Economics Working Papers - PDF document

Wor King Papers Economics Working Papers 201 3 - 06 Do Marital Prospects Dissuade Unmarried Fertility? John Kennes and John Knowles singlesintosexuallypromiscuousandabstinentgroupsinresponsetoimprovementsincontraceptiontechnology.Allofthelatterpapershoweverabstractfrommarriedfertilitydecisions.Amongthefewpublishedmarriage-equilibriummodelswithbothmarginsoffertility,thereisNeal(2004),whichexaminestheinteractionbetweenwelfarepaymentsandmarriage-marketequilibriathatdi!erinunmarriedfertilityrates,andGreenwood,Guner,andKnowles(2000)(GGKhereafter),whichshowshowmarriage-marketdynamicsandhuman-capitalinvestmentperpetuatethee!ectofrisingwelfarepaymentsonunmarriedfertility.2Animportantfeatureofthesepapersisthattheymodel,interalia,theimpactofpre-maritalfertilityonthehouseholdallocationsofmarriedcouplesthroughthemechanismofmarriage-marketequilibrium.Howeverthesepaperssu!erhoweverfromanextremecompressionofthelifecycle;onlyGGKallowsfordivorceandremarriage,buteventhere,marriageis Wealsoseethatmarriageratesare35%lowerforblackwomenaged20-25withoutchildrenthanforwhites.Understandingthesedi!erentialsinmarriageandfertility,acrosscohortandrace,willbethemainapplicationofthemodelwedevelopinthispaper.Casualempiricalevidenceforthebasicmechanisminthemodelcomesfromthelowermarriageratesofsinglemothers,thelowershareofthemarriageoutputallocatedtosinglemotherswhentheydomarryandahostofanecdotesacrossmanyculturesillustratingthetensionbetweenchildrenandstepparents(seePinker(1999)forasummary)4.Beaujouan(2009)Þndsthatre-partneringratesinFrancearesigniÞcantlylowerforsinglemothersthanforchild-lesswomenorsinglemenwithorwithoutchildren.Sheshowshoweverthatthisasymmetrybetweenmenandwomenisentirelyaccountedforbythefactthatsinglemothersaremuchmorelikelytolivewiththeirpreviouschildrenthanaresinglemales.SimilarlyBrowningandBonke(2006)Þndthathavingchildrenfromapreviousmarriagedoesnotreducetheintra-householdallocationtoDanishhusbandsinsubsequentmarriages,buthasastrongnegativee!ectontheallocationforwives.Againtheexplanationappearslikelytobeco-residenceofmotherswiththeirchildren,althoughthesurveylacksthevariablesrequiredtotestthishypothesis.Despitesuchdisincentives,thefractionofU.S.birthsaccountedforbyunmarriedwomenhasrisensteadily,from5%in1945to40%in2009,accordingtoVentura(2009).Theyshowthattherehasbeensteadygrowthintheunmarriedbirthratesince1940,andintheunmarriedshareofbirthssinceatleast1960.Thislatterincreasehasproceededatroughlythesamerateinallagegroupsfrom15-17to Thematchingprocessconsistsoftheuniformrandomassignmentofmentowomenwithinaseparatemarriagesub-marketforeachfemaletype.Thenumberofsuitorsperwomanisthereforearandomvariable $.WecanwritetheexpectedvaluesofwomenwithandwithoutchildrenasEVk=A %pM1=%#1# ö"isgivenby"!" ;forinstanceanincreaseinthevalueofsinglelifeforwomenwhoarenotmothers. isnotconsistentinourmodelwithlowermarriageratesforsinglemothers,althoughplausibleextensionsinwhichchildrenincreasethemarriagefrictionsmightgeneratethis.However,assumingthatbothmarriageratestendtowardsoneas!goestoinÞnitythenitispossiblethatadeclineinthesexratiogivesrisetoadeclineinunmarried-birthratesforasu" Fbelowabaselinefertilityrate&"mFkisgivenbythefunction" 4.1PreferencesTheindirectutilityfunctions%uSM,%uSF(k)and%uM(k,k,for,respectively,singlemales,singlewomenandmarried-couples,torepresentthemaximizedutilityßoweachperiodfromconsumptionandchil-dren.Thecriticalassumptionisthatchildrengeneratemoreutilitywithinamarriagethanwithout:%uSF(k+1) NF(k).Wealsoassumethatwhileentryintothemarriagemarketiscostlessforwomen,thereisanentrycost&�0thatsinglemenmustpay.EachperiodthereisrandommatchingwithinK+1marriagesub-markets,oneforeachtypeofsinglewoman.Foreachsub-marketk,thenumberofwomenisdenotedNF( 1/z,whichonaverageisequalto!1# denotetheexpectedvalue,onenteringtheperiod,ofamarriageconsistingofawomanwithkkidsofherown,ofwhichkmarechildrenofhercurrenthusband,conditionalon,theprevious-periodÕsrealizationofq.Letthee!ectivediscountratebedenoted÷)")(1#').Finally,letEU!"F,k,k +1|q)+!1#"F"Y (#( VRSM+V WecannowdeÞnethesurplusfromanewmarriagewherethebridehas RSM+#0($k)S(k,0)(7)4.3.3SinglesRecallingthedeÞnitionofthevaluefunctions,wecanwritetheexpostcontinuationvalueforsinglemenas:VRSM=maxk'uSM+)VESM(k)((8).Similarlyforsinglewomenwithkchildren,theexantenetvalueofenteringthemarriagemarketis:VE +1) Nowsupposethatsinglemenstrictlypreferentryintoactivemarriagemarkets.Anotherwaytothinkofthisisthatthereisexcessdemandforhusbands;thesupplyconstraintbinds.Thisconstraintis ,1,...K}suchthatinequilibrium$k�0if k!$k k,km,Q)forthedistributions.Thislistmustsatisfythefollowingconditions:1.Optimality:(a)Thefertilitydecisionrulesaresolutionstotheindividualoptimizationproblems 5.1AssetEquationsTosolvetheassetequationsforagivenlevelofk,wesolveforthepolicyrules'"D(k,k 444445VESF(k)YE(k,0,q1)...YE!k,0,qnq"6777778=A1 YE(k,0,q1)...YE!k,0,qnq k,k separatelyforthehouseholdswith m=0asthelinearsystem:3444445N!F(k)M! )...M!k, ThisistheÞxedpointofthelinearsystemdeÞnedbyT(k,km,Q):M!(k,km,Q)=D1k,kmM(k,km,Q)+D0k,km(20)Becauseanyincreasein kchildrenisnotrequiredtosolvetheseequations.5.3Market-ClearingTheequilibriumsolutioncanbereducedtotheappropriatechoiceoftheexpostvalueformen,VRSM. (22).Thismeanstheelasticityoffertilitywithrespectto!Vdeclinestozeroas+2increases.6.2.2NormalizedparametersThevaluesofsomeparametersareÞxedarbitrarily.Thusthedivorcecostissetto2,andthevariance changedwithouta!ectingtheoverallresults;thecalibrationprocedurewillresetthevaluesofthefreeparameterstorestorethebehaviorofthemodel.Theprobabilityofmarriage,conditionalonmatching,alsoappearsinthetable.Thiswasimplicitlysetto"mc=1inthetheorydiscussion;inthecalibrationwesetit0.6toensurethatmenarenotinexcesssupply.ThevaluesoftheseparametersarelistedinTable4(a).6.2.3FreeParametersTheeightremainingparameters,alsolistedinTable4(a),aresetinthestandardway:weidentifya 1.9%inthedataand2.1%inthemodel,a10%deviation. assumesastationarydistribution,whileunmarriedbehaviorintheearly1970s,asshownbyVentura(2009),wasalreadychangingrelativeto1960andearlier.Nevertheless,theÞrsttwocolumnsshowthatthemodeldeliversreasonablyaccuratevaluesforthefractionofwomenmarried(74%)andtheaveragebirthrate(15%).Itdoessharplyunderestimatetheshareoffertilityduetounmarriedwomen(6%insteadof10%),thefractionoffamilieswithkidsfromdi!erentfathers(1%insteadof6%)andthefractionofchildreninsingle-motherhouseholds(4%insteadof13%);overallthemodeldeliversapictureofaneconomydominatedbynuclearfamiliestoanextentthatissomewhatgreaterthanweobservein1973.Table6showsthedecisionrulesforfertilityandthemarriageprobabilities,conditionalonbeingactive.Thee!ectsofmarriagequalityonfertilityareseentobesmall.Marriedcoupleswithnochildrenalwayswantchildren,sotheyhavethemaximumfertilityrate,0.3.Theshadedsquaresinpanel6(a)showfamilieswithnostepchildren;thesealwayshavelowerfertilitythansame-sizefamilieswithstepchildren;forinstanceactivefamilieswithtwochildrenhaveabirthrateof0.19ifnoneofthechildrenarethehusbandÕs,butthisdeclinesto0.12asthenumberofthehusbandÕschildrenincreases.Intable6(b)weseeamarriagerateof0.41foractivewomenwithoutchildren;giventhattheyhavenochildren,womenaremuchlesslikelytobeactiveinthesimulation,sohighmarriageratesarerequired.Womenwithonechildmarryatrate0.18andwithtwochildrenatrate0.096.Thetablealsoshowstheimpactoffertilityonmaritalprospects;thesurplusis1.79forwomenwithoutkids,decliningto1.21forwomenwithtwokids;furthermorethe(unconditional)probabilitythatthewomangetsthesurplusis10%forwomenwithoutchildrenanddeclinesto0.04%forwomenwithtwokids.Themarriageratesofwomenwithmorethantwochildrenarezero,anartifactofsettingK=3,whichreducesthegainsfrommarriageforthesewomen.Sinceunmarriedwomenwithmorethantwochildrenaresuchasmallfractionofthepopulationinthe1970s,thissimpliÞcationseemsjustiÞed.7.1ComparativeStaticsThepremiseofthemodelisthatmarriageandfertilitydecisionsareconnectedthroughmaritalprospects,soitisusefultoseehowfertilityrespondstoparametersthata!ectmarriage.Wedo marriageanddivorcerateswithoutdirectlya!ectingtheutilityofhavingchildren.Inthissectionweexploitthisfeaturebyresettingthreeparameterstomatchthe1990svaluesofthreetargets:themarriageratesofwomenwithoutchildren,themarriagerateofwomenwithonechild,andtheaveragedivorcerate.Aswiththebenchmarkcalibrationfor1973,thetargetsconsistofthepredictedvaluesforage-25womenwithoutcollegeeducation,derivedfromtheprobitestimatesinTable3.Wethenasktowhatextentthechangeinmaritalprospectsassociatedwithdecliningmarriageratescanaccountfortheobservedincreaseinthebirthratestounmarriedwomen.Thethreeparametersare:theutilityofsinglelife,thee!ectofstepchildrenonthemarriedutility,andthecostofdivorce.Thenewvaluesareshownincolumn2ofTable4(a).andthetargetandmodelstatisticsareshownincolumns3and4ofTable4(b).Theshadedcellsinthetablecorrespondtostatisticsthatwerenottargets.Tohitthe1995targetsrequiredthenegativee!ectofstepkidsonmarriedutilitytoshrinkfrom-.05to-.008,thecontributionofsinglelifetoutilitytogrowfrom-0.511to-0.487,andthecostofdivorcetoincreasefrom2to5.3213.Thee!ectonfertilityofunmarriedwomenisstriking:birthratesfornon-mothersincreasefrom0.017annuallyto0.045,mirroringtheincreaseobservedinUSdata.Someoftheotherchangesinnon-targetedstatisticsalsoappearremarkablysimilartotheircoun-terpartsinthedata:marriageratesofwomenwithtwochildren,forexample,risefrom8%annuallyto12%annuallyinbothmodelanddata.Thebirthrateformarriedwomenwith1childrisesfrom19%to21%inbothmodelanddata.Othernon-targets,suchasthebirthratestomarriedwomenwithno13Thereasondivorcecostsincreaseisthatwhenmarriageratesdecline,divorcerates,ifmarriagequalitywereiid,wouldhavetorisemuchmorethanweseeinthedata.Thecalibratedpersistence(0.55)appearsinsu"cienttoo!setthise!ectthroughhigherqualityofmarriages.Itmaybethatincreasingthecardinalityofthesupportofthepersistentqualityshock(currentlysetat3)mayhelptoincreasemarriagequalityandhencereducetherequiredincreaseindivorce whetherourmodelisexaggeratingormerelysimplifyingthechannelsthroughwhichthee!ectsoccur.Thecriticalparameterforgeneratingbirth-rateresponsestoshiftingmaritalprospectsisthecur-vatureparameter+2inthee!ort-fertilityfrontier.Itshouldbestressedthatinrealitythisfrontiercomprisesanumberofmarginsthatarenotmodeledexplicitlyhere;mostimportantlyperhapsthemarginsforsexualactivity,forcontraceptive-methodchoice,andforabortion.ThereforeÒe!ortÓcor-respondsto,interalia,foregoneutilityfromsexualabstention,thecostanddisutilityofcontraception,andtherisksandutilitycostsassociatedwithabortion.Thispaperfoundthatmaritalprospectscouldexplainwhyfertilityofunmarriedwomenwassolowinthe1970s,providedthat+2wassu"cientlyclosetozero.Whetherthisisaplausiblerepresentationof anotherrouteforextendingtheanalysispresentedhere,byaddingamarginforco-habitation,perhapsevenaseparatesetofmatchingmarkets.Thetimingofeventssuggestthatfarfrombeingacauseofthedeclineofmarriage,cohabitationisratherasymptomofthatdeclinewhichcouldbeanalyzedbyputtingmorestructureontheoptionsforunmarriedwomeninthemodel.9ConclusionsTheresultsdemonstratethatthegreaterimportanceofmaritalprospectsinthe1970sthaninthe1990smaybesu"cienttoaccountforthelowerbirthratesofunmarriedwomenatthetime.Weexploitedthefactthatunmarriedmothersmarryatalowerratethannon-motherstocalibratethee!ectofmaritalprospectsinthematchingmodel.Althoughtheexerciseshedslittlelightonwhymaritalpatternschanged,thecomparativestaticsexercisessuggestanimportantroleforshocksthatincreasetheutilityofsinglelife.Apossiblecandidateexplanationforthischange,thearrivalofhighly-e!ectivecontraceptionforsinglewomen,isexploredinKennesandKnowles(2011),whichextendsthecurrenttheorytotheanalysisofsexualactivityofunmarriedpeople.Analternativeexplanationlessamenabletomeasurement,isincreasingfrictionsinthemarriage-matchingprocess,perhapsduetohigherratesoffemalelabor-marketparticipation.Wealsoappliedourmodeltounderstandingracialdi!erentialsinmarriageratesandunmarried (2009):ÒSeremettreencouple:contrasteshommes-femmes.(Repartnering:contrastsbetweenmenandwomen),ÓinEntrefamilleettravail,desarrangementsdecouplesauxpratiquesdesemployeurs,ed.byR.-L.Arnaud.Ined-laDŽcouverte,Paris.Becker,G.S.(1981):ATreatiseontheFamily ofmarriagequalityareknown,as:"Dk,km(q)=2q"&Qf(q!;q)#((#(k,km,q!)),where(#(k,k ##0($k)])1#"Dk,0(öq)*,where"mc%[0,1],aparameterdenotingtheprobabilitythatmatchedcouplesareallowedtomarry,generalizesthemodelslightlytoallowformarket-frictions.Whenwesolvethelevel-ksystemforkK,weassumethatwealreadyknowthesolutionforthek+1systemofassetequations.Thesystematk=Kisrelativelyeasytosolvebecausewithfertilityassumedtobezero,therearenotransitionstohigher whereS(k,0)=k,km,öq)#VRSF(k)#VRSMdenotesthesurplus.BythedeÞnitionofVRSF(k),wecanwrite:VRSF(k)=÷d1+)(1#')!1#"SFk"VESF(k)(23),wherethetermsin #')!1#"SFk"[1#pS($k d1=[1#pS($k "&Q#((#( ##((#(k,k q)(24)+"Dm(q))VRSF(k,$)+VRSM#-*(25)Assumingthemarriagesurvivesthedivorcestage,thevalueofthemarriage,beforethefertilityreal-izationisknown,isYR(k,0|$ +!1# +"MFk,0( ))(1#' ))]f(q! (öq)*S N!F(0)='+a 0,q),wherea11=!1#"SF0 ,0(q)MarriedCouplesTheßowoutofthemarriedchildlessstateincludesbothfertilityanddivorce,whiletheonlyßowisfrommarriageofchildlesssingles:M! ##0)NF(0)+2q&Qf(qj;q) )isthefractionofwomennextperiodwhoarebothchildlessandmarried,and.0( 1#"MF0 )=aj+1,1NF(0)+nq2i=1aj+1,i+1M(0,0,qj)whereaj+1,1=.0(qj .0(qj)f(qj,qi).LetC1k=[ai,j]. g0k,km(qj)=?@A.0k,km(qj)f(qj,öq)"mc!1 km�1.0m (k#1,km#1,qj 0k,km(qj)+.0k,km(qj)2 ,...k !1#"MFk,km(qj)" k#1 #')"SF d13(qi)*,whered13(q )+d1wherea11=(1#')!1#"SFk"(1#µk)a1i+1=!1#"SFk" d1=d11+d12+(1#')!1#"SFk"2q .Thereforethecoe" Figure 1(b) on US Census, 1980, 2000 and 2010 waves. Figure 1(a) Census, 1980, 2000 and 2010 waves. plp8�plr�plr8�pls�pls8�r/�sp�sr�ss�st�s��s8�su�sy�s8�s/�tp� AdMRc�um8pmCgcaSi� FUakTm�um8pmCgBaSi� FUakTm�um8pmBaSi� plp8�plr�plr8�pls�r/�sr�st�s8�sy�s/� 41 Figure 2(c)Women never-married, never given birt Figure 2(b)Women never-married, never given birt Figure 2(a)Women never-married, never given birt; dropoutsFigure 2(b)Women never-married, never given birt eag�eai�eal�ean�eap�gm�hg�hm�ig�im�kg�BachTFeaU�CSFdM� FMBC� ARSTUT� eah�eak�eam�eao�go�hi�ho�ii�io�ki�BachTFeaU�CSFdM� FMBC� ARSTUT� eah�eai�eak�eal�eam�ean�eao�eap�go�hi�ho�ii�io�ki�BachTFeaU�CSFdM� FMBC� ARSTUT� eak�eal�eam�ean�eao�eap�BachTFeaU�CSFdM� FMBC� ARSTUT� 42 Figure 3 . Annualised marriage and birth rates per single woman. 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Kids At Home Non-cohab All Singles 43 CeghasFcnn�Tlick Figure 4(c)Estimated Age Profiles for Birth Rates; Single women without children. Figure 4(b)Estimated Age Profiles for Marriage Rates; Single Women Figure 4(d)Estimated Age Profiles for Birth Rates; Single Women with Figure 4(a)Estimated Age Profiles for Marriage Rates; Single Women with no children. dTdd�dTdk�dTed�dTek�dTgd�dTgk�dThd�gd�gk�hd�hk�id�ik� dTdd�dTde�dTdg�dTdh�dTdi�dTdk�dTdl�dTdm�dTdn�gd�gk�hd�hk�id�ik�AkkpUhgrca�Bgmoe�RUoc� dTdd�dTdg�dTdi�dTdl�dTdn�dTed�dTeg�dTei�gd�gk�hd�hk�id�ik� dTdd�dTdg�dTdi�dTdl�dTdn�dTed�dTeg�dTei�dTel�gd�gk�hd�hk�id�ik�AkkpUhgrca�Bgmoe�RUoc� 44 Figure 5(a)Figure 5(b) Figure 5(c) benchmark value =-0.1 Figure 5(d) benchmark value =-0.1 mhmm�mhmo�mhmr�mhmt�mhm8�mhnm�mhno�mhnr�mhnt�imhns�imhnp�imhnn�imhmu�imhm��imhms�imhmp�imhmn�Annual�Birth�Rate� FcBaSe� nBaS� mhn�mhns�mho�mhos�mhp�imhns�imhnp�imhnn�imhmu�imhm��imhms�imhmp�imhmn� FcBaSe� nBaS� mh�s�mh���mh�u�mh8n�mh8p�mh8s�mh8��mh8u�mhun�mhup�mhus�imhns�imhnp�imhnn�imhmu�imhm��imhms�imhmp�imhmn� mhmm�mhms�mhnm�mhns�mhom�mhos�imhns�imhnp�imhnn�imhmu�imhm��imhms�imhmp�imhmn�Unmarried�/Total� 45 Figure 6(a)Figure 6(b)Effect on aggregate birthrates of changing marriage friction; Figure 6(c) Effect onmarriage rates of changing marriage friction; benchmark value =0.6. Figure 6(d) Effect on unmarried shares of births and mothers of changing mhmm�mhms�mhnm�mhns�mhom�mhn�mhp�mhs�mh��mhu�Annual�Birth�Rate� FcBaSe� nBaS� mhms�mhn�mhns�mho�mhos�mhp�mhps�mhr�mhn�mho�mhp�mhr�mhs�mht�mh��mh8�mhu�n� FcBaSe� nBaS� mhmr�mhms�mhmt�mhm��mhm8�mhn�mhp�mhs�mh��mhu�Annual�Birth�Rate� mhms�mhn�mhns�mho�mhos�mhp�mhps�mhr�mhrs�mhs�mhn�mhp�mhs�mh��mhu�Unmarried�/Total� 46 Figure 7(c) on Probit predictions from 1973 wave; model series based on 1973 benchmark simulation. Figure 7(a) Figure 7(b) kekk�kekp�kelk�kelp�kemk�kemp�kenk�kenp�keok�ml�mr�nl�nr�ol� FcagCcUd�FMAB� FcagCcUd�CcRST� CcUd�FMAB� kekk�kekl�kekm�kekn�keko�kekp�kekr�keks�kekt�ml�mr�nl�nr�ol�Aggn�Bckmal�iTk�FcgUdT�MheRg� FcagCcUd�FMAB� FcagCcUd�CcRST� CcUd�FMAB� kekp�kel�kelp�kem�kemp�ken�ml�mr�nl�nr�ol�Aggn�Bckmal�iTk�CRkkcTS�MheRg� FcagCcUd�FMAB� FcagCcUd�CcRST� CcUd�FMAB� 47 Figure 8(a) Effect on unmarried birthrates of changing population ratio of men Figure 8(b)Effect on aggregate birthrates of changing population ratio of Figure 8(c) Effect on marriage rates of changing population ratio of men to women; benchmark value =1.0. Figure 8(d) Effect on unmarried shares of births and mothers of changing lhll�lhlm�lhln�lhlo�lhlp�lhlr�lhls�lhlt�lhl��lhl8�lhp�lhr�lhs�lht�lh��lh8�mhl�mhm�Amm8ak�Bipsh�Rase� FcBaSe� mBaS� lhm�lhmr�lhn�lhnr�lho�lhp�lhr�lhs�lht�lh��lh8�m�mhm� FcBaSe� mBaS� lhsl�lhsr�lhtl�lhtr�lh�l�lh�r�lh8l�lh8r�mhll�lhp�lhr�lhs�lht�lh��lh8�mhl�mhm� lhln�lhlp�lhls�lhl��lhm�lhmn�lhmp�lhms�lhm��lhn�lhr�lhs�lht�lh��lh8�m�mhm�Tmlappied�ySnsak� 48 1970s1990s0.740.53-28%0.130.2269%Living Arrangements of Children Under 18 Years Old: 1960 to Present0.190.2532%0.820.62-24%0.10.3200%0.060.167%Average birth rate 0.180.08-56%National Vital Statistics Reports, Vol. 48, No. 16, October 18, 2000 Table 1Changes in Aggregate Marital Indicators . Census computations based on women aged 18-44. StatisticData% ChangeSource 49 NoKidsSinMomNoKidsSinMom20.4930.84723.18731.03(2.210)(3.151)(5.411)(4.462)0.110.0540.3120.138(0.675)(0.102)(0.366)(0.227)0.000390.0060.0020.005(0.043)(0.034)(0.038)(0.047)0.000110.000350.0320.087(0.023)(0.008)(0.139)(0.185)0.4740.120.5330.244(1.076)(0.146)(0.394)(0.283)0.9380.5630.8430.739(0.520)(0.223)(0.287)(0.290)0.0060.2160.0670.557(0.172)(0.185)(0.198)(0.327)0.002470.0060.0060.007(0.107)(0.036)(0.061)(0.055) High-School VariableTable 2 1973 1995 AgeCollege DegreeBirth RateCohabitingAttended College 50 birthmarbirthmar-5.603-4.183-4.012-4.666(0.006)(0.004)(0.003)(0.002)0.758-0.4070.2260.048(0.001)(0.001)(0.001)(0.001)-0.031-0.094-0.060-0.018(0.001)(0.001)(0.000)(0.000)0.0610.151-0.037-0.051(0.001)(0.001)(0.001)(0.001)-0.016-0.2250.024-0.123(0.002)(0.002)(0.001)(0.001)0.3770.2010.1150.139(0.002)(0.002)(0.002)(0.002)1.073-2.957-0.0580.054(0.005)(0.586)(0.001)(0.000)0.0510.6710.194-1.588(0.001)(0.001)(0.000)(0.004)0.1940.0810.026-0.088(0.000)(0.000)(0.001)(0.000)-0.004-0.0020.1420.169(0.000)(0.000)(0.000)(0.000)0.014-0.010-0.003-0.003(0.000)(0.000)(0.000)(0.000)-0.107-0.112-0.325-0.282(0.003)(0.001)(0.001)(0.000)0.4421.371-0.1770.042(0.001)(0.000)(0.000)(0.000)-0.1840.030-0.200-0.040(0.001)(0.001)(0.001)(0.000)-0.3940.273-0.2680.008(0.009)(0.003)(0.001)(0.000) 1970-73 1990-95 Variable Table 3: Probit Estimates of unmarried women's monthly marriage 51 Value19731995-0.2060.019Effect of first step child on marriage outputWomens utility for kids, intercept0.011Women's utility for kids, slope-1.125-0.503Utility bonus for singlesAdditional step-children effect 25.232Divorce Cost Discount factor Table 4(b) Free-Parameter Values for Calibrated Models. Effort-fertility curvature parameter Table 4(a) Normalized and Fixed Parameter Values in Benchmark calibration 52 NSFGModelNSFGModel0.230.250.1290.127Marriage Rate, non-mothers0.130.1490.1140.117Marriage rate, mothers of one child0.0910.1080.1180.181Marriage rate, mothers of two children0.2270.2050.2240.214Birth Rate, married couples with no kids0.1870.1860.2150.24Birth Rate, married couples with one kid0.0980.1130.10.196Birth Rate, married couples with two kids0.0190.0210.0460.145Birth rate, single women with no kids0.0560.040.090.097Birth rate, single women with one child0.020.0190.0440.045Divorce RateDataModelDataModel0.740.750.530.61Fraction married 0.130.040.220.29Fraction of kids in single-mom households 0.820.950.620.50 Fraction of kids living with both parents 0.100.040.300.33Share of fertility due to unmarried women 0.060.010.100.29Fraction of families with mixed kids 0.180.150.080.08Average birth rate Table 5(a) . NSFG statistics consist of Unshaded cells correspond to calibration targets.Table 5(b) Results from NSFG Surveys and Benchmark Model Calibrations . Based on population of women aged 18-44. 1973 1995 StatisticStatistic 53 0120.0350.0820.163qWife's Kids01200.30----10.300.21--20.190.160.1200.30----10.300.20--20.190.160.1200.30----10.300.19--20.190.150.12WomenWife Gets Value of Value of Woman00.391.175.620.3321.04-1.9410.220.573.510.1117.01-4.7120.200.513.330.0915.68-5.9130.000.000.000.00-99.00-6.97Table 6(b) Kids to Date (Parity) Table 6(a) 54 Marr-73Birth-73Marr-95Birth-95Marr-73Birth-73Marr-95Birth-95210.3010.0210.1170.0720.1220.1690.1030.134220.3040.0220.1220.0690.1240.1750.1080.128230.3050.0220.1260.0650.1250.1780.111240.3040.0220.1280.0610.1240.1770.1130.114250.3010.0210.1300.0560.1220.1730.1140.106260.2960.0200.1300.0510.1200.1660.1150.098270.2890.0190.1290.0460.1160.1560.1140.090280.2800.0170.1270.0410.1110.1430.1120.081290.2690.0140.1230.0370.1060.1290.1090.073300.2570.0120.1190.0320.1000.1130.1050.064310.2430.0100.1140.0280.0930.0970.1000.056320.2290.0080.1080.0240.0860.0810.0950.049330.2130.0060.1010.0200.0790.0660.0880.042340.1960.0040.0930.0170.0710.0520.0820.035350.1790.0030.0860.0140.0640.0400.0750.029360.1620.0020.0780.0110.0560.0290.0680.024370.1450.0010.0700.0090.0490.0210.0610.020380.1280.0010.0620.0070.0420.0140.0530.0160.1110.0010.0540.0050.0360.0090.0470.012400.0960.0000.0460.0040.0300.0060.0400.009410.0820.0000.0390.0030.0250.0030.0340.007420.0680.0000.0330.0020.0200.0020.0280.005430.0560.0000.0270.0020.0160.0010.0230.004440.0460.0000.0220.0010.0130.0010.0190.000Table A1Predicted Age Profiles for Marriage and Child-Birthsingle-woman samples from NSFG 1973 and 1995. To compensate lack of never-married non-mothers in Non-Moms Single Moms 1973 1995 1973 1995 55 NSFGModelNSFGModel-2.9897-3.1434210.28180.27610.21880.2309(0.003)(0.003)220.2690.27410.20940.2291-0.00480.0598230.25330.26950.19990.225(0.000)(0.000)240.23310.26220.19030.2185-0.1004-0.0186250.21120.25250.18060.21(0.000)(0.000)260.19210.24050.17090.1994-0.2567-0.3201270.17470.22650.16110.1872(0.000)(0.000)280.16020.21080.15110.1735-0.0160-0.0552290.14580.19370.13990.1587(0.000)(0.000)300.13050.17570.12840.14320.07930.0276310.11580.15710.11680.1273(0.001)(0.001)320.1010.13830.10510.11150.16190.0036330.0870.11990.09360.096(0.001)(0.002)340.07350.10220.08240.08130.0951-0.0247350.06160.08550.07180.0676(0.001)(0.002)360.0440.07020.06280.05510.10540.1190370.02990.05650.05410.044(0.000)(0.000)380.01980.04450.04540.0344-0.0025-0.0028390.01390.03430.03680.0263(0.000)(0.000)400.00790.02580.02830.01960.02370.0327410.00560.0190.020.0143(0.000)(0.000)420.00480.01360.01170.0101-0.2405-0.1408430.00380.00940.00360.007(0.002)(0.000)440.00210.0064-0.00440.0047-0.0513-0.0789(0.000)(0.000)-0.07190.0123(0.000)(0.000)-0.6788-0.9559(0.003)(0.001)Table A2:Probit Estimates of married 19731995 Non-Moms Table A3: Predicted Age-Birthrate profiles, based on Probit Estimates Variable Moms CohabitingPreviously MarriedAgeAge SquaredAge x BA 56 Economics Working Papers 2012 - 23: Astrid Würtz Rasmussen and Leslie S. Stratton : How Distance to a Non - Residential Parent Relates to Child Outcomes 2012 - 24: Nabanita Datta Gupta, Mette Lausten and Dario Pozzoli : Does Mother Know Best? Parental Discrepancies in Assessing Child Functioning 2012 - 25: Nabanita Datta Gupta, Daniel Lau and Dar io Pozzoli : The Impact of Education and Occupation on Temporary and Permanent Work Incapacity 2012 - 26: Jonas Maibom Pedersen, Michael Rosholm and Michael Svarer : Experimental Evidence on the Effects of Early Meetings and Activation 2012 - 27: Pieter Gautier, Paul Muller, Bas van der Klaauw, Michael Rosholm and Michael Svarer: Estimating Equilibrium Effects of Job Search Assistance 2012 - 28: Elena Cottini and Paolo Ghinetti : Working Conditions, Lifestyles and Health 2012 - 29: Casper Worm Hansen : Causes of mortality and development: Evidence from large health shocks in 20th century America 2013 - 01: Juanna Schrøter Joensen and Helena Skyt Nielsen: Math and Gender: Is Math a Route to a High - Powered Career? 2013 - 02: Valerie Smeets, Michael Waldman and Frederic Warzynski : Performance, Career Dynamics, and Span of Control 2013 - 03: Rasmus Landersø, Helena Skyt Nielsen and Marianne Simonsen: School Starting Age and Crime 2013 - 04: Nabanita Datta Gupta and Lene Kromann : An Equilibrium Search Model of the Labor Market Entry of Second - Generation Immigrants and Ethnic Danes 2013 - 0 5 : Niels Skipper and Rune Vejlin : Determinants of Generic vs. Brand Drug Choice: Evidence from Population - wide Danish Data 2013 - 06: John Kennes and John Knowles : Do Marital Prospects Dissuade Unmarried Fertility?