the least number of essential elements in the modelsimplifying the realitywhileeasing theanalytical computations. Inotherwords,whilethere is the drawback of parsimony leading tomodels that have certain assumptionsandmakingthemodelattimesfarawayfromrealityandcomplexityofactualproblems,thereisalsoavalueinthesimplificationoftherealityviamodelling,whichmakesit—atleast, analytically—easier formodellers to find solution(s) to a complex phenomenonsuchasinthecaseofeconomicandsocialchallenges.

Consideringtheseaspects,weadoptaparsimoniousmodelapproach,which isoneof the desirable features in economics and inference analysis (Zellner et al., 2001;Varian, 1997; Varian, 2009). The well-known microeconomist and author of manyundergraduateandgraduatemicroeconomicstextbooks,Varian(2009)remindsthatthewholepointofamodelistogiveasimplifiedrepresentationofreality.Inotherwords,thissuggeststhatthemodelhastheleastnumberofelementsforsimplicity,butitisstill

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able to produce testable hypotheses and eventually capture a reasonable amount ofpattern and behaviour that are happening in the real world. This is the startingapproach of the model presented in the next sub-section. Nevertheless, given thefeedbackalongtheSIMPACTproject’slifespan,ourparsimoniousapproachhasevolvedand enriched in order to better reflect the sophistication andmulti-faceted nature ofsocialinnovations.

4.2 Modelingredients

In this section,we describe all themain elements forming the basis of themodelincluding the agents, their characteristics, preferences and utilities, choices, andconditions.

Actors. For simplicity, we start with three main agents (or actors). The socialinnovatororcreator,whocreatesorcomesupwithaninnovativeidea(eitherbyfindingnew ideas or by creating new combinations using existing ideas); the users orbeneficiaries,whoarepeopleorgroupsofpeople thatare targetedor impacted inonewayoranother fromthesolutionorsocial innovationcreatedby thesocial innovator.Finally, themodel also embeds the connectors(orfacilitators) as another actor in thisframework.Theconnectorsaretheactorswhohelprealisinganideasuchasinstitutionsor(large-scale)entrepreneurs.Thisstartingpointisinlinewiththeideaofamicrolayerof social innovation as suggested by Howaldt et al. (2015). With regard to ourunderstanding of social innovation, distinct forms of collaboration reflect theinteractions between the various actors involving processes of co-creation. Althoughthis frameworkdoesnotexcludesuch interactions, theseparationof theactors in thiswayhelpsdistinguishtheirdistinctiveroleinthesocialinnovationprocessthatwewillsubsequentlysimulate.

A social innovator is a person with certain characteristics or skills such asinnovative,creative,motivated,benevolent,andresilientetc.,buts/hedoesnotneedtohaveall these traits at the same time.Weconsiderher/his jobas to comeupwithaninnovativeideaorbringtogetherexistingideasinaninnovativewayinordertoaddressasocialproblemthatpotentiallyaffectsanumberofpeople.

Withoutlossofgenerality,weassumethattherearexnumberofsocialinnovatorsina society, which takes a value in the interval [0,1]. If we assume that each socialinnovatorislinkedtoadistinctsocialinnovation,thenxalsorepresentsthenumberofsocial innovationsinanecosystem.Onecaninterpretthisvalueasthesupplyofsocialinnovation.

We denote the number of users or people who are the target group of a socialinnovationbyz.Withoutlossofgenerality,wealsonormalizez,thenumberofusers,or

SIMPACT–D2.1|11

alternativelytheshareofthepopulationwhoistargetedormeanttobeimpactedbythesocialinnovation,andassumethatittakesavalueintheinterval[0,1].Onecaninterpretthisvalueasthesizeofthedemand,dependingonthecontextofsocialinnovation.Themodelisgenericenoughtoadaptdifferentinterpretations.

Intrinsic utility. In economics, the neoclassical approach to modelling individualpreferences usually involves only monetary (pecuniary) – also known as extrinsic –utility. However, Benabou and Tirole (2003) and Besley and Ghatak (2005), amongothers, highlight the non-pecuniary part of a utility function driving individualbehaviourviautilitymaximisation.Theintrinsicutilityisawaytodescribepreferencesreflecting non-pecuniary aspects, such as social values. Given the context of socialinnovation, we argue that the intrinsic utility is a relevant and important part of theutilityofthesocialinnovator.

Moreover,theintrinsicutilityisoneoftheelementsthatcantakethemodelbeyondtherepresentativeagentapproach.Forexample,onewaytoincorporateheterogeneityamongagentsusingthistool is torankpeoplebytheir intrinsicutilityasa functionoftheirtypes.Theideabehindtherankingofutilitiesisthatitallowsfindingthresholdstoget the number of social innovators in the equilibrium. Moreover, we augment theintrinsicutilityby riskpreferencesof thesocial innovators, sinceevidenceshows thatrisk attitudes are an important element in any innovation activity (Acemoglu, 2009).Overall,wedenotetheintrinsicutilitybyr(x)wherexreflectsthetypeofanindividualandsreflectsriskpreferences.Thissummarizestheintrinsicvalueofsocialinnovationtothe innovator.Hereweusethedual interpretationofxasthetypeofthe individual(on top of the interpretation as the number of social innovators) over the continuum[0,1].Wecanusethisdualinterpretationmainlybecauseofthepropertyoftheintrinsicutility,whichisadecreasingfunctionofx.

To illustrate the dual interpretation of x and assuming that altruism can beassociatedwithbeingasocialinnovator,imaginethatthecontinuumof[0,1]representsthespectrumofbehaviourofanindividual,where0representsthemostaltruistictypeand 1 represents the least altruist (or selfish) individuals. Imagine that there are xnumberofsocialinnovators,wherexliessomewhereinthesameinterval[0,1].Becausethe intrinsic utility is ranked and is a decreasing function of x, this implies that anyindividualwho lies to the leftofx in the intervalhashigher intrinsicutilityofbeingasocialinnovatorcomparedtoindividualswholietotherightofx.Inotherwords,ifwecanassociatesocialinnovatorsasbeingaltruistpeople,thismeansthatthemostaltruistindividualhasthehighestintrinsicutilityofbeingasocialinnovatorthananindividualwho is less altruist. Assuming a linear functional form,r x = 1 − x,we can see thisillustrationgraphicallyasinFigure2.

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Figure2.IntrinsicUtilityofSocialInnovators

Riskpreferences.Weaugment the intrinsicutility such that it takes into accountriskattitudes.Inparticular,weadopttheconceptofriskaversionascommonlyusedineconomicsandfinancebasedonthebehaviourofhumanswhileexposedtouncertaintyto attempt to reduce that uncertainty. Intuitively, risk aversion is the reluctance of aperson to accept abargainwithanuncertainpayoff rather thananotherbargainwithmore certain, but possibly lower, expected payoff (Gollier, 2001). There are severalmeasures of risk aversion in the literature. In our context, we include a relative riskaversionparameterdenotedbyσ,whichisdefinedbasedontheArrow-Pratt-DeFinettimeasureofrelativeriskaversion(RRA)asfollowsforagivenfunctionr x :

(1) RRA = −x. +,,

+,,

Wherer-andr--denote the first and second derivatives ofr x , respectively, withrespecttoitsargumentx.Wedenotetheaugmentedintrinsicutilityfunctionincludingriskpreferencesbyr x, σ .

Utility fromotherswhobenefit fromor targetedby thesocial innovation. Asthesocialinnovatorsareusuallyindividualswhocareabouttheothersandhencetrytofindinnovativesolutionstoaddressabottleneck,societalchallenge,oramarketfailureinfluencingsuchpeople,itisrelevanttoincludeacomponentinher/hisutilityfunctionthat includes a parts generated by how many others use the social innovation. Weassume that this additional utility component is increasing in the number of peopleimpactedbythesocialinnovation.

0.2

.4.6

.81

r(x,s

igm

a)

0 .2 .4 .6 .8 1x

beta=1 & gamma=.1 & sigma=1& no uncertaintyIntrinsic utility

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However, there could be many reasons influencing how a social innovation cansuccessfully expand or contract its user base. We summarize all such impacts by anefficiency parameterβ, which could be interpreted—depending on the context andecosystem of the social innovation—as social trust, cohesion, ease of adaptation tochange,socialcapitalandsoon.Theideaisthatthisparametercapturesthesmoothnessforthesocialinnovationtotakeitsdesiredeffectsonthetargetgroups.

Taking into account the number of users and the efficiency with which socialinnovation takesplace,wedefineasmooth functionf(z, β)with these twoelementsasthe second component—related to the positive impact that the target group getsthroughthesocialinnovation—oftheutilityofsocialinnovator.

Networkeffects.EasleyandKleinberg(2010)describe thenetworkeffectswithinthe context of adoption of technologies for which interaction and compatibility withothers is important. Accordingly, network effects happen when for some kind ofdecisions,individualsincuranexplicitbenefitwhentheyaligntheirbehaviourwiththebehaviourofothers. Ineconomicsandbusiness,whenanetworkeffect ispresent, thevalueofaproductorserviceisdependentonthenumberofothersusingit.

Inthecontextofsocialinnovation,networkeffects(andexternalities)constituteanimportant aspect to consider. As we think of social innovators with motivation anddesiretohelpothers,wearguethatthisaspectcanbehighlyrelevant.Inthissense,weadoptthenetworkeffectsfromthepointofviewofthesocialinnovator’sutilityasourmicro-levelmodellingapproachrevolvesaroundthedecisionprocessof the individualsocialinnovator.Specifically,wecombinetheprevioustwocomponentsoftheutilityinamultiplicativeformtoreflectnetworkeffects:

(2) r x, σ f z, β

The multiplicative form means that those social innovators who place a greaterintrinsicvalueonsocialinnovation(higherr)getahigherutilityfromanincreaseinthenumber of the people affected by the social innovation (higher f) than those socialinnovators who place a smaller intrinsic value on social innovation (smaller r), ingeneral. With this network externality effect, the utility of the social innovator isaugmentedandthewholedecisionprocesswillbeinfluencedbytheinteractingfactors.

Costs. The last bit of the utility function of the social innovator is the cost. Weassume that it takeseffort, time,andpossiblyothermaterialelementsor resources tocomeup,developandsustainasocial innovation.Anotherway to interpret this in themodelling framework is by considering it as a disutility parameter within the globalutility of the social innovator. Following this approach,we incorporate this resource-constraintaspectbyaddingacostparameterdenotedbyγ.Forsimplicity,wetakethis

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parameter as given and constant that is to bededucted from the overall utility of thesocialinnovator.Regardingthecostdimension,oneextensionoftheanalysiswouldbeto make the cost variable dependent on the number of users and/or other modelparameters.Similarly,theresourceparametercouldalsoextendedtotakeintoaccountthe issue that some social innovations are more resource-intensive than others toimplement,wherebyoneneedstodifferentiatecost functionpersocial innovation.Weletthisvaryingfeatureofthecostparametertobeexploredasfutureresearch.

Globalutilityofthesocialinnovator.Uptonow,wedescribedthemainelementsoftheutilityofthesocialinnovatorandnowwecanwritetheglobalutilityfunction,u,takingallthevariablesandparametersintoaccount:

(3) u x, z, σ, β, c = r x, σ f z, β − γ

4.3 Functionalformsandassumptions

Inordertofindananalyticalsolutiontotheutilitymaximisationproblem,weneedtodefinesomefunctionalformsfortherespectivemodelcomponents.

Reflecting the decreasing nature of the intrinsic utility in x with a risk aversioncharacteristic1,weassumethefollowingsmoothfunctionalformforr:

(4) 𝑟 𝑥, 𝜎 = 1 − 𝑥9:.

Regarding the second component of the utility function, f, reflecting the utilityreceived when others are affected by the social innovation in an efficient way, weassume a smooth function that increases in z, the number of users or beneficiariestargetedbythesocialinnovation:

(5) 𝑓 𝑧, 𝛽 = 1 − exp −𝛽𝑧

Combining the two separate components, the social innovator's global utilityfunctionthatneedstobemaximisedinordertodeterminethelevelofsocialinnovation,x,becomesasfollows:

(6) 𝑢 𝑥, 𝑧; 𝜎, 𝛽, 𝛾 = 𝑟 𝑥, 𝜎 𝑓 𝑧, 𝛽 − 𝛾

𝑢 𝑥, 𝑧; 𝜎, 𝛽, 𝛾 = 1 − 𝑥9: 1 − exp −𝛽𝑧 − 𝛾

1WhentheexactdefinitionoftherelativeriskaversionàlaArrow-Pratt-DeFinettiisappliedtotheintrinsicutilityfunction,theriskaversionparameterisnots,but(s-1)/s.Seeappendixforthecalculationoftheriskaversionparameterandhowitcanstillbesummarizedby𝜎.

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Furthermore, in order to have a workable and analytical solution, the model hasseveralsimplifyingassumptionsasdescribedanddiscussedinthesequel.

In the language of the research focusing on for-profit innovation,we assume thatthereisamonopolisticcompetitionwhenasocialinnovationtakesplace,whichmeansthatattheonsetofthesocialinnovation,theexistingservicesormodelsarenotactive.This is a strong assumption, as theremight be competing social innovations or otherexistingnetworks,organizationalstructurestargetingthevulnerablegroups.However,for thesakeof findingastableandanalytical solution to themodelabove,weassumeaway the incumbency issues. Nevertheless, we acknowledge that in reality, newsolutions toa social challengemightneed to confront theexisting solutionsand therecanevenbeapowerclashbetweenincumbentactorsandnewcomers.Ourmodelcouldembed such frictions through other parameters in the ecosystem through efficiencyparameter,𝛽, for example. In this case, resistance to social innovation from theincumbent actors can be represented by higher values of this parameter creatingfrictionsandeventuallybarrierstosocialinnovationprocess.

Even though we acknowledge the possibility that rationality is not a necessarycharacteristic of a social innovator, we assume that the social innovator has somerationality in her/his choice set such as taking a decision when his utility is non-negative. This allows finding an analytical solution as regards the level of socialinnovation.

Regarding the timing of themodel, we do not insist on a specific timing of socialinnovationprocess,astherecouldbemanypossiblecombinationsofeventsdependingon the context of social innovations. However, it can still be helpful to think of thefollowingchainofactionswhenconceptualisingthetheoreticalmodel:first,weassumethattherehappenstobeasocialproblemandchallengethatneedsattentionandaction.In case of a public intervention, the problem is addressed in someway or another orperhapsnoactionistakenatall.Supposethatsomemotivatedindividualsreacttothisproblem and contemplate an innovative solution to tackle it – at least partially. Thisindividual does not have a prior on whether the solution will work or not—in somesense, there isanuncertainty in the"market".Givenhis/herpreferencesandresourceconstraints,thisindividual(orindividuals)offersasolutionandeventuallyimplementsittothesocialprobleminquestion.Basedonthemodel'snetworkeffectassumption,themoreusersbenefitfromthesolution,thehigherthesatisfactionoftheinnovator(giventhedependenceof theutility functionon the sizeof thepopulation targeted)and it islikely that more innovation will follow suite, but not necessarily from the sameinnovator.

Togetherwith these assumptions, overall, our flexiblemodel allowsmimicking allsortsofcasessuchaswhenthereisasituationwithasocialproblem,butnoserviceis

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provided to address the challenges. The model is also able to cover situations whenthereisasolutionaddressingtheproblem,butthereisagapincoverageofvulnerablepopulation faced with the challenge, such that some individuals or groups are notaddressedsufficientlyorthequalityoftheserviceprovidedinmeetingtheneedsofthetargetgroupisnotveryhigh.Inanyofthesecases,socialinnovationcouldbebeneficialforvulnerablegroupsfacingavarietyofsocietalchallenges.

4.4 Decisionmakinginthemodel

Imposing a minimum rationality on the social innovator, we write the decisionmakingconditionforthesocialinnovatorasfollows:

(7) ∃socialinnovationifu(x, z; σ, β, γ) ≥ 0

Inotherwords, thesocial innovatorwill takeapositivedecision to implement thesolution if the utility is non-negative. To find the number of individuals who willproducesocial innovation(orto findthenumberofsocial innovations),weequatetheglobalutilityfunctiontozeroandsolveforananalyticalexpressionofx.Inotherwords,thethresholdvalueofxisgivenbysolvingu x, z; σ, β, γ = 0.

The model suggests that, in practice, given the model ingredients and functionalformssofarandasindividualsarerankedbyanintrinsicutilityfunction,eachindividual(potential social innovator) decides whether to come up with a social innovation bycheckingtheaboveconditionontheutility,u x, z; σ, β, γ = 0.

Toillustratethemechanismbehindthemodel,imaginethatthereisapopulationof10individualsinasociety.SupposethatthefirstindividualhasautilityleveluOandthatit issothat uO ≥ 0, thenaccordingtothedecisionrule,hewill innovate.SupposethatthesecondindividualhasautilityleveluPandthatitissothatuP ≥ 0,thenaccordingtothe decision rule, he will decide to innovate, too. Notice that because individuals areranked (assuming the same number of users and efficiency), we have that uO > uP.SupposenowthatthethirdpersonhasuR < 0,andthenaccordingtothedecisionrule,hewilldecidetonotinnovate,giventhepreferences.Moreover,wecanstillpredictthebehaviourof theremainingseven individuals in thepopulationsinceasweknowthatindividualsarerankedbytheirtype,thenwealsoknowthatthe4th,5th,…,10thpeoplewillnotinnovateeithersinceinthiscasewehave:

(8) uTUO > uTanduW < 0

fori = 2, … ,10; j = 3, … , 10

Hence applying our model’s decision rule in this hypothetical population, thenumber of social innovators will be 2 over 10 (the threshold value). Our model willdeliverthisnumberofsocialinnovatorsasafunctionofthenumberofusersandothermodelparametersasrepresentedintheglobalutilityfunction.

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4.5 Baselineanalyticalsolutionofthemodel

Regarding the analytical expression of the number of social innovations (orinnovators),wereplacethespecifiedfunctionalformsintheglobalutilityfunctionandsolveforxintermsoftheothermodelvariablesandparametersasfollows:

(9.1) u x, z, σ, β, γ = 0

(9.2) r x, σ f z, β − γ = 0

(9.3) 1 − x9\ 1 − exp −βz − γ = 0

(9.4) 1 − x9\ 1 − exp −βz = γ

(9.5) 1 − x9\ = ]

OU^_` Uab

(9.6) x9\ = 1 − ]

OU^_` Uab

(9.7) x = 1 − ]OU^_` Uab

c.

Thelastexpressionformsthemainequationforthesimulationexerciseasdescribedinthenextsection.

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5 IMPLEMENTATIONOFTHETHEORETICALMODEL:SIMULATIONRESULTS

In the previous section,we described themain elements of the theoreticalmodeland found an analytical solution, which offers the possibility to further analyse themodelbehaviourwhensomeofthemodelelementsaremodified.Thisispartofamoregeneral exerciseknownas comparativestatics,which allows running simulationson arangeofparametervaluesceterisparibus. Inthiscontext,asimulationisaquantitativeresultofthemodeloncethemodelisfedwithinputdata–eitherartificialorbasedonempiricaldata.Usingcomputationaltechniques,onecancomparedifferentsimulationsof the samemodel,which canpotentially reflect different realities and circumstances.Our simulation exercise is conducted using artificial data points and by changing oneparameterata time inorder toobserve thebehaviourof themodelsolution,which isthelevelofsocial innovation.Inthispart,weusedSTATAasthestatisticalsoftwaretoprogramthefunctionalrelationsforsimulation.Wenotethatthegoalofthisexerciseisnot tomatch the actual numbers representing each element in themodel (e.g. costs)from reality, but rather assess hypothetical scenarios as to what would havehappened—intermsofthedirectionofchange—hadaparameterofinterestmovedupordown.Therefore, the sequel shouldbe readbykeeping inmind thepurposeof theexercise.

Figure 3 shows the change in the shape of the intrinsic utility when the riskpreferencesaremodified:astheriskaversionparameterσincreases,theintrinsicutilityshrinks. In otherwords, for a given value of x, the intrinsic value of social innovationdecreases as the risk aversion increases. Another interpretation is that for a givenintrinsic valuer x, σ —imagine you draw a horizontal line cutting through the otherlines—therearemoresocialinnovators(x)whentheriskaversionislower(towardstherightanduntil1-xline).

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Figure3.IntrinsicUtilityandRiskAversion

Regarding theutilityof the social innovatorwhen the target groupsuse the socialinnovation (f z, β ), Figure 4 shows how that utility is dependent on the efficiencyparameter.

Figure4.UtilityfromOthersUsingSIandSocietalFrictions

Figure 5 displays the level of social innovation in this baseline case using therelevant model parameters (for given values, as indicated in the graph title) and afunctionofthenumberofusers(overagrid)inthedeterministiccase(nouncertainty).

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r(x,s

igm

a)

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r_1 r_2r_3 r_4r_5

Intrinsic utility

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f_1 f_2f_3 f_4f_5

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This figure is mainly a representation of the main equation of interest—that is theanalytical solution to the number of social innovation at equilibrium—using artificialvaluesfortheparametersandtherelevantgrid.Thisparticularfigureshowsthatatverylowlevelsofusers(z),nosocialinnovationiscreated.However,aftera“tippingpoint”,thelevelofsocialinnovationincreasesinthenumberofusersofit,butthecurvestartstoflattenforverylargenumbersofusers.

Figure5.LevelofSocialInnovation(baseline)

Suppose that foragivennumberofpotentialusersandcosts—ceterisparibus, theriskpreferencesof thepotential innovatorshavechangedso that theyare likely tobemoreriskaverse.Wecansimulate this changeby increasing the levelof riskaversionparameter in themodel and checkhow the level of social innovation reacts to it. Thefollowingfiguredisplaysthisscenario.

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Figure6.IncreaseinRiskAversion

We observe that a higher level of risk aversion induce a lower level of socialinnovation holding everything else—i.e. number of users, costs, and efficiency—constant.WealsoseethatthemaximumofthecurveislowerthantheinitialcaseasinFigure5andthismaximumisattainedonlyatveryhighvaluesofz(users).

Nowletusdosimulatethelevelofsocialinnovationunderdifferentcostscenarios.Supposewestartwiththeextremecasethattherearenocostsassociatedtocreatingasocial innovationand thenwesuddenly increase thecosts,bykeepingeverythingelsethesame.Figure7and8displaytheconsequenceintermsofthesocialinnovationlevel.

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Figure7.SILevelatZeroCostScenario

Figure8.SILevelatHighCostScenario

Thelastfiguresshowhowthelevelofsocialinnovationdependsontheavailabilityof funds to cover increased costs. In the extreme casewith zero costs, together withgivenparametervalues, the social innovationattains themaximum level veryquickly.On the contrary, the higher the costs of social innovation, the less will be the levelgeneratedforgivennumberofusers,efficiency,andindividualpreferences.

Next,wesimulatethechangesinthelevelofefficiencyinordertoassesstheimpacton the levelof social innovation.Efficiency in thiscontextcouldbeunderstoodasanyfactorthatfacilitatesandeasesthesocialinnovationprocesstoexpandamongthetargetgroup.We start fromanextreme case,where the efficiencyparameter is at its lowestlevel and gradually increase it to observehow the social innovation curve reacts. Thesimulation exercise implies that higher social efficiency—because of social trust,enabling factors in the social innovation ecosystem and so on—the level of socialinnovation and the target groups reached are larger,while all othermodel inputs areheldconstant.TheresultingpatternsaredisplayedinFigures9-11.

0.0

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Figure9.SILevelwithLowestEfficiency

Figure10.SILevelwithModerateEfficiency

-11

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beta=0 & gamma=.2 & sigma=1& no uncertaintyLevel of SI

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Figure11.SILevelwithHighEfficiency

Overall, these simulation exercises allow us to get several interesting conclusionsbased on the baseline model. More importantly, the simulations based on thecomparative statics analysis predicts interesting two-way relations between socialinnovationlevelandmodelelements.Accordingly,ouranalysissuggeststhatforagivennumber of users and taking the impact of a change of an element one at a time, anincreaseintheriskaversion,costs,andinefficiencyiseachassociatedwithlowerlevelsofsocialinnovations,or—usingthedualinterpretationofthemodel—inthenumberofsocialinnovators.Resultsarelargelyrobusttosmoothchangesinfunctionalformsandflexiblewithdifferentparametervalues.

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z)

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6 MODELEXTENSIONSANDSOCIALINNOVATIONSCENARIOBUILDINGBASEDONSIMULATIONRESULTS

Inthissection,wepresentanddiscussseveralextensionstothebaselinesimulationmodel as different possible scenarios in an attempt to better reflect the complexeconomic and social phenomenon of social innovation, its actors, and ecosystems, byaugmenting and extending the parsimonious economic model.2The social innovationscenariospresentedinthesequelshouldbeunderstoodasintermsoftheprobabilityofsocialinnovationgivencertainsetsofinteractionsbetweenindividualsinandwiththeirenvironment to support social innovation stakeholders in coping with uncertaintiesassociatedwithsocial innovation.Thesesocial innovationscenariosbring thebaselinesimulationmodelclosertotherealityandreflectonthefuturepossibleeventstoguidepolicymaking.

6.1 ScenarioI:TheRoleofEnablingFactorsforSI

So far the baselinemodel of the previous section has a broadly defined efficiencyparameter,𝛽.Onecanalsointerpretthisparameterinotherways;forexample,itcouldbe any element that can facilitate the social innovation process. In this scenario, weconsider the trust interpretation.The seminal quote fromGeorg Simmel suggests that“trust is one of the most important synthetic forces within society” (Wolff, 1950).Empiricalevidencealsoshowsthatmostofthesocialinnovationsrelyonrelationshipsbasedonconfidence,trustandsolidaritybetweenactors(Terstriepetal.,2015).Thisisespecially important in the case of social innovation, where the social innovators areconfronted with an evolving target group and a constantly changing environmentcoupledwithscarcityofresources(cf.Terstriepetal.,2015;Rizzoetal,2015).Insuchacomplex setting, strong trust relations between and surrounding the social innovatorandthetargetgroups,orevenamongthetargetedindividualsthemselves,caninfluencethesuccessofthesocial innovationbyservingasasmoothingelementthroughoutthesocialinnovation’sorlifecycle.

2WewouldliketothankallSIMPACTpartnersandparticipantsatthepreviousSIMPACTprogressmeetingsandworkshopsforsuggestingvaluableideasandcomments.However,giventhecomplexityanddifficultyinfindingananalyticalsolutionandhenceconductingsimulations,wewerenotabletoaccommodateallofthem,butwetrytoaddresstheminthisreportandacknowledgesomeofthelimitationsofourapproach.

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Atthesametime,therecouldbeseveraltypesoftrustthatcandifferentlyinfluencethe social innovation process. Two commonly cited trusts notions in this context aresocial trust and political trust. Social trust is an important notion relating howindividuals feel about each other in a society. Prominent political economist FrancisFukuyama asserts that trust and social capital are notmutually exclusive and definesthemasfollows:

“Trust is the expectation that arises within a community of regular, honest, andcooperativebehaviour,basedoncommonlysharednorms,onthepartofothermembersofthatcommunity…Socialcapitalisacapabilitythatarisesfromtheprevalenceoftrustinasocietyor incertainpartsof it. It canbeembodied in the smallestandmostbasic socialgroup,thefamily,aswellasthelargestofallgroups,thenation,andinalltheothergroupsinbetween.Socialcapitaldiffersfromotherformsofhumancapitalinsofarasitisusuallycreatedandtransmittedthroughculturalmechanismslikereligion,tradition,orhistoricalhabit.”(Fukuyama,1996).

Anotherformoftrustthatweconsiderispoliticaltrust,whichisthebeliefthatthepoliticalsystemorsomepartofitwillproducepreferredoutcomesevenifleftuntended(Shi,2001). In that sense,political trust isalsoclosely related tostatecapacity, as thelatter can determine the former through (in)effective government administration ineconomic, social, andpublic affairs. In the context of social innovation, one can see atleast two different ways of interactions between political trust and social innovationdependingonthecontext.Ontheonehand,ifthestateorthepoliticalactorsarefailingtoaddressasocialchallengefacedbyvulnerablegroups(e.g.longtermunemployment),thiscantriggeradecreaseinthepoliticaltrustand,inturn,thesocialinnovatorscanbemorewillingtointerveneviatheirproposedsolutiontohelpaddressthechallenge.Thiswouldimplyanegativeassociationbetweenthepoliticaltrustandsocialinnovation.Ontheotherhand,ifthepoliticalsystemorstateisratherpro-activeandsupportiveinthecontextofsocial innovation—ontopofthealreadyprovidedpublicservices—inawaytoimprovesocialchallenges,thepoliticaltrustwouldbelikelybehigh,butsowillbethelevel of social innovation as such initiativeswould get state support. In this case, wewould rather observe a positive association between the political trust and socialinnovation.

Giventhesetwotypesoftrustsdescribedbrieflyinthisextension,wewouldratheradaptthebroaderconceptofsocialtrustasafacilitatorinthesocialinnovationprocess.This extension does not necessarily imply an analytical modification in terms of ourmodelandequation3,buttheinterpretationofthemodelresultswouldbeenrichedifwe

3 Inanextendedversionof themodel,we incorporated twodifferent trustvariables (social andpolitical)intothemodelequationsandsimulatedthelevelofsocialinnovation.Usingtheassumedfunctionalformsandinverselyrelatingthetwotrustvariablesintherelevantutilitycomponent,wefindthathigherlevelofsocial(political)trustisassociatedwithhigher(lower)levelofsocialinnovation.However,giventhetwo-

SIMPACT–D2.1|27

incorporatethetrust,oreventuallysocialcapital,asanimportantelementinthesocialinnovation process. All in all, these notions such as efficiency, social trust, and socialcapitalendupasbeingpartofenablingfactorsintheecosystemofsocialinnovations.

In several of the stakeholder experiment workshops (organisedwithinWP2), thescenariowithenabling factors in the formof social trustwasdiscussedand tested. Inparticular, highlighting its importance, the stakeholders mutually agreed that socialtrust among individuals is a catalyst for social innovation and is a prerequisite forenhancedsolidarityinsocieties(PelkaandWascher,2015).

6.2 ScenarioII:ConsequencesofUncertaintyintheProcessofSI

The model that is used to generate the simulations has been based on thedeterministiccase,wherebyweassumedawayanykindofuncertaintyorshockinthemodel.However,thismightnotexactlyreflecttherealityofaninnovationandperhapsevenlessthesocialinnovation.

Toillustratethisscenariointhemodel,supposethatthereisuncertaintyrelatedtothesocial innovationonsetorprocess.Onecanalsothinkofthisasuncertaintyonthesuccess chance of the social innovation. In reality, there could be many factorsinfluencing the chance of success of a social innovation. For example, there could beshocksrangingfromforcemajeure,disaster,extremescarcityofresources,exponentialincrease in costs of social innovation to issues like a severe lack of interest, non-complianceortake-upofthesociallyinnovativesolutionbythetargetedgroupalongtheprocesssothatthesocialinnovationdoesnotreachthedesiredoutcomeorevenitcanevenstopexistingatsomepointdue tosuchshocks.Such failurescanhappendespitetheinitialintentionsofthesocialinnovators.

Intermsoftheeconomicmodellingapproachadoptedinthispaperandasregardstotherangeofpossibilitieslistedabove,imaginethatoncetheinnovatorcomesupwitha socially innovative idea, this idea does not generate a high demand on the targetgroup—inotherwords,itdoesnotnecessarilymatchwithacorrespondingdemandforareasonoranother—andhencethesocialinnovationriskstofail.Thismightimplythatonlyafew(ornone)peopleareimpactedbythesocial innovation,andthusinfluencesthepartofthesocialinnovator’sutilitythatisrelatedtothesizeofthebenefitsaccruedtothevulnerabletargetgroups.

Onewaytoincorporatethisriskdimensioninthepreferencesofthesocialinnovatoris to augment the utility function by a random component. The utility of the social

directional relationbetweenpolitical trust and social innovation,wedonotpursue the latterextension,butmainlyadoptthesocialtrustintheextension.Theadditionalresultsusingtwotrustvariablesarenotreportedinthepaper,butareavailableuponrequestfromtheauthors.

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innovator includes the element𝑓(𝑧, 𝛽),which depends on the size of the “demand” bythetargetgroups,sinceourmodelassumesthatthesocialinnovatorenjoystheimpacttotheothers.Inordertoincorporatethisrandomcomponentinthemodel,weincludearandom variable,𝜀, as a multiplicative factor next to the f function. The resultingcalculations of the equilibrium level of social innovation after this addition gives thefollowingequilibriumlevelofsocialinnovation:

(10) 𝑥 = 1 − eOU^_` Ufg .h

i.

Introductionoftherandomelementintheutilityfunctionofthesocialinnovator,asaway to incorporate risks and shocks in the “market”, allows comparing the level ofsocial innovation between deterministic and uncertain scenarios. Moreover, thisextensioncanalsobeuseful incapturinguncertainties inthesocial innovationsuccessacrossdifferent sectors. For example, theuncertaintyor success/failure chanceof thesocialinnovationinthecontextofeducationalservicesmightbeverydifferentfromthatofuncertaintyofrisksinthesocialinnovationscasesinthecontextofhealthsector.

Methodologically, the simulationof a functionwitha randomcomponent couldbedone viaMonte Carlo simulations. Monte Carlo simulationmethod is part of a broadclass of computational algorithms relying on iteratively evaluating a deterministicmodel and repeated random sampling to obtain numerical results. To this end, weassume that the randomvariable𝜀has the followingnormal distributionwithmean𝜃andstandarddeviation𝛿:

(11) 𝜀~𝑁(𝜃, 𝛿P).

WeconducttheMonteCarlosimulationsbyrandomlydrawingvaluesfor𝜀fromitsdistributionandthensimulatethelevelofsocialinnovationforeachrandom𝜀overthegridof z. For simplicity,weassume that𝜃 = 1, 𝛿 = 0.8.From thisdistributionof𝜀,werun 500 replications of themodel, giving us 500 different values of social innovationlevel.Thismeansthatwiththeadditionoftherandomcomponentintheutilityfunction,wegetadistributionofthelevelofsocialinnovation,whichisnolongeradeterministicvalue given z (number of users) and other model parameters. In the simulationspresented below,we calculate and display themean value of the social innovation aswellasthevaluesatthe25thand75thpercentilesofthexdistribution.

To illustrate the volatility in the level of social innovation when a randomcomponentintheutilitymodelisembedded,letusstartwiththedeterministiccaseasinthe baselinemodel for a given set of parameter values. Now imagine that there is anuncertainty(inapositiveornegativedirection)thatinfluencesthesuccessofthesocialinnovationprocessforareasonoranotherandtheutilityoftheinnovatorisnolongercertainandincludesarandomcomponentthathasaprobabilisticdistribution.Wefirst

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startwithasmallenoughstandarddeviationandsimulatethelevelofsocialinnovationoverthenumberofusersforgivenparametervalues.Intheuncertaintycase,wedisplaythelevelofsocialinnovationatthe25thand75thpercentileofitsdistributionoverz.Inaway, the percentile graphs mimic the confidence interval of a randomly distributedvariable.

Figure12showsthelevelofsocialinnovationinthedeterministic(continuousline)anduncertaincasewithdashedlines,wheredashedlinesaboveandbelowrepresentingthe75thand25thpercentiles,respectively.Statistically,thepercentilegraphsarereadasfollows:thegraphofxwillbeatthep-thpercentilelineorbelowwithp%(whereinourcase,pcanbe25or75).Thenextfiguredisplaysthesamegraphafterfurtherincreasingthe volatility parameter. These two figures basically show how the level of socialinnovationshifts—inapositiveornegativeway—whenthereisevenaslightvolatilityin the social innovation process. For example,we observe that for a given number ofusers andmodel parameters andwith high volatility, the level of social innovation ismuch lower in a “bad” scenario, which happens with a (low) probability of 25%,compared to a “better” scenario. In otherwords, the range of possible values for thelevel of social innovation expands largely with the extent of the uncertainty in themodel.

Figure12.SILevelwithUncertainty(1)

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Figure13.SILevelwithUncertainty(2)

Moreover,wecancontinuethecomparativestaticexerciseinthisextendedcaseaswell. For example, Figure 14 displays the level of social innovation in the uncertaintycase as displayed in Figure 13, but nowwhen costs of innovation (or diffusion) alsorises.This lastgraphshowshowchancesof social innovationaredecreasedwithhighvolatilityfacedwithhigherfinancialcostsormoreresource-intensiveinnovations.

Figure14.SILevelwithUncertaintyandHigherCosts

The issue of uncertainty of social innovation has been highlighted in variousdiscussions during the stakeholder experiments as well. As any innovation activity

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involvesrisks in termsofsuccessor failure, thisscenariowasconsideredasanaddedvalue in the simulation model reflecting the unpredictability of social innovationinitiativesincertaincontext.

Beforemovingintothenextsocialinnovationscenario,wenotethatinnoneofthecaseswithuncertainty,wedonotneedtoidentifyspecificallythecauseofthevolatilityor randomness in the social innovation process; therefore, in that sense ourmodel isflexible enough to accommodate various settings. Nevertheless, what this scenarioshows is that innovation can be a risky endeavour, with positive or negative shockshappeningalongtheonsetorprocess,wherebytheseshocksimpacttheoveralllevelofthesocialinnovationaccordingly.

6.3 Scenario III: Bureaucratic Barriers, Managerial Burden andImplicationsforScalabilityofSI

In this extension, we address the issue of scalability of social innovation. Thescalability or diffusion of social innovation is an important element in the theoreticalunderstanding of social innovations as it relates to how various solutions offered bysocialinnovationcouldbetransferredoradaptedtootherplaceswithdifferenttargetedgroups(orsimplyextendingthecoverageoftheinitialtargetedgroup)facingasimilarsocialchallengeorproblem.

Whilethescalabilityisahighlydiscussedissuewhenwethinkofsocialinnovationinthepublicdebate,wealsoacknowledge thata social innovationsometimesstartsasaresponsetoaspecificandlocalchallengeandhencetheproposedapproachisrelevantonlyinthatcontextwithouttheneedtonecessarilyscaleitup.Atthesametime,somesociallyinnovativesolutionsaimingatvulnerablegroupscanbeadaptedtootherlocalcontextsandappliedelsewherewhensimilarsocialchallengesariseinotherplaces.

Bearing these aspects in mind and taking a positive—rather than a normative—approach,wesimulatescenariosofsituations,wherethereisthepossibilitytoscaleupthesocialinnovationandwetrytounderstandwhatfactorshaveanimpactandifyes,how, in this process using our modelling approach. We also note that the contextdependencyofsocialinnovationimpliesthatscalabilitycouldtakemanydifferentformssuch as conditional transferability, “copy-paste” adoption, adaptation and so onreflectinglocal,regional,ornationalcharacteristicsasregardsthesocialproblemtobeaddressedandrelevantvulnerabletargetgroups.

Inthecontextofthetheoreticalmodelofthispaper,weusethenotionofscalabilityasthesituationwherethesolutionofferedbysocialinnovation(orsocialinnovator)canreach out a larger user base or target group. For example, in our model’sconceptualization of scalability, each of the following two cases can be counted as a

32|SIMPACT–D2.1

another social innovation: the same social innovation applied to additional targetgroups, say, in different regions, and a different social innovator addressing the samesocialproblemofthetargetgroupinadifferentway.Sofar, theutilitymodelassumesthatsocialinnovatorsgetutilityfromtheimpactofthesocialinnovationonthetargetedgroups using it. This implies, as shown in the graphs so far, that the level of socialinnovationis increasing–eventhoughitgetsflatatsomepoint–whenthenumberofusersincrease.4Imaginenowthecasewheretheutilityofthesocialinnovatordoesnotmonotonouslyincreaseasmorepeopleusethissociallyinnovativesolution.Onewaytothink of why the utility of a social innovator can be non-increasing even though thenumberofpeoplebenefiting fromher/his social innovation increasesmightbedue tothe issue that at first the innovator enjoys as s/he touches the lives of people via thesocialinnovationaddressingasocialchallenge.Atthisinitialstagewithrelativelysmallnumber of beneficiaries, social innovator can benefit from the direct impact of theinnovation to the others. However, as more and more people become part of thesolution,thesocialinnovatorlosestheimmediatecontactwiththeusers,whichinturncangenerateadisutilityor it canbecomemanagerially socumbersome todealwithalarger-than-initially-expectednumberofusersthattheintrinsicutilityofhavingasocialinnovationtohelpothersinvulnerabilitiesisnotlargeenoughtosatisfytheequilibriumcondition of the social innovator’s threshold utility determining the level of socialinnovation.Thispossibledisutilitytothesocialinnovatorofhavingatoolargenumberof users implies that there would be limits to scaling the social innovation across apopulation.

This issue of non-increasing utility in “demand” also implies a deviation from theclassical innovationmodels, inwhichcase theutilityof the innovator ismainlyprofit-driven, and thus profits normally increase when there is a higher demand for theproduct. In thecontextof social innovation,whichdoesnotnecessarily involveprofit-maximisingobjectives,thisneednotbethecase.Inthatsense,thisextensionishelpfulin illustrating the different nature in scalability or diffusion of social innovationcompared to market-driven innovation. Given that different utility function—hencedifferentpreferences—ofthetwotypesofinnovatorsandtheirlikelyself-selectionintodifferent kinds of innovation (social innovation versus profit/market-orientedinnovation),thesizeofthe“demand”doesnotnecessarilyincreasethe“production”ofsocialinnovation,asitwouldbeinamarket-orientedinnovation.

Intermsofthemodelequations,onewaytoincorporatethisextensionistoredefinetheintrinsicutilityfunction𝑟 𝑥, 𝜎 ofthesocialinnovatorandmakeitdependentontwomore elements: z, size of the target group benefiting from social innovation, and𝜇, aparameterthatmeasuresthedegreeof(managerial)bureaucracyinthemanagementof

4 Thisisanaturalresultasthexfunctionisconcaveinz.

SIMPACT–D2.1|33

socialinnovationdirectlyrelatedtothesizeoftheusers.5Wemodifytheinitialintrinsicutilityfunctionasfollows(wedenotethenewonewithr’):

(12) 𝑟-(𝑥, 𝑧; 𝜎, 𝜇) = p(q,i)gr

With this functional form,we posit that the intrinsic utility function is decreasingvis-à-visz(thesizeoftheusersofsocialinnovation)forgiven𝜇 ∈ 0,1 .

Until now, the baseline model assumes that𝜇 = 0, i.e. there is no additionalbureaucraticormanagerialburdentogetherwiththesizeofthetargetgroupnegativelyaffectingtheintrinsicutilityofthesocialinnovator.However,oncethisisthecase(𝜇 >0), then the threshold utility of the social innovator determining the level of socialinnovationwillbemodified,henceaffectingtheonsetofsocialinnovation.

Weillustratethisextensiononthelimitstoscalabilityofsocialinnovationwithourmodel simulations and using similar parameter values as previously taken in thefollowing graphs. Figure 15 starts with the baseline case (including the volatilityextension)withouttheadditionofthebureaucracyparameter—i.e.weassumethat𝜇 =0.

Figure15.SILevelintheBaselineCase

Nowimaginethat it isnolongerthecasethatthe largerthenumberof individualsthat can be addressed by the social innovation, the higher the intrinsic utility theinnovatorcanget,mainlybecausealargenumberofpotentialbeneficiariesofthesocial5 Weassumethat𝜇 ∈ [0,1].

0.2

.4.6

.8x(

z)

0 .2 .4 .6 .8 1z

x P25_x_epsP75_x_eps

(beta=3 &gamma=.1 &sigma=4 &sd=.8 &mu=0)Level of SI

34|SIMPACT–D2.1

innovation also requires a more complex management, involve possible bureaucraticbarriers,orotherkindsofbottlenecksintermsoftheprovisionofthesociallyorientedsolutionaimedat these individuals. In termsofourmodel,wecansummarizeallsuchbarriers with a positive value of the𝜇parameter. Using this approach, the followingFigure16displays there-simulatedbaselinemodelafter incorporating themanagerialburdenorbureaucracyparameter,startingwitharelativelylowvalue.

Figure16.SILevelwithLowManagerial/BureaucraticBurden

Weobserve thatat a relatively low levelof thebureaucracyparameter, themodelalmostdoesnotchangeintermsofthepredictedlevelofsocialinnovation.Thiscanberelatedtothemotivationandperseveranceofthesocialinnovatordealingwithmultiplecomplexities, as it is generally the case, such as lack of funds, uncertainty of theinnovationprocess, andbureaucratic barriers to expansion.However,when the latterissuebecomesmoreconsiderableinmagnitudesuchthatthethresholdlevelofutilityisimpactedmorestrongly,thenwemightobserveahaltofprovisionofthesocialserviceprovidedatlargernumberofuserbase.ThefollowingFigure17describesthisscenario,where the managerial or bureaucratic burdens to accommodate the needs of a largetargetgroupismuchhigher.Thesimulationofthelevelofsocialinnovationinthiscasesuggests that these factors canactually serve asbarriers to scaleup social innovationandcanprohibit the lattertoexpandfurthertoaccommodatemorevulnerablegroupsafterathresholdvalueofthesizeoftheusers.

In further simulations that we conducted (not reported here, but available uponrequestfromtheauthors)wherethemanagerialburdenparameterisfurtherincreased,theresultingoutcomeisthatthelevelofsocialinnovationstopsatanearlierpointoverthegridofthenumberofusers.Thismeansthatwhenthelevelofsuchburdenisveryhigh,therearecorrespondinglylessnumberofsocialinnovationhappening.

0.2

.4.6

.8x(

z)

0 .2 .4 .6 .8 1z

x P25_x_epsP75_x_eps

(beta=3 &gamma=.1 &sigma=4 &sd=.8 &mu=.1)Level of SI

SIMPACT–D2.1|35

Figure17.SILevelwithHighManagerial/BureaucraticBurden

Overall, with this extension we illustrated the scalability or diffusion of socialinnovationprocessandhowthemodelcanbeaugmentedtoincorporatesuchissues.Wedidthisbyaddingamanagerialorbureaucraticburdenparameter,whichplaysaroleindeterminingwhetherthesocialinnovationcanbescaledup.Inparticular,eachpotentialinnovatorenjoyscreatingasocialinnovation,astherearemoreuserstobenefitfromituptoapoint;however,thelevelofsocialinnovationcancometoahaltifthedisutilityofdealingwithtoomanypeopleoutweighsthebenefitsfromhelpingthem.Inreality,suchsituationsmight arisewhen new innovatorsmight decide not to pursue (or adapt analready existing one to a new target group) a socially innovative idea due to suchbureaucratic burdens coupled with scarcity of resources—including managerialresources. Mulgan (2006) also asserts that organizational capacity to grow togetherwith a propitious environment is two necessary conditions to scale up socialinnovations.

A related important issue raised by the participants in SIMPACT’s stakeholderworkshops is related to theknowledgeaspectofsocial innovation. Inparticular, therewasanagreementthatsocial innovatorsarenotonlyexpectedtobestrongexpertsofsocialproblemsandcommittedtoasocialproblems,butatthesametime,theyshouldalsobeexpertsofmanagerialaspectsandknowtheindustryandsectorspecificitiesfortheir social innovation (Pelka and Markmann, 2015). The importance of managerialknowledge or capacity for the sustainability and scalability of social innovations is inlinewiththecurrentscenarioextensionofthetheoreticalmodelpresentedinthissub-section.

0.2

.4.6

.8x(

z)

0 .2 .4 .6 .8 1z

x P25_x_epsP75_x_eps

(beta=3 &gamma=.1 &sigma=4 &sd=.8 &mu=.25)Level of SI

36|SIMPACT–D2.1

Nevertheless, once the fundamental question of whether scalability of socialinnovationmakes sense in the first place is dealtwith (extensivemargin), the second-level issue on the barriers to scalability could be somewhat overcome (intensivemargin).Thisdependsonthesocialinnovationcontext,giventhepaceoftechnologicaladvanceand increasingusageof ICT, internetandweb-basedplatforms,eachofwhichcanhelpscale-upsocialinnovationsatrelativelylowcoststhesedays.Nevertheless,wenotethatsuchtoolsmaynotberelevantforallsocialinnovationcontexts.

6.4 Summary of SI scenarios based on simulation modelextensions

Wesummarize theextendedversionof thebaselinesimulationmodel in the followingscenarios:

SIScenarios Implicationsforsocialinnovation

Enablingfactorsandecosystem(e.g.efficiency,trust–socialand/political)

Byincreasingsolidarityandefficiencyinsociety,enablingfactorssuchassocialtrustworksasacatalystforsocialinnovation

UncertaintyintheprocessorsuccessofSI

Uncertaintyandvolatilityaremostlypresentinsocialinnovationinitiativesleadingthesociallyinnovativesolutiontowardsvarioustrajectoriesdependingontheextentandtypeoftherisksfacedalongthesocialinnovationprocess

Bureaucraticbarriers;managerialburden

Thebureaucraticandmanagerialbarrierscouldpreventsocialinnovationsfromextendingtolargertargetgroups

Table1SIScenariosandSimulationResults

SIMPACT–D2.1|37

7 CONCLUDINGREMARKS

This report presented a theoretical approach to economically underpin socialinnovation.The theoreticaleconomicmodeldeveloped in thiscontext isanattempt tounderstand what we can learn from a modelling perspective to understand theprocesses that leads to social innovation initiatives. Themodel incorporates elementslike individual preferences (risk preferences, caring for others etc.), intrinsic values,network effects, resource constraints, institutional efficiencies, uncertainty andbureaucratic issues within the context of social innovation targeting disadvantagedindividuals facingsocial challengesandothervulnerabilities inorder to comeupwithsolutionsthatcanempowerthem.

Themodelisbuiltinawaythatthemainequationofinterestsummarizesthelevelof social innovation as a function of all the other model parameters and variables.Accordingly,someofthemodelpredictionssuggestthatthelevelofsocialinnovationispositively associated with the risk-lovingness of the innovator, efficiency or otherfacilitating factors such as social trust. The social innovation simulationmodel is fedwith feedback from empirical findings from SIMPACT as well as from stakeholderexperimentsbyconductingarealitycheckof theresultsenables toelaboratedifferentbehaviourscenarios.

In particular, the report presents various possible scenarios of the extendedsimulationmodel covering issues such as enabling factors in the form of social trust,uncertainty in the process of social innovation and the existence of bureaucratic andmanagerialbarrierstoscalingupsocial innovation. Inparticular, thescenariospredictthat the levelof social innovation isnegativelyassociatedwithcostsof innovation (orresourcescarcity)andmanagerialburdenorbureaucraticbarriersfacedwhentherearetoomanyuserstargetedbythesocialinnovation,whichcouldalsobeinterpretedastheissue of capacity constraint of the social innovation in addressing the totality of thetarget group. As confirmed with the stakeholder feedback, these scenarios bring thetheoreticalandsimulationmodelofSIMPACTclosertothereality.

Thevalueaddedofa theoreticalmodellingandsimulationapproachmainlycomesfrom its complementarynature to othermethods (such as sociological approach, casestudyanalysis,andsoon), its flexibilitytoadapttodifferentscenarios,simplicityforatractablesolutionandavailability forempiricalvalidation. Italsogivesanexante ideaon what kind of situations could be expected when certain model parameters aremodified. The output of such an approach, when communicated in a non-technicalmanner to ensure to pass the main ideas, can inform in advance the relevant actors

38|SIMPACT–D2.1

involved in social innovation process. Moreover, this can also help generate publicawarenessaboutthesocialinnovation.

Withthisattempt,weareawarethatmoreresearchneedstobedoneinordertogetfurtherinsightstowards“theorizing”socialinnovationprocess.Inthatsense,economictheoryandsimulationsprovideaninterestingsetoftoolbox,wherebyonecangetusefulinformationandassesshypotheticalscenariostoinformdecisionsandpolicymaking.

SIMPACT–D2.1|39

REFERENCES

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Moghadam, S. andA. Kaderabkova (2015b). Social Innovation inNewMember States:PartII–SurveyofExpertPanel.SIMPACTWorkingPaper,2015(2).Gelsenkirchen:InstituteforWorkandTechnology.

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SIMPACT–D2.1|41

ANNEX

Calculationoftheactualrelativeriskaversionparameteranditsrelationwith𝝈

Whendescribing the riskpreferencesof the social innovator,we simplyused𝜎as theparameter summarising the risk attitudes. However, given the functional form of theintrinsicutilityfunctionandthedefinitionoftheriskaversionbasedonArrow-Pratt-DeFinetti,thetruerelativeriskaversionparameterisnot𝜎,butiUO

iwhichiscalculatedas

follows:

𝑟- 𝑥, 𝜎 = −1𝜎𝑥

9w::

𝑟-- 𝑥, 𝜎 = −1 − 𝜎𝜎P

𝑥9wx::

𝑅𝑅𝐴 = −𝑥𝑟--

𝑟-= −𝑥

− OUiix

𝑥9wx::

− Oi𝑥

9w::

𝑅𝑅𝐴 = −𝑥1 − 𝜎𝜎

𝑥UO

𝑅𝑅𝐴 =𝜎 − 1𝜎

.

However,becauseiUOiisanincreasingfunctionof𝜎(i.e.

{:w9:{i

> 0),theinterpretationof

relativeriskaversion,iUOi,isthesameastheinterpretationoftheparameter𝜎.

sfs

socialinnovation

C EP S

WestphalianUniversity

Institute for Work & Technology