The dynamics of welfare participation in Québec

TheDynamicsof WelfareParticipationin Québec

by

Jean-YvesDuclos

Bernard Fortin

Guy Lacroix

and

HélèneRoberge

Departmentof EconomicsandCRÉFAUniversitéLaval

Ste-Foy, Québec,Canada,G1K 7P4

Abstract

Few studieshaveexaminedthedynamicsof participationin welfare in Québecandelse-where in Canada.Thispapershedssomelight on that importanttopic, which is crucialfor the understandingof the featuresand of the effectsof welfare programmes,and fortheanalysisof possiblereforms.For this,weusea large representativesampleof welfareparticipantsbetween1979and1993.We find that themajority of new spellslast for lessthanoneyear. Nevertheless,that a large proportionof ongoingspellsare of long dura-tion. We estimatefor instancethat the50%shortestspellsaccountfor only 10%of totalwelfare spending. Overall, singlemenleavewelfare more rapidly than singlewomen,youngpeoplefasterthantheir elders,andmoreeducatedindividualssoonerthanthelesseducated.Thewelfare reformof 1989appears to havereducedsignificantlythe rateofexit amongparticipantsunder30. Returnsontowelfaregenerally occurshortlyafterexit,andat a ratewhich diminishesrapidly with time. Finally, weproposea measure of wel-faredependencewhich comesupbeingalmosttwiceaslarge for single-parentfamiliesasfor all othercategories.

Keywords SocialAssistance,SocialPolicy, WelfareDynamics,DurationAnalysis.

This researchwassupportedby HealthandWelfareCanadaandby the Ministèrede laSécurtiédurevenuof theGovernmentof Québec.Wearegratefulto PierreLanctôt,Jean-Paul Boudraux,JeanSt-Gelais,DenisThiboutotandGéraldTremblayfor their precioushelp in accessingandprocessingthe data,andto GhyslaineMorin, SuzanneLévesque,SergeHamelandMarie-RenéeRoy for theirusefulcommentsandadvice.Wefinally wishto thankNicolasBeaulieu,ClaudeBilodeau,Éric Couture,Patrick Déry, Éric Simard,ChristineSoucy andJean-FrançoisThibeaultfor their excellentresearchassistance.Re-mainingerrorsareoursalone.

August,1998

1 Intr oductionThemaingoalof provincial welfareprogrammesin Canadais to guaranteea basicmin-imum incomefor poor individuals and households.Up until recently, however, someworrying trendsin thenumberof welfaredependenthouseholdsandin the level of pro-grammespendinghave emerged. In every province therehasbeena dramaticincreasein welfarecaseloadandin programmeexpenditures.In Québec,for instance,between1980and1993,disbursementsrosefrom $1.860bto $3.146b(1991dollars),anincreaseof nearly60%.Over thesameperiod,thenumberof householdsonassistancegrew from285,174to 450,675,anincreaseof 58%.

Not surprisingly, this growth in the costsand in the numberof claimantshasledmostprovincial governmentsto considerreformingtheir welfareprogrammes.Already,Ontario,British ColumbiaandAlberta have introducedsignificantchanges;Québecisalsoenvisaginga majoroverhaulof its socialassistanceprogramme,which wasalreadyrevisedin 1989.Despitethispolitical interestin reforms,very few studieshaveexaminedthedynamicsof participationin welfarein Canada1. This lack of researchis particularlytimely for Québec,which,upuntil 1990,hadcaseloadshigherthanof any otherprovince(includingOntario,which hasa populationalmost50%larger)andwherethepercapitawelfarespendingof 400$wasby1992by farthelargestin Canada(seeCanadaAssistancePlan,AnnualReport1992).Wehave little or no information,for example,on theflow ofbeneficiariesinto andout of welfarein Québec,on householdslikely to experiencelongor frequentwelfarespells,ontheaveragedurationof welfarespells,or ontheincidenceofwelfarere-entries.Someclaim thatlengthyspellsonwelfare(i.e. definedby thenumberof consecutive monthson welfare)createa dynamicdependencewhich hastheeffect ofreducingtherecipients’chancesof exit. Is this true?Moreover, very little is known abouttheimpacton themajorreformthatoccurredin Québecin 1989.

A deeperknowledgeof thedynamicsof participationin theseprogrammesis of coursean essentialelementof a soundunderstandingof the characteristicsand of the effectsof the programmes,andof any discussionleadingto an eventualreform of the system.This papershedssomelight on someaspectsof theseimportantissuesby providing adescriptive examinationof welfareparticipationin Québec.In particular, it presentsananalysisof welfareexit andre-entryfor different categoriesof households.Exit ratesmeasurethe probability that a householdof a particulartype will leave assistancein aspecificinterval (e.g. during the sixth monthon assistance),given that it hasremainedon welfareuntil then. Similarly, re-entryratesmeasuretherisk thata household(whichhasalreadybeenin receiptof benefits)returnsto welfareduring a given time interval,given that it hasremainedoff social aid until then. Furthermore,we characterizethe

1Yet,seeBarrettandCragg(1998).Lacroix (1997)comparestheCanadianlongitudinalevidenceonwelfareparticipationavailablefor Québecandfor British Columbia. Cross-sectionalresearchon the determinantsofwelfareparticipationin CanadaincludesAllen (1993),CharetteandMeng(1994),andDooley (1994). For theUS evidence,seeBaneand Ellwood (1994) and Moffitt (1992), and, for a comparisonof the CanadianandAmericansystemsof assistance,BlankandHanratty(1993).

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averagedurationof spellson andoff welfarefor differentcategoriesof households.Wealsoderive thedistributionsof boththestartingandtheongoingspellsat agivenpoint intime. Finally, thispaperexaminestheoverall rateof dependenceonsocialassistance(i.e.theexpectedproportionof timespentonsocialassistance)afterahouseholdhasreceivedit once.Thisoverall ratecombinesourestimatesof bothentryandexit rates.

Amongotherthings,thepaperthusseeksto answerthefollowing questions:

1. How canonecharacterizethedynamicsof participationin socialassistance?Forex-ample,doexit ratestendto diminishwith thelengthof welfarespells?Conversely,how do re-entryratestendto varywith thelengthof timespentoff welfare?

2. Doesthisdynamicsvarywith thecharacteristicsof households?

3. Whichclaimantsareat risk for lengthyor frequentwelfarespells?

4. What is therelative importanceof shortandlong spellsin aggregatewelfarebud-gets?

5. Which socio-economiccharacteristicsseemassociatedwith a high overall rateofwelfaredependence?

To answerthesequestions,we usea representative sampleof individualswho hadaclaim between1979and1993,andmadeavailableto usby theMinistèrede la SécuritéduRevenu.Our analysisis thereforeconditionalon participatingin welfareat leastonceover the sampleperiodanddoesnot provide any informationon the decisionto claimsocialassistancefor thefirst timeover thelife cycle. This limitation,alsofoundin BarretandCragg(1998),mustbekeptin mind in whatfollows. Section2 of thepaperprovidesa detaileddescriptionof thesedata.Section3 presentsthebasicstatisticaltoolsutilizedto characterizethedynamicsof participation.Thesetoolsarethenappliedto thedatainSection4. Finally, Section5 providesa syntheticmeasureof welfaredependencebasedon theresultsof theprevioussection.Weconcludein Section6.

2 Samplingprocedureand basicdata descriptionThe datausedfor this study was drawn from the recordsof Québec’s ministèrede laSécuritédu Revenu. Thesefiles containinformationon all individualshaving receivedwelfarebenefitsatsometimebetween1979and1993.

The sizeof theseadministrative recordsmakesa studybasedon the entiredatabaseimpracticable,sowe drew a randomsample.Our samplingprocedureusedthe fact thatindividualfilesareorganizedby socialinsurancenumbers(SIN). Thus,eachSIN appearsexactly oncein thefiles, regardlessof the lengthor frequency of spells.A randomdrawfrom a uniform distribution generateda sampleof 95,514cases2. It shouldbenotedthatfor certainindividualsthestayonwelfarecanbeconsidered,for all intentsandpurposes,

2Thesamplingmethodologyandsamplesizearesimilar to thoseof BarrettandCragg(1998).

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permanent.Theseare individuals whosephysicalor mentalstateis suchthat, for anindeterminatelengthof time or even for life, they areunableto work. For obvious rea-sons,theseindividualsareexcludedfrom thesample.Thefinal sampleis thuscomprisedof individualshaving no handicapor only a minor, intermediate,or temporaryphysicalhandicap.Furthermore,they arefit to work.

Thesampleperiodrunsfrom January1979to December1993.A window of thissizeis necessaryto analyselengthyandrepeatedspellson welfare. Thesamplingprocedurewill pick up somespellswhich were ongoingin January1979 and somewhich havenot endedin December1993. In the first casewe have truncationon the left, in thesecond,truncationon the right. Truncationon the right doesnot poseany particularmethodologicaldifficulty, but truncationon the left is more delicate. For this reason,spellswhich wereongoingin January1979werefollowedbackasfar asJanuary1975.3

Spellsthatwereongoingat thatdateweresimply droppedfrom thesample.Thus,whilethe randomsamplewasdrawn from welfare recordsfrom the periodbetweenJanuary1979andDecember1993,somespellsactuallybegin asearlyasFebruary1975.

Tables1 and2 presentseveralcharacteristicsof thesample.Sincetheinformationistabulatedfor theperiod1979–1993,it providesaportraitof welfarerecipientsoverfifteenyears,andmaynot berepresentative of any givenyearwithin thatperiod.Table1 belowshows a decompositionof householdsby agegroups4. Thedistinctionbetween“coupleswith children” and“childlesscouples”is basedon the presenceor absenceof childrenundertheageof eighteenin thehouseholdduringthewelfarespell.

Readingrow-wise acrossthe rows of the table,we seethe distribution of typesofhouseholdsamongthe differentagegroups.We noticethat nearlyhalf of coupleswithchildrenarebetween31 and45 yearsold, andthat only 11.5%arebetween18 and24.Childlesscouplesareprimarily situatedin the18–24andthe56+ groups,asonewouldexpect. As to single-parentfamilies,over 45%of themarebetween31 and45 yearsofage.Finally, singlesarerelatively young,sinceover58%of themarein the18–24group.

Readingcolumn-wiseyieldsinformationabouttheagegroupsby householdtype.Weobserve thatsinglepeopleconstitutethe largestsegmentof all agegroups,which is notsurprisingsincethey represent62%of all householdsin oursample.Similarly, the18–24groupaccountsfor over 42% of the entiresample. The secondlargestgroup includesindividuals31–45yearsold, whomake up26%of thesample.

Table2 presentsthe joint distribution of ageandeducation.This datashows clearlythatyoungerpeopletendto bemoreeducatedthantheirelders,reflectingthatfactthatthelevel of schoolinghasgenerallyincreasedover time. Readingcolumn-wiserevealsthatindividualsin the18–24,25–30,and31–45agegroupsareconcentratedin theranges6–11 and11–14yearsof schooling.Individualsin groups46–55and56+ areconcentratedin the � 6 and6–11years-of-schoolingrange.

It is alsoof someinterestto examinethelevel of educationof differenttypesof house-

3Theadministrativerecordshaveonly beencomputerizedasof 1975.4Householdcharacteristicsdescribethoseobservedat the beginningof the first spell in the sampleperiod,

andpertainto theclaimantin thecaseof couples.

4

holds.Table3 below shows thatthemajority of individualson welfarehave betweensixandeleven yearsof schooling,i.e. have not completedhigh school. This is true for alltypesof households.Couplestendto bemoreheavily representedin the leasteducatedgroup( �� years),but thatpartly reflectsthefactthattheiraverageagetendsto behigherthanthatof othertypesof households.

3 MethodologyFor the purposesof our presentstudy, a welfarespell is definedasan uninterruptedse-quenceof monthsduringwhich a householdreceiveswelfarebenefits.Analogously, anoff-welfarespellis definedasanuninterruptedsequenceof monthsduringwhichahouse-hold doesnot receive welfarebenefits,following at leastonemonthof previouswelfarereceipt.Theprincipaladvantageof usingtheconceptof spellsis that thedistribution oftheirdurationscharacterizeexhaustively thedynamicsof welfareparticipation.

A usefultool for studyingthedurationof welfarespellsis theexit rate. For a house-holdreceiving welfare,theexit ratein month� correspondsto theprobabilitythatthespellwill endin thatmonth,giventhatit haslastedat least�� months.It is thusaconditionalprobability. For somepurposesit maybepracticalto divide thedurationof a spell into“windows.” Eachwindow encompassesa givennumberof months.An exit ratecanthenbeinterpretedastheprobabilitythata spellendsin window �� giventhat it wasongoingat theendof window �� Finally, theunit of observationfor estimatingexit ratesis thespell— a personhaving morethanonespell between1979and1993appearsasa newobservationat thebeginningof eachnew spell.

3.1 Derivation of the exit rates and of the associateddistribu-tions

The exit rate �� is simply computedasthenumberof spellsendingin the window �� dividedby thenumberof remainingparticipantsat thebeginningof thewindow,� �� , whosespellsareuntruncatedat thebeginningof or within thewindow. Formally,��! #"$ �! #" � Startingwith theexit rate,wecanderive two interestingdistributions:

1. Thedistribution of new spells

Thisdistributionyieldsthefrequency of thedurationof anew spell. Imaginethatwewereto draw 100new spellsat random.Let %&�� betheproportionof householdswhosespellslastexactly � windows. To obtaintheproportionof new spellswhichwill enduplasting� windows,it is sufficientto multiply theporportionof new spellsstill ongoingafter ��'� windows by theconditionalprobabilityof leaving duringwindow �� Recursively, weobtain:%(�)�*�+� ��)�*��%(�-,.�+� ��-,.�0/1�2�3%(��*�546�

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... (1)%&��7� �� 89 �:� <;0=>?@ = %(�BA��5CDE�Thefirst termontheright-handsideof thelastexpressionis simply theconditionalprobability of exit in window �� The secondterm is the probability of remaining(“surviving”) after �F�G� windows.

2. Thedistribution of ongoingspells

Imaginethat we wereto draw 100 spellsat randomout of all thoseongoingat aparticularpoint in time. How many of themwould eventuallyhave a total spelllengthof � windows? Notefirst that theprobabilityof drawing at randomamongall ongoingspellsa spell of long durationis higher than it is for one of shorterduration. For example,even if a sameproportionof householdsbeganone-andten-yearspellsat every point in time ( %H�)�*� and %I�)�KJ6� would thenbe equal),thelongerspellswould necessarilyconstitutea greatershareof a sampleof ongoingspellsat aparticularpoint in time(a shareabout10 timesgreater).Let LG�� betheproportionof ongoingspellsat any instantthatwill endup having a durationof �windows. Thisproportioncanbeestimatedin thefollowing manner:

LG�<��M� �)%&�<��NPO?�@ = A.%Q�1A�� (2)

Thesetwo estimateddistributionsshall beusefulfor understandingthedynamicsofwelfareparticipation.Off-assistancespellsaresimilarlyusedto estimatethere-entryratesandthedistribution of off-welfaredurations5.

3.2 Unobservedheterogeneity

An importantelementof thewelfareparticipationdynamicsis therelationbetweenspelldurationandexit rates. A negative relationis referredto as “negative durationdepen-dence”in the literature. Many factorsmay be responsiblefor negative durationdepen-dence.For example,a lengtheningspell on welfaremay senda badsignalto potentialemployersconcerningthebeneficiary’s level of motivation. Similarly, theerosionof hu-mancapitalmay have the effect of diminishingthe numberof job offers or simply theemploymentprospectsof thewelfarerecipient.Furthermore,theindividual’s tastesmaychangeover thecourseof thespellsoasto reducetherateof exit (e.g. discouragement).

5Given informationaboutthebeginningandthe lengthof repeatedspellson welfare,it is possibleto char-acterizethedurationof off-assistancespells.After transformationof thedata,calculatingthere-entryrateaftertheendof a spellon welfareis analogousto finding theexit rate: it is theratio of thenumberof spellsoff-aidwhichend(returnto welfare)over thenumberof spellswhichcouldbeending.Fromtheserates,wecanderivedistributionsthatareanalogousto thetwo describedabove.

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Finally, it is possiblethatalengthystayonwelfaremaymodifydemographicchoices(e.g.marriagerates,fertility, separation)which in turncandecreasetheprobabilityof exit.

Decreasingexit ratesmayalsobedueto “unobservedheterogeneity”within thewel-farepopulation.A decreasingprofile of exit ratesis thena purelystatisticalartifactwithnoconnectionto negative temporaldependence.To seehow, imaginethatwithin apopu-lation comprisinghouseholdswith differentexit probabilitiesbut with no “negative tem-poraldependence”,anexit ratefor thefirst window is calculatedfrom thebehaviour oftheentiresample.For subsequentwindows,let theexit ratebederivedfrom thebehaviourof thehouseholdswhosespellshave not ended.Theseestimateswill show progressivelysmallerexit probabilities,sincethe higher-rate groupswill disproportionatelyhave al-readyleft thesample.This observationcouldwrongly suggestnegative temporaldepen-dence.Wemustthereforebeprudentwheninferringcausalexplanationsfor thebehaviourof theexit ratesacrosstime.

4 Descriptiveanalysisof welfaredynamicsThissectionprovidesadetailedanalysisof theexit ratesfrom socialassistancealongwiththeir two associateddistributions. First, we examinetheentiresamplein orderto char-acterizethe behaviour of the “average”welfarerecipient. Subsequently, the analysisisrepeatedfor varioussocio-demographicgroups.Unlessotherwisestated,our datacoversthe interval from 1979to 1993,so that the calculatedexit ratesanddurationsrepresentaveragesover severalbusinesscyclesandin a changingenvironment.

4.1 Welfareexit rates

Table4 andFigure1 illustrateexit ratesfor theentiresample.As canbeseen,theseratesremainconstantfor thefirst two windows andthendecreasesignificantly. Thewindowscover a six-monthperiod,thoughthedatais monthly. In calculatingexit ratesfor thesewindows,wearein factcomputinganaverageof theexit ratesfor themonthsit comprises.This tableshows thatmany householdsexit welfaresoonafterentry. In fact,over34%ofnew entrantsleave within thefirst six months6. Of thoseremaining,33.9%leave withinthe following six months. Conditionalexit ratesdiminish regularly and thenstabilizearound8%.

Table5 andFigure2 decomposethe exit ratesamongfive householdtypes: singlemen and women,coupleswith and without children, and single-parentfamilies. Theexit ratefor thefirst six-monthwindow variesbetween25.4%for single-parentfamiliesand40.6%for coupleswith children. Thus,barelyonesingle-parenthouseholdin fourmanagesto getoff welfarein thefirst six months,while four in tencoupleswith childrendoso.Exit ratesremainfairly constantduringthefirst two windows for all of thegroupsin the table,thendropsubstantiallybeginningwith the third window. They converge to

6This is, however, low relative to the75%foundfor British Columbiaby BarrettandCragg(1998).

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8.0%for singlemenandwomenandfor single-parentfamilies,for childlesscouplestheyrapidly converge to 14% while for coupleswith childrenthey converge moreslowly to11%.

Figure3 decomposesexit ratesby agegroups.It is of interestto notethat increasingexit ratesarefound primarily amongyoungpeople. In fact, theseratesfor 18–24yearoldsclimb from 39.6%to 43.9%from thefirst to thesecondwindow beforefalling backto 36.5%in the third. This groupdemonstratesrelatively high exit rates— above 30%for many windows. However, very few individualsin this grouphave spellswhich lastmorethanfiveyears.The25–30and31–45agegroupspresentaconstantexit ratefor thefirst two windows while the46+ groupis characterizedby a decliningrateasof thefirstwindow. As canbeseen,theexit ratesprofile is highly correlatedwith age.

Figure4 presentsa breakdown of exit ratesby level of education.As expected,moreeducationimplies higher exit rates. The picture may however be complicatedby theexistenceof anegativecorrelationbetweenageandlevel of education.Sincemembersoftheyoungeragegroupsgenerallyhave moreschoolingthattheir elders(cf. Table1), andsinceyoungpeopletendto have higherexit rates,thevariationsin exit ratesattributableto educationmayin factbepartlyexplainedby age.

Figure5presentsexit ratesfor spellsbeginningin eachyearfrom1979to 1993andforwindowsof 1-6monthsand7-12months.As canbeseen,thesetwo seriesof exit ratesarepositively correlatedandserve to illustratetheimpactof businesscycleson thedynamicsof welfareparticipation. We candistinguishtwo cycles,startingwith the recessionofthe early 1980’s and that of the late 1980’s. It would neverthelessbe inappropriatetoattribute all the variationsin exit ratesto macroeconomicfluctuations.Several factors,perhapsin conjunctionwith thesecycles,mayplayarole. The1989reformof theQuébecwelfaresystementaileda sizablejump in benefitsto singlesandchildlesscouplesundertheageof 30. With theabolitionof discriminationbasedonage,theseclaimantsbecameeligible for thesamebenefitsastheir elders,yielding themanincreasein incomesupportof nearly100%. It is possiblethatthis increasein thebenefitsscaleis partly responsiblefor the fall in exit rates.Furthermore,we shouldnotethat theunemploymentinsuranceprogrammebecamesignificantlylessgenerousafter1989,measuredin termsof theratioof themaximumnumberof weeksof benefitsto theminimumnumberof weeksof workrequiredto qualify. This typeof changerenderswork lessattractive to individualswith aweakattachmentto thelabourmarket,especiallyto theextentthatthey anticipateperiodsof unemployment in the future. Finally, the real minimum wagestagnatedat a historiclow in theperiodbetween1986and19937. A priori, theeffect of theminimumwageontheexit rateis ambiguous.A low minimumwageunderminestheattractivenessof work,reducingthesupplyof unskilledlabour, but it simultaneouslyincreasesits demand.Allthesefactorscombineto explain at leastpartly theobserved fall in the rateof exit from1989.

Oneway of partially isolating the effect of the 1989reform which doesn’t rely on

7Between1975and1993, the minimum wageaveraged$4.84in 1986dollars. In 1976-1977it peaked at$6.00,andthenfell to a low of $3.97in August1986.It hassincehoveredaround$4.30in 1986dollars.

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sophisticatedstatisticaltechniquesis to examinetheprofileof exit ratesbeginningbefore1989andto compareit with thepost-1989data8. Assumingthat thebusinesscycle, theU.I. programandtheminimumwageaffect all agegroupsequally, observed changesintheexit rateacrossagegroupsmaybeattributableto thereform. Needlessto say, to theextent that changesin the economicenvironmentdo not affect all agegroupsequally,the observed effectsmay not be entirely due to the reform. The analysisis presentedin Figures6 to 8 for eachperiod. We seethat before1989youngpeoplehadexit ratessignificantlyhigherthanthoseof theirelders.Theseexit ratesfell after1989to levelsthataresignificantlycloserto theirelders’.It is of interestto notethatexit ratesfor the31–45agegroupdid not really changeacrossthetwo periods9. We thusobserve acrossthetwoperiodsan increaseor stagnationof exit ratesfor the30+ groupalongwith a significantdeclinefor theunder30groups.Of course,therecessionof 1989–93maywell have hurtyoungpeopleharderthanothers,but thevariationsin their exit ratesarelargeenoughtosuspectthatthereformprobablyhadasignificantimpacton thedurationof theirspells.

4.2 Averagedurations on welfare

The precedingsectionprovided a detailedanalysisof the exit profilesof several socio-demographicgroups. This information may be condensedinto a measureof averageduration. Recall that the exit rate, � , representingthe probability of exit from welfareduringwindow � given that thehouseholdreceivedbenefitsuntil at leastwindow ��R� �canbewrittenas: ��<��M� � �� (3)

Theexpression� �� represents“survival” until �� We caneasilyshow that

� �� maybeexpressedas: � ��TS VUXWY /1�2�Z��<� ? �546� �\[GJ]� (4)

Finally, we canalsoshow that the expecteddurationon welfaremay be expressedasafunctionof

� �� : ^ �<��M� O>?�@`_ � �1A�� (5)

Thislastexpressionsimplysaysthattheexpecteddurationis thesumof thesurvival func-tionsover all theperiods.In theprecedingsection,exit rateswerecalculatedfor only 17windows. Consequently, to calculateexpecteddurations,we needto make somefurtherassumptionsconcerningthesurvival ratebeyondthewindowsused.Twoapproacheshavebeenproposedin theliterature:

1. Onemayassumethat theexit rateof the lastwindow consideredremainsconstantfor all subsequentwindows (e.g. BaneandEllwood(1983)).

8Spellsbeginningbefore1989andcontinuingpastDecember1988arecensored.9In fact,exit ratesfor theover45groupincreasedafter1989.

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2. Onecanusetheexit ratesfrom thewindows we have beenconsideringto estimatea second-or third-orderautoregressive function. Theestimatedparametersmaybeusedto predicttheexit ratefor subsequentwindows (e.g. KatzandMeyer (1990)).

We usethe secondapproachin this paper. In all cases,third-orderautoregressivefunctionswereusedto calculatetheexit ratefor subsequentwindows10. Usingthis, wefind thattheexpecteddurationof a spellon welfareis slightly lessthantwo years.Table6 disaggregatesthis variableover varioustypesof households.Exceptfor single-parentfamilies,it is around22months.Singlewomenhaveslightly longerspellsthansinglemen(23.49vs. 21.28months)andcoupleswith childrenalsohave spellsmarginally longerthat childlesscouples(22.57vs. 19.70months). Furthermore,it is interestingto notethat the averagedurationof spellsfor single-parentfamilies is essentiallythe sameasthatobtainedby BaneandEllwood(1983)in their studyof AFDC (Aid to FamilieswithDependentChildren). In fact,our resultsshow that theexpecteddurationis 41 months,while thecorrespondingfigurewas48monthsin theirstudy.

Table6 alsoclearly indicatesthe positive correlationbetweenthe durationof spellsandtheageof claimantson onehand,andthenegative correlationbetweenthis durationandthe level of educationon theotherhand.Welfarespellsof 18–24year-oldshave anmeandurationof barely12.8months,while claimantsover 45 have spellsof morethan49 monthson average.Also, they aremuchlongerfor individualswith little schoolingthanfor theirmoreeducatedcounterparts(37.30vs.17.14months).

4.3 Distributions of newand ongoingspells

In section3.1 we introducedtwo distributionswhich canbecalculateddirectly from theexit rates.Thefirst, %(��a� is thedistribution of the lengthof a spell randomlyselectedamongall startingspells,andthesecond,Lb�� is thedistribution of thelengthof aspellrandomlyselectedamongall ongoingspells. Table7 presentstheseestimateddistribu-tions for the entiresample,illustrating the flow andstockeffectsof participationin thewelfareprogramme.Thus,thereis a 34%probabilitythatanew spellwill endwithin sixmonths(column %I�� ). Overhalf of thenew spells(56%)will endwithin twelvemonths.Thus,few of thenew spellswill beof long duration11. Conversely, spellslastingmorethanfiveyearsaccountfor 54%of thespellsongoingatany point in time(column LE�� ),andspellslongerthaneightyearsaccountfor 39%.

Table7 alsopresentstheseestimatesfor differenthouseholdtypes.Thedistributionsof new andongoingspellsfor singlewomenis slightly tilted forward comparedto thatof men. This simply confirmsthat they have marginally longerdurationsthanmendo.Similarly, the distribution for coupleswith childrenis slightly offset from thatof child-lesscouples.Themoststriking informationinformationin this table,however, concerns

10Expecteddurationswerein factcomputedusingmoredisaggregatedmonthlyexit rates.11They areevenfewerin BritishColumbia,whereonly 10%of new spellsarestill ongoingafter1 year(Barrett

andCragg(1998)).

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single-parentfamilies.Over half of ongoingspellsat any timewill eventuallyhave a du-rationof overeightyears.Only25%of new spellswill endin lessthansixmonths.Again,theseresultshavearemarkableresemblanceto thosefoundby BaneandEllwood(1983).In their study, 29%of single-parentfamiliesbeginninga spellon welfareleave it withinsix months,and19%within thefollowing six months(17%in ourstudy).Moreover, longspells(8+ years)accountfor 45.7%of theongoingspellsatany time.

Anotherwayof illustratingthedistributionof welfarespellsis byplottingtheirLorenzcurve(Figure9). Onthehorizontalaxis,wefirstorderspellsby theirlengths,startingwiththeshortestonesandendingwith the longest.On theverticalaxis,we expressthepro-portionof theaggregatewelfareduration(or of ongoingspells,andthusapproximatelyofaggregatewelfarespending)accountedfor by a certainpercentageof thesmallestspells.We find that the 50% shortestwelfarespellsaccountfor only 10%of the total ongoingwelfarespellsandspending.Conversely, the50%longestspellsaccountfor 90%of to-tal welfareoutlays.Figure9 alsoindicatesthatthe20%shortestspellscontributeto littlemorethan2%of aggregatewelfarespending,whereasthelongest20%accountfor around70%of aggregatewelfareduration.

4.4 Ratesof welfare re-entries

Oneof thekey elementsof theoveralldynamicsof welfareparticipationconcernstherateof re-entryto welfareafterhaving exited. Table8 andFigure10presentsuchratesof re-entryfor theentiresample.We find that22%of householdsleaving welfareat any pointin time will returnwithin six months,andanother11% within the following six monthperiod. In British Columbia,a full 50%returnwithin a year(BarrettandCragg,1998).Re-entryratesslowly declineto about2%. Thus,the longerthepersonis off assistance,the lesslikely he or sheis to return. Column3 of Table8 containsinformationon thedistribution of new off-welfarespells. It revealsthat over 42% of theseexiting welfareparticipantswill returnto welfarewithin two years.Furthermore,38.6%of householdsleaving welfareatany point in timewill remainoff welfarefor at leasteightyears.

Figures11, 12 and13 provide informationon re-entryratesandcontaindisaggrega-tionsanalogousto thoseof Figures2, 3 and4. Themainresultsareasfollows:

1. While singlewomenhave a longeraveragedurationonwelfarethanmen,thelatterhave higherre-entryrates.

2. Childlesscoupleshave bothhigherexit ratesandlower re-entryratesthancoupleswith children.

3. Single-parenthouseholdshave re-entryrateswhicharebarelyhigherthantheover-all re-entryrates.

4. There-entryratesof theagegroups18–24,25–30,and31–45arepracticallyiden-tical. The46+grouppresentsa returnprofile lower thantheothergroups.

5. Theratesof re-entrydecomposedby level of educationarevirtually identical.

11

Otherresults,notshown here,indicatethatre-entryratesprofilesarecounter-cyclical,unlike exit rates. We also found two peaksof monthly re-entryratesat about12–13monthsand17–18months12, sothereappearto bemarkedincreasesin returnsto welfareafter aboutoneandone-and-a-halfyearsoff aid. Sincewe do not have the reasonsforentryandexit, it is difficult to explain this phenomenon.Nonetheless,to theextent thatindividuals quit welfare to take a job, the increasein re-entryratesmay be relatedtothe parametersof the unemployment insuranceprogramme.In fact, dependingon theyearandthe region, theminimumnumberof weeksof work requiredto qualify for theprogrammevariesbetweentenandtwelve, with benefitsbeingpaid for 42 to 52 weeks.Consequently, individualsquittingwelfareto takea job providing therequirednumberofweeks,andthenexhaustingtheirinsurancebenefits,wouldindeedcauseapeakin re-entryratesat about12–13months.

A possibleexplanationfor the eighteenmonth peak is the existenceof the “Pro-grammed’Aide àl’intégrationàl’emploi”. Underthisprogramme,afirm hiring awelfarerecipientmayhave a part of thewagereimbursedfor a periodof up to 26 weeks.Dur-ing this probationperiodthe individual contributesto theunemploymentinsurancepro-gramme,andthusmaybecomeeligible for benefits.At theendof this periodthetraineemay not receive a permanentjob offer, andmay thenreceive unemployment insurancebenefitsfor up to 42 weeks.In all, this individual will have beenoff-assistancefor about17–18months,correspondingto thesecondpeak.

4.5 Mean durations of off-welfarespells

Table6 showsthemeandurationsof off-assistancespellsfor differentsocio-demographicgroups.Takentogether, theprofileof off-aid durationsdifferssomewhatfrom theon-aidprofile. Thus,while the lengthof spellson welfareis slightly shorterfor menthanforwomen,the off-welfarespellsof the latter areconsiderablylonger. Also, coupleswithchildrenhave on-aidspellswhich arelongerthanthoseof childlesscouples,andoff-aidspellswhichareshorter. Moreover, the18–24,25–30and31–45agegroupsseemto haveoff-aid durationswhich aresimilar to, but lower than,thoseobserved for the46+group.Finally, theredoesnot appearto be a strongcorrelationbetweenthe level of educationandtheexpectedlengthof off-assistancespells.

5 Overall ratesof welfaredependenceThedescriptive analysisof theprecedingsectionshasshedsomelight onthedynamicsofparticipationin welfarefor theperiod1979–1993.It hasamongotherthingsallowedustoidentify groupswhosebehaviour is characterizedeitherby lengthyspellsonwelfareor byfrequentreturnsto welfare.Now, theresultspresentedthusfar donot combinethesetwo

12BarrettandCragg(1998)alsofind a peakin re-entryratesat abouteleven monthsin their samplefromBritish Colombia.They partiallyattributeit to seasonality.

12

essentialcomponentsof the dynamicsof welfareparticipationinto a syntheticmeasureof dependence.Sucha measureis requiredif we wish to compareobjectively differentgroupscharacterizedby varyingaveragedurationsonandoff- welfare.

Thereare several ways to definewelfare dependence.For our purposes,we shallproposea measurewhich combinestheadvantagesof computationalsimplicity with anintuitive interpretation.We definethe rate of dependenceasfollows. Let %dcHe be theaveragedurationof on-welfarespellsfor group f��]%hg�cHe thecorrespondingoff-welfareaverage,and %Ei e �j%hc elk %hg�c e thetotal meandurationof anon-aid/ off-aid cycle.Onemeasureof therateof dependence,mneo� is thus:

mnep� %hc e%Ei�e � (6)� %hcIeaq �%Eiè (7)

The rateof dependencethuscorrespondsto the proportionof an entirecycle which isspenton welfare.Thesecondtermon theright-handsideof equation�5rs� is a measureofthefrequency with which agivengroupbeginsanew cycle. For example,if %EièF�Q�KJsJ]�then =tFuwv ��J]�xJy� � andgroup f hasonechancein 100of startinganew cycle in any month.Multiplying thisby %dcHe givesustheexpectedproportionof aperiodof timeweexpectamemberof group f to spendonwelfareafterhe/shehasenteredwelfarefor thefirst time.It shouldbenotedthatagrouphaving ahighaveragedurationof welfarespellsandalongcycle (rarereturns)mayhave thesamevaluefor its rateof dependenceasa groupwith ashorteraveragelengthof welfarespellscombinedwith a shortercycle (frequentreturns).

Table9 presentsdependenceratesby householdtype.Thetableshowsthatsinglemenexhibit adependenceratehigherthandowomen,despitethefactthattheirwelfarespellsareshorteronaverage.Theirgreaterdependenceis explainedby morefrequentre-entriesinto welfare.Single-parentfamiliesclearlyhave a high rateof dependencebecausetheirlongerspellscombinewith morefrequentreturns;oncethey have claimedwelfarea firsttime,weexpectsingleparentsto spendonwelfare37.7%of thesubsequenttimeperiods.Finally, childlesscouplesshow a dependenceratesignificantlylower thancoupleswithchildrenbecausethey returnto welfaremuchlessfrequently13.

Tables10 and11 presentoverall welfaredependenceratesby agegroupandeduca-tion level for menandwomen. We seethatmenandwomenarequitedifferentin theirbehaviour vis-à-viswelfare.While thelengthof welfarespellsis shorterfor menthanforwomenin all groups,theformersystematicallyreturnto socialassistancemorequickly.Nonetheless,thishigherfrequency doesnot entirelycompensatefor their shorterwelfarespells,sothatwomen’s rateof welfaredependenceis generallyhigherthanmen’s. Ratesof dependencearestronglypositively correlatedwith age,andnegatively with education.

13Lacroix (1997)alsoshows thatdespitethefact thatthey stayoff welfarelonger, Québecwelfarerecipientsexhibit greaterwelfaredependencethanin British Columbia,exceptfor singleparents(this is dueto a signifi-cantlygreaterz�{}| ).

13

Rising from lessthan6 yearsof educationto morethan15 decreasesthe proportionoftimespentonwelfareby asmuchas15%for menor women.

6 ConclusionThegrowth in expenditureson Canadiansocialassistanceprogrammesandthe increasein thenumberof claimantsupuntil recentlyhasledto many callsfor thoroughreformsoftheprogrammes.To ourknowledgevery few studieshaveexaminedthedynamicsof wel-fareparticipationin Canada.A detailedunderstandingof thesedynamicsis neverthelessessentialfor any enlighteneddiscussionof possiblereforms.

To contributeto abetterunderstandingof thefeaturesandof theeffectsof theQuébecsocial assistanceprogramme,we usein this papera representative sampleof welfarerecipientsbetweenthe years1979and1993,madeavailable to us by the ministèredela Sécuritédu Revenu. Descriptive tools thenenableus to characterizethe durations,exit andre-entryratesfor severalcategoriesof householdsandthusto identify high-riskgroups.

Wefind thatthemajorityof startingspells(56%)will lastfor lessthanoneyear. Exitratestendto decreasequitesharplywith the lengthof thespell. While mostnew spellsareof fairly shortduration,it remainsthata largeproportionof ongoingspellsareof longduration.We estimatefor instancethat70%of aggregatewelfaredurationandspendingis accountedfor by the20%longestspells.

Overall, single men leave welfare more rapidly than single women,young peoplefasterthan their elders,andmoreeducatedindividuals soonerthan their lesseducatedcounterparts.It alsoappearsthat the businesscycle hasa significantinfluenceon thatdynamics.Thus,theexit ratein thefirst six monthsof 1986,a yearof economicgrowth,was37%, while the correspondingnumberfor the first six monthsof 1991wasbarely29%.

Theimportantwelfarereformthatoccurredin Québecin 1989eliminateddiscrimina-tion on thebasisof age.As aconsequence,thebenefitsscalefor singleindividualsunderthirty morethandoubledbetween1988and1990,rising from $2072to $5108annually(1986dollars).Conversely, it fell slightly for thethirty plusgroup,from $5495to $5108.Theexit rateof participantsover thirty remainedrelatively stablebeforeandafter1989.After 1989,we neverthelesswitnessa sharpdrop in the exit ratesfor the underthirtygroup. Thereformthusappearsto have hadanimportantimpacton theexit ratesof theyoungergroup.

Between1979and1993,we estimatethattheexpectedlengthof anongoingwelfarespellwas25.5months,but thatof a starting(or new) spellwasaround17 months.Thatlengthis twiceaslongfor single-parenthouselholdsasfor otherhouseholdtypes.Returnsontowelfaregenerallyoccurshortlyafterexit, andat a ratewhich diminisheswith time.Single-parenthouseholdstakeanaverageof 67monthsto returnto welfareoncethey haveleft; singlewomenandchildlesscouplesreturnafter92 monthson average.Re-Entryis

14

fasterfor youngpeopleandvarieslittle with education.Finally, ourresultsindicatethatwelfaredependenceisalmosttwiceaslargefor single-

parenthouseholdsasfor any othertypesof households.The dependencerateof singlemenalsoexceedsthat of singlewomen. Finally, theseratesincreasesignificantlywithageanddecreasewith theclaimant’s level of education.

References

Allen, DouglasW. (1993),"Welfareandthefamily: theCanadianexperience,"Journalof LaborEconomics11,s201-s221

Bane,Mary JoandDavid T. Ellwood(1983),"Thedynamicsof dependence:theroutesto self sufficiency," Reportpreparedfor theU.S.Departmentof HealthandHumanServices

Bane,Mary Jo andDavid T. Ellwood (1994), "Welfare realities: from rhetoric to re-form," Harvard University Press

Barrett,GarryF. andMichael I. Cragg(1998),"An untoldstory: thecharacteristicsofwelfareusein British Columbia,"CanadianJournalof Economics31,165-188

Blank,RebeccaM. andMariaJ.Hanratty(1993),"Respondingto need:acomparisonofsocialsafetynetsin CanadaandtheUnitedStates,"in D. CardandR.B. Freeman,eds,SmallDifferencesthatmatter, ChicagoUniversityPress,190-231

Charette,MichaelF. andRonaldMeng(1994),"The determinantsof welfareparticipa-tion of femaleheadsof householdin Canada,"CanadianJournalof Economics27,290-306

Dooley, Martin D. (1994), "The useof social assistanceby Canadianlone mothers,"Mimeo,Departmentof Economics,McMasterUniversity

Lacroix, Guy (1997),"Reformingthe welfaresystem:in searchof the optimal policymix," preparedfor theIRPPconference:"AdaptingPublicPolicy to aLabourMar-ket in Transition"

Katz,L.F. andB.D. Meyer (1990),"The Impactof thePotentialDurationof Unemploy-mentBenefitsontheDurationof Unemployment,"Journalof PublicEconomics41,45–72.

Moffitt, Robert(1992),"Incentive effectsof theU.S.welfaresystem:areview," Journalof EconomicLiterature 30,1-61

15

Table1: Distributionof agegroupsby householdtype~(Proportionof therow total)

[Proportionof thecolumntotal]Household 18–24 25–30 31–45 46–55 56+ TotalCouples 2003 3425 8554 2297 1092 17371with (0.115) (0.197) (0.492) (0.132) (0.062) (1.00)children [0.049] [0.228] [0.343] [0.312] [0.150] [0.182]Childless 2079 1094 1289 914 2173 7549couples (0.275) (0.144) (0.170) (0.121) (0.287) (1.00)

[0.051] [0.073] [0.011] [0.124] [0.298] [0.079]Single- 2297 2246 5055 1115 467 11180parent (0.205) (0.200) (0.452) (0.099) (0.041) (1.00)families [0.056] [0.149] [0.202] [0.151] [0.064] [0.117]Single 34248 8223 10018 3029 3545 59063persons (0.579) (0.139) (0.169) (0.051) (0.060) (1.00)

[0.843] [0.548] [0.402] [0.411] [0.487] [0.620]Total 40627 14988 24916 7355 7277 95163

(0.426) (0.157) (0.261) (0.077) (0.076)[1.00] [1.00] [1.00] [1.00] [1.00] [1.00]�

In thecaseof couples,ageappliesto theclaimant.

Table2: Distributionof agegroupsby level of education(Proportionof therow total)

[Proportionof thecolumntotal]Education 18–24 25–30 31–45 46–55 56+ Total�I� 1598 950 3267 2275 3704 11794

(0.135) (0.080) (0.277) (0.192) [0.314) (1.00)[0.039] [0.063] [0.131] [0.308] (0.508] [0.123]

6 – 11 27144 8583 13978 3986 2992 56683(0.478) (0.151) (0.246) (0.070) [0.052) (1.00)[0.668] [0.572] [0.560] [0.540] (0.410] [0.595]

11– 14 10568 3787 5041 729 426 20551(0.514) (0.184) (0.245) (0.035) [0.020) (1.00)[0.260] [0.252] [0.202] [0.098] (0.058] [0.215]

14+ 1326 1678 2650 380 168 6202(0.213) (0.270) (0.427) (0.061) [0.027) (1.00)[0.032] [0.111] [0.106] [0.051] (0.023] [0.065]

Total 40636 14998 24936 7370 7290 95230(0.426) (0.157) (0.261) (0.077) (0.076) (1.00)[1.00] [1.00] [1.00] [1.00] [1.00] [1.00]

16

Table3: Distributionof householdtypesby educationlevel(Proportionof therow total)

[Proportionof thecolumntotal]Education Childless Couples Single- Singles Total

Couples with parent personschildren families�I� 3296 1848 1339 5335 11818

(0.279) (0.156) (0.184) (0.451) (1.00)(0.194] [0.243] [0.118] [0.090] [0.124]

6 – 11 10363 3966 7356 35151 56836(0.182) (0.069) (0.129) (0.618) (1.00)[0.612] [0.523] [0.652] [0.594] [0.598]

11– 14 2766 1257 2094 14427 20544(0.134) (0.061) (0.101) (0.702) (1.00)[0.163] [0.165] [0.185] [0.244] [0.216]

14+ 509 509 492 4225 5735(0.088) (0.088) (0.085) (0.736) (1.00)[0.030] [0.067] [0.043] [0.071] [0.060]

Total 16934 7580 11281 59138 94933(0.178) (0.079) (0.118) (0.622) (1.00)[1.00] [1.00] [1.00] [1.00] [1.00]

17

Table 4Welfare exit rates, total sample

Windows�

Exit rates(months)

1 to 6 0.34047 to 12 0.339213 to 18 0.248619 to 24 0.200325 to 30 0.172331 to 36�

0.150937 to 42�

0.141643 to 48�

0.126549 to 54�

0.125055 to 60 0.110861 to 66 0.105367 to 72 0.100673 to 78 0.096679 to 84 0.090185 to 90�

0.089391 to 96 0.0878

more than 96 0.0800� � � � � � ��

0.0000�0.0500�0.1000�0.1500�0.2000�0.2500�0.3000�0.3500�0.4000�

1 to

6

7 to

12

13 to

18

19 to

24

25 to

30

31 to

36

37 to

42

43 to

48

49 to

54

55 to

60

61 to

66

67 to

72

73 to

78

79 to

84

85 to

90

91 to

96

mor

e th

an 9

6

18

Table 5Welfare exit rates by type of households

Windows�

Single men Single women Single heads Couples Couples(months) (without children) (with children)

1 to 6 0.3627 0.3330 0.2543 0.4064 0.36057 to 12 0.3864 0.3407 0.2291 0.3889 0.358513 to 18 0.2957 0.2806 0.1709 0.2580 0.248619 to 24 0.2391 0.2150 0.1381 0.2074 0.215525 to 30 0.2047 0.1965 0.1248 0.1787 0.179931 to 36�

0.1758 0.1646 0.1073 0.1621 0.170637 to 42�

0.1554 0.1671 0.1045 0.1410 0.162543 to 48�

0.1396 0.1399 0.0989 0.1532 0.138549 to 54�

0.1230 0.1305 0.1084 0.1493 0.141555 to 60 0.1154 0.1150 0.0840 0.1453 0.135561 to 66 0.0984 0.1246 0.0863 0.1491 0.118867 to 72 0.1017 0.1234 0.0740 0.1436 0.118473 to 78 0.0836 0.1002 0.0844 0.1533 0.113479 to 84 0.0871 0.0847 0.0788 0.1417 0.104085 to 90�

0.0862 0.0934 0.0776 0.1548 0.096391 to 96 0.0697 0.0922 0.0740 0.1390 0.1157

more than 96 0.0700 0.0900 0.0700 0.1300 0.1050� � ¡ ¢ £ ¤¥ ¦ § ¨ © ª « ¬ ® ¯ ° ± ² ³ ´ µ ¶ · ¸ ¹ º » ¼ ½ ¾ ¿ À Á Â Ã Ä Å Æ

0.0000�0.0500�0.1000�0.1500�0.2000�0.2500�0.3000�0.3500�0.4000�0.4500�

1 to

6

7 to

12

13 to

18

19 to

24

25 to

30

31 to

36

37 to

42

43 to

48

49 to

54

55 to

60

61 to

66

67 to

72

73 to

78

79 to

84

85 to

90

91 to

96

mor

e th

an 9

6

Single headsÇSingle womenÇCouples (with children)ÈSingle menÇCouples (without children)È

19

Table 6Expected durations

On welfare Out of welfare(months) (months)

By type of householdSingle men 21.28

É73.44

Single women 23.49É

92.47Single heads 40.81

�67.24

Couples (without children) 19.70 91.95Couples (with children) 22.57

É77.78

By age18-24 years old 12.82 76.4825-29 years oldÉ

20.00É

72.3830-45 years old�

29.29É

74.81more than 45 years old 48.92 98.91

By education0-5 years 37.30

�85.71�

6-10 years 26.10 72.8811-13 years 18.33 87.16

�more than 13 years 17.14 91.31

20

Tab

le 7

Dis

trib

utio

ns o

f new

spe

lls (

D(t

)) a

nd o

f ong

oing

spe

lls (

F(t

)) b

y ty

pe o

f hou

seho

lds

Win

dow

sS

ingl

e m

enS

ingl

e w

omen

Sin

gle

head

sC

oupl

es

Cou

ples

T

otal

sam

ple

(mon

ths)

(with

out c

hild

ren)

(with

chi

ldre

n)D

(t)

F(t

)D

(t)

F(t

)D

(t)

F(t

)D

(t)

F(t

)D

(t)

F(t

)D

(t)

F(t

)1

to 6

36.2

700

5.11

3933

.300

04.

2536

25.4

300

1.86

5740

.640

06.

1900

36.0

500

4.79

1134

.040

04.

0106

7 to

12

24.6

253

10.4

162

22.7

247

8.70

8417

.084

03.

7602

23.0

851

10.5

484

22.9

261

9.14

0722

.373

67.

9082

13 to

18

11.5

633

8.15

1912

.339

57.

8810

9.82

443.

6039

9.35

897.

1274

10.1

985

6.77

7010

.835

66.

3832

19 to

24

6.58

526.

4994

6.80

176.

0818

6.58

213.

3803

5.58

245.

9518

6.64

296.

1799

6.56

005.

4103

25 to

30

4.28

985.

4435

4.87

995.

6101

5.12

673.

3852

3.81

235.

2260

4.35

045.

2036

4.51

274.

7851

31 to

36

2.93

004.

5443

3.28

454.

6150

3.85

773.

1133

2.84

024.

7586

3.38

344.

9461

3.27

124.

2396

37 to

42

2.13

473.

9127

2.78

554.

6256

3.35

393.

1989

2.07

004.

0988

2.67

294.

6180

2.60

643.

9921

43 to

48

1.61

963.

4254

1.94

243.

7218

2.84

253.

1281

1.93

204.

4140

1.90

793.

8035

1.99

883.

5324

49 to

54

1.22

782.

9430

1.55

843.

3841

2.80

743.

5015

1.59

444.

1283

1.67

933.

7941

1.72

523.

4555

55 to

60

1.01

032.

7064

1.19

412.

8981

1.93

972.

7038

1.32

003.

8200

1.38

053.

4860

1.33

812.

9954

61 to

66

0.76

202.

2563

1.14

503.

0714

1.82

542.

8123

1.15

773.

7030

1.04

642.

9204

1.13

082.

7977

67 to

72

0.71

012.

3027

0.99

272.

9164

1.43

012.

4132

0.94

883.

3237

0.91

902.

8090

0.96

652.

6192

73 to

78

0.52

431.

8483

0.70

662.

2564

1.51

042.

7704

0.86

743.

3029

0.77

602.

5781

0.83

472.

4587

79 to

84

0.50

061.

9058

0.53

741.

8535

1.29

122.

5577

0.67

892.

7917

0.63

092.

2640

0.70

342.

2375

85 to

90

0.45

231.

8494

0.54

242.

0094

1.17

132.

4921

0.63

652.

8116

0.52

352.

0175

0.63

432.

1673

91 to

96

0.33

421.

4607

0.48

551.

9223

1.03

032.

3433

0.48

312.

2810

0.56

842.

3416

0.56

802.

0744

mor

e th

an 9

64.

4606

35.2

200

4.77

9834

.191

012

.892

852

.970

12.

9923

25.5

230

4.34

3932

.329

45.

9000

38.9

437

21

Ê Ë Ì Í Î Ï ÐÑ Ò Ó Ô Õ Ö × Ø Ù Ú Û Ü Ý Þ ß à á â ã ä å

0.0000�0.1000�0.2000�0.3000�0.4000�0.5000�0.6000�

1 to

6

7 to

12

13 to

18

19 to

24

25 to

30

31 to

36

37 to

42

43 to

48

49 to

54

55 to

60

61 to

66

67 to

72

73 to

78

79 to

84

85 to

90

91 to

96

mor

e th

an 9

6

18-24 years old

25-29 years oldæ30-45 years oldçmore than 45 years old

è é ê ë ì í îï ð ñ ò ó ô õ ö ÷ ø ù ú û ü ý þ ÿ � � � � � � � � �

0.0000�0.0500�0.1000�0.1500�0.2000�0.2500�0.3000�0.3500�0.4000�0.4500�

1 to

6

7 to

12

13 to

18

19 to

24

25 to

30

31 to

36

37 to

42

43 to

48

49 to

54

55 to

60

61 to

66

67 to

72

73 to

78

79 to

84

85 to

90

91 to

96

mor

e th

an 9

6

0-5 years�6-10 years

11-13 years

more than 13 years�

22

� � � � � �� ! " # $ % & ' ( ) * + , - . / 0 1

0.0000�0.1000�0.2000�0.3000�0.4000�0.5000�0.6000�

1979

1980

1981

1982

1983

1984

1985

1986

1987

1988

1989

1990

1991

1992

1993

1-6 months

7-12 months2

23

3 4 5 6 7 8 9: ; < = > ? @ A B C D E F G H I J K L M N O P Q R S T U V W

0.0000�0.0500�0.1000�0.1500�0.2000�0.2500�0.3000�0.3500�0.4000�0.4500�0.5000�

1 to

6

7 to

12

13 to

18

19 to

24

25 to

30

31 to

36

37 to

42

43 to

48

49 to

54

55 to

60

before 1989Xafter 1989Y

Z [ \ ] ^ _ à b c d e f g h i j k l m n o p q r s t u v w x y z { | } ~

0.0000�0.0500�0.1000�0.1500�0.2000�0.2500�0.3000�0.3500�0.4000�0.4500�

1 to

6

7 to

12

13 to

18

19 to

24

25 to

30

31 to

36

37 to

42

43 to

48

49 to

54

55 to

60


� � � � � � �� ¡ ¢ £

0.0000�0.0500�0.1000�0.1500�0.2000�0.2500�0.3000�0.3500�

1 to

6

7 to

12

13 to

18

19 to

24

25 to

30

31 to

36

37 to

42

43 to

48

49 to

54

55 to

60


24

Figure 9Lorenz curve of the distribution of

welfare spells¤

0¥

20 40 60 80 1000

¥

20¦

40

60

80

100

% of smallest welfare spells

% of aggregate welfare duration

25

Windows�(months)

1 to 6 0.2182 0.2182 0.04537 to 12 0.1057 0.0826 0.051513 to 18 0.1042 0.0729 0.075619 to 24 0.0733 0.0459 0.066725 to 30 0.0604 0.0351 0.065531 to 36�

0.0508 0.0277 0.063337 to 42�

0.0434 0.0225 0.060643 to 48�

0.0394 0.0195 0.060749 to 54�

0.0344 0.0164 0.057755 to 60 0.0302 0.0139 0.054761 to 66 0.0287 0.0128 0.055767 to 72 0.0268 0.0116 0.055473 to 78 0.0242 0.0102 0.052979 to 84 0.0212 0.0087 0.048885 to 90�

0.0207 0.0083 0.050191 to 96 0.0198 0.0078 0.0502

more than 96 0.0190 0.3860 0.0853

Welfare re-entry rates

Re-entry rates D(t) F(t)

Table 8§

¨ © ª « ¬ ® ¯° ± ² ³ ´ µ ¶ · ¸ ¹ º » ¼ ½ ¾ ¿ À Á Â Ã

0.0000�0.0500�0.1000�0.1500�0.2000�0.2500�

1 to

6

7 to

12

13 to

18

19 to

24

25 to

30

31 to

36

37 to

42

43 to

48

49 to

54

55 to

60

61 to

66

67 to

72

73 to

78

79 to

84

85 to

90

91 to

96

mor

e th

an 9

6

26

Ä Å Æ Ç È É Ê ËÌ Í Î Ï Ð Ñ Ò Ó Ô Õ Ö × Ø Ù Ú Û Ü Ý Þ ß à á â ã ä

0.0000�0.0500�0.1000�0.1500�0.2000�0.2500�

1 to

6

7 to

12

13 to

18

19 to

24

25 to

30

31 to

36

37 to

42

43 to

48

49 to

54

55 to

60

61 to

66

67 to

72

73 to

78

79 to

84

85 to

90

91 to

96

mor

e th

an 9

6

18-24 years old

25-29 years oldæ30-45 years oldçmore than 45 years old�

å æ ç è é ê ë ìí î ï ð ñ ò ó ô õ ö ÷ ø ù ú û ü ý þ ÿ � � � � � � � � � �

0.0000�0.0500�0.1000�0.1500�0.2000�0.2500�

1 to

6

7 to

12

13 to

18

19 to

24

25 to

30

31 to

36

37 to

42

43 to

48

49 to

54

55 to

60

61 to

66

67 to

72

73 to

78

79 to

84

85 to

90

91 to

96

mor

e th

an 9

6

0-5 years�6-10 years

11-13 years

more than 13 years

27

� � � � � � �� ! " # $ % & ' ( ) * + , - . / 0 1 2 3 4 5 6 7 8 9

0.0000�0.0500�0.1000�0.1500�0.2000�0.2500�0.3000�

1 to

6

7 to

12

13 to

18

19 to

24

25 to

30

31 to

36

37 to

42

43 to

48

49 to

54

55 to

60

61 to

66

67 to

72

73 to

78

79 to

84

85 to

90

91 to

96

mor

e th

an 9

6

Couples without children

Single women

Couples with children

Single men

Single heads

28

Table9: Dependenceratesby householdtypes:<; :>=?; @

Singlemen 21.279 73.440 0.224Singlewomen 23.486 92.467 0.202Single-parentfamilies 40.807 67.240 0.377Childlesscouples 19.699 91.952 0.176Coupleswith children 22.571 77.782 0.224

Table10: Dependenceratesby agegroupsMEN WOMEN

18-24 25-30 31-45 46+ 18-24 25-30 31-45 46+:<;

11.215 15.064 23.300 44.625 14.683 25.280 35.930 53.688:>=?;72.951 68.782 71.022 93.002 80.566 76.526 79.414 [email protected] 0.180 0.247 0.324 0.154 0.248 0.312 0.337

Table11: Dependenceratesby levelsof educationMEN WOMEN

ACB7-11 12-14 15+

ACB7-11 12-14 15+

:<;32.958 21.001 15.869 17.295 42.473 31.887 20.669 16.930:>=?;80.292 68.994 84.656 88.360 92.537 77.613 89.579 [email protected] 0.233 0.158 0.164 0.315 0.291 0.187 0.151

29

The dynamics of welfare participation in Québec

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