Growth or Profitability First?: The Case of Small and ... · PDF fileGrowth or Profitability First? ... , the independent and control variables are integrated and allow ... The Case

Growth or Profitability First? The Case of Small and Medium-Sized Enterprises in Canada

October 2014

Small Business Branch Research and Analysis DirectoratePatrice Rivard, PhD

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Growth or Profitability First? The Case of Small and Medium-Sized Enterprises in Canada—October 2014

Contents

Abstract .............................................................................................................................. 21. Introduction ................................................................................................................ 32. DefinitionsandMeasures .......................................................................................... 43. DataandMethodology ............................................................................................. 5

3.1 Data .................................................................................................................... 53.2 Methodology ...................................................................................................... 5

3.2.1 Classification .............................................................................................. 63.2.2 TransitionmatricesandMarkovchains ...................................................... 73.2.3 Orderedandunordereddynamicprobitmodelswithrandomeffects forpaneldata .............................................................................................. 8

3.2.4 Modelvariables .......................................................................................... 94. Results ....................................................................................................................... 12

4.1 Transitionmatricesoffirmsfrom2006to2011 ............................................... 124.2 Estimationofmodels ....................................................................................... 134.3 Otherresults ..................................................................................................... 16

5. Conclusions ............................................................................................................... 17Bibliography .................................................................................................................... 19Appendices ....................................................................................................................... 22A EmpiricalResearchontheRelationshipbetweenGrowthandProfitability ..... 22B EconometricModels ................................................................................................ 23C HypothesisTesting ................................................................................................... 29D EmpiricalResearchonDeterminantsofGrowth .................................................. 30E ResultsofOtherMeasuresUsed ............................................................................. 31


AbstractBasedonasampleofsmallandmedium-sizedenterprisesinCanada,weexaminetherelationshipbetweenafirm’sgrowthandprofitabilityfortheperiodfrom2006to2011.Usingadynamicprobitmodelwithrandomeffects,weshowthatafirmwithahighlevelofprofitabilityandalowlevelofgrowthhasagreaterchanceofsubsequentlyachievinghighgrowthandhighprofitabilitythanafirmwithahighlevelofgrowthandalowlevelofprofitability.Inaddition,thisstudyshowsthathumancapitalisadeterminingfactorasitplaysapositiveroleinafirmachievingsuperiorperformanceinbothgrowthandprofitability.Afirm’sdebtisalsoasignificantfactorthatcanslowprogress.Finally,theresultsofmodelestimationsshowthatafirm’sagehasnoeffectontheevolutionofitssituationintermsofgrowthandprofitability.

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1. IntroductionGrowthisatopicthatisincreasinglythefocusofgovernmentconcern.However,theprerequisitesforsustainablegrowtharestillpoorlyunderstood,andparticularlytherelationshipbetweengrowthandprofitability.Governmentsoftenconcentrateonfinancingorbarrierstoentry,butthereisrecognitionthatafirm’sgrowthstrategiesarejustasimportant.Giventheconclusionsofourresearch,creatingtheconditionsforprofitabilityappearsessentialtosustainablegrowth.

AccordingtotheempiricalfindingsofCoad(2007),thereislittleresearchontherelationshipbetweengrowthandprofitability.Thisrelationshipisrathercomplexandresearchersdisagreeonitsnature.Infact,certainstudiesshowthatthetwoareunrelated,whileothersshowanegativeorpositiverelationship.1Forexample,Penrose(2009)suggeststhattherelationshipbetweengrowthandprofitabilitymaybenegative.Thisassertionreferstothefactthatagrowingfirmmayreachapointwhereitbecomesineffective,subjectedtoeverhigheradministrativecoststhateatawayprofits.

Morerecently,Davidssonetal.(2009)studiedthenatureoftherelationshipbetweengrowthandprofitabilitybyestablishinghowfirmsfitintocategoriesbasedonthesetwovariablesandbyexaminingthetransitionoffirmsfromonecategorytoanotherovertime.Thismethod,calledtransitional analysis,shednewlightonthesubject.Theauthorsestablishedthathighlyprofitablefirmswithlowgrowtharemostlikelytoachievebothhighgrowthandhighprofitability,thecategoryofthemostsuccessfulfirms.Inaddition,thesefirmsarealsolesslikelytobecomelessprofitableandtoseetheirgrowthdecline,thecategoryoftheleastsuccessfulfirms.Brännbacketal.(2009),buildingontheworkofDavidssonetal.(2009),arrivedessentiallyatthesameresults.Theyconcluded,inparticular,thatpriorgrowthisapoorparameterfordeterminingafirm’sfutureperformance.TheresultsandconclusionsofDavidssonetal.(2009)arealsosupportedbytheworkofJang(2011).TheworkofDavidssonetal.(2009)isessentiallylimitedtoadescriptivestudyofafirm’stransitioneveryyear,andtheiranalysisdoesnotexplicitlyidentifyotherpotentialcauseswithasignificantinfluenceonafirm’ssituation.2

Thegeneralpurposeofthisstudy,therefore,istoimproveourempiricalunderstandingoftheapplicabletransitionsinexistingrelationshipsbetweengrowthandprofitabilityforsmallandmedium-sizedenterprises(SMEs)inCanada.Todoso,weproposeatwofoldprocess.

1) WeusethetransitionalanalysismethodologyofDavidssonetal.(2009)tocompareourrespectivedatabanks.

1.SeeTable10inAppendixA,whichprovidesanoverviewofresearchontherelationshipbetweengrowthandprofitability.2.Theauthorsdeclarethattheyonlyconductedadditionalanalysesusingamultiplelogisticmodelandconcludethatthemodel’s(unspecified)controlvariablesarenotsignificant.However,theirconclusionsaresupportedbytheirmodel.


2) Wetaketheanalysisfurtherbyusingadynamicprobitmodelwithrandomeffects.Inthiseconometricmodel,theindependentandcontrolvariablesareintegratedandallowustodeterminetheirinfluenceonafirm’sprobabilityofbeinginonecategoryoranother.

Useofthelattermodelalsoallowsforcalculatingafirm’sprobabilityofbeinginthemostsuccessfulorleastsuccessfulcategorybasedonitsprevioussituation.ThisisaninterestingaspectthatisnotaddressedintheworkofDavidssonetal.(2009).

Webeginthisstudybydefiningthetermsgrowthandprofitability.Wethenpresentthemeasuresthatarecommonlyusedtodeterminegrowthandprofitabilityandthatserveasindicatorsoftherelationshipbetweenthesetwovariables.Next,wedescribethedataunderlyingthiswork,aswellasthemethodologyweuse,whichisbasedonthatofDavidssonetal.(2009).WeexplaintheprimaryresultsandtheirconsequencesforCanadianSMEs.Finally,weconcludethisworkwithadiscussiononfutureresearchthatmightbeundertakenintheareaofgrowthandprofitability.

2. Definitions and MeasuresIntheclassicworkbyPenrose(2009),The Theory of the Growth of the Firm,twomeaningsaregenerallyattributedtothetermgrowth.3Ontheonehand,growthisanincreaseinquantity,whichcanbeapplied,forexample,inreferencetogrowthinsalesorexports.Ontheotherhand,asecondconnotationreferstoanincreaseinsizeorinqualityandisseenastheresultofadevelopmentprocesssimilartoabiologicalprocess,whereaseriesofinternalchangesleadstoanincreaseinthesizeandtoachangeinthecharacteristicsofthegrowingobject.Forourownwork,weconsiderthefirstdefinitionofgrowth.Thetermprofitability relatestoafirm’sabilitytogenerateprofits.

Growthofabusinesscanbemeasuredinvariousways.Threemeasuresarecommonlyused:total sales,number of employeesandtotal assets.Studiesongrowthuseoneoranotherofthesemeasures.Thesemaybecorrelated,butareconceptuallydifferent.Thatiswhyitissometimesdifficulttocomparethemandtodeterminewhichisthemostappropriate.However,Weinzimmeretal.(1998)presentalternativesformeasuringgrowth,aswellasafewsuggestionstohelpresearcherschoosethemostsuitablemeasurebasedonthedataused.Intheirview,salesgrowthisanappropriatemeasureinmanysituations.4

Anumberofindicatorscanalsobeusedtomeasureprofitability.Theprofitmarginratioorthereturnoncapitalratio(Lafrance,2012)isgenerallyusedforthispurpose.Thefirstcorrespondstotheratiobetween

3.SeealsoDavidssonetal.(2007).4.Anheuristicargumentwouldbetosaythatsalesgrowthoftenprecedesotherindicators:anincreaseinsalesfrequentlyrequiresmoreassetsandmoreemployees.Morerecently,ShepherdandWiklund(2009)delveddeeplyintotherelationshipsbetweenthevariousmeasurescited.Inparticular,theyshowempiricallycaseswherethemeasuresareequivalent.Itisalsoagoodreferenceforresearcherswhowishtouseanappropriatemeasureforgrowthinaspecificcontext.

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5


profitsandtotaloperatingrevenues(grosssalesorgrossrevenues),whereasthesecondiscalculatedasbeingtheprofitsontotalcapitalortotalassets.Inthiscase,werefertoreturn on assets or return on investment.5Forthepurposesofthisstudy,wehavechosentheprofitmarginratio.

3. Data and MethodologyInthissection,wepresentrelevantinformationonthedatausedinthisstudyaswellasonthemethodology.

3.1 Data

ThedatausedforthisworkaresourcedfromStatisticsCanada’s2007Survey on Financing of Small and Medium Enterprises.6Theinitialsampleexaminedconsistsof15,808firms.Inthepresentstudy,SMEsaredefinedashavingfrom1to499employees.7Moreover,financialinformationonparticipatingSMEs,providedbytheCanadaRevenueAgency(CRA),wasmatchedwiththeStatisticsCanadadataforeveryyearfrom2002to2011.

Thisinformationhastheadvantageofbeinghighlyreliableandaccurategivenitsofficialnature.Assuch,wecreatedalongitudinaldataset(paneldata)basedondatafromStatisticsCanada’ssurveyandfromtheCRA.Inaddition,thesampleisbalanced,thatis,allofthedataforeachfirmareknownforeveryvariableandforeachyear.Whenthisisnotthecase,thesampleissaidtobeunbalanced.8

Tooptimizethenumberoffirmsinoursample,welimitedourstudytotheyears2006to2011ascertainfinancialinformationwasmissingforseveralfirmsbetween2002and2005.Theresultsofthisstudy,therefore,mustbeinterpretedbasedonthissample.Finally,weprocessedthedatatoeliminateextremevaluesaswellasobservationswheretotalsales,totalassetsorthenumberofemployeeswerenil.

3.2 Methodology

Thisstudyinvolvestwosteps.

1) ThefirststepconsistsofclassifyingtheSMEsintofivecategoriesbasedoncharacteristicsrelatedtogrowthandprofitability.Then,astudyontheSMEs’transitionovertheyearswillbeconductedtodeterminetheproportionoffirmschangingfromonecategorytoanother.

5.NotethatSchmalensee(1989)(Table1,p.340)uses12differentindicatorsforprofitability.Profitscanalsobecalculatedbeforeoraftertaxinallcases.AccordingtoHallandWeiss(1967),itisbettertocalculateprofitsaftertaxastaxesvarywidelyacrossindustrysectors.ThesameargumentcanbemadewhenconsideringCanadianprovincesandterritoriesindividuallyaseachhasitsowntaxationsystem.

6.StatisticsCanadachose35,055SMEsfromtheBusinessRegister.Ofthese,18,532werecontactedand15,808agreedtofilloutthequestionnaire.

7.InStatisticsCanada’ssurvey,SMEsaredefinedasbusinesseswithfewerthan500full-timeemployeesandgrossrevenueoflessthan$50million.

8.Astheresultsofunbalancedsamplesaresimilartothoseofbalancedsamples,theyarenotpresentedinthisstudy.


2) Forthesecondstep,weusetheunorderedandordereddynamicprobitmodelswithrandomeffectsforpaneldatatoestimateafirm’sprobabilityofbeinginacategorybasedoncertaincontrolvariables.Wecomparethevariousresultsinthiscaseanddeterminewhethergivinganordertothevariouspotentialsituationsforthefirmseveryyearhasanotableeffectonafirm’sprobabilityofbeinginonecategoryoranother.

3.2.1 Classification

Asthegeneralpurposeofthisstudyistoshedlightontherelationshipbetweengrowthandprofitabilityforsmallandmedium-sizedenterprisesinCanada,wefirstpresentthevariousmeasuresofgrowthandprofitabilityusedinourwork.

Forthepurposesofthisstudy,threegrowthindicatorsareconsidered:totalsales,numberofemployeesandtotalassets.Weusethesemeasurestotestwhetherornotsimilarresultsareobtained.IfC,oneofthesethreemeasures,isconsidered,growthisdeterminedbythefollowingequation:

×100

Aswemustcalculaterelativegrowthrates,thefirstyearcannotbeconsideredintheanalysis.Asweareusingonlyobservationsfrom2006to2011,however,wecanuse2006tocalculateafirm’srateofgrowth.

Tomeasureprofitability,weusethereturnonassetsofDavidssonetal.(2009),whichisdefinedasfollows:

Netincomeaftertax Total assets

Usingthedefinitionsofgrowthandprofitability,SMEscanbebrokendownintofivecategories:

1) Mediocre:lowprofitabilityandlowgrowth(belowthemedianforbothvariablesandinthelowestquartileforatleastoneofthetwo);

2) Average:averageperformance(inthesecondorthirdquartileforprofitabilityandgrowth);

3) Growth:lowprofitabilityandhighgrowth(belowthemedianforprofitabilityandaboveforgrowth,butwithoutqualifyingfortheAveragecategory);

4) Profit:highprofitabilityandlowgrowth(abovethemedianforprofitabilityandbelowforgrowth,butwithoutqualifyingfortheAveragecategory);and

5) Star:highprofitabilityandhighgrowth(abovethemedianforbothvariablesandinthehighestquartileforatleastoneofthetwo).

Table1showsthisclassificationindetail,where(a,b)representsthequartileforprofitability(a)andgrowth(b).

Ct‒Ct−1

Ct−1

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Table1:ClassificationofSMEsbasedongrowthandprofitability

ThespecificobjectivesofthisstudyaretodeterminethecategoryinwhichaCanadianSMEmustbeattimet−1tobeintheStarcategoryontheonehandandtheMediocrecategoryontheotherhandattimet. The Starcategoryrepresentsthemostsuccessfulfirmsintermsofprofitabilityandgrowth,whereasthe Mediocrecategoryrepresentstheleastsuccessfulfirms.Itisclearthatourattentionmustfocusonthesetwocategoriesoffirms.BasedontheresultsofDavidssonetal.(2009),wealsoassertthetwofollowinghypotheses:

H1:Firmswithhighprofitabilityandlowgrowth(thoseintheProfitcategory)attimet−1aremorelikelytoachievehighgrowthandhighprofitability(i.e.,tobepartoftheStarcategory)attimetthanfirmswithhighgrowthandlowprofitability(thoseintheGrowthcategory).

H2:Firmswithhighgrowthandlowprofitability(thoseintheGrowthcategory)attimet−1aremorelikelytoexperiencelowgrowthandlowprofitability(i.e.,tobepartoftheMediocrecategory)attimet thanfirmswithhighprofitabilityandlowgrowth(thoseintheProfitcategory).

3.2.2 Transition matrices and Markov chains

Thefirstmethodweemploytoverifythevalidityofourtwohypotheses(H1andH2)istoconsiderthesituationofthebusinesseseveryyearandtotracktheirevolutionusingthemethodologyofDavidssonetal.(2009).Asmentionedearlier,SMEswereclassifiedfortheyears2006to2011inclusively.Asaresult,weknowwhethereachfirmchangedcategoriesfromyeartoyear.Thisiswhatwecallthetransition matrix. Wecalculatetheproportionoffirmsthatchangesituationsforeverypossibletransitioncombinationandeveryyearfrom2006to2011.Inaddition,wepresentthefirms’transitionsbyaggregatingthedata.

OurfirstanalysisofthebehaviourofCanadianSMEsisverysimilartothestudyofvariablesfollowingadiscrete time stochastic process.Foreveryyearexamined,afirm’ssituationmaybeconsideredavariate,thevalueofwhichmayhaveafinitenumberofpossibilitiescorrespondingtothefivecategoriesdefinedearlier.Inaddition,toanalyzeafirm’spotentialtransitionsovertime,wefindourselvesinthegeneralcontextofMarkov chain theory,morespecifically,thatoftheorderofoneprocess.

QuartileforGrowth

1 2 3 4

1 (1,1) Mediocre

(1,2) Mediocre

(1,3) Growth

(1,4) Growth

2 (2,1) Mediocre

(2,2) Average

(2,3) Average

(2,4) Growth

3 (3,1) Profit

(3,2) Average

(3,3) Average

(3,4) Star

4 (4,1) Profit

(4,2) Profit

(4,3) Star

(4,4) StarQ

uart

ile fo

r pr

ofi ta

bility


Thus,thestochasticprocessrelatedtoafirm’ssituationovertheyearsformsanorder-oneMarkov chainifafirm’sprobabilityofbeinginaparticularcategorydependsonlyonthecategorytowhichitbelongedoverthepreviousperiod.Thisisareasonablehypothesisasattimet−1thecategorytowhichthefirmbelongsisdeterminedbyitsgrowthandprofitability,whichmayhaveaneffectonthefirm’ssituationattimet.

Aftercalculatingtheproportionoffirmsineachcategoryfortransitionsintheaggregatemanner,westatisticallytestthedifferencebetweencategoryproportionsbyusingstandardteststoverifythevalidityofhypothesesH1andH2.

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3.2.3 Ordered and unordered dynamic probit models with random effects for panel data

Themodelsweconsiderinthisstudyaretheordered dynamic probit model with random effects andtheunordered dynamic probit model with random effects.WereferthereadertoAppendixBforthedetailsofthismodelaswellasourhypotheses.Toconductthisstudy,wealsobasedourselveslargelyontheworkofContoyannisetal.(2004a)inthehealthfield.Weusedasimilarmodel,butadaptedittothecontextofCanadianSMEperformancedefinedontheclassificationmethodofDavidssonetal.(2009).Theestimatedmodelsarebasedonthefollowingequation:

= ßxit + γЅit−1 + ci + εit

wherei=1,...,nandT=1,...,Ti ;xitrepresentstheindependentvariablesanddoesnotcontainaconstantterm;Ѕit−1constitutesasetofdichotomousvariablesindicatingthatthefirmbelongstoacategoryattimet−1;andciisthefirm’sunobservedspecificindividualheterogeneity,whichdoesnotvaryovertime.Variableisalatentvariableofthefirm’spossiblecategoryandsitistheobservedvariable.Fortheorderedmodel,weestablishtheorderofthecategoriesasfollows:

Mediocre ≺ Average ≺ Growth ≺ Profit ≺ Star

where≺denotesthedirectionoftheorderrelation:ifa ≺ b,thenaisconsideredasituationinferiortob. TheorderofthesesituationscanbejustifiedbytheresultsofDavidssonetal.(2009)andthemannerinwhicheachsituationisdefined.Thus,dependentvariablesittakesthevalueof0,1,2,3or4dependingonwhetherthefirmbelongstotheMediocre,Average,Growth,Profit or Starcategoryrespectively.10

Fortheunorderedmodel,dependentvariablesitwillbeequalto1ifthefirmbelongstotheStarcategory,0inallothercases,andsitwillbeequalto1ifthefirmbelongstotheMediocrecategory,0inallothercases.Asthehypothesisofanorderedmodelsuggestsarigidstructurethatmaynotberepresentativeofthedata,thisjustifiesuseoftheunorderedmodel.

9.SeeAppendixD.10.Thevalueassignedtothecategoriesisarbitrary,butmustrespectthesetorder.

s * it

s * it

8

9


Wealsoassumethattheunobservedindividualheterogeneouseffects11aresuchthat

ci = c0 + α1Si0 + α2 xi + ui (1)

wherexiistheaverageofthevariablesbyfirmbasedontimeandwiththesamehypothesesasforthetheoreticalmodel.NotethatSi0representsallthedichotomousvariablesforthefirm’sinitialsituation.

Earlier,weassumedthatafirm’ssituationovertimewouldfollowaparticularstochasticprocessdefinedasbeingaMarkovchain.Inthiscase,thatmeansthatafirm’sprobabilityofreachingasituationattimetdependsonlyonitssituationattimet−1.Davidssonetal.(2009)obtainedtheirresultsinacontextsimilartothatofMarkovchaintheoryastheauthorsanalyzedthefirm’stransitionovertheyearsandcalculatedtheproportionoffirmswhosesituationchanged.Themodelweusepresentsmanyadvantages.First,itispossibletomeasuretheimpactofafirm’spositioninacategoryattimet−1ontheprobabilityofbeinginacategoryattimet.ThiswillbegivenbytheestimationofcoefficientsЅit−1. This isthedynamicaspectofthemodelrepresentedhere.Next,wecanalsoanalyzetheeffectofindependentandcontrolvariablesontheprobabilitythatthefirmwillbeinaparticularsituation.Thisisgivenbyestimatingthecoefficientsofxit.Finally,applyingtheresultsobtainedwiththismodel,wecalculatetheaverage partial effects.12Usingthese,wecan,amongotheruses,quantifytheeffectonafirm’sprobabilityofbeinginacategorywhenitsprevioussituationcorrespondstoanyofthefivedefinedcategoriesfollowingthemethodofDavidssonetal.(2009).Thevariousaspectsarisingfromthisstudy’smodelrepresentthesignificantcontributionsofthisworkastheyallowustoexamineingreaterdepththeperformanceoftheSMEsandthelinkbetweenafirm’sgrowthandprofitability.

3.2.4 Model variables

Wenowpresentthevariablesthatarepartofthemodelsusedinthisstudy.Thechoiceofthesevariablesisbasedontheworkofresearcherswhoanalyzedthedeterminantsofgrowthwithaclearinfluenceonthefirms’performanceand,inparticular,ontheirsituationfromyeartoyear.Table11,inAppendixD,providesasummaryofthisworkanddefinesthevariablesthatwereincorporatedintoourstudy’smodelsbasedontheavailabilityofdatainoursample.

• Dichotomousvariablesforprovincesorregions:Quebec,Ontario,BritishColumbia,Atlantic(NovaScotia,NewfoundlandandLabrador,PrinceEdwardIsland,NewBrunswick),Prairies(Manitoba,Alberta,Saskatchewan),Territories(Yukon,NorthwestTerritoriesandNunavut);

• Dichotomousvariablesforindustrysectors:13agriculture;mining;construction;manufacturing;wholesaletrade;retailtrade;transportationandwarehousing;informationandculturalindustries;

11.SeeAppendixBformoreinformation.12.SeeAppendixB,sectionB.1.2.13.AccordingtotheNorthAmericanIndustryClassificationSystem(NAICS),2007.


realestateandrentalandleasing;professional,scientificandtechnicalservices;administrativeservices;healthcareandsocialassistance;arts,entertainmentandrecreation;accommodationandfoodservices;otherservices;

• Dichotomousvariablesfortheyearsconsidered:2006to2011;

• Characteristicsoffirm: ◦ Ageoffirm(Age)14

◦ Numberofemployees(Emp)15

◦ Externalfinancing(Debt):16

Totalliabilities Total assets

◦ Humancapital(HumCap):17toestimatehumancapital,wedeterminetheratiobetweentheannualwagespaidtoemployeesbythebusinessandtheaverageannualwagespaidtoemployees,18calculatedbyindustrysector;

• Dichotomousvariableforeachcategoryoffirmsattimet−1;

• Dichotomousvariableforeachcategoryoffirmsattimet0,thatis,2006;

• Averageobservationsfrom2006to2011forthevariablesnumberofemployees(whereapplicable),ageoffirm,debtandhumancapital.Thesevariablesareusedinequation(1)(andinequation(4)inAppendixB).

Totalsales,assetsandliabilitiesareexpressedinmillionsofCanadiandollars.ProfitisexpressedintensofthousandsofCanadiandollars.Also,allamountswereadjustedbasedon2006pricesusingtheconsumerpriceindex.19

Tables2,3and4provideinformationonthesampleusedinthisstudywhenthefirms’totalsalesareusedasameasureofgrowth.20

14.FirmageisestimatedusingthedateatwhichthefirmfirstappearsintheBusinessRegister.15.Thisisthefirm’saveragenumberofemployeesasreportedtotheCanadaRevenueAgency.Thisvariableisexcludedfrom

certainregressions,wherethenumberofemployeesisusedasameasureofgrowth.16.Todefinecertainfinancialvariables,weconsultedStatisticsCanada’sFinancial Performance Indicators for Canadian Business

(1995).17.WeestimatedhumancapitalinthesamemannerasLopez-GarciaandPuente(2012).18.Firmsreporttheiremployees’annualwagestotheCanadaRevenueAgency.19.Source:StatisticsCanada,CANSIM,Table326-0021.20.RefertoAppendixEforothermeasuresconsidered(totalnumberofemployeesandtotalassets).

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Table2providesinformationoncertainvariables.Wenotethatforfirmsinthesample,onaverage,liabilitiesrepresentthreequartersofassets.Table2alsoshowsthatthefirms’averageageisabout25yearsandthattheaveragenumberofemployeesisjustover30.

Table2:Averageofselectedvariablesformodels

Standarddeviationinparentheses. *Numberofobservationsxnumberofyears.

Table3breaksdownthefirmsbyprovinceorregion.ItshowsthatOntarioandQuebecaccountforalmosthalfofallfirmsinCanada,thatis,27percentforOntarioand22percentforQuebec,whereasthethreeterritoriestogetherhavethefewestSMEsinCanada.

Table3:Distributionoffirmsbyprovinceorregion

*Numberofobservationsxnumberofyears.

Finally,Table4breaksdownfirmsinthesamplebyindustrysector.Itshowsthatthegreatestproportionoffirmsisfoundinthreesectors:professional,scientificandtechnicalservices;manufacturing;andretailtrade.Theprofessional,scientificandtechnicalservicessectoraccountsfor17.3percentofallfirms,followedbythemanufacturingsector(15.5percentofallfirms)andtheretailtradesector(12.8percentofallfirms).

Variable Average

Debt 0.73 (0.76)

HumCap 1.00 (1.77)

Age 25.00 (16.60)

Emp 33.05 (55.34)

TN* 20,920

Province/region PercentageOntario 27.56Quebec 22.80Prairies 19.93BritishColumbia 12.40Atlantic 13.86Territories 3.44NT* 20,920

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Table4:Distributionoffirmsbyindustrysector


4. ResultsThissectionpresenttheresults.Asthreemeasuresareusedforgrowth,andtoavoidrepetition,thissectionprovidesonlyresultsforwhichthemeasureisthetotalnumberofsales.ResultsforothermeasuresarepresentedinAppendixE.

4.1 Transition matrices of firms from 2006 to 2011

Thissubsectionpresentsthetransitionmatrixobservedforaggregateddatafrom2006to2011(seeTable5).Firmpositionattimet−1isfoundinthecolumns,whilefirmpositionattimetisfoundintherows.Thetransitionmatricesforeachyearhavebeenomittedastheresultsbearcloseresemblancetothoseoftheaggregateddata.WenotethattheproportionoffirmsintheProfitcategoryattimet−1andintheStar categoryattimetismuchhigherthanthatoffirmsintheGrowthcategoryattimet−1andintheStar categoryattimet(nearlydouble).However,theproportionoffirmsintheProfitcategoryattimet−1andintheMediocrecategoryattimetismuchlowerthanthatoffirmsintheGrowthcategoryattimet−1andintheMediocrecategoryattimet(twotimessmaller).Thesefindingsarealsovalidforeverytransitionyearconsidered(seeAppendixE).Furthermore,wenotethat,ingeneral,firmstendtoremaininthesamecategoryfromyeartoyear.

Industrysector Percentage

Professional,scientificandtechnicalservices 17.30Manufacturing 15.54Retailtrade 12.79Construction 9.99Accommodationandfoodservices 9.75Mining 8.13Wholesale trade 7.36Transportationandwarehousing 4.45Agriculture 3.61Administrativeservices 3.08Otherservices 2.84Informationandculturalindustries 1.74Healthcareandsocialassistance 1.58Arts,entertainmentandrecreation 0.96Realestateandrentalandleasing 0.88TN* 20,920

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Table5:Transitionmatrixforfirms,aggregateddatafrom2006to2011(percentage)

Table6presentstheresults(asapercentage)ofthetestsofhypothesesH1andH2foreachtransitionyearandfortheaggregateddatafrom2006to2011.

Table6:Hypothesistesting(percentage)

***p<0.001.

Ineverycase,wefindthathypothesesH1andH2aretrueforeachtransitionyearandfortheaggregateddata.Inshort,agreaterproportionoffirmsinitiallyinaProfitsituationreachesthehighestsuccesscategory,Star,thanfirmsinitiallyinaGrowthsituation.TheproportionoffirmsinitiallyinaGrowth situationthatendupintheMediocrecategory,thecategoryofleastsuccess,isgreaterthantheproportionoffirmsinitiallyinaProfitsituation.

4.2 Estimation of modelsTable7presentstheresultsofestimationsbasedontheorderedandunordereddynamicprobitmodelswithrandomeffects.

Certaincontrolvariables,suchasdichotomousvariablesforyearsandforindustrysectors,havebeenomitted.Inaddition,referencecategoriesforthecorrespondingdichotomousvariablesareOntariofortheprovincesorregions,firmsintheGrowthcategoryforthefirm’ssituationattimet−1andthemanufacturingsectorfortheindustrysectorvariable.Intheorderedmodel,theapproximatedthresholdparameters21arecalledThreshold1,Threshold2,Threshold3andThreshold4.

Positionattimet −1Mediocre Average Growth Profit Star

Mediocre 33.65 19.26 30.34 16.42 15.60Average 22.15 45.24 23.16 20.82 20.18Growth 23.32 10.16 25.10 5.28 5.17Profit 5.58 8.54 6.03 26.97 23.97Star 15.29 16.80 15.37 30.50 35.08Po

sitio

n at

tim

e t

Finalsituation Star Mediocre

Initialsituation Growth H1 Profit Growth H2 Profit2006–2007 15.26 *** 26.55 30.51 *** 15.002007–2008 14.80 *** 27.77 28.23 *** 16.362008–2009 17.85 *** 31.28 29.64 *** 18.902009–2010 14.07 *** 36.17 33.02 *** 14.202010–2011 14.73 *** 31.39 30.55 *** 17.342006–2011 15.37 *** 30.50 30.34 *** 16.42

21.SeeAppendixB.2.

13


Table7:Resultsofestimationsbasedontheorderedandunordereddynamicprobitmodelswithrandomeffects

Statistictinparentheses. *p<0.05,**p<0.01,***p<0.001. (1)Dynamicprobitmodelwithrandomeffects(RE).(2)Dynamicprobitmodelwithrandomeffectsanddependentvariable=1iffirmbelongstoStarand0otherwise.(3)Dynamicprobitmodelwithrandomeffectsanddependentvariable=1iffirmbelongstoMediocre and0otherwise. †Numberofobservationsxnumberofyears.

FirstwenotethatafirmintheProfitcategoryattimet−1ismorelikelytoachievetheStarcategoryattimetthanafirmintheGrowthcategoryfortheorderedmodel(1).Asweimposedanorderofpotentialsituationsforfirms,itwastobeexpectedthattheestimatedcoefficientsforsituationsattimet−1wouldfollowagradientofvalues,thatis,theywouldbenegativeforMediocreandAveragesituationsandpositiveforProfitandStarsituations,allconsideredwithrespecttotheGrowthsituation.Theestimationsobtaineddidnotdoso,exceptfortheProfitandStarsituations.Infact,afirmintheMediocrecategoryattimet−1hasabetterchance,allotherthingsbeingequal,ofachievingtheStarcategoryattimetthanafirmin

Orderedmodel UnorderedmodelRE(1) RE-Star(2) RE-Mediocre(3)

Mediocret−1

0.0863*** -0.0131 0.122**(3.03) (-0.32) (-3.25)

Profitt−1

0.299*** 0.288*** 0.272***(8.84) (6.43) (-6.13)

Averaget−1

0.0728** -0.00620 -0.193***(2.62) (-0.15) (-5.28)

Start−1

0.291*** 0.208*** -0.308***(9.20) (4.55) (-7.78)

Debt-0.202*** -0.334*** 0.174***(-8.73) (-8.23) (6.20)

Emp0.00286*** 0.00416*** -0.00430***(3.31) (3.36) (-3.40)

Age0.00609 0.00183 -0.0254(0.26) (0.06) (-0.78)

HumCap0.121*** 0.140*** -0.184***(4.83) (3.79) (-4.87)

Prairies0.0853** 0.0994** -0.00469(2.78) (2.60) (-0.12)

Quebec0.0563* 0.0816* -0.0625(2.01) (2.32) (-1.72)

Threshold1-0.688***

(-12.51)

Threshold20.166**(3.04)

Threshold30.562***(10.27)

Threshold41.024***(18.60)

Loglikelihood -31,707.211 -10,329.857 -10,614.673TN† 20,920 20,920 20,920

14


the Growthcategory.ThesameruleappliestofirmsintheAveragecategoryattimet−1.Assuch,thissituationisnotanabsoluteindicatoroffutureperformance.

Moreover,astheestimatedcoefficientofProfitt–1ispositiveandthecontextisanorderedmodel,wecanconcludethatafirminthiscategoryislesslikelytoendupintheMediocrecategorythanafirmintheGrowthcategoryattimet−1.Thus,forthesemodels,hypothesesH1andH2areverifiedfortheCanadianfirmsinoursample.

Table8presentstheaveragepartialeffectsfortheorderedmodel,whichindicatetheeffectontheprobabilityofachievingtheStarandMediocrecategoriesbasedonthefirm’scategoryattimet−1.Ifweconsidermodel(1a),wefindthatifafirmisintheProfitcategoryattimet−1,itsprobabilityofbeingintheStar categoryattimetisabout8percentagepointshigherthanifitisintheGrowthcategoryattimet−1.Thus,theProfitcategoryisamongthosethatfosterthemostchancesforafirmtosubsequentlyachievegreatersuccess.Inaddition,afirmintheProfitcategoryattimet−1,is7percentagepointslesslikelytobeintheMediocrecategory,accordingtomodel(1b).

Table8:Averagepartialeffectsontheprobabilityofachieving the StarandMediocrecategoriesfortheordereddynamic probitmodelwithrandomeffects

Standarddeviationinparentheses. (1)Dynamicprobitmodelwithrandomeffects(RE). *Numberofobservationsxnumberofyears.

Intermsoftheunorderedmodel,thatis,models(2)and(3),hypothesesH1andH2arealsoverified.Formodel(2),firmsintheProfitcategoryattimet−1aremorelikelytoachievethesubsequentStar categorythaniftheyareintheGrowthcategory.Model(3)revealsthatafirmintheProfitcategoryattimet−1islesslikelytoendupintheMediocrecategoryattimetthanafirmintheGrowthcategory.Table9indicatesthatformodel(1),afirmintheProfitcategoryattimet−1isabout8percentagepointsmorelikelytobeintheStarcategoryattimetthanafirmintheGrowthcategory.Ontheotherhand,model(2)showsthatbeingintheProfitcategoryattimet−1,makesafirm7percentagepointslesslikelytobeinthe Mediocrecategoryattimet.

OrderedmodelRE(1a) RE(1b)

Star Mediocre

Mediocret−1

0.0218 -0.0220(0.00489) (0.00494)

Profitt−1

0.0803 -0.07143(0.0145) (0.0155)

Averaget−1

0.0183 -0.0187(0.00409) (0.00414)

Start−1

0.0770 -0.0712(0.0135) (0.0141)

TN* 20,920 20,920

15


Table9:AveragepartialeffectsontheprobabilityofreachingtheStarcategoryandofbeingintheMediocrecategoryfortheunordereddynamicprobitmodelwithrandomeffects

Standarddeviationinparentheses. (1)Dynamicprobitmodelwithrandomeffectsanddependentvariable=1iffirmbelongstoStarand0otherwise.(2)Dynamicprobitmodelwithrandomeffectsanddependentvariable=1iffirmbelongstoMediocreand0otherwise. *Numberofobservationsxnumberofyears.

Inshort,theorderedandunorderedmodelsgivethesameresultsfortheeffectoftheProfitandGrowth situationsattimet−1ontheprobabilityofachievingthehighestsuccesscategory(Star)orbeingintheleastsuccessfulcategory(Mediocre).

4.3 Other results

External financing or debt

Anotherimportantresultconcernsthevariableforfirms’externalfinancingordebt,expressedastheratiooftotalliabilitiestototalassets.Inallmodels,thisvariableissignificantandtheestimatedcoefficientisnegative.Therefore,wecanconcludethatexcessivedebtmayimpedeachievementoftheStarcategoryandfavourstheprobabilityofbeingintheMediocrecategory.Intermsofthenumberofemployees,Table7revealsthatthisvariableissignificantandfavoursafirm’sprobabilityofbeingintheStarcategory.Hence,thesizeofabusinessappearstohaveasubstantialeffectonachievingsuccess.

Age

Inthecaseathand,afirm’sageisnotsignificantinexplainingthetransitionovertime.Intheliteratureonthesubject,empiricalresearchhasshownthattherelationshipbetweenafirm’sgrowthanditsageisnegative.Thissuggeststhatyoungerfirmsaremorelikelytorecordhighergrowththanolderfirms.22 However,thisdoesnotappeartobethecaseforthesampleofCanadianfirmsinthisstudy.ThismaybeduetosamplingissuesastheSurvey on Financing of Small and Medium EnterprisesisbiasedtowardsolderfirmsasseeninTable2.

UnorderedmodelRE-Star(1) RE-Mediocre(2)

Mediocret−1

-0.00340 -0.0313(0.000830) (0.00686)

Profitt−1

0.0804 -0.0669(0.0163) (0.0144)

Averaget−1

-0.00161 -0.0495(0.000394) (0.0105)

Start−1

0.0565 -0.0765(0.0119) (0.0156)

TN* 20,920 20,920

22.SeetheworkofEvans(1987),Coadetal.(2013),Lottietal.(2009)andNunesetal.(2013).

16


Human capital

Thisstudy’smodelshighlightanimportantaspectofSMEsinrelationtotheiremployeesandtheirhumancapital.Asexplainedearlier,toestimatethelatterweusedtheratiooftotalwagespaidtotheaveragewagesoffirmsinthesameindustrysector.Whilethisisanapproximation,highlyeducatedandexperiencedworkersgenerallytendtoearnhigherwages.23Thiscanalsobeexplainedbythefactthatthemarketattributesahigherproductivityvaluetocertainworkers.Theseassumptionsareconsistentwiththetheoryofhumancapital.

Wefind,inTable7,thattheindependentvariablerelatedtohumancapitalhasapositiveestimatedcoefficient.Thus,afirmwithhighhumancapitalhasagreaterchanceofachievinghighgrowthandhighprofitability.Thisdemonstrates,inparticular,thelinkbetweenhumancapitalandafirm’sperformance.

Geography

Thefirms’geographicsituationforcertainprovincesorregionsalsoappearstohaveanon-negligibleeffectontheirperformance.Table7showstheestimatedcoefficientsobtainedinthemodelsfortwooftheprovinceswhosecoefficientwassignificant.Hence,wefindthatbeingbasedinQuebecorinthePrairiesincreasestheprobabilitythatafirmwillreachtheStarcategory,formodels(1)and(2),versusafirmbasedinOntario,anddiminishestheprobabilitythatafirmwillbeintheMediocrecategoryformodel(1).

5. ConclusionsThepurposeofthisstudywastoshednewlightonthenatureoftherelationshipbetweengrowthandprofitabilityforCanadianSMEs.LikeDavidssonetal.(2009),wefoundthatahighlyprofitablefirmhasagreaterchanceofgoingontoreachthehighestsuccesscategorythanafirminahigh-growthcategory.Perhapsthemaincontributionofthispaperowesmuchtotheuseofadynamicprobitmodelwithrandomeffects,whichallowedforamorein-depthanalysisthanthatcarriedoutbyDavidssonetal.(2009).

Thismodelenabledustocapturetheeffectofafirm’ssituationatagiventimeontheprobabilitythatitwillbeinacertaincategoryatasubsequentpointintimeandtomeasuretheeffectofotherindependentvariablesonafirm’sprobabilityofbeinginacertaincategory.Assuch,wewereabletoshow,forthesampleinquestion,thefollowingelements:

• Humancapitalisapositiveandsignificantfactorinfirmsreachingahighlevelofsuccess,intermsofbothgrowthandprofitability.Conversely,humancapitalallowsafirmtoreduceitschancesofbeingintheleastsuccessfulcategory.

23.SeeWeiss(1995).

17


• Debtisalsoasignificantvariablethatcanimpedeafirm’sabilitytoperformwellintermsofgrowthandprofitability.

• Althoughnumerousempiricalstudieshaveshowntheconsiderableinfluenceofafirm’sageonitsgrowth,thisvariableisnotsignificantinthemodelsweused.

• ThereappearstobeadegreeofdifferenceamongCanadianprovincesorregionswithrespecttoafirm’sperformance.

Intermsoffutureresearchonthesubject,anumberofavenuescouldbeexplored.Ourstudyconsideredthehumancapitalofemployees,butnottheowners’characteristics.Indeed,severalworks24indicatethatthecharacteristicsofafirm’sowner,notablyhisorherexperienceandlevelofeducation,canhaveaninfluenceonafirm’sgrowth.Thisresearchcouldbeundertakenusingthe2011Survey on Financing and Growth of Small and Medium Enterprises,whichcontainsinformationonowners’characteristics.Asecondsubjectcouldexploretherelationshipbetweenafirm’sperformanceanditsexportsofgoodsorservices.Thisresearchcouldexaminewhetherexportsenablethefirmtoachieveahigherlevelofperformanceintermsofgrowthandprofitability.

24.See,forexample,theworkofDobbsandHamilton(2007),HamiltonandLawrence(2001),Barkham(1994)andKangasharju(2000).

18


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21


Appendices

A Empirical Research on the Relationship between Growth and Profitability

Table10:Empiricalresearchontherelationshipbetweengrowthandprofitability

ReferenceMeasureofgrowth

Measureofprofitability Years Samplesize Country Sector

Growth–profitabilityrelationship

Reid(1995) Assets N/A 1985–1988 73 Scotland N/A Negative

Glancey(1998) Assets Returnonassets Assetstosales 1988–1990 38 Scotland Manufacturing None

Roper(1999) Total sales Returnonassets Assetstosales 1993–1994 703 Ireland Manufacturing Low

Nakanoand Kim(2011) Assets Returnon

investment 1987–2007 1,633 Japan Manufacturing Positiveandnegative

Markmanand Gartner(2002)

Sales Employees Profits

1992–1997 1993–1997 1994–1998

1,233 UnitedStates Allsectors None

Cowling(2004) Sales Returnon investment 1991–1993 256 United

Kingdom N/A Positive

Coad(2007)Sales Employees Valueadded

Grossoperatingsurplusonvalueadded

1996–2004 8,405 France Manufacturing Positive

22


B Econometric Models

Thisappendixpresents,inageneralcontext,theeconometricmodelsusedinthisstudy.

B.1 Dynamic probit model for panel data

B.1.1 Theoretical elements of the model

Oneofthemodelsweuseinthisprojectisbasedlargelyonthedynamic probit model for panel data(orlongitudinaldata).DetailsregardingthismodelcanbefoundintheexcellentworkofWooldridge(2010).

Astheterminologyindicates,themodelcombinesthreeessentialaspects.First,wewillconsiderpaneldata.Thedataconsistofindividuals(i)thatareobservedoveraperiodoftime(T).Inthiscontext,thenotationyitindicatesthatweobserveindividual

25 iattimet,fori=1,...,nandt=1,...,T. 26Ingeneral,nwillbelargeandTrelativelysmall.Thetermdynamicreferstothefactthatwewillusevariablesfromthepreviousperiod(laggedvariables)attimet–1.Finally,thetermprobitmeansthatthemodelisprobabilisticandthattheerrortermfollowsaparticulardistribution,whichisanormaldistributioninthecaseathand.Thevariable isalatentvariable.Thisisanunobservedvariableforwhichanindicator,notedasyit ,isobservedandlinkedtothisvariableinthemannerexplainedbelow.Letusconsiderthefollowinglatentregression:

= ßxit + ρyit-1 + ci + εit (2)

wherexitisavectorofdimension1×Kformedbyindependentvariables,ci representstheunobservedheterogeneouseffectsandεit istheerrorterm,whichfollowsastandardizednormaldistribution,notedasN(0,1).Giventherelationshipbetweenci andxit,therearetwotypesofmodel:therandom effectsmodel,ifitisassumedthatci andxitarenon-correlated,andthefixed effectsmodel,ifitisassumedthatthesetermsarecorrelated.Wewillalsohypothesizethatεit isstrictlyexogenous,thatis,xitisnon-correlatedwithεis foranytimetands.Thishypothesiscanbeexpressedasfollows:

E(εit|xi1, xi2,...,xiT ,ci )=0

Thelatentvariableanditsindicatoryitarerelatedasfollows:

yit =1, if >0

yit =0, if≤0

y * it

y * it

25.Thetermindividualisusedinthebroadersenseofthetermandincludes,forexample,firms.26.InsteadofT,wecouldconsiderTi ,whichmeansthemodelisunbalanced.Ifthemodelisbalanced,thenTi = T foranyi.

y * it

y * it

y * it

23


Consideringthedistributionoftheerrorterm,itfollowsthat:

P(>0|xit ,yit−1,ci )=P(yit = 1|xit,yit−1,ci )=Φ(ßxit + ρyit−1 + ci )

P(≤0|xit,yit−1,ci )=P(yit=0|xit,yit−1,ci )=1−Φ(ßxit + ρyit−1 + ci )

whereΦisthedistributionfunctionofthestandardizednormaldistribution:

Φ(x)=exp�−�dtFinally,itisalsofoundthat:

E�yit|xit ,yit−1,ci � =Φ( ßxit + ρyit−1 + ci ) (3)

Asmentionedearlier,twotypesofmodelcanbeuseddependingonthehypotheseswithrespecttothecorrelationofindependentvariablesandtheunobservedheterogeneouseffect.Theinterestintherandomeffectsmodelresidesessentiallyinthepossibilityofestimatingthecoefficientsofvariablesthataresetintime(e.g.,gender,ethnicity,skill).Thisisnotpossiblewithfixedeffectsmodels.Thus,inthiscase,itisimpossibletodeterminehowthisparticulartypeofvariableaffectsthedependentvariable.Usingadynamicmodelmayalsoposeaproblemwhenestimatingcoefficients.Variableyit−1 isendogenousasitiscorrelatedwiththeerrorterm.Thisstemsprimarilyfromthefactthatthe“real”initialobservationyi 0isnotknownaswebegintoobserveindividualsfromanarbitraryinitialtime.Thepriorinformationisunknown.Thismeansthattheinitialobservationiscontainedintheerrorterm,hencethecorrelationwiththelaggedvariableyit−1. This is the initial condition problem. Wooldridge (2000,2005)dealtwiththisprobleminrelationtodynamicnon-linearrandomeffectmodels.Thesolutionconsistedessentiallyofmodellingthedistributionofunobservedeffectsconditionaltotheinitialvaluesandtotheexogenousindependentvariables.BasedontheWooldridgesolution,wewillthereforeassumethat:

ci = c0 + α1yi0 + α2xi + ui (4)

wherexiistheaveragevariablesbyindividualatagiventime,thatis:

xi = xit

Itisassumedthattheerrortermuiisnon-correlatedwiththevariablesandisdistributed,conditionaltoxit ,suchthatN(0,).Notethatthedichotomous(orbinary)variablesareexcludedfromthecalculationofxitoavoidcollinearity.Thus,equation(3)maybewritten:

E�yit|xit ,yit−1,ci � =Φ(ßxit + ρyit−1+c0 + α1 yi0 + α2 xi + ui)

y * it

y * it

1

�2π

x

∫ -∞

1 t 2 2

1 T

T

� i=1

σ 2 u

24


and,intheformoflatentregression:

= ßxit + ρyit−1 + c0 + α1 yi0 + α2 xi + ui + ɛit

Theabovesolutionentailsanumberofadvantages.First,itcanbeappliedeasilybycertainstatisticalsoftwareprograms(e.g.,Stata)toestimatetheordereddynamicprobitmodelwithrandomeffectsbythemaximumlikelihoodmethod.Thismethodcanalsobeusedtoestimatethecoefficientsofvariablesthatdonotvaryovertime.

Notethatthismethodhasbeenusedextensivelyintheliterature,notablyintheworksofContoyannisetal.(2004a,2004b),Heiss(2011)and,morerecently,Lopez-GarciaandPuente(2012).

B.1.2 Average partial effects

Theinterestinusingtheprobitmodelresidesinthefactthatitispossibletoquantifythepotentialeffectofcertainspecificindependentvariablesontheprobabilitythatthedependentvariablewilltakeonacertainvalue.Thesignoftheestimatedcoefficientsofßwillgivethedirectionoftheeffect(positiveornegative),butnotthemagnitude.Thatiswhywewilldefinetheaverage partial effects,whichallowustoobtainthisinformation.

Generally,ifwehavethefollowingmodel:

E(yit|xit ,ci )=P(yit = 1|xit ,ci )=Φ (xit + ci ),t=1,...,T

then,bysimplifyingthenotationbydroppingsubscripti,thepartialeffectforacontinuousvariablextj is givenby:

= ßjφ(xt + c)

whereφisthestandardizednormaldistribution:

φ(ȥ)=exp(−ȥ 2/ 2)

Fordiscretevariables,thepartialeffectiscalculatedbasedon

Φ(xt(1) + c)−Φ(xt

(0) + c) (5)

wherext(0)andxt

(1)aretherespectivevaluesofthevariableconsidered.27

Thedifficultyofcalculatingpartialeffectsresidesessentiallyinthefactthattheheterogeneouseffects,c, arenotobserved.Ameasurecommonlyusedfortheeffectofindependentvariablesconsistsofcalculating

y * it

27.WeusethesamenotationasPapkeandWooldridge(2008).

�P(yt = 1|xt ,c)�xtj

1

√2π

25


theexpectationonthepartialeffectsbasedonthedistributionofc.Thus,theaverage partial effect,notedas APE,evaluatedinxtisdefinedby:

APE(xt)=Ec �ßjφ(xt + c)�

wheretheexpectationisconditionaltoc.Asaresult,theaveragepartialeffectnolongerdependsonc. Theaveragepartialeffectcanbeobtainedfordiscretevariablesbytakingtheaverageofthedifferencecalculatedin(5).

Similarto(4),wewillassumethat:

ci = Ψ + ξxi + ui

withuidistributedbasedonN(0,).

Wooldridge(2010)showsthatthepartialeffectsmaybeobtainedbyderiving,orbycalculating, thedifferenceforthefollowingexpression:

Exi �Φ(Ψα + ßα xt + ξα xi)� (6)

wheresubscriptαindicatesthatthecoefficientsweredividedby�1+.Theexpressionfoundin(6)canbeestimatedby:

Φ (Ψα + ßα xt + ξα xi) (7)

Notethatconvergentestimatorsofthecoefficientsmaybeuseddirectlyin(7)toobtainconvergentestimatorsoftheaveragepartialeffects.

Inshort,aconvergentestimatoroftheaveragepartialeffectsisobtainedbyderiving,orbycalculating,thedifferenceforthefollowingexpression:

Φ(Ψα + ßα xt + ξα xi)

wherethenotation�meansanestimationofthecoefficientandsubscriptαmeansthatthecoefficientsweredividedby�1 + .

Inthecontextofthemodelspecifiedin(2)andthehypothesisformulatedontheunobservedheterogeneouseffectsin(4),aconvergentestimatoroftheaveragepartialeffectsisgivenbyderiving,orbycalculating,thedifference:

Φ(c0α + α1α + α2α xi + ßαxit + ρα yit−1)

σ 2 u

σ 2 u

σ 2 u

1 N

N

� i=1

1 N

N

� i=1

1 N

N

� i=1

26


Itisalsopossibletocalculatetheaveragepartialeffectsforanytimetandi.Inthiscase,thedifferencemustbederivedorcalculated:

Φ(c0α + α1α + α2α xi + ßαxit + ρα yit−1)

B.2 Ordered dynamic probit model for panel data

Thetheorywepresentedconcerningthedynamicprobitmodelforpaneldatacanbegeneralizeddirectlytoanorderedmodel.Thismodelwillalsobeusedinthisstudy.Asbefore,thelatentvariableisnotedasandthedummyvariableasyit .Weassumethatyittakesitsvaluesintheset{0,1,...,J},whereJ is a positiveinteger.Thelatentregressionmodelissimilarandisgivenby:

= ßxit + ρyit−1 + ci + εit

Thesamehypothesesasintheunorderedcaseapplytothismodelaswell.Letμ1<...<μJrepresentthreshold parametersandletusdefine:

yit=0,if≤μ1

yit=1,ifμ1<≤μ2

⋮ yit = J,if>μJ

Thus,thevalueofyitisdeterminedbasedontheintervalinwhichvariableislocated.Theseintervalsaregivenbythethresholdparameters.

Assumingthattheerrortermisnormallydistributed,itfollowsthattheprobabilitiesthatthedependentvariabletakesoneitherofthepreviousvalues,conditionaltotheindependentvariables,aregivenby:

Pit0 = P(yit =0|xit,yit−1,ci )=Φ(μ1−ßxit−ρyit−1−ci ) (8)

Pit1 = P(yit = 1|xit ,yit−1,ci )=Φ(μ2−ßxit−ρyit−1−ci )−Φ(μ1−ßxit−ρyit−1−ci ) (9)

⋮ PitJ = P(yit = J|xit ,yit−1,ci )=Φ(μJ−ßxit−ρyit−1−ci ) (10)

Note,inthiscase,parametersμjarealsotobeestimatedasforßandρ.Again,thismodelmaybeestimatedbythemaximumlikelihoodmethod.28

1 NT

N

� i=1

T

� t=1

y * it

y * it

y * it

y * it

y * it

y * it

28.Weusedthereoprob.adoprogram,writtenbyGuillaumeR.Fréchette(Stata Technical Bulletin,Vol.59,January2001).

27


Thehypothesesweformulatedontheunorderedmodelaretransferabletotheorderedmodel,particularlythehypothesisonthedistributionoftheunobservedheterogeneouseffectofindividuals(givenby(4)).Generalizationoftheconceptspresentedintheprevioussectionisalmostdirect.Itisamatterofusingthepreviousdefinitions,whicharesimplyanextensionofthoseoftheunorderedmodel.However,oneexceptionconcernsthesignificanceoftheestimatedcoefficients.Foranorderedmodel,thesignofthecoefficientindicatestheeffectonprobabilityonlyforextremecases.Wecaneasilyseebyderiving(8)and(10)thatapositivecoefficientincreasesprobabilityPitJandthatanegativecoefficientincreasesprobabilityPit0.Forintermediatevalues,thesignofthecoefficientdoesnotgenerallyindicatetheeffectonprobability.29Thiscanbeobservedbyderivingexpression(9).

29.RefertoWooldridge(2010)formoredetails.

28


C Hypothesis Testing

Belowweusep1tosignifytheproportionoffirmsintheProfitsituationattimet−1andtheStarsituationattimet,andp2tosignifytheproportionoffirmsintheGrowthsituationattimet−1andtheStarsituationattimet.Ourhypothesesare:

H0:p1 = p2

and

H1:p1 > p2

ThiscorrespondstohypothesisH1.Let~p1representtheproportionoffirmsintheProfitsituationattimet−1andtheMediocresituationattimetand~p2representtheproportionoffirmsintheGrowthsituationattimet−1andtheMediocresituationattimet.Thehypothesesinthiscaseare:

H0:~p1 = ~p2

and

H1:~p1<~p2

ThelatterarerelatedtohypothesisH2 .

Letp,sandzbedefined,respectively,by:

p =

s = �p(1−p)� 1 �

z =

wherep1correspondstotheestimatedvalueof�p1 or ~p1 andp2istheestimatedvalueof�p2 or ~p2.Sincewehaveaone-tailedtest,thestatisticzαcanbefoundusinganormaltablewithasignificancelevelofα%,whereα ∈{1,5,10}.Ifzα<z,thisresultsinrejectionofH0infavourofH1inthefirstcase.Ifzα > z,H0isrejectedinfavourofH1inthesecondcase.

p1· n1 + p2· n2

n1 + n2

n1 + n2

p1 − p2 s

29


D Empirical Research on Determinants of Growth

Table11:Empiricalresearchondeterminantsofgrowth

ReferenceMeasureofgrowth Years Samplesize Country Sector

Determinant ofgrowth

HartandPrais(1956) Marketvalue

1885–1896 1896–1907 1907–1924 1924–1939 1939–1950

Variesaccordingto years considered

UnitedKingdom

Mining Manufacturing Distribution

Size

SimonandBonini(1958)

Sales Assets Employees Valueadded Profits

1954–1955 1954–1956 500 UnitedStates Manufacturing Size

HymerandPashigian(1962) Assets 1946–1955 1,000 UnitedStates Manufacturing Size

SinghandWhittington(1975)

Assets 1948–1960 2,000 UnitedKingdom

Manufacturing Construction Distribution Otherservices

Size

Evans(1987) Employees 1976–1980 100 UnitedStates Manufacturing Size Age

Hall(1987) Employees 1972–1979 1976–1983

1,349 1,098 UnitedStates Manufacturing Size

Heshmati(2001)Employees Sales Assets

1993–1998 N/A Sweden N/ASize Age Externalfinancing Humancapital

BecchettiandTrovato(2002) Employees 1989–1997 5,000+ Italy Manufacturing

Size Age Externalfinancing

Lottietal.(2009) Employees 1987–1994 3,285 ItalyRadio Television Communicationsequipment

Size Age

Levrattoetal.(2010) Employees 1997–2007 12,811 France Manufacturing

Age Size Humancapital Externalfinancing

NakanoandKim(2011) Assets 1987–2007 1,633 Japan Manufacturing Size

Chandler(2012)Wages Employees Revenues Profits

1996–2003 2,304 Canada 14specificsectors

Externalfinancing Age Size

Lopez-GarciaandPuente(2012)

Employees 1996–2003 1,411 SpainAllsectors,exceptagricultureandfinance

Humancapital Externalfinancing Age

Coad et al. (2013)

Employees Sales 1998–2006 62,259 Spain Manufacturing Age

DaunfeldtandElert(2013)

Employees Revenues 1998–2004 288,757 Sweden Allsectors Size

Nunesetal.(2013) Sales 1999–2006

495 and

1,350Portugal

Agriculture,forestryandmining Construction Manufacturing Commerce Services Tourism

Age Externalfinancing

30


E Results of Other Measures Used

Thissectionprovidestheresultsfortwoothermeasuresusedinthisstudy:totalnumberofemployeesandtotal assets.

E.1 Total number of employees







Variable Average

Debt 0.73 (0.74)

HumCap 1.00 (1.78)

Age 25.12 (16.60)

Emp 32.16 (54.42)

TN* 22,800

Province/region Percentage

Ontario 27.57Quebec 22.85Prairies 20.04BritishColumbia 12.39Atlantic 13.88Territories 3.27TN* 22,800



31




***p<0.001.

Positionattimet −1

Mediocre Average Growth Profit StarMediocre 34.45 16.09 31.11 11.30 11.46Average 22.23 45.87 20.41 30.74 19.42Growth 22.89 12.79 27.17 8.67 10.13Profit 10.31 12.38 9.89 29.57 24.86Star 10.11 12.87 11.41 29.72 34.13


Initialsituation Growth H1 Profit Growth H2 Profit

2006–2007 11.01 *** 25.52 29.80 *** 12.112007–2008 12.21 *** 28.38 28.19 *** 10.202008–2009 10.23 *** 30.63 33.02 *** 11.392009–2010 10.96 *** 30.89 33.56 *** 12.252010–2011 12.64 *** 33.29 31.11 *** 10.622006–2011 11.41 *** 29.72 31.11 *** 11.30

Posi

tion

at ti

me

t

32


Table17:Resultsofestimationsbasedontheorderedandunordereddynamicprobitmodels withrandomeffects,usingthenumberofemployeesasameasureofgrowth

Statistictinparentheses. *p<0.05,**p<0.01,***p<0.001. (1)Dynamicprobitmodelwithrandomeffects(RE).(2)Dynamicprobitmodelwithrandomeffectsanddependentvariable=1iffirmbelongstoStarand0otherwise.(3)Dynamicprobitmodelwithrandomeffectsanddependentvariable=1iffirmbelongstoMediocreand0otherwise. †Numberofobservationsxnumberofyears.


Mediocret−1

0.0667* -0.0281 -0.0962** (2.53) (-0.70) (-2.71)

Profitt−1

0.542*** 0.572*** 0.626***(18.96) (14.57) (-16.16)

Averaget−1

0.154*** 0.0668 -0.398*** (6.22) (1.76) (-12.19)

Start−1

0.489*** 0.495*** -0.597***(16.64) (11.45) (-15.86)

Debt -0.232*** -0.329*** 0.196***

(-9.93) (-8.01) (6.86)

Age 0.0135 0.0464 0.00597 (0.60) (1.42) (-0.19)

HumCap 0.235*** 0.276*** 0.416***

(12.43) (9.82) (-13.89)

Prairies 0.0458 0.0536 0.0463 (1.66) (1.48) (1.32)

Quebec 0.0502* 0.0749* -0.0610

(1.97) (2.25) (-1.85)

Threshold1 -0.702***

(-14.40)

Threshold2 0.165***

(3.40)

Threshold3 0.637***

(13.11)

Threshold4 1.241***

(25.30)Loglikelihood -34,614.743 -10,136.976 -10,675.734TN† 22,800 22,800 22,800

33


Table18:AveragepartialeffectsontheprobabilityofachievingtheStarandMediocrecategoriesfortheordereddynamicprobitmodelwithrandomeffects, usingthenumberofemployeesasameasureofgrowth


Table19:AveragepartialeffectsontheprobabilityofreachingtheStarcategory andofbeingintheMediocrecategoryfortheunordereddynamicprobitmodel withrandomeffects,usingthenumberofemployeesasameasureofgrowth

Standarddeviationinparentheses. (1)Dynamicprobitmodelwithrandomeffectsanddependentvariable=1iffirmbelongstoStarand0otherwise.(2)Dynamicprobitmodelwithrandomeffectsanddependentvariable=1iffirmbelongstoMediocreand0otherwise. *Numberofobservationsxnumberofyears.


Star Mediocre

Mediocret−1

0.015 -0.016(0.00484) (0.00482)

Profitt−1

0.138 -0.114(0.0307) (0.0322)

Averaget−1

0.0351 -0.0366(0.0114) (0.0115)

Start−1

0.123 -0.105(0.0278) (0.0289)

NT* 22,800 22,800

UnorderedmodelRE-Star(1) RE-Mediocre(2)

Mediocret−1

-0.00660 -0.0235(0.00217) (0.00735)

Profitt−1

0.155 -0.133(0.0340) (0.0432)

Averaget−1

0.0160 -0.0933(0.00527) (0.0307)

Start−1

0.131 -0.129(0.0300) (0.0411)

NT* 22,800 22,800

34


E.2 Total assets







Variable Average

Debt 0.72 (0.75)

HumCap 1.00 (1.78)

Age 25.21 (16.70)

Emp 32.23 (55.52)

TN* 22,695

Province/region PercentageOntario 27.74Quebec 22.74Prairies 20.27BritishColumbia 12.23Atlantic 13.77Territories 3.26TN* 22,695



35




***p<0.001.

Positionattimet −1

Mediocre Average Growth Profit StarMediocre 36.79 17.78 33.95 12.94 12.85Average 24.23 48.37 26.85 17.93 21.94Growth 18.94 10.07 20.65 9.24 6.63Profit 7.37 9.01 8.27 22.55 20.57Star 12.66 14.77 10.27 37.34 38.01Po

sitio

n at

tim

e t


Initialsituation Growth H1 Profit Growth H2 Profit2006–2007 10.96 *** 35.42 32.23 *** 12.332007–2008 10.54 *** 36.01 36.74 *** 11.622008–2009 10.17 *** 40.30 34.14 *** 14.802009–2010 8.93 *** 38.64 33.33 *** 12.522010–2011 10.53 *** 36.27 32.98 *** 13.382006–2011 10.27 *** 37.34 33.95 *** 12.94

36


Table25:Resultsofestimationsbasedontheorderedandunordereddynamicprobitmodels withrandomeffects,usingtotalassetsasameasureofgrowth

Statistictinparentheses. *p<0.05,**p<0.01,***p<0.001. (1)Dynamicprobitmodelwithrandomeffects(RE).(2)Dynamicprobitmodelwithrandomeffectsanddependentvariable=1iffirmbelongstoStarand0otherwise.(3)Dynamicprobitmodelwithrandomeffectsanddependentvariable=1iffirmbelongstoMediocreand0otherwise. †Numberofobservationsxnumberofyears.


Mediocret−1

0.152*** 0.125** -0.170*** (5.38) (2.93) (-4.59)

Profitt−1

0.681*** 0.782*** -0.612***(21.12) (17.51) (-14.00)

Averaget−1

0.231*** 0.161*** -0.395*** (8.67) (3.89) (-11.43)

Start−1

0.540*** 0.560*** -0.566***(17.70) (12.19) (-14.60)

Debt -0.311*** -0.515*** 0.282***

(-12.15) (-11.48) (9.00)

Emp 0.000904 0.00142 -0.00241

(1.07) (1.15) (-1.95)

Age -0.0327 -0.0173 0.0248(-1.44) (-0.54) (0.78)

HumCap 0.0906*** 0.0629 -0.138***

(3.80) (1.78) (-3.93)

Prairies 0.0466 0.0465 -0.00639 (1.64) (1.29) (-0.17)

Quebec 0.000996 -0.0288 -0.0641

(1.97) (2.25) (-1.85)

Threshold1 -0.578***

(-11.20)

Threshold2 0.363***

(7.06)

Threshold3 0.745***

(14.43)

Threshold4 1.202***

(23.12)Loglikelihood -33,535.943 -10,661.585 -11,131.342TN† 22,695 22,695 22,695

37


Table26:AveragepartialeffectsontheprobabilityofachievingtheStarandMediocrecategoriesfortheordereddynamicprobitmodelwithrandomeffects,usingtotalassetsasameasureofgrowth


Table27:AveragepartialeffectsontheprobabilityofreachingtheStarcategory andofbeingintheMediocrecategoryfortheunordereddynamicprobitmodel withrandomeffects,usingtotalassetsasameasureofgrowth

Standarddeviationinparentheses. (1)Dynamicprobitmodelwithrandomeffectsanddependentvariable=1iffirmbelongstoStar and0otherwise.(2)Dynamicprobitmodelwithrandomeffectsanddependentvariable=1 iffirmbelongstoMediocreand0otherwise. *Numberofobservationsxnumberofyears.


Star Mediocre

Mediocret−1

0.0375 -0.0376(0.0113) (0.012)

Profitt−1

0.193 -0.141(0.0357) (0.0420)

Averaget−1

0.0569 -0.0571(0.0172) (0.0181)

Start−1

0.145 -0.123(0.0289) (0.0322)

TN* 22,695 22,695

UnorderedmodelRE-Star(1) RE-Mediocre (2)

Mediocret−1

0.03183 -0.0417(0.0101) (0.0118)

Profitt−1

0.231 -0.132(0.0427) (0.0390)

Averaget−1

0.0407 -0.0960(0.0131) (0.0275)

Start−1

0.155 -0.129(0.0326) (0.0340)

TN* 22,695 22,695

38

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