Strategic Labor Supply


 Baldric Cross
 2 years ago
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1 Prelmnry drft My 1999 Do not quote wthout permsson of uthor Comments re welcome Strtegc Lor Supply A dynmc rgnng model nd ts econometrc mplementton Mrm Belo Free nversty of Berln Astrct In ths pper dynmc rgnng model of ntrfmly tme llocton s presented wth dvorce s the thret pont. Rtonl ehvor leds to overnvestment n humn cptl nd neffcent tme llocton regrdng housework nd mrket work the ltter of whch s lso suppled s n nsurnce gnst the rsk of dvorce. For mrred women n the Germn SocoEconomc Pnel lor supply s estmted: A durton model on mrtl stlty s performed to otn predcted dvorce proltes. Then nstrumentlvrle estmton of femle lor supply s performed wth ftted wges nd ftted thret ponts weghted y the ndvdul prolty of dvorce. The emprcl results support the rgnng rgument of strtegc spect to femle lor supply. Keywords: tme use, femle lor supply, ntrfmly rgnng, dvorce, durton model, nstrumentl vrle estmton JEL Clssfcton: J, C71, C35 Insttut für öffentlche Fnnzen und Sozlpoltk Boltzmnnstr Berln fon: fx: eml:
2 Strtegc Lor Supply A dynmc rgnng model nd ts econometrc mplementton Introducton Over the lst four decdes there hs een n enormous ncrese n the lor force prtcpton of mrred women. Wheres overll prtcpton rtes n Germny hve een fllng due to reducton n lfe tme work (lter entry nto the lor force s well s erler retrement), mrred women s prtcpton rtes for ge 5 to 50 lmost douled from the sxtes to the lte nnetes, gong from 37% to 70% (Frnz 1996 nd Sttstsches Bundesmt 1997). Over the sme perod dvorce rtes hve contnuously ncresed. The prolty of dvorce n 5 yers of mrrge hs trpled from 11% n 1955 to 9% n 1986 (Lengsfeld nd Lnke 1988). Whether the ncresng rsk of dvorce s cused y hgher femle lor force prtcpton, s mny studes suggest, or whether mrred women now supply more lor due to the hgher rsk of dvorce, s other studes rgue (see for nstnce Dekmnn (1994)), the decson to work certnly nvolves n spect of nsurnce tht hs een mssed y trdtonl models of household lor supply. It s ths nsurnce spect tht wll e ncorported n the theoretcl modelng nd econometrc estmtng of femle lor supply n the present pper. In the conventonl common preference model (Becker 1965, Gronu 1973 nd 1977) tme llocton decsons of fmly memers nvolve nether humn cptl consdertons of jo experence nor strtegc rgnng spects of ndvdul control over fnncl resources. Insted ndvdul lor supply s derved from the mxmzton of household utlty functon suject to udget nd tme constrnts. Aprt from the fct tht t stll remns to e clrfed just how such jont utlty functon cn e developed, whether t e socl welfre functon of the sort proposed y Smuelson (1956), the utlty functon of n ltrustc hed of the household s Becker suggested n 1974 or some other ggregton of the ndvdul utlty functons of ll fmly memers, the trdtonl frmework fls to correctly expln the ctul lor force prtcpton of mrred women. In prtculr wth regrd to rsng chldren women re often oserved to work for much less thn wht could possly e ther vlue of home tme when djustng ther lor supply untl the wge rte equls the mrgnl product of housework equls the mrgnl rte of susttuton etween lesure nd consumpton. 1 Prt of the dscrepncy etween oservton nd trdtonl economc theory ws tken up y Lehrer nd Nerlove (1981). In ther humn cptl model for lor supply nd fertlty ehvor of mrred women, the lfe cycle s dvded nto three stges dstngushed y the presence nd ge of chldren or, n other words, the demnd for household producton. A wfe lloctes her tme mong work n the lor force, work t home nd lesure. She lso decdes out her nvestment n humn cptl whch ffects her wge rte n the susequent perods. If the ncrese n future ernngs s suffcently lrge, she wll work n the lor mrket even f her wge does not rech the shdow prce of her tme spent t home rerng kds. Besdes the mntennce of ther humn cptl nd the fer of foregong future chnces on the lor mrket fter the chldrerng phse, mny women stte tht they wnt to cheve some 1 Ths s true esp. n lght of the Germn tx system (Ehegttensplttng), whch dscourges mrket work y mrred women snce women s ernngs re ht y hgh mrgnl tx rtes. 1
3 ndependence from ther husnds ernngs. Often ths mens workng for low wge rte. Strtegc ehvor nd ts dstrutonl spect of control over fnncl resources does seem to ply some role n fmly decson mkng, though. Emprcl studes (e.g. the survey y Dekmnn nd Klen, 1991) ndcte tht n the lght of fdng fmly stlty nd ncresng dvorce rtes, lor force prtcpton lso serves s n nsurnce gnst the rsk of dvorce. Ths strtegc spect of lor force prtcpton ws frst tken nto consderton y uthors followng gme theoretc pproch. In ther semnl works Mnser nd Brown (1980) nd McElroy nd Horney (1981) ppled Nsh coopertve rgnng theory to household decson mkng. In these models the dstruton of utlty wthn the household s determned y the fesle consumpton set of the two prtners nd ther outsde optons 3 whch re the snglestte utltes. Any chnge n the reltve conflct pyoffs, e.g. n ncrese n ncome of one of the prtners, wll ffect the household utlty dstruton n tht spouse s fvor. An lterntve Nsh rgnng model wth noncoopertve mrrge reflectng trdtonl gender roles nsted of dvorce s the outsde opton ws proposed y Lunderg nd Pollck (1993) 4. The seprtespheres model, n contrst to the dvorcethret model, lso explns dfferent equlrum dstrutons n exstng mrrges mpled y trnsfer pyments to ether of the prtners, even f these do not ffect the sngle stte utltes. Ott (199) tkes ccount of ntertemporl dependences of household decsons n proposng dynmc rgnng model wth sugme consstency. In ths settng the prtners outsde optons re not gven exogenously ny more, nsted they re endogenously determned y the precedng perod s tme llocton. An ndvdul s decson to supply lor s mde llowng for the ccompnyng mpct on her future conflct pyoff. The prtners reltve rgnng powers therefore drectly depend on pst tme use decsons nd the resultng humn cptl ccumulton. Sequentl noncooperton does not llow to sgn ndng contrcts etween the perods. Ths frmework seems to e most pproprte for explnng the lor force prtcpton of mny women who not only consder ctul lor ncome ut lso the humn cptl spect of jo experence s well s ther future rgnng power wthn the household when mkng tme llocton decsons. Ths pper s dvded nto two prts: In the theoretcl prt dynmc rgnng model of fmly lor supply s dscussed, n the emprcl second prt the mplctons of the theoretcl model re ncorported nto n econometrc estmton of femle lor supply. In the followng secton I propose dynmc rgnng model tht extends the work of Ott (199). Tme llocton s determned y ntrfmly rgnng tkng plce wthn threeperod lfe cycle. Wheres n the frst stge humn cptl nvestments re mde noncoopertvely y ech ndvdul, n the susequent stges,.e. the fmly phse, tme llocton decsons (esp. tme devoted to housework s opposed to tme spent n the lor mrket) re determned through Nsh rgnng etween the prtners wth seprton s ther thret pont. In ths model rtonl ndvduls not only tend to overnvest n humn cptl durng the frst perod of lfe ut lso hve n ncentve to choose suoptml tme ptterns t the egnnng of the fmly phse should ths mprove ther rgnng poston n the followng perod. Ths result s due to n symmetry of the lernng effects from mrket work versus housework nd to the symmetry of the mrketlty of the dfferent lor sklls. nless ndng longterm contrcts cn e mde etween the prtners, rtonl ehvor lwys leds to neffcent See e.g. Gugler (1984). 3 The terms outsde opton, thret pont nd conflct pyoff re used synonymously. They ll ndcte person s est lterntve to the rgnng outcome. 4 Woolley (1988) s well s Konrd nd Lommerud (1996) lso model ntrfmly decson mkng s Nsh rgnng model wth nternl thret ponts.
4 outcomes wth respect to tme llocton nd household producton wthn the fmly. Extendng the trdtonl frmework, n ths model lor supply decsons re lso determned y strtegc rgnng consdertons. In the econometrc prt of the pper these strtegc spects re tken nto ccount when estmtng femle lor supply n fvestge procedure usng dt from the Germn Socoeconomc Pnel. Frst the dt set s ntroduced nd comprson of smple chrcterstcs y ncdence of future dvorce s presented. The pprent nterdependence etween prtcpton nd mrtl stlty suggests tht lor supply mght n fct e cused y the ndvdul rsk of dvorce. The fvestge procedure s crred out for model specfcton wth vrtul conflct pyoffs. A loglner durton model on mrtl survvl or stlty s estmted. The resultng condtonl proltes of dvorce serve s weghts for the conflct pyoffs otned from susmple OLS conflct pyoff equton estmtes. The resultng expected conflct pyoffs s entered s n nstrumentl vrle nto the prot estmton of lor force prtcpton nd nto the OLS estmton of femle hours worked. Wth the explct ncluson of the ndvdul outsde opton the resultng lor supply equton tkes nto consderton strtegc spects of ntrfmly tme llocton. The pper concludes wth summry of the theoretcl nd emprcl results from nlyzng lor supply wthn dynmc rgnng frmework. 3
5 I A threeperod rgnng model I consder model 5 n whch n ndvdul s lfe cycle s dvded nto three perods of dfferng length: In the frst perod decsons on humn cptl nvestment re mde, tht s, the vlle tme hs to e llocted mong educton ctvtes K nd lesure L. At the egnnng of the second perod ech ndvdul s rndomly mtched to prtner wth whom she forms fmly n order to rse chldren 6. In the second nd the thrd perod the fmly phse, tme s llocted mong three competng ctvtes: work n the lor force M, whch yelds mrket goods, work t home H, whch yelds home produced goods such s chld servces, nd lesure L whch yelds drect utlty. The two perods re dstngushed y the chldren's ge or ther demnd for cre (.e. household producton), respectvely. Ths tkes hgh vlue n perod when nfnts hve to e looked fter 4 hours dy nd, from certn ge on, dmnshes stedly n the lte fmly phse. 7 Wheres n the frst perod tme llocton nd consumpton decsons re mde ndependently y ech ndvdul, the fmly phse s chrcterzed y twostge coopertve Nsh rgnng gme: the dstruton of lesure nd consumpton goods wthn the household s, ccordng to the xomtc Nsh soluton of the gme, determned y the mxmum product of the ndvdul cooperton gns n the two stges. Agreements mde t the egnnng of the fmly phse re only ndng for one perod. Humn cptl ccumulton n one perod does not tke effect untl the susequent perod. Hence, the outsde optons nd the pyoff spce n the second nd thrd perod re determned y decsons mde n the prevlng preperod. Although the utlty functon s ntertemporlly seprle, the lfe perods re nonetheless nterrelted through the determnton of the conflct pyoffs. Becuse of ths nterdependence the threestge optmzton prolem hs to e solved through ckwrds nducton ccordng to the de of sugme consstency. The optmzton prolem of spouse s llustrted wth the followng pcture: lfe cycle: + + ( + C )( + C ) ( C )( C ) tme use: K, L1 M, H, L M, H, L ckwrds nducton: W ( V C )( V C ) ( C )( C ) 5 The model proposed extends the work of Ott (199, 1995) y tkng nto ccount prefmly humn cptl decsons. 6 In ths model the term fmly generlly descres household n whch two persons mutully gree on lvng together nd where sustntl mount of household jos hve to e tken cre of. These jos do not necessrly hve to e lnked to the erng nd rerng of chldren, they could lso nclude the nursng of reltves n need of cre. 7 The exct ge of dstncton etween stge nd stge 3 depends on the nsttutonl crcumstnces regrdng the mount of chld cre servces provded y schools e.g.. In Germny fmles wth chldren rechng school ge certnly do not enter the thrd stge s ths mens even less nsttutonlly provded chld cre thn n kndergrten; here, the dstngushng ge level hs to e ssumed much hgher. 4
6 where t nd t re ndvdul utlty functons dependng on the level of prvte t consumpton nd the mount of lesure nd V, V, W nd W re soclled mxmumnshsoluton functons of the prtners nd t tme t. C nd C re the correspondng conflct pyoffs. The conflct pyoff s the soluton to the mxmzton of snglestte utlty represents the mxmum utlty tht could e cheved outsde the prtnershp 8, n other words, t reflects the opportunty costs of fmly lfe tht re determned y the spouse s productvty fctors, such s wge rte, household productvty, nd nonlor ncome. The soluton to the threeperod model s derved recursvely s follows: t Perod 3: mx ( C )( C ) Perod : mx ( V C )( V C + + ) Perod 1: mx + W for 1 =, Frst, the condtonl rgnng soluton for perod 3 wll yeld mxmumnshsoluton functons V nd V whch depend on tme llocton decsons mde n the precedng perod. sng these ndrect utlty functons the decson prolem of the second perod wll e solved, gn provdng mxmumnshsoluton functons W for ths perod. The sme procedure s then repeted for the frst perod. Perod 3 mx N3 = ( 3 ( X3, L3) C3 )( 3 ( X3, L3) C3 ) = ( C )( C ) where X + X = X = X + X nd X = Z( H + H ) s.t. T = M + H + L for =, M nd w M + w M X X + Z( H + H ) + I + I 0 H H In ths lst perod sttc Nshrgnng gme hs to e solved. The product of the ndvdul cooperton gns s mxmzed wth regrd to prvte consumpton X nd lesure L, suject to udget nd tme constrnts. The prvte consumpton goods of the two prtners cn ether e produced t home ( X H ) ccordng to the household producton functon Z or purchsed on the mrket. The totl mount of mrket goods X M must not exceed pooled household ncome generted y lor ncome w M + w M plus nonlor ncome I + I. 9 Optml tme llocton n ths sttc settng s known from trdtonl results,.e. n equlrum tme s llocted mong mrket work nd household producton ccordng to the equlty 8 It s ssumed tht such mportnt decsons concernng lor force prtcpton nd home work justfy the use of the dvorcethret model s opposed to fll cks wth noncoopertve ehvor (see dscusson n the ntroducton). 9 The prce of the mrket good s set to unty. 5
7 etween the prevlng productvty fctors w nd z (wth of lesure reltve to tht of consumpton: L X = z = w z Z = ) nd the mrgnl utlty H As n the Beckern frmework dfferent wges for men nd women led to speclzton of the prtners ccordng to ther comprtve dvntges. The mn dstncton etween ths sttc rgnng model nd the trdtonl model les n the dstruton of utlty wthn the fmly. Wheres n the common preference theory the queston of ntrfmly dstruton s smply not ddressed, here t s condtoned on the reltve rgnng postons of the prtners. Thus, rse n s conflct pyoff, e.g. due to n ncrese n ths spouse's nonlor ncome, results n n ntrfmly redstruton fvorng. nd X X = C C L L = w w C = C z z C C Perod The optmzton prolem of the second perod s solved usng the mxmumnshsoluton * * * * * * X, L = X, L from the rgnng gme ove. Wth functons N 3 = 3 ( 3 3 ) nd N 3 3 ( 3 3 ) * V ( w w z z I I ) V ( M M C ( M ) C ( M N )) =,,,,, =,,,, V s determned y tme llocton decsons mde n perod. Second perod s tme llocton s then optmzed ccordng to: s.t. For the optml level of M L X ( 3 )( 3 ) ( V C )( V C ) mx N = + C + C = + + udget nd tme constrnts s ove. the followng condton must e stsfed: 1 V V dc V V = z = w + + X M C M + 1 X M + C dc M If equlty holds, tme wll e llocted mong mrket work, work t home nd lesure ccordng to the mrgnl outputs of these tme uses 10. In contrst to the trdtonl (1) 10 For smplcty the mrgnl eneft of household work s restrcted to the ctul household productvty z whle pd lor lso yelds humn cptl effects. A consderton of humn cptl ccumulton n household producton, however, would not lter the results qulttvely s long s the humn cptl gned from speclzton n the household s less mrketle thn the humn cptl ccumulted n mrket work. 6
8 frmework, here, the mrgnl output of lor s not restrcted to the hourly wge rte ut lso ncludes the mpct of current lor force prtcpton on next perod s utlty. If the ndvdul wge rte s postvely relted to the humn cptl ccumulted, hence t 1 functon of the form wt = w( K, L t= 1 t) wth w K w K > 0, < 0, > 0 nd w < 0, the decson L t to work wll hve dfferent longrun effects: Due to hgher wge level n enlrgement of the fesle consumpton set, tht s n outwrd shft of the utlty posslty fronter, wll result. I cll ths the pure fronter effect. At the sme tme chnge of the conflct pyoff wll led to dstrutonl rgnng effect. Both fronter effect nd dstrutonl rgnng effect rse from the mpct of mrket work on own future utlty nd spouse s future utlty weghted y the respectve mrgnl utltes of consumpton 1 nd 1, respectvely. Snce tme spent n X X the lor mrket typclly hs the descred postve mpct on future utlty through shft of the utlty posslty fronter or n mproved rgnng poston, tme s llocted to mrket work even t wge rte much elow household productvty. Hence, n comprson wth trdtonl theory reltvely more tme wll e dedcted to mrket work nd less to household producton. (Even t z = w speclzton n mrket work tkes plce.) Ths s due to the symmetry etween the ccompnyng lernng effects resultng from the lower mrketlty of household ltes. Or, n other words, the dfferng effects from nvestments n mrketspecfc humn cptl nd nvestments n fmlyspecfc humn cptl on rgnng power countereffect the dvntges of speclzton. Consderng the longrun effects of tme use,.e. the mrgnl output of tme spent n mrket producton s opposed to tme spent n household producton, even dfferent wge structures of men nd women do not necessrly led to complete speclzton s would e the cse n trdtonl theory. Insted, the nteror soluton of oth prtner s tme eng llocted to ll dfferent tme uses, to pd s well s unpd work n prtculr, tht one oserves n relty cn now e explned. Lor supply cn e descred s functon of oth spouses wges, household productvtes, nonlor ncome nd conflct pyoffs: w L t ( w, w, z, z, V, V, C C ) M M, =. Perod 1 The optmzton prolem of the frst perod s solved usng the mxmumnshsoluton * * * * * * X, L = X, L from the rgnng gme ove. Wth functons N = ( ) nd N ( ) * N W ( w w z z3 I I ) W K K C ( K ) C ( K ) ( ) =,,,,, =,,,, W s determned y tme llocton decsons mde n perod. Now, frst perod s tme use s optmzed ccordng to: mx = + W s.t. T = M + K + L nd w M + I X 0 for =, 7
9 Snce n the prefmly stge decsons on tme use re mde ndependently, ndvdul mxmzton s now suject to ndvdul udget constrnts. Optml tme llocton decsons hve to meet the frst order condton: L X 1 W W = + K C X dc dk () The mount of eductonl nvestment should e chosen so s to equlze the shdow prce of tme nd the mrgnl eneft ssocted wth n ddtonl unt of schoolng. Snce humn cptl nvestment tkes effect on future wge rtes, the mrgnl output of educton hs two components: The frst s the drect mpct of educton on utlty possltes, the fronter effect, the second s the dstrutonl rgnng effect tht rses from chnge of the ndvdul conflct pyoff. More humn cptl leds to hgher returns from mrket work nd thus mproves the fnncl stuton of the household s whole. At the sme tme t strengthens the ndvdul rgnng power through n mprovement of the sngle stte utlty. Due to these longrun effects of tme use more humn cptl nvestment wll typclly result n comprson wth trdtonl theory or even compred wth the dynmc model of Lehrer/Nerlove whch explctly consders humn cptl ccumulton. Implctons Snce n the fmly phse the dstruton of utlty wthn the household s unquely determned y the utlty posslty fronter of the two prtners s well s ther outsde optons, ll decsons tht ffect these prmeters re of gret mportnce for the ntrfmly llocton of tme. The mount of humn cptl nvestment chosen y ech ndvdul n the frst perod of lfe wll set the ss for the fmly rgnng gme n the followng perods wth regrd to the orgn of the fesle pyoff spce nd the conflct pyoff. Lkewse, ntrfmly tme llocton n the second perod hs mplctons not only for tht perod's outcome ut lso decdes out the prtner's rgnng postons n the lte fmly phse (3rd perod). Prefmly humn cptl nvestment There re two effects resultng from ny chnge n humn cptl nvestment: shft of the utlty posslty fronter nd n ltered dvson of resources etween the prtners. Strtng from gven optml educton level,.e. for effcent choces n the prefmly stge, the fronter effect of n extr unt of schoolng (n equton ) hs to e zero. The dstrutonl rgnng effect, however, nduces move long the effcency fronter fvorng so tht hs n ncentve to overnvest n humn cptl compred to the householdeffcent level K *. Overnvestment occurs s long s dc dk > L tht s, s long s, y ccumultng n extr unt of humn cptl exceedng the effcent level, the mprovement of s rgnng poston s hgher thn her utlty loss from reduced lesure, 8
10 tme n perod 1. Ths condton holds f optml humn cptl nvestment s sngle s hgher thn wthn fmly 11. In trdtonl models no ncentve for overnvestment exsts. Snce the outsde opton s neglected, the totl effect of n extr unt of educton would e zero. The trdtonl result could therefore e consdered s specl cse of the rgnng pproch where optml humn cptl nvestment s sngle equls tht wthn fmly. Hence, educton exceedng the optml level would hve no effect on the ndvdul rgnng poston. Ths would lso e true for settng wth ndng longterm contrcts etween the prtners, where the ndvdul rgnng powers re ssumed to remn unchnged regrdless of eductonl decsons. Thus the lck of dstrutonl ncentves would sustn n optml level of humn cptl nvestment. As opposed to the humn cptl model y Lehrer nd Nerlove (1981) where the optml level of nvestment n humn cptl s functon of the extent to whch ths cptl s utlzed n the susequent stges of lfe, here the humn cptl endowment serves for mprovng the ndvdul rgnng poston regrdless of ts ctul utlzton. In other words, the humn cptl endowment s employed rther mplctly thn explctly n the tme llocton decson. It serves s strtegc vrle for determnng ntrfmly dstruton. Intrfmly lor supply Rtonl ndvduls not only tend to overnvest n humn cptl t the prefmly stge ut lso hve n ncentve to choose suoptml tme ptterns t the egnnng of the fmly phse f ths wll mprove ther rgnng poston n the followng perod. Agn, there re two effects rsng from chnge n second perod's lor supply on the rgnng set of the lte fmly phse: shft of the utlty posslty fronter nd n ltered dvson of resources etween the spouses. Snce for effcent choces the fronter effect equls zero, n ddtonl unt spent n the lor force does not chnge the utlty spce ut nduces move on the effcency fronter towrds hgher utlty level for. As we cn see from equton (1) n oversupply of mrket work n the second perod wll occur f, strtng from gven optml tme llocton, n ncrese of one prtner's lor force prtcpton wll rse her nextperod's conflct pyoff () nd f the dstrutonl rgnng effect fvorng her own future utlty exceeds tht of her spouse s (): () C M > 0 3 X 3 () 1 V 1 V > C C X The frst condton holds f optml lor supply s sngle s hgher thn wthn fmly. In the trdtonl frmework no ncentve for oversupply exsts. Snce the outsde opton s neglected, the totl effect of n extr unt of mrket work would e zero. The trdtonl result could therefore e consdered s specl cse of the rgnng pproch where optml tme llocton s sngle equls tht wthn fmly. Hence, lor supply exceedng the optml level would hve no effect on the ndvdul rgnng poston. Ths would lso e the cse n settng wth ndng longterm contrcts etween the prtners, where the ndvdul rgnng powers re ssumed to remn unchnged regrdless of the chosen tme uses n perod. Thus 11 Ths mplcton corresponds wth the results of Konrd nd Lommerud s twostge gme of mrrge (1996) where the wge rte s chosen noncoopertvely n the frst stge nd Nsh rgnng gme etween the prtners s solved n the second stge. 9
11 the lck of dstrutonl ncentves would sustn n optml level of lor supply. nless ndng longterm contrcts cn e mde etween the prtners rgnng outcomes wll e suoptml wth respect to tme llocton nd household producton 1. Due to ntrfmly rgnng, ndvdul optmzton s not exclusvely focussed on the mxmzton of fmly outcome ut lso one s own shre of tht outcome. Snce utlty wthn household s dstruted ccordng to the prtner s externl lterntves, tme llocton decsons hve to e mde n the lght of ther effects on these externl lterntves. Even though wth the presence of smll chldren n the erly fmly phse more tme devoted to household producton, prtculrly speclzton of the prtners, would e effcent n the short run, none of the prtners wll e wllng to weken her future rgnng poston. As result, not ll producton possltes n the household cn e exhusted. On ccount of eductonl overnvestment efore nd suoptml tme llocton wthn the erly fmly phse the gns from speclzton wthn the household wll e less those technclly fesle. In the dynmc rgnng model wth endogenously determned conflct pyoffs pd lor serves s strtegc vrle for ntrfmly utlty dstruton. Dscusson of the theoretcl results In the model presented rtonl ndvduls tend to overnvest n humn cptl n the prefmly perod. At the egnnng of the fmly phse they lso hve n ncentve to choose n mount of lor supply exceedng the optml level or n mount of household producton fllng short of the optml level, respectvely, should ths mprove ther rgnng poston n the followng perod. nless ndng longterm contrcts cn e mde etween the prtners, rtonl ehvor lwys leds to neffcent outcomes wth respect to tme llocton nd household producton wthn the fmly. One mjor mplcton of ntrfmly rgnng concerns the estmton of lor supply. For the resons just descred, the decson to prtcpte n the lor mrket n the dynmc rgnng pproch s not only determned y productvty ndctors, such s wge rtes nd household productvtes, ut lso ncludes humn cptl ccumulton s well s strtegc spects regrdng the ndvdul rgnng poston. A consderton of these strtegc spects n econometrc specfcton wll therefore led to more dequte estmtons of ndvdul lor supply. Wth ts ssumpton out the tme structure of lfe ths model descres n extreme cse of fmly formton. Humn cptl nvestments re mde efore prtners n lfe meet rndomly nd strt erng nd rerng chldren. Another extreme cse of lfestyle would e the sngle stte. Relty must le somewhere n etween these two cses. If prolty s ssgned to ech extreme, then n ndvdul s expected lfetme utlty tkes some vlue weghted y the lkelness of these two lfestyles. As for the nvestment n educton, f the prolty of styng sngle s greter thn zero nd f the suffcent condtons for overnvestment hold,.e. optml humn cptl nvestments s sngle re hgher thn wthn mrrge, even greter overnvestment wll result. Ths s ecuse no one cn e sure tht he or she wll meet Mrs. or Mr. Rght nd e le to tke dvntge from cooperton surplus, esp. tht shre generted y ntrhousehold speclzton. Thus, the fndng of neffcent eductonl decsons stys, even n more generl verson of ths model. II Emprcl evdence of the dynmc rgnng model 1 On dscusson concernng the enforcement of ntrfmly greements see Ott (1993). 10
12 In ths secton the strtegc spect of fmly tme use decsons tht hs een derved theoretclly s mplemented n n estmton of femle lor supply, tkng nto ccount mrtl stlty nd the outsde opton to mrrge s determnnts of femle lor force prtcpton 13. A numer of studes nvestgted how dvorce proltes nfluence femle lor supply decsons (Peters 1986, Hurn 1989, Prkmn 199, Johnson nd Sknner 199, Boln 1997, Butrc 1998, Gry 1998). Wllm R. Johnson nd Jonthn Sknner (1986) ccounted for the effect of mrtl stlty on lor force prtcpton n estmtng smultneous model of future dvorce prolty nd current lor supply for mrred women. sng 197 dt from the Pnel Study of Income Dynmcs (PSID) for couples who were mrred n tht yer nd some of whom seprted prtlly n the followng 6 yers, ther results support the hypothess tht sujectve dvorce proltes ncrese lor supply. In crossntonl comprson Brr Butrc (1998) fnds lrge dfferences etween the nted Sttes nd Germny. Her estmtons, sed on the 1986 smples of the PSID nd the Germn SocoEconomc Pnel (GSOEP), suggest tht the prolty of dvorce hs no sgnfcnt mpct on lor supply or hours decsons of women n the.s. wheres Germny very much resemles the.s. n the 1970s. Krstn Boln (1996) dopted smlr pproch wth Swedsh dt. He lso ncluded the rsk of dvorce s n ddtonl regressor n the lor supply equton. Wheres Johnson/Sknner nd Butrc estmted lor supply wthn mrrge, Boln ws nterested n lor supply t the tme of mrrge. Hs results lso convey sgnfcnt mpct of predcted dvorce rsks on femle lor force prtcpton. sng 1979.S.dt the rtcles y H. Elzeth Peters nd y Allen M. Prkmn oth conclude tht the ntroducton of unlterl dvorce hs ncresed the lor force prtcpton rte of mrred women. But wheres Peters ttrutes ths response to the lck of compenston for mrrgespecfc nvestment t dvorce tht cretes n ncentve for mrred women to enter the lor force nd ncrese ther mrketle cptl, Prkmn rgues wth the lck of compenston for mrred women s reduced humn cptl. He fnds greter effect of unlterl dvorce on the lor supply of younger nd etter educted women who could experence lrger reductons n ther future ernng cpcty f they reduced ther prtcpton n the lor force. Although Prkmn mplctly consders the dynmc effects of humn cptl deprecton for mrred women, overll the cted studes restrct ther nlyss to the reltonshp etween lor supply nd the rsk of dvorce s such rther thn the mpct of the externl lterntve or outsde opton to fmly decson mkng,.e. the mpct of the underlyng rgnng power. Jeffrey S. Gry ccounts for the relevnce of the wfe s rgnng poston when nvestgtng.s. mrred women s lor supply ehvor wth chnge n mrtl property lws. Snce stte s dpton of unlterl dvorce cn e nterpreted s n exogenous nd unexpected shft of the extrhousehold envronmentl prmeters (EEPs) of fmly lfe. In contrst to Peters nd Prkmn he fnds tht unlterl dvorce s opposed to mutulconsent dvorce hs no mpct on mrred women s lor force prtcpton unless the underlyng mrtlproperty lws n ech stte re consdered (1998: 69). By nlyzng exogenous chnges of EEPs Gry concludes tht the wfe s lor supply s n ncresng functon of her rgnng poston wthn mrrge. 13 Theoretclly, mle lor supply s just the sme suject to these strtegc consdertons. Prctclly, however, men s hours worked show much less vrton thn women s. Snce the model proposed hs n ny cse ntlly een chosen to motvte the oservton of mrred mothers lor force prtcpton, the nlyss wll e restrcted to women only. 11
13 In the present pper the emprcl pplcton of rgnng power n fmly decson mkng s even further developed: Women s outsde optons re estmted nd ther mpct on femle lor supply re nvestgted to drectly test the theoretcl reltonshp derved n the dynmc rgnng model ove, therey pplyng the concept of the vrtul conflct pyoff. The vrtul conflct pyoff The concept of the vrtul conflct pyoff ccounts for the endogenety of ndvdul rgnng power on ndvdul tme llocton, prtculrly lor force prtcpton. It proceeds from the fct tht everyody hs n outsde opton to fmly rgnng regrdless whether t wll ever e relzed or not. Wheres for seprtng couples we re le to oserve ther economc performnce fter rekup nd, thus, relzton of ther outsde opton to styng wth ther spouses, for ntct prtnershps we do not know the conflct pyoffs. Ths s where the vrtul comes nto ply: Why not pply whtever cn e oserved wth seprtng spouses to the nonseprtng ones n order to generte vrtul conflct pyoff for every sngle person no mtter whether household dssoluton hs ctully tken plce? The mpct of the vrtul or expected conflct pyoff on ndvdul tme llocton cn then e exmned. In other words, the strtegc spects of supplyng lor tht hve een derved n the theoretcl model re now nvestgted emprclly. Allowng for humn cptl nd other ndvdul endowment fctors, the ndvdul outsde opton s chosen s n ddtonl determnnt for the supply of lor. Ths extends the conventonl estmton of femle lor supply y strtegc element 14. Dt set nd smple chrcterstcs To explore the reltonshp etween femle lor supply nd mrtl stlty n Germny I use dt from the Germn SocoEconomc Pnel (GSOEP) 15. As n ndvdul household mcrodt pnel the GSOEP s rch dt source for nlyzng lor force prtcpton y mens of vrous ndvdul s well s household chrcterstcs. The emprcl results re sed on dt from the West Germn susmple of the GSOEP coverng the yers from 1985 to Mkng use of the pnel structure of the dt the longterm mpct of the rsk of dvorce on current lor supply hs een ccounted for: crosssecton smple of couples tht were mrred n 1985 (nd wve of the GSOEP) hs een nlyzed hvng ddtonl nformton on ther mrtl sttus s well s ther economc sttus n the twelve susequent yers untl The nlyss s restrcted to couples wth the wfe not younger thn 0 nd not older thn 45 yers of ge s well s to couples where oth spouses hve completed ther schoolng n 1985, n order to cover tme llocton decsons mde n the erly fmly phse when (ccordng to the theoretcl model) humn cptl nvestments n educton hve lredy een done. The fnl smple conssts of 538 couples, 44 of whom remned mrred durng the followng 1yer perod nd 96 of whom seprted or dvorced n one of the susequent yers The smultneous modelng of tme llocton decsons nd household dssoluton chrcterzes n extenson of the conventonl estmton procedures for femle lor supply (for n overvew of the emprcl lterture see e.g. Lyrd et l. 1980, Kllngsworth 1983, Kllngsworth nd Jmes J. Heckmn 1986, Mroz 1987). 15 For more nformton on the GSOEP see Wgner et l. (1993). 16 The smple s not lmted to complete couples, though. In other words t prtly conssts of women whose husnds hve left the pnel t some stge nd t ncludes men whose wves dd not prtcpte n the ntervews durng the whole tme perod. To e precse, nformton on 44 women lvng n stle mrrges nd 96 seprtng women s eng used together wth the oservtons of 416 nonseprtng nd 83 seprtng men. 1
14 In Tle X (NOT DISPLAYED IN THIS VERSION) the summry sttstcs of the two su smples, sed on women wth hgh mrtl stlty nd sed on seprtng women, re lsted. The two smples revel gret dfferences n ther humn cptl endowment, ther current lor force prtcpton nd n personl chrcterstcs s regrds mrtl nd culturl ckgrounds. The verge nonseprtng couple s older thn seprtng couple. It got mrred t younger ge nd hs een mrred for longer tme. Also the shre of frst mrrges s sustntlly hgher wth stle prtnershps. Nonseprtng women re on verge less educted (.e. less yers of schoolng), hve less fulltme work experence n fulltme employment, ther lor force prtcpton nd monthly work hours re lower thn those of dvorcng women. Ther husnds, on the contrry, hve more work experence nd re currently workng to hgher extent thn n seprtng couples. Overll we cn sy tht gender dfferences wth regrd to humn cptl endowment nd lor force sttus re smller mong seprtng couples. Femle nd mle educton, work experences, current lor force prtcpton nd hours of work re ll more equted n the seprtng sugroup. Even the ge dfference etween husnd nd wfe s greter wth nonseprtng spouses. These complementrtes wthn stle couples mght e n ndcton for the Beckern rgument of comprtve dvntges. Tht s, wth dmnshng gender dfferences the returns from speclzton wthn the household re loosng mportnce. For the seprtng su smple the gns from styng mrred re (or hve een) lower. Fvestge estmton: The generlzed Heckmn procedure wth vrtul conflctpyoffs The lor supply of mrred women wll e estmted ccordng to the followng equton: * * h = β1 X1 + γ w + η pow + ε1 = 1,..., N * w = β X + ε =,..., N 1 where X 1 s vector of vrles commonly used s regressors n n estmton of lor supply (educton, ge, prevous work experence, chldren, household nonlor ncome, husnd s ernngs). w * s the wfe s own (ltent) wge rte nd pow * s n ndctor of reltve rgnng power consstng of the couple s expected (ltent) ndvdul conflct pyoffs. The effects of omtted vrles re represented y the rndom error term ε 1. In order to consder the outsde opton n the lor supply equton expected conflct pyoffs hve to e generted for those spouses who dd not seprte wthn the smple perod nd hence do not yeld ny nformton on ther fll ck poston explctly. Consder pyoff equton for the ltent conflct pyoff c * of the form * c = τ Z + ε = 1,..., N c where Z s vector of vrles oserved for ll dvorced men nd women, ncludng e.g. the tenure of mrrge, ge t mrrge, humn cptl nd other socodemogrphc vrles, nd ε c s men zero normlly dstruted rndom error term representng the effects of unoserved fctors such s emotons. Snce c * s only known for the seprtng sugroup (d=1) one oserves: 13
15 * c = c f d = 1 c = 0 f d = 0 The prolem of smple selecton s hs to e crefully consdered when ssgnng conflct pyoffs to nonseprtng wves nd husnds snce the group of seprted respondents mght dffer from the group of stll mrred spouses on ccount of unoserved vrles. Otherwse the use of predcted conflct pyoffs otned from n OLS estmton sed on seprtng respondents only mght result n nconsstent prmeter estmtes due to smple selectvty prolems. Therefore, the Heckmn procedure for selectvty scorrected estmtons (Heckmn 1979, 1980) should not only e ppled to the estmton of the wge rte ut to the determnton of consstent conflct pyoffs s well. When pplyng the twostge Heckmn procedure to the estmton of conflct pyoffs, however, no roust estmton results could e otned due to collnerty prolems nd the very smll smple sze of seprtng couples (n=94). As smulton studes showed (Puhn 1997, Rendtel 199), n those cses susmple OLS stll proofs to e the most roust estmtor. As consequence, we estmte conflct pyoffs usng the susmple of seprtng couples only. Vrtul conflct pyoffs re then predcted for the whole smple ccordng to ther socodemogrphc chrcterstcs. Fgure 1: Fvestge estmton procedure 1 DRATION model on Dvorce Hzrd rtes for dvorce Condtonl conflct pyoffs for women nd men 3 PROBIT on Lor force prtcpton Selectvty correcton vrle for prtcpton 5 OLS on Hours worked OLS on Conflct pyoff (Seprtng susmple) ) women ) men Predcted conflct pyoffs for women nd men 4 OLS on Wge rte (Workng susmple) Predcted wge rtes The fvestge estmton procedure s performed s dsplyed n Fgure 1: In the frst stge loglner durton model (Weull model) on mrtl survvl or stlty s estmted for the full smple n order to lter compute conflct pyoffs condtonl on the tenure of mrrge. The resultng hzrd rtes yeld condtonl proltes of dvorce for ech ndvdul for ech yer of ther remnng (verge) lfetme. Second, mle nd femle OLS conflct pyoff 14
16 equtons re estmted usng the seprtng susmple only. Together wth the hzrds expected cumultve conflct pyoffs re computed for ll men nd women. These predcted conflct pyoffs re n the thrd step entered s n nstrumentl vrle nto the prot estmton of lor force prtcpton. From the prot estmtes the nverse Mlls rto λ l of prtcpton s computed nd dded to the OLS wge equton for workers only. Ftted vlues for wge rtes derved from the selectvty scorrected wge equton estmtes (stge 4) together wth the predcted conflct pyoffs re ncluded n the ffth nd fnl step: n OLS regresson on lor supply, gn sed on the restrcted smple of employed women only. Thus the fnl lor supply estmton uses two nstrumentl vrles, the vrtul wge rte nd the vrtul conflct pyoff. 17 The conflct pyoff mesure In the theoretcl model presented ove fmly prtners rgn over the dstruton of utlty ccordng to ther reltve rgnng powers. But how s ths rgnng power determned emprclly, n every dy lfe so to spek? Assumly there s noody explctly computng hs or her conflct pyoff tht would e relzed n cse of dvorce. In n mplct wy, however, every person comes cross conflct pyoff mesures when oservng frends, reltves or neghors who seprte. I rgue tht ech ndvdul pples ths rgnng mesure, t lest suconscously, to her own stuton, gven the ndvdul humn cptl endowment, household chrcterstcs nd EEPs. In other words, t s the perceved rgnng power drwn from personl oservtons nd expecttons tht ffects ntrfmly decson mkng. The conflct pyoff ctully drwn from the seprtng group s computed s the monthly hhnc equvlzed ncome n the second yer fter rekup ccordng to nc e =. Hence, 0.5 (hhsze) household ncome s dvded y the squre root of the numer of household memers to consder economes of scle n household consumpton. Snce durng the twelve months followng seprton enttlements to trnsfer pyments hve n most cses not een settled yet, reported ncome turns out to e suject to hevy chnges. Therefore I decded to use the second yer s fnncl sttus (fter seprton) s more roust mesure of n ndvdul s conflct pyoff 18. Once the pyoff estmton coeffcents hve een otned, vrtul conflct pyoffs cn e predcted for the whole smple nd for every susequent yer, sed on the respondents socodemogrphc chrcterstcs. Those chrcterstcs tht re strctly monotonclly ncresng over tme (such s ll ge vrles) re perpetuted, wheres ehvorl vrles such s tht porton of mrge lfe tht hs een spent n gnful employment re set constnt. The fnl conflct pyoff mesure s then computed s the weghted verge of expected future conflct pyoffs, wth the weghts ccordng to ndvdul dvorce proltes n ll yers. 17 For the wge equton ge, ge squred, yers of schoolng (pln nd squred) nd prevous work experence n fulltme nd n prttme jos (pln nd squred) re used s explntory vrles: w f = 0.5ge 0.003ge.31edu edu fullex fullex wth R of A selectvtys correcton (λ l ) s performed for the wge equton prtex prtex 18 It could e rgued tht womn s ndvdul ncome rther thn her shre of the household ncome represents her conflct pyoff n cse of dvorce. On the other hnd, the mesure used should ccount for the posslty of new prtnershp nd the ccommodtng fnncl resources whch, fter ll, re prt of the EEPs λ l
17 The rgnng power ndctor Brgnng power s determnnt of the strtegc supply of lor cn e ncluded nto the estmton equton n dfferent wys. In the theoretcl model t s the reltve rgnng coeffcent, reflected y one prtners gn from rgnng dvded y tht of the other spouse, whch condtons the ndvdul tme use decson. In the emprcl nlyss I therefore lso use reltve mesure of ndvdul rgnng power, nmely the devton from symmetry n rgnng postons 19. The symmetry ndctor s formed s functon of the spouses conflct pyoffs: c sym = 1, wth c eng the lower pyoff. The ndctor s zero for spouses wth c j equl outsde optons,.e. equl rgnng postons, nd t s hgher the more one prtner s outsde opton exceeds tht of the other. (Prelmnry) Estmton results A nested Prot estmton of femle lor force prtcpton (see Tle 3 n the Appendx) revels tht the decson to work s postvely relted to the solute sze of the wfe s expected conflct pyoff nd negtvely relted to the symmetrc rgnng ndctor even when controllng for vrles ndctng her own nd her husnd s humn cptl, the opportunty costs of mrket work (mesured y the presence of chldren) nd nonlor ncome. Ths result ndctes tht femle lor supply cn e prtly led ck to strtegc consdertons regrdng the ndvdul future rgnng poston. The more equl the couples rgnng powers the hgher s the womn s ncentve to mntn ths reltve rgnng poston. The expected reltve ttrctveness of womn s externl lterntve wth respect to tht of her prtner sgnfcntly determnes her lor force prtcpton. Includng these pyoff mesures leds to etter ft of the model (the vlue of the log lkelhood functon decreses from 44 to 6). The numer of hours worked y femle, estmted n stge 5, s lso postvely relted to her solute conflct pyoff (Tle 4). The hgher her expected outsde opton the more hours she works (for strtegc resons). The devton from symmetrc future rgnng stuton etween the spouses, however, does not sgnfcntly mtter for her decson to prtcpte n the lor mrket. One wy to understnd ths result s to see prtcptng n the lor mrket, no mtter to whch extent, s n mplct opton for economc ndependence from the prtner. By styng n the lor force mrred women try to keep ther humn cptl nd hence ther reltve rgnng power from deprectng. To hve the foot n the door (tht s to sy: n the lor mrket) nd not to e le to mke ther own lvng s wht mnly drves mrred women to supply lor. Overll the estmton results support the rgnng rgument tht there s lso strtegc spect to women prtcptng n the lor mrket. Conclusons In the theoretcl model presented rtonl ndvduls tend to overnvest n humn cptl n the prefmly perod. At the egnnng of the fmly phse they hve n ncentve to choose n mount of lor supply exceedng the optml level or n mount of household producton fllng short of the optml level, respectvely, should ths mprove ther rgnng poston n the followng perod. nless ndng longterm contrcts cn e mde etween the prtners, rtonl ehvor lwys leds to neffcent outcomes wth respect to tme llocton nd 19 The symmetry ndctor hs een used y Ott (199) for the spouses wge rto n n estmton on the prctce of rth control. 16
18 household producton wthn the fmly. Snce the model tkes nto ccount the dynmc mplctons of dfferent tme uses lor s lso suppled out of strtegc resons. It serves s n nsurnce gnst the rsk of dvorce. The emprcl results n ths pper show tht, ccordng to the theoretcl model, womn s reltve rgnng power, mesured s the devton from symmetry etween her own nd her husnd s vrtul conflct pyoffs, s negtvely relted to her lor force prtcpton nd the sze of her conflct pyoff s postvely relted to the numer of hours worked. It seems tht y styng n the lor mrket mrred women ntend to keep ther humn cptl nd, thus, ther rgnng power from deprectng. Lor force prtcpton gves them the opportunty to mntn certn level of conflct pyoff. Thus the nstrumentl vrle estmton of lor supply wth ftted wge rtes derved from selectvtys corrected wge equton estmtes nd ftted conflct pyoffs derved from pyoff equton estmtes supports the rgnng rgument tht there s strtegc spect to femle lor supply. 17
19 Appendx Tle 1 Step 1: Durton model for mrtl stlty Weull model (n w =66) Coeffcent estmte Tvlue Yers of schoolng wfe Yers of schoolng husnd Age t mrrge wfe Age t mrrge husnd Frst mrrge  dummy σ Constnt Log Lkelhood  Log Lkelhood (restrcted) Shded coeffcents re sgnfcnt t the 10%level, old coeffcents t the 5%level. Dt source: Germn SocoEconomc Pnel
20 Tle Step : Conflct pyoffs OLS (n w =96/ n h =83) Conflct pyoff wfe husnd Coeff.estmte Tvlue Coeff.estmte Tvlue Own ge Prtner s ge Educton Prtners educton Reltve work experence Prtner s rel. work experence Nonlor household ncome Dummy chld present (<16) Age of youngest chld (<16) New mrrge prtner New other prtner Constnt Adjusted R Shded coeffcents re sgnfcnt t the 10%level, old coeffcents t the 5%level. Dt source: Germn SocoEconomc Pnel
21 Tle 3 Step 3: Femle lor force prtcpton PROBIT (n w =538) Lor force prtcpton Coeff.estmte Tvlue Coeff.estmte Tvlue Constnt Age Educton Work experence (fulltme) Work experence (prttme) Nonlor household ncome Dummy chld present (<16) Age of youngest chld (<16) Husnd s wge ncome Conflct pyoff Symmetry ndctor Log Lkelhood  Log Lkelhood (restrcted) Shded coeffcents re sgnfcnt t the 10%level, old coeffcents t the 5%level. Dt source: Germn SocoEconomc Pnel
22 Tle 4 Step 5: Femle work hours OLS (n w =3) Hours of work Coeff.estmte Tvlue Coeff.estmte Tvlue Constnt Age Educton Work experence (fulltme) Work experence (prttme) Nonlor household ncome Dummy chld present (<16) Age of youngest chld (<16) Husnd s wge ncome Predcted wge rte Lmd Conflct pyoff Symmetry ndctor Adjusted R Shded coeffcents re sgnfcnt t the 10%level, old coeffcents t the 5%level. Dt source: Germn SocoEconomc Pnel
23 References Becker, G.S. (1965), A Theory of the Allocton of Tme, Economc Journl, 75, S Becker, G.S. (1974), A Theory of Socl Interctons, Journl of Poltcl Economy, 8 (6), Boln, K. (1996), An Economc Anlyss of Mrrge nd Dvorce, Lund Economc Studes 6, Lund nversty. Dekmnn, A. (1994), Ht ds stegende Eheschedungsrsko ds eruflche Enggement von Fruen gefördert?, Sozle Welt, Jg. XXXXV, Dekmnn, A; Klen, T. (1991), Bestmmungsgruende des Eheschedungsrskos. Ene emprsche ntersuchung mt den Dten des sozooekonomschen Pnels, Koelner Zetschrft fuer Sozloge und Sozlpsychologe, 43, Frnz, W. (1996), Aretsmrktoekonomk, Sprnger: Berln Hedelerg. Gugler, E.; Schch, E.; Vollmer, M. (1984), Wederenglederung von Fruen n qulfzerte Berufstätgket nch längerer Berufsunterrechung, Mnnhem. Gry, J.S. (1998), DvorceLw Chnges, Household Brgnng, nd Mrred Women s Lor Supply, n: The Amercn Economc Revew, 88 (3), Gronu, R. (1973): The Intrfmly Allocton of Tme: The Vlue of the Housewves Tme, Amercn Economc Revew 63, Gronu, R. (1977): Lesure, Home Producton, nd Work: The Theory of the Allocton of Tme Revsted, Journl of Poltcl Economy 85 (6), Heckmn, J. (1979), Smple selecton s s specfcton error, Econometrc 47 (1), Heckmn, J. (1980), Smple selecton s s specfcton error wth n pplcton to the estmton of lor supply, n: J. P. Smth (ed.), Femle Lor Supply: Theory nd Estmton, Prnceton nversty Press, Horney, M.J.; McElroy, M.B. (1988), The Household Allocton Prolem: Emprcl Results from Brgnng Model, Reserch n Populton Economcs, 6, Johnson, W.R.; Sknner, J. (1986), Lor supply nd mrtl seprton, The Amercn Economc Revew, 76 (3), Kllngsworth, M.R. (1983), Lor Supply, New York: Cmrdge nversty Press. Kllngsworth, M.R.; Heckmn, J.J. (1986), Femle Lor Supply: A Survey, Chpter n Ashenfelter, O.; Lyrd, R. (eds.), Hndook of Lor Economcs, Vol. 1, New York: Elsever Scence Pulshers BV, Konrd, K.; Lommerud; K.E. (1996): The Brgnng Fmly Revsted, CEPR Dscusson Pper No Lyrd, R.; Brton, M.; Zlz, A. (1980), Mrred Women s Prtcpton nd Hours, Economc, 47 (185), Lehrer, E.; Nerlove, M. (1981), The Lor Supply nd Fertlty Behvor of Mrred Women: A ThreePerod Model, Reserch n Populton Economcs, 3,
24 Lengsfeld, W.; Lnke, W. (1988), De demogrphsche Lge n der Bundesrepulk Deutschlnd, n: Zetschrft für Bevölkerungswssenschft 14, Lunderg, S.; Pollck, R. (1993), Seprte Spheres Brgnng nd the Mrrge Mrket, Journl Poltcl Economy, 101, Mnser, M.; Brown, M. (1979), Brgnng Anlyss of Household Decsons, n: Lloyd, C.B.; Andrews, E.S.; Golroy, C.L. (eds.), Women n the lor mrket, New York: Colum nversty Press. Mnser, M.; Brown, M. (1980), Mrrge nd Household Decson Mkng: A Brgnng Anlyss, Interntonl Economc Revew 1 (1), McElroy, M. (1990): The Emprcl Content of Nshrgned Household Behvor, Journl of Humn Resources 5 (4), McElroy, M.; Horney, M. (1981): Nshrgned Household Decsons: Towrd Generlzton of the Theory of Demnd, Interntonl Economc Revew, (), Mroz, T.A. (1987), The Senstvty of n Emprcl Model of Mrred Women s Hours of Work to Economc nd Sttstcl Assumptons, Econometrc, 55 (4), Ott, N. (199), Intrfmly Brgnng nd Household Decsons, Hedelerg: Sprnger. Ott, N. (1993), De Rtonltet nnerfmller Entschedungen ls Betrg zur Dskrmnerung welcher Aret, Groeznger et l. (ed.): Jensets von Dskrmnerung, Mrurg: Metropols. Ott, N. (1995): Fertlty nd Dvson of Work n the Fmly: A Gme Theoretc Model of Household Decsons, n: Kuper, E.; Sp, J. (ed.), Out of the Mrgn, London, New York, Ronnng, G. (1991), Mkroökonometre, Berln Hedelerg: Sprnger. Smuelson, P. (1956), Socl Indfference Curves, Qurterly Journl of Economcs, 10 (1), 1. Sttstsches Bundesmt (ed.) (1997), Sttstsches Jhruch 1997, Wesden: Metzler/Poeschel. Wgner, G. et l., (1993), The Englsh Lnguge Pulc se Fle of the Germn Soco Economc Pnel, Journl of Humn Resources, 8(), Woolley, F. R. (1988): A Noncoopertve Model of Fmly Decson Mkng, London School of Economcs, mmeo. 3
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