Employmen, Family Union, and Childbearing Decisions in Grea Briain Arnsein Aassve Simon Burgess Carol Propper Ma Dickson Conens 1. Inroducion... 1 2. Daa... 3 Union formaion and dissoluion... 3 Employmen and non-employmen... 4 The birh evens... 5 Descripive saisics... 5 3. Empirical modelling of he demographic and labour marke evens... 7 4. Esimaion Resuls... 9 Background variables and educaion, and endogenous evens... 9 Time varying variables... 11 Duraion and age dependence... 13 Unobserved heerogeneiy... 14 5. Micro Simulaion Analysis... 16 6. Conclusions... 20 References... 22 CASEpaper 84 April 2004 Cenre for Analysis of Social Exclusion London School of Economics Houghon Sree London WC2A 2AE CASE enquiries el: 44 0)20 7955 6679 i
Cenre for Analysis of Social Exclusion The ESRC Research Cenre for Analysis of Social Exclusion CASE) was esablished in Ocober 1997 wih funding from he Economic and Social Research Council. I is locaed wihin he Sunory and Toyoa Inernaional Cenres for Economics and Relaed Disciplines STICERD) a he London School of Economics and Poliical Science, and benefis from suppor from STICERD. I is direced by Howard Glennerser, John Hills, Kahleen Kiernan, Julian Le Grand, Anne Power and Carol Propper. Our Discussion Paper series is available free of charge. We also produce summaries of our research in CASEbriefs, and repors from various conferences and aciviies in CASErepors. To subscribe o he CASEpaper series, or for furher informaion on he work of he Cenre and our seminar series, please conac he Cenre Adminisraor, Jane Dickson, on: Telephone: UK20 7955 6679 Fax: UK20 7955 6951 Email: j.dickson@lse.ac.uk Web sie: hp://sicerd.lse.ac.uk/case Arnsein Aassve Simon Burgess Carol Propper Ma Dickson All righs reserved. Shor secions of ex, no o exceed wo paragraphs, may be quoed wihou explici permission provided ha full credi, including noice, is given o he source. ii
Ediorial Noe Arnsein Aassve is a lecurer in he Deparmen of Economics, Universiy of Leiceser, and a research associae of CASE, London School of Economics. Simon Burgess is Professor of Economics in he Deparmen of Economics and he Leverhulme Cenre for Marke and Public Organisaion CMPO), Universiy of Brisol, and a research associae a CASE. Carol Propper is Professor of Economics in he Deparmen of Economics and he CMPO, and a co-direcor of CASE. Ma Dickson is a research assisan a CMPO. Acknowledgemens A large par of his work was underaken while Aassve was working as a research Scienis a he Max Planck Insiue for Demographic Research. The auhors hank he Insiue for ousanding suppor. We would like o acknowledge Riccardo Borgoni and San Panis for heir excepional help and advice in his work. We are graeful o he ESRC for funding his projec: gran number R000237943. Aassve would also like o hank RAND for generous suppor in developing he simulaion framework for his analysis. We are also graeful o workshop paricipans a Souhampon, Mancheser, Brisol, Leiceser, and paricipans a he ESPE 2003. The responsibiliy for any errors lies wih he auhors. Corresponding auhor: Arnsein Aassve Deparmen of Economics Universiy of Leiceser Universiy Road Leiceser LE1 7RH Email: aa128@le.ac.uk iii
Absrac The paper invesigaes he relaionship beween work and family life in Briain. Using appropriae saisical echniques we esimae a five-equaion model, which includes birh evens, union formaion, union dissoluion, employmen and non-employmen evens. The model allows for unobserved heerogeneiy ha is correlaed across all five equaions. We use informaion from he Briish Household Panel Survey, including he rerospecive hisories concerning work, union, and child bearing, o esimae his model. We obain well-defined parameer esimaes, including significan and correlaed unobserved heerogeneiy. We find ha ransiions in and ou of employmen for men are relaively independen of oher ransiions. In conras, here are srong links beween female employmen, having children and union formaion. By underaking a deailed micro simulaions analysis, we show ha differen levels of female labour force paricipaion do no necessarily lead o large changes in feriliy levels. Changes in union formaion and feriliy levels, on he oher hand, do have a significan impac on employmen raes. JEL numbers: J12, J13, J22 Keywords: demographic ransiions, marriage, divorce, birh, employmen iv
1. Inroducion Over he las few decades Briain has seen large changes in paerns of employmen and family life. The mos noiceable change is perhaps he increase in he female employmen rae which, in 1999, sood a 72%. A he same ime here have also been imporan demographic changes. Marriage raes have generally declined and have only parly been offse by higher cohabiaion raes. Thus, overall boh men and women end o say single for much longer han was he case in he pas. Compared o oher European counries, feriliy raes have remained high in Briain. Given hese observed changes in boh family life and employmen, i is naural o ask he quesion o wha exen hese processes are linked. The conribuion of his paper is o address his quesion using appropriae saisical models, in which individuals employmen decisions are modelled joinly wih heir feriliy and union formaion decisions. I has been argued for insance, ha as women have increased heir employmen raes, and consequenly heir economic independence, his has marginalized he imporance of marriage as an insiuion o rear children. Increasingly researchers have recognized ha many of hese demographic and labour marke decisions are made joinly and ha he ransiions are herefore iner-linked. For insance McElroy 1985) suggesed ha he process of leaving he parenal home and finding he firs job could no been seen as independen evens. An imporan insigh of her work was ha from a saisical poin of view, failing o conrol for he joinness of he decisions produced heavily biased parameer esimaes. Recenly, join modelling of processes suspeced o be inerrelaed has become more feasible. Willis 1999) proposed a join model of childbearing and marriage, analysing women s decision o have children ouside marriage. Alhough no esimaing an empirical model, Willis s approach highlighs he inherenly join decision-making presen in demographic processes. An imporan conribuion o he empirical lieraure is Lillard 1993), who esimaed a join model of feriliy and marial dissoluion using simulaneous hazard regression. He also esimaed he correlaion beween he wo processes and showed ha failing o conrol for simulaneiy produced biased parameer esimaes. Following his paper, a range of work has focussed on conrolling for he possible bias creaed by he simulaneiy of processes. Examples include Lillard and Waie 1993) modelling childbearing and marial dissoluion; Brien 1997) invesigaing he role of he marriage marke for differen race groups in he US; Brien e al 1999), Baizan e al 2002), considering he issue of cohabiaion, marriage and non-marial childbearing; Upchurch e al 2002) analysing he iner-relaionship beween union formaion, childbearing and educaional choice; and van der Klauuw 1996) analysing he relaionship beween work and marriage. All of hese papers demonsrae he imporance of 1
he joinness of he processes, and ha failing o ake his ino accoun generally produces biased parameer esimaes, which would oherwise be misleading for policy purposes. Anoher se of papers consider he impac of income on various dimensions of demographic behaviour. For insance, Duncan and Hoffman 1990), Wolfe e al 2001), and Aassve 2003) consider he impac of economic resources and opporuniy coss on women s propensiy o have children ouside marriage. Aassve e al 2002) invesigae he impac of earnings and family income on he decision o leave he parenal home and o ge married. A cenral heme in hese papers is ha income, mainly earnings, is endogenous wih respec o he demographic processes under sudy. They highligh he fac ha he income generaion process is driven by demographic evens, and vice versa. There are neverheless some imporan shorcomings of he curren lieraure. Alhough i is frequenly emphasised ha work and family formaion are inerrelaed processes, researchers ypically analyse only cerain aspecs of demographic behaviour ogeher wih he employmen ransiions. Furhermore, researchers rarely analyse demographic evens in heir compleeness: ypically he issue is abou iming of firs birh or firs union formaion, no considering wha happens afer such evens. Here we aemp o provide a fuller picure of boh employmen ransiions and demographic processes. Our approach is novel in several respecs. Firs we specify a simulaneous hazard regression framework similar o Lillard 1993) ha includes birh evens, union formaion, union dissoluion, employmen and non-employmen evens and addiionally, allows for unobserved heerogeneiy ha is correlaed across all five equaions. Employmen, child bearing, and family formaion ransiions are all specified in separae equaions, bu esimaed in a join maximum likelihood procedure. This allows us o analyse he impac of employmen ransiions explicily, conrolling for is poenial endogeneiy wih respec o feriliy and union formaion. Second, we esimae his model using daa from he Briish Household Panel Survey BHPS), where panel informaion for 1991-1998) is merged wih rerospecive informaion provided in 1992 o consruc complee hisories for employmen, child bearing and union formaion for all respondens in he panel. We hus creae hisories sreching back o he 1940s, which enables us o provide esimaes for several cohors of he UK populaion, and also avoids he problem of lef censoring, which is ofen a problem when using he panel componen only. Third, we make use of exensive simulaions o provide furher insigh ino he dynamics of hese processes, which is no necessarily easy o infer from he parameer esimaes alone. 2
The nex secion discusses he daa in deail, and secion 3 he economeric model. Secions 4 and 5 presens he resuls, and a final secion offers some conclusions. 2. Daa The daases we use are from he Briish Household Panel Survey for 1991-1998. The firs wave of he BHPS was designed as a naionally represenaive sample of he populaion of Grea Briain living in privae households in he auumn of 1991. Approximaely 5,500 households, conaining abou 10,000 persons, were inerviewed. These original sample members are re-inerviewed each successive year, and if hey spli off from heir original households o form new households, all adul members of hese new households are also inerviewed. Similarly, children in he original sample households are inerviewed when hey reach 16 years of age. Thus, he sample remains broadly represenaive of he populaion of Grea Briain as i changes hrough he 1990s. In addiion o providing informaion on respondens wihin he Panel survey period 1991 onwards) he BHPS asked respondens o provide deailed rerospecive work, family and feriliy hisories in 1992. These rerospecive daa are mached o he wihin panel daa o consruc deailed marriage, feriliy and work hisories from age 13 for all adul respondens. By using he rerospecive hisories individual specific behaviour is modelled from he person s 13h birhday, hus avoiding he iniial condiions problem normally encounered when esimaing duraion models based on he panel componen only. We have creaed five deailed even hisories for each individual: forming and dissolving a parnership, having anoher) child, enering and leaving employmen. Union formaion and dissoluion As cohabiaion is an increasing form of union in he UK eiher as a precursor o legal marriage or as a subsiue), we define marriage as living in union wih a person of he opposie gender, regardless of legal marial saus. For he wihin panel daa we use he self-repored marial saus, which akes he following caegories: married, living as a couple, separaed, divorced, widowed and never married. We classify married and living as a couple as de faco married, wih he remaining caegories being de faco no married. For he rerospecive sample daa, we use he daase BMARRIAG. 1 This provides he individual s marriage hisory from he age of 16 years up o he dae of inerview in wave wo. The monh and he year of cohabiaions leading o 1 The names of hese daa ses are he same as hey appear in he BHPS daa base. 3
marriages are provided, as well as daes for which marriages ended as separaions. Thus similar de faco marriage informaion is provided boh from he panel and he rerospecive par. The rerospecive cohabiaion hisories are compleed by using informaion from he daase BCOHABIT, which records he deails of cohabiaions ha are never made ino legal marriages. 2 The even hisories are consequenly consruced by using informaion from boh daa sources. We impue missing marial hisory daes if we know here is a change in marial saus and we know he year of he change bu he monh is missing. Employmen and non-employmen Individuals are defined as being employed if hey are in full ime paid employmen, par ime paid employmen or paid self-employmen. Individuals who are on long-erm leave due o sickness or on maerniy leave 3 ) are classified as no-employed. An individual is classified as changing employmen saus only if s/he moves ino or ou of paid employmen. Thus, cases where individuals change employer bu remain coninuously employed are no implemened as a change in employmen. Similarly, individuals changing from full ime o par ime are no recorded wih any change. Moreover, individuals moving from full ime educaion o job seeking are recorded wih no change. For he wihin Panel daa, we use he variable wjbstat which is an annual self-repored employmen saus. In addiion we use wave-by-wave employmen hisory files from wave hree o wave eigh wjobhist). Each file conains deails of all employmen saus spells since he 1s Sepember in he year before he inerview. In cases where individuals have employmen changes, he gaps beween he annual wjbstat are filled wih spells from he wjobhist files and recoded as in paid employmen and no in paid employmen as defined above. For he rerospecive hisory we use he BLIFEMST file, which records he individuals complee paid employmen hisories from he age ha hey firs lef full ime educaion up o 1992. We assume ha all individuals are in full ime educaion and herefore non-employed a age 13. The panel and rerospecive hisories are subsequenly used o creae wo even hisories for each responden, all of which are daed o he monh. There are a number of 2 3 In oal here are 1272 such unions, which are never made ino legal marriages recorded in he rerospecive cohabiaion hisory file. Moreover, ou of he 1258 unions ha begin afer wave 2 81.3% are no iniially legal marriages. In he rerospecive marriage hisory daa, 1403 of he marriages which is 18.1%) begin in cohabiaion and 640 which is 30.8% of he uncensored rerospecive legal marriages) end in separaion. We only wan o include individuals who are a paid work, herefore maerniy leave does no coun in his insance as being in paid employmen. There are 1039 observaions ha are maerniy leave in he employmen hisory daases ha we use, his represens jus 0.8% of he oal number of observaions. 4
cases where he individual records he sar monh for a spell as a season raher han a monh, and in hese cases we apply he BHPS season codes. 4 The monh of July is used for impuaion, whenever he monh is missing bu no he year. Employmen evens are no impued if an individual is missing from any years of he panel. The daa is reaed as censored from he firs dae he responden leaves he panel. 5 The birh evens Birhs occurring during he panel years are consruced from he household record of he responden. In each wave deails of new household members are recorded in he daase windall. The variable wnewhy provides informaion abou wheher he new household member is new baby. If his is he case he even is daed by using monh and year variables. In he majoriy of cases, here is only one birh even in he household in given wave, bu we also idenify muliple birhs. 6 The rerospecive hisory colleced in 1992 records he daes of birh of all he responden s children o ha dae. The deails for an individual s naural children are recorded in he daase BCHILDNT. 7 These daa are recoded ino a monhly panel of daa covering he birh evens in each individual s life up o he ime of heir inerview in wave wo. These daa are hen merged wih he wihin panel daa o creae one even hisory file, which records he concepions of children, where he concepions are assumed o have aken place 9 monhs before he birh dae. We do no model children leaving home, so do no creae a file of children leaving home daes. These daa are also used o creae socks of each process as well as duraions. In he case of socks of children, we assume ha children leave home a 21, so decrease any posiive sock by 1 a he dae a which he oldes child will be 21. Descripive saisics Table 1 presens saisics for he ransiions. The able provides mean duraion unil birh, union formaion, union dissoluion, employmen, and nonemploymen, all measured in years. Noe here ha all duraions include also 4 5 6 7 The BHPS season codes are: winer=january, spring=april, summer=july and auumn=ocober. The number of individuals who become censored afer each wave are as follows: afer wave wo 872), wave hree 920), wave four 700), wave five 398), wave six 349), wave seven 386). There are 6839 individuals who only become censored a he end of he daa we use wave 8, 1998). The grea majoriy of individuals only ever have one birh even in any one wave. There are nine households where here are wo birh evens wihin one wave and one household where here are hree birh evens wihin one wave. We use only he records of individual s naural children. 5
hose individuals censored a he end of he survey. In addiion, he able indicaes he proporions experiencing he evens. The relevan figures are given in he firs and hird columns i.e. he column shown as sample ). From he able we see ha he mean duraion unil firs childbearing is 13.57 years for women, and 16.46 years for men, so mean ages of firs birh are 26.57 and 29.46 years respecively. The second row shows he mean ime unil second birh, saring from he ime of he firs birh. Thus he mean imes unil he second childbearing evens are 4.36 and 4.62 for men and women, which correspond o mean ages of 30.9 for women and 34 for men. The daa indicae ha once he firs birh has occurred, boh men and women accelerae he iming of he second birh, whereas hird or fourh birhs generally end o ake place a a much laer age. Abou 68 percen of all women and 58 percen of all men are recorded as having a leas one child and he percenages are slighly higher for he proporion of hose who have one child ha go on o have a leas one more child. Given wo children, relaively few go on o have a hird birh. For union formaion, he mean age of firs union formaion is 23.37 for women and around 26 for men. The mean ime unil firs union dissoluion is quie long, indicaing ha a large proporion of hose enering he firs union end o remain in his union, and in he majoriy of cases, unil he censoring dae. Of hose who experience a union dissoluion 35 percen of women and 28 percen of men) he mean ime o second union is 5.26 years for women and 4.10 years for men. Employmen and non-employmen ransiions, on he oher hand, are much more frequen evens. Boh men and women find employmen on average a he same age, and ineresingly, almos all women in his sample have a leas one employmen spell. The difference beween men and women becomes apparen when looking a any subsequen employmen ransiion, as well as he nonemploymen ransiions. The mean ime for he firs non-employmen ransiion is 7.47 years for women and 14.53 years for men. Furhermore, 80 percen of women who were employed a leas once become non-employed a some sage in heir career. The equivalen figure for men is considerably lower 53 percen). Once non-employed, men end o find employmen considerably quicker han women. For insance, he ime unil second employmen for women is on average 4.89 years, whereas for men he mean ime is only 1.62 years, and similar discrepancies exis beween men and women for subsequen employmen ransiions. 6
7 3. Empirical modelling of he demographic and labour marke evens In our model we specify five hazards, which arise from hree processes childbearing, union formaion, and employmen ransiions). We assume ha hese hazards are no exogenous o each oher and depend on boh he pas occurrence of he own and oher processes, he pariy of own and oher evens, on duraion, age, a se of ime invarian observed characerisics, and ime invarian unobserved characerisics. The se of hazards is as follows: 1) B B B B B B P b x b A b T b U E f b D M f b h ε = 8 7 4 3 2 1 ) ) )) ), )) ), ) ln 2) M M M M M i i i M x m P m A m T m U E f m m B h ε = = 11 10 9 8 7 6 1 ) ) )) ), ) ) ln 3) D D D D D i i i D x d P d A d T d U E f d B d h ε = = 11 10 9 8 7 6 1 ) ) )) ), ) ) ln 4) E E E E E i i i E x e P e A e T e D M f e B e h ε = = 11 10 9 8 7 6 1 ) ) )) ), ) ) ln 5) U U U U U i i i U x u P u A u T u D M f u B u h ε = = 11 10 9 8 7 6 1 ) ) )) ), ) ) ln where h j, j = B, M, D, E, U are he hazards of a birh, union formaion, union dissoluion, employmen and non-employmen respecively. Equaion 1) is he log hazard rae of experiencing a birh even, equaion 2) he log hazard of a union even, equaion 3) he log hazard of a union dissoluion, equaion 4) he log hazard of an employmen even, and equaion 5) is he hazard rae of experiencing an non-employmen even. The funcions f.,.) denoes he endogenous variables, and are consruced as ime varying dummy variables. For insance marial saus is included as a ime varying variable in equaions 1, 4 and 5, and akes he value 1 in he segmens which an individual is married or in a union), and zero oherwise. Employmen saus is implemened similarly. Individuals may have many children and experience several unions, employmen and non-employmen spells. In oher words, evens migh be repeaed over ime. We do no specify separae equaions for differen spells: for insance, he equaion for a marriage even, equaion 2), includes firs, second, and up o he sixh birh. Bu as he process of, say, firs child bearing migh be very differen from he process of second
birh even, each hazard is modelled as a funcion of a se dummy variables P j, where j B, M, D, E, U, o conrol for he pariies of he own even. In addiion, we include deailed conrols for age, which is capured by A j ). This is a vecor of N A 1 spline variables whose coefficiens are allowed o differ beween inervals separaed by N A nodes. Denoing he nodes as w k, we can define he spline variable for he kh inerval as: j A ) = max[0, min wk 1, wk wk 1)]; j B, M, D, E, U ) 6) The baseline hazard funcion, T j ), is defined in a similar way, a piecewise coninuous linear Gomperz funcion. By specifying several node poins, he formulaion allows for a variey of paerns of he duraion dependence in he hazard funcion. To complee he specificaion of equaions 5) 9) we include a range of non ime varying variables, denoed x j. These are educaion in 5 groups), cohor of birh in 4 groups), 8 parenal socio-economic saus, ehnic origin, and a dummy variable indicaing wheher he responden lived wih boh parens a age 14. 9 Leaving each ε j as independen univariae random variables will capure unobserved heerogeneiy wihin each process, bu no capure any correlaion in unobserved heerogeneiy across processes. To deal wih his we specify ε j o have a mulivariae join normal disribuion. Formally: B ε 2 0 σ B M ε 0 ρ BM D ε ~ N 0, ρ BD E 0 ε ρ BE U ε 0 ρ BU ρ σ ρ ρ ρ MB 2 M MD ME MU ρ ρ σ ρ ρ DB DM 2 D DE DU ρ ρ ρ σ ρ EB EM ED 2 E EU ρ ρ ρ ρ σ UB UM UD UE 2 U 7) By esimaing he correlaions beween equaions we are in effec able o conrol for he fac ha he five processes migh be endogenous o each oher. To illusrae he problem, assume for he momen ha we only esimaed he firs wo equaions. Furhermore, le us assume ha he correlaion beween childbearing and union formaion, here given as ρ BM, is posiive, bu ha we fail o conrol for his correlaion in he regression. Under hese circumsances he 8 9 The cohors are defined by decade of birh beginning in 1940. The lowes educaional group have no qualificaions; he highes have universiy level qualificaions. As i sands his specificaion does no include any ineracion erms. Clearly several ineracion formulaion could be ineresing and bring a deeper undersanding o individuals behaviour. However, currenly he model conains 185 parameers, and esimaion is no rivial. Given ha he curren specificaion is able o replicae he original daa reasonably well we decided no o include furher covariaes. 8
esimaes of he direc effec of union formaion he ime varying variable) in he childbearing equaion, and he ime varying birh variables in he union formaion equaion, will be biased. In fac, as long as he rue correlaion is posiive here will be an upward bias in he direc effecs. 10 In a sysem of five equaions, where each even ineracs wih each of he ohers, i becomes more difficul o predic he direcion of he bias. An addiional imporan feaure of he unobserved heerogeneiy erms is ha hey are assumed fixed over an individual s lifeime. Clearly, unobserved characerisics influencing he hazard migh change as he various evens ake place. 11 4. Esimaion Resuls This secion presens he parameer esimaes of he economeric model see Tables 2A 2E). Background variables and educaion, and endogenous evens We sar by discussing he esimaed coefficiens of he non-ime varying background variables. These show ha family background is an imporan deerminan for an individual s family formaion evens, whereas i has less impac on he employmen ransiions. Boh men and women coming from disruped families have more children, form and dissolve unions quicker. The effecs are weaker for he non-employmen ransiions, alhough we do find ha women from disruped families are more likely o leave employmen, which is consisen wih he fac ha hey have more children. Men and women from non-whie ehnic origins show quie differen behaviour o he res of he populaion. They generally end o delay union formaion, bu have a considerable higher feriliy rae once in a union. They also have a lower rae of enering employmen, whereas here is no difference in erms of leaving employmen. Parenal occupaional saus has a more limied impac. I is 10 11 This argumen ress on he assumpion ha he mulivariae normal disribuion is able o capure he unobserved heerogeneiy reasonably well. Heckman and Singer 1984) argue agains using parameric disribuions since he specific choice of he disribuion funcion migh affec he parameer esimaes. However, his conclusion has laer been conesed see for insance Ridder 1987) and references herein). I has been argued ha differen impacs of choosing a parameric disribuion is jus as likely o be affeced by using an inflexible funcion for he baseline hazard funcion. If he baseline is flexible, i.e. he piecewise coninuous linear Gomperz formulaion used here, i is no clear ha he parameric choice of he unobserved heerogeneiy should have much impac on he parameer esimaes. See Aassve e al 2002) for a specificaion where he unobserved heerogeneiy erms are differen, bu correlaed, across ime. 9
sronges in he feriliy ransiions, where a high male parenal socio-economic saus is associaed wih a significan reducion in he feriliy rae. Moher s occupaional saus has very lile or no impac. The impac of faher s occupaional saus on enering employmen is negaive boh for men and women. This is somewha surprising given ha we also conrol for educaional aainmen. A possible explanaion is ha he faher s occupaional saus is posiively correlaed wih family income. The negaive impac suggess ha young individuals from wealhy family backgrounds end o delay enry o employmen, which migh be due o longer ime spen in educaion. We now urn o he impac of educaion. 12 Mos of he esimaes are consisen wih previous findings, alhough we do find some unexpeced non-linear effecs. For childbearing, we find ha highly educaed women have a lower rae of child bearing. Furhermore, here is a monoonic gradien for he five caegories of educaional aainmen. The impac of educaion on having children is weaker for men and only men wih higher educaional aainmen levels have a feriliy rae ha is significanly lower han ha of he oher educaion groups. For union formaion, he impac is very similar o hose of feriliy, alhough he magniude of he effecs is generally smaller. These findings are generally consisen wih our expecaions. Educaion generally delays boh feriliy and union formaion and he impac is generally monoonic. For union dissoluion on he oher hand, educaional level has no significan impac. In erms of enering employmen, he resuls are more mixed. Women wih medium levels of qualificaions have a higher enry rae ino employmen compared o hose wih lower educaion. Women wih very high educaional aainmen have a considerable lower ransiion rae ino employmen han all oher groups. For men he impac is slighly differen. Low and medium levels of educaion do no seem o have any differenial impac on he enry ino employmen. However, as for women, hose wih he highes educaional aainmen have a lower rae of enry ino work. Ineresingly, higher educaion among men is negaively associaed wih leaving employmen. Consequenly he resuls sugges ha, alhough highly educaed men are less likely o leave employmen, once hey have lef, hey spend longer searching for he nex job. For women he educaional effec on non-employmen is also negaive, bu here is no monoonic gradien. I is imporan o keep in mind ha hese paerns migh be driven by he fac ha boh men and women who spend longer ime in educaion will necessarily delay enry ino employmen. 12 Noe ha we rea educaion as exogenous, hough properly i should be modelled as par of he se of choices individuals make abou heir pos compulsory school leaving behaviour. However, modelling he level of educaion would add oo much complexiy. 10
Our esimaes indicae imporan behavioural differences beween he four cohors. In general we find ha he younger cohors have lower feriliy raes and a lower rae of enering unions. Once in a union hey are considerably more likely o dissolve he union, compared o he oldes cohor, which indicaes ha individuals in he younger cohors end o spend longer ime being single. The resuls are more mixed for he employmen and non-employmen ransiions. Among women we see ha he second oldes cohor ener employmen a a higher rae han he oldes cohor, whereas here is no significan difference beween he oldes cohor and he wo younges cohors. For men, compared o he oldes cohor, he individuals in he younger cohors all have lower ransiion raes ino employmen. For boh genders here are clear posiive gradiens for enry ino non-employmen, indicaing ha he younger cohors have a much higher ransiion raes ou of work han he oldes cohor. The combinaion of hese rends indicaes ha individuals in he younger cohors, paricularly he men, spend more ime unemployed han hose in he older cohors. Time varying variables We sar by analysing he impac of marial saus and employmen saus on child bearing. Noe ha marial saus incorporaes cohabiaion, and employmen includes full ime and par ime work. The esimaes in Table 2A indicae ha marial saus has a large posiive impac on feriliy evens, and ha he effec remains srong when conrolling for unobserved heerogeneiy. As we would expec, being in employmen has a negaive impac on concepions. Alhough he parameer is highly significan, i is no exremely large, implying ha working is no a paricularly srong deerren o having children. I is possible ha he relaively weak effec is somewha influenced by he fac ha we incorporae par ime and full ime work ino he same caegory. I is possible, for insance, ha women in full ime work have a much lower feriliy rae han women working par ime. Obviously he recorded employmen spells migh mask ransiions beween par ime and full ime work, which migh play an imporan role in feriliy decisions. 13 The posiive impac of employmen for men on having children is also according o expecaions. The parameer is highly significan, bu again he magniude is somewha small. Noe, however, ha he parameer esimae here averages over all birh orders. Thus i is possible ha he impac would have been sronger for iming of firs birh, and even weaker for subsequen birhs. 13 While i is noed ha ransiion o par ime work usually occurs afer he birh of a child raher han prior o concepion, i may be he case ha he negaive effec on feriliy of ransiion ino full ime work from par ime work is masked by he inclusion of par ime work in he employmen definiion. 11
When considering he impac of child bearing on union formaion, we see ha he impac very much depends on he birh order. Noe here ha he birh evens represen he sock of children and should be inerpreed accordingly. For insance, experiencing a firs birh has a srong posiive impac on forming a union, and his is he case for boh genders. However, having a second birh ouside a union acually lowers he rae of union formaion rae. The opposing signs of he firs and he second birh evens are ineresing. The posiive impac of he firs birh even is consisen wih economic heories in ha individuals consider a cohabiing union or a marriage more beneficial once hey have acquired marial specific capial. However, here migh also be normaive forces a play, in he sense ha individuals migh feel a pressure o legiimise he child. The negaive sign of second birh-even indicaes ha hose who do no form a union afer he firs birh are a a disadvanage in he marriage marke when hey have he second child. 14 The subsequen birh evens have no significan impac on union formaion. Work saus has a posiive and srongly significan impac on union formaion for boh men and women, a finding consisen wih mos previous research. Turning o he union dissoluion hazard, we find parameer esimaes consisen wih our expecaions. The negaive impac of firs and second birh on dissoluion indicaes he role of children as marial specific capial. Thus having children reduces he separaion rae. 15 Our specificaion does no include duraion splines for he birh evens, so we do no examine he impac of he age of he children on he rae of dissoluion. 16 I is noeworhy ha he impac of children becomes sronger once we conrol for unobserved heerogeneiy. In fac, he negaive impac of he second birh even is only significan for women when unobserved heerogeneiy is included. The hird birh even does no have any saisically significan impac on dissoluion. Higher birh orders generally have a posiive impac, bu hese variables are no paricularly well defined due o small sample sizes. The impac of work saus on divorce is no paricularly srong, especially for men, independen of wheher unobserved heerogeneiy is 14 15 16 The second birh even ouside a union will also include women who migh have had he firs birh wihin a union. We allow for individual specific fixed effecs in he modelling process which can ake ino accoun ases for marriage and herefore conrol for his. The individual fixed effecs conrol for ases for marriage such ha i is no simply he case ha children are born in more sable relaionships. Therefore hough here are no fixed effecs for specific unions o conrol for he sabiliy of a union, he effec of ases for union are conrolled for somewha in he individual fixed effecs. See, for insance, Lillard and Waie 1993) who show how dissoluion depends on he age of he children. 12
conrolled for. For women, on he oher hand, work has posiive impac only when we conrol for unobserved heerogeneiy. The rae of enering employmen is negaively associaed wih a firs birh even. Alhough he impac is negaive for boh genders, i is considerably weaker for men. This negaive impac for men is somewha surprising, as he financial coss associaed wih childbearing, and he radiional division of labour beween men and women jus afer child-birh, would sugges a greaer incenive for men o ener employmen. For second birhs, here is no significan effec for women, whereas here is sill a weak negaive effec for men when unobserved heerogeneiy is included. For higher birh orders he negaive impac for women and men apar from he hird birh order) persiss. Being in a union reduces he employmen rae for women, independen of wheher he specificaion conrols for unobserved heerogeneiy or no. For men, here is a srong posiive impac, bu ineresingly, his disappears once we conrol for unobserved heerogeneiy. Our esimaes of he relaionship beween enering non-employmen and childbearing show ineresing, alhough no enirely unexpeced resuls. For women, he firs birh even has a srong and posiive impac on leaving employmen, whereas for men here is no significan effec. The impac of he second birh even on enering non-employmen is negaive and significan for women, suggesing ha hose having he second child are more likely o hang ono o heir jobs, implying ha more women now reurn o work immediaely afer he maerniy leave. Again, he birh even does no have any impac on men s employmen decision. Marial saus has a similar effec as he birh evens. Tha is, women in a union have a considerably higher rae of enering non-employmen compared o hose who are single. For men he impac is negaive, alhough his again disappears once we conrol for unobserved heerogeneiy. Duraion and age dependence Tables 3A 3E repor he parameer esimaes of he baseline hazard and age splines. These esimaes provide a picure of he duraion dependence and he age effec in he five processes. Saring from Table 3A, which repors he esimaes for he birh evens, we noe ha he hazard is iniially increasing and hen declining for all inervals, apar from a posiive jump in he second las inerval. I is imporan o remember ha his refers o he baseline for all birh evens. As is well known in he lieraure e.g. Newman and McCulloch 1984)), he shape of he baseline for he firs birh even is very differen compared o any subsequen birhs. In he former he shape of he baseline ends o have a pronounced invered U-shape. Here, where he baseline parameers refer o he average of all birh pariies, he shape is much less pronounced. Looking a he 13
impac of age we see a much more disinc paern. The rae of childbearing increases sharply wih age iniially, hen becoming fla or slighly decreasing. 17 For union formaion we find less marked paerns, especially in erms of he baseline hazard. Again, his is in conras o he ypical shape of he baseline of firs union even, which is normally srongly increasing and hen declining. Again he age splines are more prominen and increasing unil age 23 before hey sar o decline weakly. For dissoluion he paerns are more mixed. The baseline hazard is fla for he firs wo inervals, hen someimes declining and someimes increasing, every ime a very small magniudes. A mixed paern also appears for he age splines. For men i is difficul o esimae more han wo age splines. Overall he esimaes for dissoluion indicae lile duraion dependence or age effecs. The age effec for employmen ransiions is considerably sronger. The hazard increases srongly wih he firs age inerval, hen rises a a slower rae and hen becomes approximaely fla. The risk of employmen has negaive duraion dependence, alhough he paern is no monoonic. In oher words, he risk of employmen falls he longer he individual remains unemployed, alhough he hazard evenually becomes fla. For non-employmen ransiions our esimaes indicae very lile duraion dependence alhough here does seem o be weak age dependence a he early ages. Unobserved heerogeneiy The esimaes of he parameers of he unobserved heerogeneiy erms are repored in Table 4. The firs panel gives he esimaes of he sandard errors of he five equaions. The impac of he unobserved heerogeneiy is paricularly pronounced for he shape of he baseline hazard, he pariy variables, and he age effec. For women mos of he sandard errors are close o uniy, excep for he employmen hazard. 18 The second panel of Table 4 repors he esimaes of he correlaions beween he error erms. Before looking a he correlaions in deail, i is useful o say a few words abou heir inerpreaion. In he case of single spell muliple processes, a posiive correlaion, say, would indicae ha hose wo evens are 17 18 An ineresing quesion is wheher only one hazard rae funcion for all birh pariies is a sufficien specificaion he alernaive being separae hazard funcion for each birh-pariy. However, as he nex secions shows, compuing descripive saisics from simulaing he model and comparing hem wih he original sample shows a quie close fi, which we ake as an indicaion ha our specificaion is sufficien in replicaing he observed ransiion paerns. Pu differenly, compared o he oher processes, he variaion in employmen ransiions among women seem o be fairly well capured by he observed covariaes. 14
deermined joinly. For insance, a posiive correlaion in a model of iming unil firs childbearing and firs union formaion, would sugges ha hese decisions were no made independenly of each oher. Or pu differenly individuals would rarely make a decision abou marriage independenly of having had he firs birh. In our specificaion evens are repeaed: individuals may have many marriages and hey may have many children. As such a posiive correlaion reflecs ha he more likely you are o have children no only he firs child) he more likely you are o ge married ha is, i may reflec long run ase and capabiliies. 19 Looking a he correlaions we see ha hey are mosly non-zero and significan, indicaing he endogeneiy of he processes. In addiion o he correlaions beween feriliy childbearing) and union formaion, here is a posiive correlaion beween childbearing and union dissoluion and beween childbearing and employmen and non-employmen. Thus, individuals more prone o childbearing are also more likely o have more marriages and more employmen spells i.e. have a more variable marriage and employmen hisory. Ineresingly, and no unexpecedly, he correlaions beween childbearing and employmen and childbearing and non-employmen are considerably smaller for men. The esimaes also reflec a significan posiive correlaion beween union formaion and dissoluion. The esimae indicaes ha here are women he correlaion for men is no significan) ha have a srong preference for living in a union bu who a he same ime are no saisfied wih heir curren union. Thus, hey have sronger endency o move ino and ou of unions. The posiive correlaions beween feriliy and union formaion, feriliy and union dissoluion, and union formaion and union dissoluion, are all consisen wih he findings of Upchurch e al 2002) using US daa. We also find a srong posiive correlaion beween union formaion and employmen. Thus hose who are more likely o form a union are also more likely o ge employmen quickly. There is lile evidence o sugges any correlaion beween union and non-employmen, and employmen and union 19 The issue of inerpreaion is more suble han his. Frequenly in he demography lieraure, unobserved heerogeneiy is referred o as differences in ase for family life. Those who marry and have he firs birh quickly normally refleced by a posiive correlaion) are ofen said o have a preference for family life, which in he daa is unobserved. Bu of course unobserved heerogeneiy is by definiion unobserved. Consequenly we canno know for sure wha underlies a posiive or negaive correlaion. However no daa source is likely o be rich enough o provide much clues abou he exac naure of he unobserved facors. 15
dissoluion. In addiion, here is lile o sugges ha here are any common unobserved facors driving employmen and non-employmen ransiions. This is an ineresing resul, as i suggess ha, conrolling for he oher endogenous processes, here is no significan correlaion beween he wo. In oher words, hose who end o find employmen quickly, condiioning on he observed covariaes, do no necessarily have a higher rae of becoming non-employed. As such, he case is differen o union formaion and union dissoluion, where he correlaion is srong and significan for women. In summary, he effec of conrolling for unobserved heerogeneiy is o affec he coefficien esimaes on he socks of he 5 processes, on he baseline hazard and age. In addiion, he esimaed unobserved heerogeneiy beween processes is somewha differen o ha which has previously emerged from esimaes of only a subse of he processes considered here. 5. Micro Simulaion Analysis As a means o provide furher insigh ino he iner-relaionships beween hese processes we underake a deailed micro simulaion analysis. The basic principle behind he simulaions is o make random draws from he uniform disribuion in which he random values are convered o simulaed duraions, via he invered survivor funcions. 20 Forunaely, simulaing a sysem of simulaneous hazards is quie similar o he case of single equaion models wih repeaed spells, or any fully sequenial model, such as he compeing risk model. Despie he fac ha he principle remains he same, simulaing a sysem will necessarily involve a higher level of complexiy. This is mainly driven by he fac ha any of he evens aking place mus be incorporaed as ime varying variables in he oher equaions. In oher words, any ime varying evens included as regressors in he esimaion procedure mus also be incorporaed in he simulaions. 21 Here every individual is simulaed from he age 13. From his age, we simulae he iming of 1) he firs birh even, 2) he firs union even, and 3) he firs employmen even. We do no simulae iming of non-employmen and union dissoluion, since a age 13 all individuals are assumed and consisen wih he original daa no o be working nor in a union. The lenghs of he hree 20 21 See Aassve e al 2002) and Aassve 2003) for applicaions of his approach. As an example, consider he wo equaions of birh evens and union formaion. If an individual is simulaed o marry prior o any birh evens, he marriage union even has o be included as a ime varying variable in he birh equaion. Similarly, if a person is simulaed o experience firs childbirh prior o marriage, his even mus be included as a ime varying variable in he marriage equaion. 16
simulaed duraions are compared, and he shores is seleced and aken o be he firs even for his simulaed individual. Based on he iming of he even he baseline duraion dependence and he age dependency are updaed. Tha is, if he lengh of he firs simulaed duraion is five years, hen he nex evens are simulaed from age 17. Saring from he ime of he firs even, now assuming ha he individual is in a union, a birh even, a union dissoluion even, and an employmen even are simulaed. Again, he shores of he hree duraions are seleced and recorded. This procedure is repeaed unil he censoring dae is reached. Noe being in a union and being single are aken o be muually exclusive saes as are being in employmen and being unemployed. Feriliy evens, in conras, are repeaed and irreversible evens. Consequenly, an individual will always be a risk of anoher child, provided he or she has no reached he censoring dae imposed in he original daa. 22 The simulaions are performed separaely by gender, wih 52600 replicaions for women and 49980 replicaions for men. These simulaed individuals have he same background characerisics such as ehnic background, cohor, parens characerisics, and so on) as he original sample. In conras, he ime varying variables will depend direcly on he simulaed pahs, as hey are generaed from he simulaion hemselves. Simulaion of he unobserved heerogeneiy erms is relaively sraighforward. Each simulaed individual is given a value drawn from he five-dimensional join normal disribuion, as shown in equaion 7), and repored in Table 4. This value is simply added o he log hazard, which is used o consruc he invered survival funcion. Table 1 compares descripive saisics from he daa and he simulaions. The descripive saisics from he simulaions coincide well wih hose of he sample. This is paricularly he case for he demographic ransiions. For he firs hree birh evens i is clear ha he differences are very small. The same is he case for union formaion and union dissoluion. The discrepancies become somewha larger for evens ha are less frequen in he original sample e.g. he fourh birh). For he employmen and non-employmen ransiions he fi is also saisfacory, alhough again he discrepancies become larger as evens become less frequen. We classify individuals ino overall saes defined by he combinaion of marial, employmen and child saes. 16 saes are defined by he 2 marial saes * 2 employmen saes * 4 child saes. Occupancy of hese overall saes differs by gender. The mos common sae for females is single, employed, no children 21%), followed by married, employed, no children 17%). 6% of 22 The censoring dae for childbearing was se o 45 years of age for women, and 55 years of age for men. 17
females are single, no employed, wih no children, and around 4% are single, no employed wih children. For men, he mos common group is single, employed, no children 31%), followed by married, employed, no children 17%). Around 9% are single, unemployed, wih no children, and jus under 1% are single, no employed wih children. These sae occupancy paerns for women and men agains age are illusraed Figures 1 and 2, respecively. To simplify he presenaion we graph only seleced saes for each age and by cohor. The 4 groups represened for females are single, non-employed, parens, single working wih no children, married, no working, wih children and married, working, wih children. These saes accoun for abou 66 percen of all female observaions. All 4 graphs show he sharp fall in he single, working wih no children group beween he ages of 18 and 30 and he rise in he number married wih children boh working and no working). The cohor differences can again be seen clearly: across cohors, he fall in he single, working, no children group akes place a laer ages he younger he cohor. The wo graphs for he wo older cohors shows he relaive increase wih age in he share of married women wih children ha are employed compared o hose who are no employed. Figure 2 races ou he occupancy of 4 saes by age for 4 cohors for males. The four saes are no married, no employed, no children, no married, employed, no children, married, no employed, children and married, employed, wih children. Togeher, hese groups accoun for 73 percen of all observaions. The graphs for all four cohors show he fall in he wo unmarried groups over ime and he rise in he number married working wih kids. This fall and rise ake place a a younger age he older he cohor. Compared o females, he number who are married wih children bu no employed is much lower, reflecing he higher employmen rae for men. Of crucial ineres in his analysis is he exen o which feriliy, union formaion and employmen influence each oher. For insance, wha is he impac on feriliy and union formaion raes from an increase in employmen among women? Or similarly, wha is he impac on feriliy and employmen levels from increasing he raes a which men and women form unions? Given he complex naure of he model, predominanly driven by non-lineariies and inricae feedback mechanisms, he parameer esimaes alone are no necessarily very useful in answering hese quesions. In conras, simulaions faciliae informaive sensiiviy analysis in a simple way. Our approach is he following. For each of he hree processes, we increase he hazard of each even occurring in urn. For he feriliy process we increase he inercep by 10%, for unions we increase he inercep of enering a union by 10% and decrease he inercep for dissolving by he same amoun, and for employmen we increase 18