Barganng at Dvorce: The Allocaton of Custody Martn Halla Unversty of Lnz & IZA Chrstne Hölzl Unversty of Lnz December 2007 Abstract We model the barganng process of parents over custody at the tme of dvorce. Frst we assume an nsttutonal settng where only sole custody s avalable. In a second step we reform ths nsttutonal settng and ntroduce the possblty of jont custody. We show that some parents, who would not be able to fnd an agreement n the sole custody regme, can fnd an agreement after the reform. Accordngly, our emprcal analyss shows that the ntroducton of jont custody enables more parents to dvorce by mutual consent. A detaled analyss of court record data reveals that the reform had no mpact on the odds that chldren are manly lvng wth ther mother. However, we observe a shft n the determnants of the custody allocaton. JEL Classfcaton: J13, J12, K36, D1, C78. Keywords: (Jont) custody, dvorce, famly law, barganng. Contact author: Johannes Kepler Unversty of Lnz, Department of Economcs, Altenbergerstr. 69, 4040 Lnz, Ph.: +43 70 2468 8219, Fax: +43 70 2468 28219, emal: martn.halla@jku.at. Helpful comments of René Böhem, Johann K. Brunner, Rener Buchegger, Uwe Dulleck, Peter Egger, and Rudolf Wnter-Ebmer are gratefully acknowledged. The usual dsclamer apples.
1 Introducton In recent decades, throughout the western world an ncreasng ncdence of dvorce could be observed (OECD, 2007). 1 Martal breakdown can have severe economc and socal consequences for all partes nvolved. Polcy-makers and scholars are especally concerned about the welfare of affected chldren. Recent economc research has stressed the fundamental role of legal nsttutons at the tme of dvorce (e. g. Del Boca, 2003). Obvously, the legal framework consttutes the choce-set and defnes the rules of the dvorce process. Moreover, t can affect the dstrbuton of welfare wthn non-ntact famles. Legal nsttutons determne the famles post-dvorce well-beng and should be desgned to mnmze the negatve consequences of dvorce. A crucal feature of every dvorce s the allocaton of custody and consequently custody law s a partcular mportant aspect of the legal framework. In fact, t governs the actual lvng arrangement after dvorce. Snce the 1970s many developed countres have ntroduced varous forms of jont custody after dvorce to supplement or to replace sole custody arrangements. 2 One typcally dstngushes between jont legal custody and jont physcal custody. Jont legal custody means that both parents share the rght and the oblgaton of makng major decsons about ther chld s upbrngng (e. g. about schoolng, relgon, and health care.) Jont physcal custody means that the chld spends a sgnfcant amount of tme wth each parent. In any case polcy-makers ntended thereby to mtgate the pan of dvorce for all partes nvolved. Snce then an ongong debate across academc dscplnes ncludng economcs, law, psychology and socology between proponents and opponents of jont custody has started. Researchers have prmarly focused on the effect of dfferent custody arrangements on chldren s well beng after dvorce. Proponents of jont custody typcally argue that chldren beneft from ongong support and resources from both parents. Ths s captured n varous dmensons such as behavoral and emotonal adjustment (Bauserman, 2002), economc well-beng (Seltzer, 1991; Del Boca and Rbero, 1998), educatonal attanment (Teng Wah, 2006) and parental nvolvement (Bowman and Ahrons, 1985; Huang, Han and Garfnkel, 2003) among others. Opponents object that chldren under jont custody are exposed to ongong parental conflct (Kuehl, 1989). However, the causal relatonshp between certan custody arrangements and chld outcomes s far from clear and the emprcal evdence s mostly nconclusve. In ths paper, we go one step back n order to make progress n a comprehensve evaluaton of jont custody. We analyze the mmedate effects of jont custody at the tme of dvorce. In partcular, we focus on the mpact of jont custody on the dvorce process. 1 However, n the Unted States the dvorce rate peaked n the early 1980s and has been declnng snce then (Stevenson and Wolfers, 2007a,b). 2 In the Unted States jont custody was frst ntroduced n Indana n 1973 and has snce then spread to nearly all states (Brng and Buckley, 1998). In Europe, jont custody has been ntroduced, for nstance, n Sweden n 1976 (Jänterä-Jareborg, 2003), n Norway n 1981 (Sverdrup and Lødrup, 2003), n Germany n 1997 (Dethloff and Martny, 2003) and n Austra n 2001 (Roth, 2003). 2
The arrangements at the tme of dvorce are decsve for post-dvorce development and outcomes. Therefore, we model the barganng process of parents over custody at the tme of dvorce. 3 Frst we assume an nsttutonal settng where only sole custody s avalable. In a second step we reform ths nsttutonal settng and ntroduce the possblty of jont custody. The barganng process s characterzed by alternatng offers. Parents are mpatent but want to fnd a custody agreement that allows both to be better off than wth havng the judge assgn custody. We show that some parents, who would not be able to fnd an agreement n a sole custody regme, can fnd an agreement after a jont custody reform. Ths s a strkng argument n favor of jont custody. In the emprcal part of the paper we present evdence whch supports our model s predcton. Explotng the control group nature of couples wthout mnors we show that the ntroducton of jont custody n Austra has ncreased the fracton of dvorces by mutual consent. In addton, we employ rch mcro data of court records to explore n detal the barganng process of parents over custody before and after ths reform. Whle the custody reform has not changed the odds that chldren are (manly) lvng n the mother s household after dvorce, we observe that the reform has altered the determnants of ths allocaton. In sum, the results ndcate that the addtonal opton of jont custody has a medatng effect on the dvorce process. The ntroducton of jont custody substantally reduces monetary and emotonal cost of dvorce. A larger fracton of couples s now able to fnd a custody agreement wthout heavly resortng to courtroom adjudcaton. Ths mnmzes both prvate and publc cost of ltgaton. Whether jont custody has apart from that desrable effects s an open ssue. However, n the fnal secton of the paper we hghlght that parents wth favorable characterstcs self-select themselves nto jont custody. Ths fndng s of partcular mportance for other studes analyzng the effect of jont custody on varous (chld) outcomes. We dscuss potental dentfcaton strateges for future research. Apart from the lterature studyng the effect of jont custody after dvorce a couple of papers are related to our theoretcal work. Cooter, Marks and Mnookn (1982) use a barganng model wth alternatng offers to model negotatons that are nfluenced by the legal stuaton, but they do not explctly refer to dvorce and custody. They fnd that optmsm about the outcome n court as well as uncertanty about how much the other party s wllng to concede durng negotatons can lead to a tral nstead of an agreement between the partes. Mnookn and Kornhauser (1979) refer explctly to dvorce, but do not use an explct model. They examne n detal how the legal stuaton at dvorce nfluences a couple s barganng over the dvson of matrmonal property, comprsng tangble and ntangble assets. They show that the judge s preferences over dfferent arrangements affect the parents barganng behavor. Fella, Manzn and Marott (2004) derve an explct barganng model between spouses where the transferablty of matrmonal property 3 Rasul (2006) and Francescon and Muthoo (2003) model the allocaton of chld custody as a prenuptal contract. 3
serves as a crucal determnant of whether to dvorce or not. Wthn ths model they examne the effcency of dfferent dvorce laws. In our paper we take the dvorce decson as gven and nvestgate how parents bargan over custody under dfferent custody law regmes. 2 A barganng model of the custody allocaton To model the barganng process over custody, we presume that parents have to fnd a custody arrangement for ther mnor n order to dssolve marrage legally. 4 Preferably they agree on t, but f they are not able to fnd any agreement, a judge assgns sole custody to one parent. There are two dfferent types of dvorce avalable: () dvorce by mutual consent and () dvorce by fault. Dvorce by mutual consent s cheaper and easer to obtan than dvorce by fault, but t requres that parents cooperate and fnd a mutually bndng agreement concernng custody. If parents do not manage to agree they have to proceed wth dvorce by fault. In order to fnd an agreement, parents can bargan over the custody allocaton. 5 Frstly, we assume a sole custody regme where parents can choose from two possble arrangements. They can assgn sole custody ether to the mother or to the father. Then we ntroduce the possblty of jont custody. In partcular, we consder a combnaton of jont legal and jont physcal custody. After the reform the parents can choose from four possble arrangements. The mnor can lve wth ether parent n a sole custody or n a jont custody, where the parents have to choose a man resdence for the chld. 6 However, parents can only keep jont custody wth an explct agreement to do so. Snce the avalable type of dvorce depends on whether the parents can fnd an agreement or not, the barganng over custody has to take place before flng for dvorce. The negotaton over custody can be modeled n the followng way, whch s based on Rubnsten (1982). The parents N = {m, f} have preferences over tme T and over a set of agreements X. 7 There are two agreements x n the sole custody regme X S = {ms, fs} and four agreements x after the jont custody reform X J = {ms, fs, mj, fj}, where S stands for sole custody and J for jont custody. Each agreement leads to a certan amount of utlty for each parent, whch s dscounted accordng to the tme t T = {0, 1, 2..., t C } that t has taken to come to the agreement. We assume that parents have constant dscount rates δ [0, 1], so that the utlty of parent of an agreement x that has been found at 4 We assume that there s only one mnor to smplfy the negotaton and rule out the case where parents splt ther chldren. 5 The negotaton at dvorce typcally ncludes the dvson of the whole matrmonal property. Therefore, dvorce settlements nclude, besde the allocaton of custody, an agreement on monetary ssues such as the dvson of assets, almony awards and chld support payments. In the barganng model we solely focus on the allocaton of custody under dfferent regmes. We dsregard monetary ssues snce they affect the allocaton of custody n each regme equally. However, we wll pck up ths ssue n the emprcal part of the paper. 6 Consequently, we refer to the parent where the chld s lvng manly n a jont custody as the resdent parent. In secton 2.4 we wll dscuss varyng legal systems. 7 The terms m and f can stand for mother and father or for male and female. 4
tme t s gven by u (x, t) = δ t u (x). Furthermore, parents are completely and perfectly nformed about each others preferences due to ther closeness durng marrage. The parents have to follow certan rules n the barganng process. We arbtrarly assume that parent m makes the frst proposal x out of the set of agreements X. The parents then alternate n makng offers, whch the other parent can accept (whch ends the game) or reject (whch leads to a new perod and a new offer). Moreover, n each perod the parent who decdes about an offer can opt out (whch also ends the game) and let the judge assgn custody, henceforth called gong to court. 8 The negotaton does not go on ndefntely. It ends n perod t C wth an assgnment by the judge. Ths date s set exogenously before the negotaton begns. It can be an appontment at court, that s set before the negotaton starts and at whch the arrangement has to be fxed. In perod t C the judge assgns sole custody to parent m wth probablty p and to parent f wth probablty (1 p). 9 Ths lottery yelds utlty δ t C U C = δ t C [pu ms + (1 p)u fs ε ] for parent, where ε are addtonal monetary and emotonal cost of a dvorce by fault compared to a dvorce by mutual consent for short, cost of dsagreement. 10 When a parent ends the game by optng out, the same lottery less the cost of dsagreement apples as n the case of an exogenous end of the negotaton, [pu ms + (1 p)u fs ε ], but now utlty s dscounted to a smaller degree, snce the game ends sooner and less cost of watng occur. Every game conssts of a set of hstores H, where a hstory h H s composed of a seres of proposals and reactons to them. The utlty of a parent of a certan outcome (x, t) does not depend on the hstory though, but only on the agreement x and on the pont n tme t when t was agreed upon. In order to rank the utltes of the parents we have to make assumptons about ther preferences: () Preferences are statonary; (x, t) (y, t + 1) ff (x, 0) (y, 1) and (x, t) (y, t) ff (x, 0) (y, 0). () Parents prefer to reach an outcome as soon as possble, due to the dscountng of the utlty; (x, t) (x, t + 1). () If an agreement x s preferred to agreement y, then each parent wll wat for one perod to acheve the preferred agreement as opposed to gettng the less preferred agreement now; (x, t + 1) (y, t) ff (x, t) (y, t). Gven the model s setup and these assumptons t remans to specfy the utlty orderngs of the parents. The utlty orderngs depend on the set of agreements, whch n turn depends on the custody regme. In the next secton we specfy the utlty orderngs for the baselne case of a sole custody regme and then solve the model for subgame-perfect Nash-equlbra. 11 After that we dscuss the barganng n a jont custody regme. We wll 8 If gong to court was a possble agreement, nstead of an outsde opton, the results would not change. 9 The parents can deduce the probablty from former court rulngs n smlar cases. We assume that both parents have access to the same nformaton and, therefore, form smlar belefs about the probablty p. Ths rules optmsm of both parents out. 10 Emotonal cost could result from parents nternalzng the utlty of the chld, whch would be lower n case of dvorce by fault compared to dvorce by mutual consent due to the ongong dsagreements of the parents. We assume that the cost of dsagreement do not vary over tme. 11 By concentratng on subgame-perfect Nash-equlbra nstead of Nash-equlbra we exclude equlbra wth non-credble threats. 5
then compare the outcomes of the two regmes to dentfy the effect of allowng for jont custody after dvorce. 2.1 Solvng the model n a sole custody regme In a sole custody regme the utlty orderng of each parent ncludes two possble agreements X S = {ms, fs} and the outsde opton of gong to court (the exogenous end of the game). We assume that havng custody leads to a hgher utlty for each parent than gvng custody to the other parent. 12 The outsde opton of gong to court yelds an expected utlty between the two agreements, as t s not clear who wll become custodan. The lottery tself leads to a hgher utlty level than gong to court snce no cost of dsagreement ε arse. Therefore, there are two possble utlty orderngs for each parent n every perod, U > U C > U j and U > U j > UC. (1) Whether the utlty of the outsde opton s larger or smaller than the utlty of the other parent havng custody depends on the relatve magntudes of p and ε. If the probablty of becomng custodan s large enough and/or the cost of dsagreement are small enough, then parent prefers gong to court nstead of agreeng to gve custody to the other parent. The two possble utlty orderngs for each parent lead to four possble stuatons. These stuatons and ther solutons are summarzed n Table 1. The stuatons have three dfferent outcomes: () The parents do not agree and go to court mmedately. () The parents fnd a sngle agreement n the frst perod t = 0. () The parents fnd an agreement mmedately, but t depends on who can make the frst proposal and on ther relatve (m)patence whch parent can get her/hs preferred agreement. In a real settng, one may assocate the rght for the frst proposal and hgh patence wth any gven advantage. For smplcty, we wll refer to t as relatve barganng power. The model s solved by Table 1: Summary of the results n a sole custody regme. f fs C ms fs ms C ms C fs C ms m ms fs C fs ms / fs backward-nducton: The parents know that eventually (at the exogenous end of the game) 12 Ths analyss assumes as most economc analyzes of the famly do (e.g. Becker, 1993; Ermsch, 2003) that parents are altrustc towards ther chldren n the sense that ther utlty depends on the welfare of ther chldren. Therefore, t seems to be a natural startng pont that parents are nterested n spendng tme wth ther chldren and that they want to reman custodan after dvorce. However, other preference orderngs would not change the basc result. 6
the judge wll assgn custody to one of them. The parents want to mprove ther stuaton (.e. ncrease ther utltes) by fndng an agreement that s better for both of them, or at least by gong to court mmedately (whch saves the cost of watng). Case 1 When the subset of possble agreements X X, whch contans only those agreements that both parents prefer to the outsde opton, s empty the parents cannot fnd an agreement and go to court mmedately. The optmal strategy for each parent n ths case s to propose that the chld should be lvng wth her/hmself, and not to accept the equvalent proposal of the other parent. Ths means that the game could go on untl the exogenous end, wth each parent proposng her/hmself as custodan and rejectng the proposals of the other parent. Therefore, t s preferable to go to court mmedately. In the case where both parents have the utlty orderng U > U C > U j, parent m, who by defnton starts the game, wll propose ms and parent f goes to court mmedately to save the cost of watng. Case 2 When the subset of possble agreements X s not empty and both parents prefer the same possble agreement,.e. x = x j = x X, where x X s the agreement that parent values most hghly of all the agreements that both parents prefer to the outsde opton, then the parents come to the agreement x mmedately. Agan, the parents try to fnd an agreement whch ncreases the utlty of both of them compared to the eventual assgnment by the judge. In ths case agreement x not only mproves the utlty of both parents, t s also the preferred agreement of both wthn the subset of possble agreements X. Therefore, the optmal strategy for each parent s to propose x and to accept ths proposal of the other parent. Consder the utlty orderng U > U C > U j and U j j > U j > U C j where S s equal to the preferred possble agreement of both parents (x ) and the only element of the subset of possble agreements X. Therefore, parent, who has the hgher valuaton of the outsde opton, gets custody mmedately. Case 3 When the subset of possble agreements X s not empty and the parents prefer dfferent possble agreements,.e. x x j wth x, x j X, then there are two possble outcomes x and x j. In ths case the outcome depends on the relatve barganng power of the parents. A pror t s not clear whch of the two agreements the parents wll choose. It depends on whch parent wll eventually gve n. Ths n turn s determned by the degree of patence of the parents (δ ) and by whch parent can make the last proposal or for short by ther relatve barganng power. 13 Consder the case where both parents have a utlty orderng of U > U j > U C. Both parents have hgh cost of dsagreement and/or a relatvely low and therefore relatvely equal probablty to get custody assgned by the judge. In ths 13 Impatence can result from altrusm of the parents toward ther chld, snce they nternalze that the chld suffers from ongong dsputes. Therefore, t s closely related to the emotonal cost of dsagreement. 7
case both parents prefer ms or fs over the exogenous end of the negotaton. Dependng on whether parent m or parent f has the relatve hgher barganng power the soluton wll be ms or fs. 14 2.2 Solvng the model n a jont custody regme For the the jont custody regme we have to make some assumptons on the preference orderngs over sole custody, jont custody and gong to court. Frstly, we assume that each parent prefers that the chld s (manly) lvng wth her/hm. However, gven that parents may ether prefer to be sole custodan or resdent parent and share parental rghts and oblgatons under a jont custody wth the former spouse. Secondly, gven that the chld s (manly) lvng wth the other spouse each parent wants to be ntegrated nto a jont custody, so that jj js. Therefore, we have two dfferent possble utlty orderngs for the set of agreements X J = {ms, fs, mj, fj}. Incorporatng the outsde opton leads to a total of seven dfferent utlty orderngs for each parent, as the utlty of gong to court relatvely to the other utltes vares wth the probablty p to get custody assgned by the judge and the cost of dsagreement ε. There are four possble utlty orderngs wth a preference for sole custody: U S > U C > U J > U jj > U js, U S U S U S > U J > U C > U jj > U js, > U J > U J > U jj > U C > U js, > U jj > U js > U C, (2) and three possble utlty orderngs wth a preference for jont custody: 15 U J U J U J > U S > U C > U jj > U js, > U S > U S > U jj > U C > U js, > U jj > U js > U C. (3) Ths results n 49 dfferent stuatons, for whch the solutons are summarzed n Table 2. However, the analyss can easly be smplfed snce there are agan only three possble outcomes: () There s no agreement from whch both parents proft, so that the parents go to court mmedately (Case 1). () They fnd a sngle agreement whch mproves the stuaton for both parents (Case 2). () There are two possble agreements whch the parents may choose, because they have dfferent preferences over the subset of possble > Um fj > Um C > Um fs and agreements (Case 3). The utlty orderngs Um ms U fs f > Uf C > U fj f > Uf mj > Uf ms > Um mj are an example of Case 1. The parents cannot fnd any 14 Refer to the Appendx A for a detaled analyss of relatve barganng power and ts effects on the chosen agreement. 15 Gong to court cannot yeld a hgher utlty than gettng a sole custody by agreement due to the lottery pu ms + (1 p)u fs and the addtonal cost of dsagreement ε. 8
m Table 2: Summary of the results after the jont custody reform. a f fs fs fs fs fj fj fj C fj fj fj fs fs fs fj C mj mj C mj mj mj mj C ms mj C ms ms ms ms C ms ms C ms C mj fj fs C C C ms C C ms ms mj C ms/ ms/ C C mj C mj fj fs mj mj ms mj fj mj/ ms/ mj/ ms/ C fj fj C fs fj fj fj fj ms mj fj fj/ mj/ ms/ mj/ ms/ fs fj fs C fs fs fs fj fj mj ms C C C mj mj C mj mj fj fs mj ms fj mj/ mj/ mj/ mj/ C fj fj C fs fj fj fj fj mj ms fj fj/ mj/ mj/ mj/ mj/ fs fj fs C fs fs fs fj fj a The whte cells n ths table correspond to the upper left case n Table 1; the lght grey cells to the upper rght and lower left case; and the dark grey cells correspond to the lower rght case n Table 1. agreement whch leads to a hgher utlty than the outsde opton for both of them. For parent f only fs yelds a hgher utlty, but for parent m ths agreement s worse than gong to court. Any other agreement whch leads to a hgher utlty for parent m yeld a lower utlty than the outsde opton for parent f. Therefore, the parents wll go to court mmedately. An example for Case 2 s gven by Um ms > Um fj > Um fs > Um C and U fj f > Um mj. In ths case, there are two agreements whch lead to a > U fs f > Uf C > U f mj > Uf ms hgher utlty than gong to court for both parents, namely fj and fs. Snce both parents prefer fj over fs they wll agree on fj mmedately. One case whch leads to an outcome > Um fj > Um C > Um fs as stated by Case 3 s gven by the utlty orderngs Um mj and U fs f > U fj f > Uf mj > Uf ms > Uf C (f) has the relatve hgher barganng power. 16 > Um ms. The parents wll agree on mj (fj) f parent m 2.3 Changes due to the jont custody reform The ntroducton of jont custody as an addtonal custody arrangement besde sole custody does not change the parents way of barganng. However, the outcome of the negotaton may change. To study these changes, we compare the outcome of a certan couple under 16 In fact fj s not the most preferred agreement of parent f n the set of agreements (t s only secondbest here), but t s the frst-best agreement n the subset of possble agreements. 9
the jont custody regme wth that ths couple would have found under the sole custody regme. Most mportantly, t turns out that some parents who would not be able to fnd an agreement n a sole custody regme (Case 1) can fnd an agreement after the reform. Let us frst consder the two stuatons from the sole custody regme where parents fnd an agreement mmedately (Case 2). These two stuatons, where parents have a dfferent valuaton of the outsde opton, can be dstngushed nto ten stuatons each n a regme wth jont custody depcted by the lght grey cells n Table 2. After the reform parents stll manage to fnd an agreement mmedately. However, here are now two possble outcomes n some stuatons, whch mprove the utlty of both parents compared to gong to court. The stuaton where the parents fnd more than one possble agreement n the sole custody regme (Case 3) can be dstngushed nto four stuatons after the ntroducton of jont custody (dark grey cells n Table 2). All four agreements are better than gong to court for both parents. The sngle stuaton wthout agreement n the sole custody regme (Case 1) can be dstngushed nto 25 stuatons n the jont custody regme (whte cells n Table 2). In 12 out of these 25 stuatons parents can fnd at least one agreement, even though ths would have not been possble before the reform. Of course, these agreements are exactly the addtonal ones contanng jont custody. If an agreement on sole custody s possble, then t would have been possble wthout allowng for jont custody as well. The affected group are the parents preferrng any jont custody agreement compared to a sole custody of the other parent. Two further ponts are worth notng: Frstly, consderng all possble preference orderngs each of the avalable agreements after the reform, X J = {ms, fs, mj, fj}, s a possble outcome. Secondly, the comparson of the types of outcome n the two regmes shows that some of the parents who fnd an agreement (on sole custody) n the sole custody regme, prefer a jont custody arrangement after the reform. These parents are the ones where at least one of them (the one wth the hgher barganng power) can mprove her/hs utlty wth a jont custody arrangement as compared to a sole custody one. 2.4 Varyng legal systems In ths secton we show that our model can be easly adapted to other legal systems. The most mportant aspects of modelng where adaptatons may apply are () the avalable types of dvorce, () the concrete type of jont custody and () the offcal channel to mantan jont custody. Ad (): The legal system may provde a type of dvorce where the monetary cost are ndependent of the parents ablty to agree on custody. In that case the cost of dsagreement ε only consst of emotonal cost. 17 Ths mples that the cost of dsagreement are 17 If the tral lasts longer due to a dspute, then ε may contan monetary cost as well, but the baselne monetary cost are the same and therefore they do not appear n the cost of dsagreement. 10
comparable lower (provded that the emotonal cost are smlar). Therefore, the rank of gong to court wll be hgher compared to the case modeled above and dvorces wthout agreement wll be more lkely. Ad (): Consder a legal system whch provdes an equally shared jont physcal custody. That means, parents do not have to agree on a resdent parent, snce law ntends that the chld spends equally or close to half the tme wth each of her/hs parents. In ths case there are only three agreements after the reform, X J = {ms, fs, J }, and the number of possble utlty orderngs per parent s reduced from seven to fve. Consequently, there are only 25 dfferent stuatons n the model nstead of 49. Ad (): In some legal systems jont custody s the default opton nstead of beng a possble arrangement. In ths case, dvorcng parents keep jont custody, except for the case where one or both of the parents apply to the court to assgn custody. If the judge can assgn sole or a jont custody the outcome of gong to court s even more uncertan than n the case modeled above. Ths leads to a lower valuaton of the outsde opton. Nevertheless, the same 49 stuatons may result. Modfyng the model n the proposed ways does not lead to changes n the prncples of how the parents negotate or n ther ablty to cooperate. Only the chosen custody arrangement n a specfc stuaton may change. Therefore, the result that ntroducng jont custody facltates fndng an agreement stll holds. 2.5 Further polcy mplcatons The cost of dsagreement ε and the probablty p affect the parents valuaton of the outsde opton. The lower the probablty of assgnment and the hgher the cost of dsagreement, the lower s the expected utlty of gong to court. A low valuaton of the outsde opton n turn promotes cooperaton and should ncrease the ncdence of mutually bndng arrangements. Ths fact can be used to desgn an nsttutonal settng whch promotes cooperaton of parents and leads to the followng polcy mplcaton: An (about) equal probablty for both parents to get custody assgned by the judge and monetary cost of a dvorce dependng on the parents wllngness to cooperate. In partcular, we suggest that maternal/paternal preference rules for custody should be replaced by neutral rules (e.g. the best nterest of the chld rule). In addton, monetary cost of dvorce by mutual consent should be sgnfcantly lower compared to those of a dvorce by fault. 3 Emprcal analyss In the emprcal part of the paper we employ Austran data. Austra s a partcular sutable case snce t had a recent reform (n the year 2001) of ts custody law and a unque data set 11
of court records, whch captures the perod before and after the reform, s avalable. The am of our emprcal analyss s threefold. Frstly, we test the model s predcton, namely that the ntroducton of jont custody facltates cooperaton between parents wth data from the Austran Statstcal Offce. Secondly, we examne the dvorce process of dvorces by mutual consent before and after the reform wth the court record data n more detal. In partcular, we test whether the custody reform has changed the odds that the mother becomes custodan/resdent parent and whether the reform has altered the determnants of ths allocaton. Thrdly, we characterze the couples who agree on jont custody after the reform. 3.1 Testng the barganng model Our barganng model predcts that by swtchng from a sole custody regme to a jont custody regme parents should be able to fnd a custody agreement more easly. Consequently, the ntroducton of jont custody should enable addtonal parents to dvorce by mutual consent. In ths secton we present evdence that the jont custody reform n Austra on the 1st of July 2001 ndeed led to an ncrease of the fracton of dvorces by mutual consent and therefore to a decrease of the fracton of dvorces by fault. We employ data that has been retreved from the Austran Statstcal Offce database. Dstrct Courts have jursdcton over dvorce proceedngs and report every sngle dvorce case wth ts basc data to the Austran Statstcal Offce. Unfortunately, the data s avalable on a Federal State level only. However, the completeness and accuracy of ths admnstratve database s ts strkng advantage. We assembled a panel data set for the nne Austran Federal States for the years 1991 to 2006. Ths balanced panel data set wth 144 observatons comprses ten years before the reform, the year of the reform (2001) and fve years after the reform. In a frst step we estmate a panel fxed effects model where the dependent varable s the percentage of dvorces by mutual consent (DMC s,t ) n state s n year t, DMC s,t = α s + βt + γjc t [+δdl t + ζd s,t ] + ε s,t, (4) s where s α s are state fxed effects and βt captures a tme trend. The explanatory varable of prmary nterest s JC t whch captures the perod after the reform ncludng the whole year 2001. We cannot dstngush the frst half of the year 2001 (before the reform came nto effect) from the later half, because we only have yearly data. 18 In an addtonal specfcaton (Ib) we control for the perod before the dvorce law reform from the year 1999 (DL t ). Ths reform abolshed adultery and the refusal to have chldren as so-called absolute reasons for dvorce but had no nfluence on custody law. For completeness, we also consder the possblty that the ntroducton of jont custody had an mpact on the 18 However, n order to check the robustness of our results we dropped the observatons of the year 2001a nd the qualtatve results dd not change. 12
ncdence of dvorce. Therefore, we ran a thrd specfcaton (Ic) where we nclude the number of dvorces per 1,000 resdents (D s,t ) as an addtonal control varable. Moreover, we re-ran all three specfcatons where we allow for state-specfc tme trends (specfcatons IIa-IIc). We use populaton weghts for our estmatons and robust standard errors are calculated throughout, allowng for clusterng by state. 19 The results for our sx estmatons of the share of dvorces by mutual consent are summarzed n Table 5. Each specfcaton shows a postve and a statstcally sgnfcant effect of the ntroducton of jont custody on the share of dvorces by mutual consent. The rcher specfcatons suggest an ncrease of about 1.7 percentage ponts. Ths effect s quanttatvely mportant snce n the year 2000 already 90 percent of all dvorces were dvorces by mutual consent (Statstk Austra, 2003). Control group approach Whle there s no evdence that the tmng of jont custody reform was endogenous,. e. t was ntroduced n a perod of an ncreasng share of dvorces by mutual consent, we provde addtonal results where we explot the control group nature of couples wthout mnors. The estmaton results above are based on a sample of all dvorcng couples (wth and wthout mnors). The jont custody reform, however, does only apply to couples wth mnors at the tme of dvorce and should have no mpact on couples wthout. Therefore, couples wthout mnors consttute a clear control group. Whle, we do not have separate fgures for the share of dvorces by mutual consent for couples wth and wthout mnors we can explot the varaton of number of dvorces wth mnors across states. In each year we rank the states accordng to ther average number of mnors per dvorce. Based on ths rankng we buld three groups: states wth a low, wth a medum and wth a hgh number of mnors per dvorce. For each group we defne a bnary varable Mt, l Mt m and Mt h whch s equal to one f the state belongs n year t to the group wth a low, a medum or a hgh number of mnors per dvorce. Notably, there s varaton n the composton of these three groups over tme. 20 Compared to equaton (4) we substtute the jont custody reform dummy wth the bnary varables dentfyng the three groups and respectve nteracton terms wth the jont custody reform dummy, DMC s,t = s α s + βt + θ m M m t + θ h M h t +γ l JC t M l t + γ m JC t M m t + γ h JC t M h t [+δdl t + ζd s,t ] + ε s,t. (5) The base group s now equal to the group wth a low number of mnors for the perod before the reform. The dea s that the effect of the jont custody reform should ncrease wth the average number of mnors per dvorce (. e. wth the share of the treatment group). 19 We have tested the potental effect of the custody reform on the ncdence of dvorce n a separate panel fxed-effects model too. We estmated a panel model for the number of dvorces per 1,000 resdents n state s n year t for the years 1991 to 2006 (see Table 4). Nether specfcaton shows a statstcally sgnfcant effect of the custody law reform on the number of dvorces. 20 Only the Federal State of Venna s n each year n the group wth the lowest average number of mnors per dvorce. 13
Accordngly, we expect ˆγ l < γˆ m < ˆγ h. The estmaton results (n Table 6) ndeed show that the quanttatve effect of the jont custody reform on the share of dvorces by mutual consent ncreases wth the number of mnors. For nstance, consderng specfcaton (IIb) we fnd for the group wth the lowest number of mnors an effect of the jont custody reform of about 1.6 percentage ponts. For the group wth a medum number of mnors the effect s equal to 1.9 percentage ponts. Fnally, for the group wth the hghest number of mnors we obtan the largest effect of two percentage ponts. The average number of mnors had no effect on the share of dvorces by mutual consent before the reform. These estmated coeffcents are strong support for the causal nterpretaton of our results. 21 Taken together, the results provde convncng evdence that the ntroducton of jont custody led to qualtatvely sgnfcant ncrease n dvorces by mutual consent. 3.2 Who gets custody? So far we have presented evdence that the ntroducton of jont custody has ncreased the share of parents who fnd an agreement and lead to more dvorces by mutual consent. In ths secton we examne the dvorce process of dvorces by mutual consent before and after the reform n more detal. We test whether the custody reform has changed the probablty that the mother becomes custodan/resdent parent and whether the reform has altered the determnants of ths allocaton. Our emprcal analyss n ths secton s based on rch mcro data from Austran court records. 22 We have collected nformaton on 7, 062 dvorce cases from fve dstrct courts n Austra. 23 These dvorces were ntated between 1997 and 2003, and completed by May 2004. A dvorce record s an offcal record comprsng all relevant nformaton on the case. 21 To check the robustness of our results we refne our control group. Accordng to Austran legal practce chldren above 14 years of age have the rght to choose ther prmary place of resdence. The judge wll only act aganst the chld s wshes f her/hs well-beng s endangered. Therefore, t seems plausble that the number of chldren below 14 years of age s more decsve for our analyss (compared to the average number of mnors,. e. chldren below the age of 19). The allocaton of custody should not complcate the conflct between parents and the dvorce process f the chld s wll s pvotal anyway. Therefore, we replcate our analyss for the average number of chldren below 14 years of age (see Table 7). Accordng to our expectaton the results show the same patterns, however, wth ncreased statstcal sgnfcance. 22 Please note, we could not use ths data set to study the mpact of the jont custody reform on the share of dvorces by mutual consent compared to the dvorces by fault n the last secton, snce dvorces by fault are undersampled n ths data set. Whle n the perod from 1997 to 2003 on average about 10 percent of all dvorces where dvorces by fault n the relevant federal states, we observe n our data set only about 2 percent dvorces by fault. Ths s due to the fact that the access to dvorce records of dvorces by fault at the data collecton was on average more dffcult compared to that of dvorce records coverng dvorces by mutual consent. Dvorces by fault are on average under longer examnaton and sent to other courts more often. On top of that dvorce records coverng dvorces by fault very often lack essental nformaton, snce parents agree on some ssues n other proceedngs documented n separate records. Whle ths fact causes no problem for the analyss n ths sectons, t would have based the results above. 23 The courts were selected to represent rural and urban areas. The courts whch gratefully cooperated wth complng the data were Hall, Ktzbuehel, Kufsten, Lnz, and the dstrct of Favorten n Venna. Data were collected on nearly all dvorces n the perod n the courts n Hall and Ktzbühel. In Kufsten data of about 90 per cent of all cases could be collected. In Lnz and Venna (Favorten) data of approxmately 80 percent of all dvorces could be collected. 14
Therefore, a dvorce record conssts of soco-economc nformaton on the whole famly, transcrpts of all proceedngs, the correspondence between the ltgants and the court, dfferent certfcates and the judgment or the settlement. Snce we are only nterested n dvorces by mutual consent wth mnors we exclude all observatons on dvorces by fault and cases wthout mnors. As the unt of nterest we use the oldest mnor n every famly whch leads to 3, 242 observatons. 24 Table 3 shows that before the jont custody reform about 90 percent of the mnors lved wth ther mother after the dvorce and about 10 percent wth ther father. 25 Smlarly, after the reform about 91 percent of the mnors are (manly) lvng wth ther mother and 9 percent wth ther father, but 45 percent of all parents have agreed upon jont custody. These smple descrptve statstcs hnt that the Table 3: Share of dfferent custody arrangements for oldest mnor. Before After the reform the reform Overall Sole custody by mother 90.29 50.63 77.58 Sole custody by father 9.71 4.33 7.99 Jont custody, manly lvng wth mother - 40.33 12.92 Jont custody, manly lvng wth father - 4.72 1.51 Number of oldest mnors 2,203 1,039 3,242 share of mnors (manly) lvng n the mother s household after dvorce has not changed due to the reform. However, n order to get a more n-depth answer we employ data from the whole tme perod and estmate a probt model explanng the probablty that the father becomes custodan/resdent parent. In other words we explan the probablty that the chld s (manly) lvng n the father s household. As the explanatory varable of prmary nterest we nclude a bnary varable capturng the perod after the reform. As addtonal control varables we employ nformaton on the chld s sex and the chld s age, on the parents ncome, on ther educaton, on ther number of jont chldren, on the length of ther marrage, on ther former marrages, on the usage of lawyers and whether the mother has been a homemaker. 26 Further we control for the judge s sex, for the courts where dvorce took place, as well as for the month and the year of dvorce. 27 Table 8 24 We have excluded all cases wth a-typcal custody arrangements where, for nstance, grandparents became custodans. 25 Takng all mnors nto account leads to vrtually the same pcture snce there are hardly any cases where mnors are splt between parents,. e. that mnors wthn one famly have dfferent custodans/resdent parents. 26 There are only four fathers n the whole data set who are homemakers. 27 Unfortunately nformaton on ncome s mssng frequently, especally for mothers. In 22 percent of the cases there s no nformaton on both parents ncome. In 50 percent of the cases only the mother s, and n 10 percent of the cases only the father s ncome s mssng. In the remanng 18 percent of the cases we have complete nformaton on both parents ncome. Fortunately, we have very detaled nformaton on the parents occupaton whch allow us to mpute for mssng ncomes based on multvarate OLS-regressons. The mputed ncomes n our estmaton analyss below are based on separate regressons for males and females. In each estmaton below we control wth bnary varables for the cases wth mssng ncome and we wll report on the robustness of our results due to mputaton. Based on the sample of all couples wth at least one mnor chld at the tme of dvorce we mputed n 32 percent of the cases for the father s ncome 15
provdes descrptve statstcs for all covarates. The estmaton results are summarzed n columns 1 and 2 of Table 9. The effect of the custody reform s postve but bascally nsgnfcant (p-value= 0.104). The estmatons results affrm the descrptve statstcs. 3.3 Determnants of the allocaton of custody To examne the determnants of the allocaton of custody before and after the reform we splt the sample. For the perod before the reform the estmaton strategy s obvous and we estmate a probt model. After the reform the stuaton s less clear. One could argue that the custody allocaton has now two dmensons: The parents can frst choose between sole and jont custody, and secondly they have to agree on a custodal or a resdent parent. Ths results n an estmaton strategy wth two bnary decsons. Consequently, we estmate a bvarate probt model on the jont determnaton of who becomes resdent/custodal parent (mother vs. father) and the custody type (sole vs. jont). Ths estmaton procedure allows for a correlaton between the two error terms of these equatons. 28 The results from the conventonal probt estmaton for the perod before the reform are lsted n columns 4 to 6 of Table 9. The dependent varable takes on the value one f the father s the sole custodan and zero f the mother s the sole custodan. Columns 7 to 12 summarze the estmaton results of the bvarate probt model. In ths secton we consder the results of the frst equaton (columns 7 to 9), where the dependent varable s equal to one f the chld s manly lvng n the father s household, and zero otherwse. Comparng these two estmatons we focus on the comparson of the determnants of the chld s man place of resdence under the two regmes. The outsde opton Snce we only consder dvorces by mutual consent the custody allocatons we observe n our data are defntely the outcome of an agreement of the parents and not due to a judgment. Nevertheless, accordng to our theoretcal consderatons we should fnd that the allocaton of custody n dvorces by mutual consent to be nfluenced by the outsde opton (probablty of assgnment and cost of dsagreement for the counterfactual case of a dvorce by fault). For nstance, a hgh probablty for parent leads to a hgher valuaton of the outsde opton and t s therefore easer for parent to get the preferred and n 72 percent of the cases for the mother s ncome. The explanatory varables n these two regressons comprse age at marrage, age at the brth of the frst chld, dummy varables for the dfferent occupatons (unsklled blue collar worker, sklled blue collar worker or craftsman, whte collar worker, cvl servant, self-employed, etc.), for the place of brth, for ctzenshp and for the place of resdence (zp code). All coeffcents show the expected sgn and are of reasonable sze. The predctve power of these two regressons s qute good wth an R 2 of 0.53 for the regresson of the females and of 0.17 for the regresson of the males. All estmaton results whch are dscussed but not presented n the paper are of course avalable upon request. 28 Alternatvely, one could argue that the custody decson has four dmensons after the reform, snce there are now four dfferent custody arrangements avalable: the mother gets sole custody, the father gets sole custody, jont custody wth the mother as resdent parent and jont custody wth the father as resdent parent. Ths vew results n a multnomal choce model. We have calculated a multnomal probt model. These estmaton results from ths are consstent wth those from the bvarate probt model dscussed below, however, provde no addtonal nsghts. 16
custody agreement. Parents can deduce the probablty of assgnment p from former dvorces by fault. Accordng to Austran legal practce derved from law and former fndngs mothers (fathers) are the preferred custodans for female (male) mnors. 29 Mothers are the preferred custodans for young chldren and n general Austran legal practce prefers homemakers as custodans, snce they have already demonstrated that they manage to take care of the chld. The estmaton results for the perod before (columns 3 and 4 n Table 9) ndeed show that f the mnor n queston s a grl, the father s less lkely to become custodan (by about two percentage ponts). Further, as expected the probablty that he gets custody ncreases wth the chld s age 30 and decreases wth the mother beng a homemaker (by about mnus three percentage ponts). For the perod after the reform (columns 5 and 6 n Table 9) we fnd a comparable effects of the chld s age and the mother beng a homemaker. However, the chld s sex seems to play no role anymore. Income & educaton Hgh-ncome parents may cope more easly wth the hgher cost of dvorce by fault than parents wth lower ncome. Therefore, the utlty equvalent of the monetary cost of dsagreement of a hgh-ncome parent may be lower than that of a lowncome parent. Ths leads to a hgher valuaton of the outsde opton and should thereby ncrease the probablty that the hgh-ncome parent gets her/hs preferred agreement. On the other hand, a hgh-ncome parent may face hgher opportunty cost of takng care of the chld. Ths may lead to a reversed utlty orderng, where, for nstance, ths parent prefers the other to be the resdent parent n a jont custody. The estmaton results for the perod before the reform suggest that n the case of mothers the second effect domnates. An ncrease n the mother s ncome slghtly rases the probablty that the father gets custody. 31 The father s ncome has no statstcally sgnfcant mpact. Possbly, the two countervalng effects cancel each other out. After the reform nether the mother s nor the father s ncome has an mpact on the resdence decson. Wth respect to the mother, ths change s plausble, snce under jont custody the effect of the opportunty cost of tme may be less crucal. The parents educaton has no effect n any perod. Lawyers Accordng to Austran law dvorcees are free to hre a lawyer. Durng the tme perod coverng our data t was also possble for dvorcng couples to hre a jont lawyer. 32 Therefore, we have to dstngush fve dfferent cases: nether parent has a lawyer, parents have a jont lawyer, both parents have a lawyer each, only the mother has a lawyer and only the father has a lawyer. In our estmatons we nclude a bnary varable for each case where the base group s equal to couples wthout any lawyer. The 29 In the followng we embrace by the term custodan/custodanshp both the custodan under the sole custody regme and the resdent parent under a jont custody. 30 An ncrease n the mnor s age from half a standard devaton below the mean to half a standard devaton above the mean (.e. from about 7.4 to about 12.5 years) ncreases the probablty of the father beng the custodan by nearly three percentage ponts. 31 An ncrease n the mother s ncome from half a standard devaton below the mean to half a standard devaton above the mean (.e. from e 461 to e 803) ncreases the probablty that the father gets custody by one percentage pont. 32 On 1st of January 2005 a new draft of the so-called Non-Contentous Proceedngs Act entered nto force and repealed the possblty of jont lawyers. 17
estmaton results for the perod before the reform show a hgher probablty of gettng custody for fathers who are they only parent who has retaned a lawyer compared to fathers of couples who have no lawyer at all (about plus 5 percentage ponts). The reversed effect s true for mothers (mnus 2 percentage ponts). We do not observe a statstcally sgnfcant effect of the nvolvement of lawyers on the custody allocaton f parents have a separate lawyer each. It seems that f both parents hre a lawyer ther effects cancel out. There s also no mpact of a jont lawyer. Although these results seem to be very suggestve t s not clear whether the statstcally sgnfcant effects are ndeed due to a causal effect of lawyers or rather due to a systematc selecton of couples wth farly dfferent characterstcs nto specfc stuatons. 33 In the sample after the reform we face the problem of separaton (Albert and Anderson, 1984): The varable only the mother has a lawyer perfectly predcts the outcome,. e. n every case where only the mother had a lawyer she became custodan/resdent parent. Fortunately, separaton has n the case of a bvarate probt model not as severe consequences as n the conventonal probt model, where ether the affected varable or observatons have to be dropped n order to ft the model (Zorn, 2005). We stll can estmate our bvarate probt model wth the full set of covarates and observatons. However, the coeffcent and standard errors of the varable only the mother has a lawyer are upward based. Compared to the perod before the reform, we do not observe a statstcal sgnfcant mpact of the father s lawyer and n the case where both parents have a lawyer the mother s lawyer outperforms the father s lawyer. Ths suggest that the jont custody reform has ncreased the relatve power of mother s lawyers. Alternatvely, the reform may have changed the sex-specfc selecton nto legal representaton. Almony In our basc specfcaton we do not control for almony payments. The allocaton of custody and almony payments may be smultaneously determned and consequently almony payments are a potentally endogenous varable. However, f we add the almony payment to the wfe as an addtonal explanatory varable the qualtatve results of all other covarates are unchanged n all estmatons (see Table 10) 34. Ths ndcates that we do not have a problem of omtted varable bas n our estmaton results. The coeffcent of the almony payment tself s throughout negatve and statstcally sgnfcant n the estmaton for the whole perod and n the perod before the reform. However, snce there s no obvous way to fx the endogenety problem of almony we do not stress ths result. The results from ths secton show that the ntroducton of jont custody had no mpact on the probablty that mnors are lvng wth ther mothers after dvorce. However, we observe some dfferences n the determnants of the man place of resdence. In general, these changes may be due to two reasons. Frstly, the avalablty of jont custody may 33 For a detaled dscusson of the role of lawyers n dvorce processes see Halla (2007). 34 In the estmaton for the whole perod the dummy for the perod after the reform, the number of chldren and the dummy ndcatng a female judge carry one astersk ndcatng a statstcally sgnfcance at a 10-percent level after controllng for almony. Please note, the p-values of these coeffcents (0.104, 0.104 and 0.101) have been pretty much the same before controllng for almony. 18
have an mpact on parent s way of barganng over the allocaton of custody. Secondly, snce the custody reform has ncreased the share of dvorces by mutually consent, we observe a potentally dfferent populaton of dvorcng couples after the reform. However, snce the share of ths addtonal parents s comparable small the latter explanaton seems to be less lkely. In sum, we nterpret the results as ndcatng that the ntroducton of jont custody had a medatng effect on the barganng process over custody after dvorce wthout changng the fnal resdent allocaton. 35 3.4 Who takes jont custody? Who are the 45 percent of all couples who agree on jont custody after the reform? In order to answer ths queston we examne the second equaton of our bvarate probt model for the perod after the reform (see Columns 10 to 12 of Table 9). Most strkngly, the estmaton results show that any nvolvement of lawyers has a tremendously negatve effect on an agreement on jont custody. We observe a reduced probablty (compared to the case wthout any lawyer) of 20 percentage ponts f only the mother has a lawyer, mnus 16 percentage ponts f only the father has a lawyer and mnus 22 percentage ponts f parents have a separate lawyer each or a jont lawyer. Agan, these negatve correlaton can be explaned by a true causal effect of lawyers or by a systematc selecton of parents wth dstnct characterstcs nto specfc stuatons. For nstance, t seems plausble that parents wth grave conflcts are more lkely to hre lawyers and would have not agreed on jont custody n the counterfactual stuaton wthout any lawyers. The second mportant results s that the probablty of a jont custody arrangement ncreases wth the parents ncome. Agan, ths result suggests sortng. Parents wth a hgher soco-economc status and hgher abltes self-select them nto jont custody. Surprsngly, the parents educaton has no statstcally sgnfcant mpact. Moreover, we fnd that the probablty of jon custody ncreases wth mother s age and decreases wth the number of the father s pror marrages. Taken together, the results suggest that parents wth favorable characterstcs self-select themselves nto jont custody. Ths fndng s crucally mportant for studes examnng the effects of jont custody on chld-outcomes. Apart from that we fnd some evdence that female judges seem to be based aganst jont custody and manage to nfluence parents n ther decson. A female judge reduces the lkelhood of an agreement on jont custody by about seven percentage ponts. Ths effect can be nterpreted causally snce couples are matched randomly to judges. Fnally, the year dummes reveal a trend towards jont custody over tme. The purpose of ths small secton s smply to hghlght the fact that 35 In order to check the robustness of our results concernng the mputaton procedure we dd the estmaton analyss based on the smaller sample wth complete ncome nformaton for both parents. The results for the whole perod and for the perod before the reform are very smlar to the results reported n Table 9. The effect of the parents ncome s unchanged, only the statstcal sgnfcance of some control varables changes. An estmaton of the bvarate probt model for the perod after the reform based on ths sample cannot be realzed, snce no convergence s acheved. Ths s caused by the few cases n ths sample where the father s the sole custodan (11) or resdent parent under jont custody (10). 19
couples wth jont custody are selected group. It may be the case that emprcal studes neglectng ths fact are based due to confoundng factors and overestmate the postve effect of jont custody. An promsng way to dsentangle causal effects of jont custody on future chld outcomes s gven by dfferent tmng of custody law reforms across countres. The tmng of the ntroducton of jont custody regmes across European countres would allow such a dfference-n-dfferences analyss. Smlarly Teng Wah (2006) explots the varaton across the Untes States to study the mpact of jont custody on educatonal attanment. 4 Summary & conclusons We have modeled the allocaton of custody at the tme of dvorce as barganng between parents wth alternatng offers and a fnte horzon for two dfferent custody regmes. Frst we assume a sole custody regme. In a second step we ntroduce jont custody as an addtonal opton. We have shown that some parents, who would not be able to fnd a custody agreement n the frst regme, can fnd an agreement after the jont custody reform. Emprcal evdence based on a recent jont custody reform n Austra supports our model. Explotng the control group nature of couples wthout mnors we fnd that the ntroducton of jont custody has ncreased the fracton of dvorces by mutual consent. Based on rch mcro data of court records we nspect the barganng process of dvorces by mutual consent before and after ths reform. The custody reform has not changed the odds that chldren are manly lvng wth ther mothers, however, some determnants of the custody allocaton are altered. Gven our fndngs we support the ntroducton of jont custody. Jont custody has medatng effects on the dvorce process and enables facltatng cooperaton among parents. Ths, n turn, mnmzes both prvate and publc cost of ltgaton. Furthermore, the crcumventon of panful adversary proceedngs and of substantal delays nduced by contested judcal proceedngs reduces emotonal stress. Above all, consensual solutons are by defnton more consstent wth the preferences of each parent, and should thereby lead to an outcome that s more stable over tme than a result mposed by a judge. The fact that female judges dstract couples to take jont custody should be observe and dscussed by the judcal professon. Whether jont custody has apart from the medatng nfluence on the dvorce process desrable effects after dvorce s an open ssue and deserves further research. However, our court data clearly shows that parents who agree on jont custody are a hghly selected group. Future research on post-dvorce outcomes has to take ths nto account. 20
References Albert, A. and J. A. Anderson (1984), On the Exstence of Maxmum Lkelhood Estmates n Logstc Regresson Models, Bometrka 71(1), 1 10. Bauserman, Robert (2002), Chld Adjustment n Jont-Custody Versus Sole-Custody Arrangements: A Meta-Analytc Revew, Journal of Famly Psychology 16(1), 91 102. Becker, Gary S. (1993), A Treatse on the Famly, Enlarged Edton, Harvard Unversty Press, Cambrdge, MA. Bowman, Madonna E. and Constance R. Ahrons (1985), Impact of Legal Custody Status on Fathers Parentng Postdvorce, Journal of Marrage and the Famly 47(2), 481 488. Brng, Margaret F. and Francs H. Buckley (1998), Jont Custody: Bondng and Montorng Theores, Indana Law Journal 73(2), 393 452. Cooter, Robert, Stephen Marks and Robert Mnookn (1982), Barganng n the Shadow of the Law: A Testable Model of Strategc Behavor, Journal of Legal Studes 11(2), 225 251. Del Boca, Danela (2003), Mothers, Fathers and Chldren After Dvorce: The Role of Insttutons, Journal of Populaton Economcs 16(3), 399 422. Del Boca, Danela and Roco Rbero (1998), Transfers n Non-Intact Households, Structural Change and Economc Dynamcs 9(4), 469 478. Dethloff, Nna and Deter Martny (2003), Country Chapter Germany, n K.Boele-Woelk, B.Braat and I.Sumner, eds, European Famly Law n Acton, Vol. III Parental Responsbltes, Intersenta, Antwerpen. Ermsch, John (2003), An Economc Analyss of the Famly, Prnceton Unversty Press, Prnceton, NJ. Fella, Gulo, Paola Manzn and Marco Marott (2004), Does Dvorce Law Matter?, Journal of the European Economc Assocaton 2(4), 607 633. Francescon, Marco and Abhnay Muthoo (2003), An Economc Model of Chld Custody, Dscusson Paper 857, Forschungsnsttut zur Zukunft der Arbet (IZA), Bonn. Halla, Martn (2007), Dvorce and the Excess Burden of Lawyers, Dscusson Paper No. 2962, Forschungsnsttut zur Zukunft der Arbet (IZA), Bonn. Huang, Chen-Chung, Wen-Ju Han and Irwn Garfnkel (2003), Chld Support Enforcement, Jont Legal Custody, and Parental Involvement, Socal Servce Revew 77(2), 255 278. 21
Jänterä-Jareborg, Maart (2003), Country Chapter Sweden, n K.Boele-Woelk, B.Braat and I.Sumner, eds, European Famly Law n Acton, Vol. III Parental Responsbltes, Intersenta, Antwerpen. Kuehl, S J. (1989), Aganst Jont Custody: A Dssent to the General Bull Moose Theory, Famly & Conclaton Courts Revew 27(2), 37 45. Mnookn, Robert H. and Lews Kornhauser (1979), Barganng n the Shadow of the Law: The Case of Dvorce, Yale Law Revew 88(5), 950 997. OECD (2007), Socety at a Glance : OECD Socal Indcators 2006, OECD, Pars. Rasul, Imran (2006), The Economcs of Chld Custody, Economca 73(1), 1 25. Roth, Maranne (2003), Country Chapter Austra, n K.Boele-Woelk, B.Braat and I.Sumner, eds, European Famly Law n Acton, Vol. III Parental Responsbltes, Intersenta, Antwerpen. Rubnsten, Arel (1982), Perfect Equlbrum n a Barganng Model, Econometrca 50, 97 109. Seltzer, Judth A. (1991), Legal Custody Arrangments and Chldren s Economc Welfare, The Amercan Journal of Socology 96(4), 895 929. Statstk Austra (2003), Demographsches Jahrbuch 2001/02, Wen. Stevenson, Betsey and Justn Wolfers (2007a), Marrage and Dvorce: Changes and ther Drvng Forces, Journal of Economc Perspectves 21(2), 27 52. Stevenson, Betsey and Justn Wolfers (2007b), Trends n Martal Stablty, Unpublshed manuscrpt, Unversty of Pennsylvana. Sverdrup, Tone and Peter Lødrup (2003), Country Chapter Norway, n K.Boele-Woelk, B.Braat and I.Sumner, eds, European Famly Law n Acton, Vol. III Parental Responsbltes, Intersenta, Antwerpen. Teng Wah, Leo (2006), From Maternal Preference to Jont Custody: The Impact of Changes n Custody Law on Chld Educatonal Attanment, Unpublshed manuscrpt, Unversty of Toronto. Zorn, Chrstopher (2005), A Soluton to Separaton n Bnary Response Models, Poltcal Analyss 13(2), 157 170. 22
Appendx A In Case 3, t s a pror not clear whch of the two possble agreements x or x j the parents wll choose. The outcome depends on ther relatve barganng power,. e. who can make the last/frst proposal and on ther relatve (m)patence.in the followng we characterze four sub-cases whch result from dfferent combnatons of who can make the last proposal and the mpatence of the parents. Defnton (x, t + z ) (x j, t). Impatence of a parent means, that there s a crtcal tme span z for whch Therefore, parent havng her/hs way after the crtcal tme span z leads to a lower (or equal) utlty for parent than lettng the other parent have her/hs way now. Hence, t s not credble for parent to reject x j now, f s/he could get x span z. Case 3.1 only after the crtcal tme If parent wth the last proposal s suffcently patent,.e. z > t C 1 and therefore (x, t C 1) (x j, 0), then the parents agree on x mmedately ndependent of parent j s patence. In the penultmate perod, when the last proposal s made, the not-proposng parent j wll agree to x, because t s stll better than havng to go to court n the next perod. The parents know that parent j wth the penultmate proposal wll fnally gve n, therefore they agree on x mmedately. Case 3.2 If parent wth the last proposal s not suffcently patent,.e. z t C 1 and therefore (x, t C 1) (x j, 1), but parent j s suffcently patent, then the parents agree on x j mmedately.36 In ths case parent has an advantage due to the last proposal, but s/he cannot use t, because t s not credble for her/hm to wat untl the penultmate perod (wth the last proposal). The reason for ths s that acceptng the proposal of the other parent n perod 0 or perod 1 leads to (at least) as much utlty as havng x n the penultmate perod. Therefore, parent cannot credbly reject, f parent j proposes x j n the begnnng (or n perod 1). Parent wll even propose x j her/hmself, to save the cost of watng. If both parents are (suffcently) mpatent, so that the other parent s preferred possble agreement now yelds at least as much utlty as the own preferred possble agreement n the penultmate perod, then there are two possble outcomes: If one parent s more patent than the other parent, then the more patent parent wll have her/hs way. both parents are equally mpatent, then the parent wth the frst move wll get her/hs preferred possble agreement. 36 We have to nclude perod 1 here. If parent j has the frst proposal and parent could become credble by watng one perod, then parent would get her/hs way. If 23
Case 3.3a If both parents are not suffcently patent,.e. (x, t C 1) (x j, 1), and parent s more patent then parent j,.e. z > z j + 1, then the parents agree on x mmedately ndependent of who can make the last proposal. The reason s that parent j wll not get the consent of parent durng z j. Parent may or may not consent to x j after z j t does not matter for parent j, for whom t s n any case better to consent to x now (and t would not be credble to do otherwse). Parent on the other hand can credbly threaten to wat longer than z j, but not long enough for the last proposal. Ths does not matter though, parent j wll consent to x as soon as parent proposes t. Parent j wll even propose x her/hmself, because (x, 1) j (x j, z j + 1) and (x, 0) j (x, 1). Case 3.3b If both parents are not suffcently patent,.e. (x, t C 1) (x j, 1), and both parents are (nearly) equally mpatent,.e. z = z j or z = z j ± 1, then the parents agree on x (x j ) mmedately f parent (parent j) makes the frst proposal. In ths case both parents know that they cannot get ther preferred possble agreement wthn ther crtcal tme spans. Therefore, each parent has an ncentve to propose the own preferred possble agreement, but also to consent to the preferred possble agreement of the other parent, as soon as t s proposed, because they cannot ncrease ther utlty by watng. Parent m (who by assumpton makes the frst proposal) proposes x m and parent f agrees to t. 24
Appendx B Table 4: The effect of jont custody on the number of dvorces. a (I) (II) (III) Jont custody reform -0.057-0.057 0.014 (0.034) (0.035) (0.090) Controllng for: Dvorce law reform Yes Yes Yes Trend Yes Yes Yes State dummes Yes Yes Yes Trend*State dummes Yes Yes Trend 2 Yes Trend 2 *State dummes Yes R-squared 0.967 0.971 0.982 a The dependent varable s the number of dvorces per 1,000 resdents n state s n year t, where s = 1,..., 9 and t = 1991,..., 2006. The number of observatons s n each estmaton equal to 144. Estmated usng state populaton weghts. Robust standard errors n parentheses. *, ** and *** ndcate statstcal sgnfcance at the 10-percent level, 5-percent level, and 1-percent level. 25
Table 5: The effect of jont custody on the share of dvorces by mutual consent. a (Ia) (Ib) (Ic) (IIa) (IIb) (IIc) Jont custody reform 2.161*** 1.775*** 1.748** 2.160*** 1.775*** 1.735** (0.438) (0.487) (0.525) (0.451) (0.501) (0.529) Constant 88.651*** 91.864*** 92.620*** 85.963*** 89.178*** 90.073*** (0.467) (0.536) (1.870) (0.210) (0.482) (1.564) Controllng for: State dummes Yes Yes Yes Yes Yes Yes Trend Yes Yes Yes Yes Yes Yes Trend*State dummes Yes Yes Yes Dvorce law reform Yes Yes Yes Yes Dvorces per 1,000 resdents Yes Yes R-squared 0.398 0.488 0.488 0.481 0.571 0.572 a The dependent varable s the percentage of dvorces by mutual consent n state s n year t, where s = 1,..., 9 and t = 1991,..., 2006. The number of observatons s n each estmaton equal to 144. Estmated usng state populaton weghts. Robust standard errors n parentheses. *, ** and *** ndcate statstcal sgnfcance at the 10-percent level, 5-percent level, and 1-percent level. 26
Table 6: The effect of JC on the share of dvorces by mutual consent by the no. of mnors. a (Ia) (Ib) (Ic) (IIa) (IIb) (IIc) JC*Low no. of mnors 1.819** 1.452** 1.409* 1.921** 1.581* 1.530 (0.600) (0.624) (0.677) (0.776) (0.796) (0.851) JC*Medum no. of mnors 2.363*** 2.022*** 2.010*** 2.191*** 1.864** 1.853** (0.402) (0.399) (0.417) (0.618) (0.582) (0.574) JC*Hgh no. of mnors 2.632** 2.167** 2.130* 2.531*** 2.019** 1.969** (0.797) (0.919) (0.939) (0.734) (0.777) (0.802) Medum no. of mnors -0.153-0.234-0.239 0.467 0.353 0.331 (0.456) (0.328) (0.338) (0.979) (0.835) (0.854) Hgh no. of mnors -0.346-0.268-0.239-0.150-0.067-0.058 (0.785) (0.844) (0.866) (1.126) (1.237) (1.235) Constant 88.775*** 91.992*** 92.876*** 86.060*** 89.160*** 90.037*** (0.758) (0.693) (1.927) (1.022) (1.112) (2.021) Controllng for: State dummes Yes Yes Yes Yes Yes Yes Trend Yes Yes Yes Yes Yes Yes Trend*State dummes Yes Yes Yes Dvorce law reform Yes Yes Yes Yes Dvorces per 1,000 resdents Yes Yes R-squared 0.404 0.493 0.494 0.492 0.577 0.579 a The dependent varable s the percentage of dvorces by mutual consent n state s n year t, where s = 1,..., 9 and t = 1991,..., 2006. The number of observatons s n each estmaton equal to 144. Estmated usng state populaton weghts. Robust standard errors n parentheses. *, ** and *** ndcate statstcal sgnfcance at the 10-percent level, 5-percent level, and 1-percent level. 27
Table 7: The effect of JC on the share of dvorces by mutual consent by the no. of kds<14. a (Ia) (Ib) (Ic) (IIa) (IIb) (IIc) JC*Low no. of kds<14 1.875** 1.508** 1.454* 2.111** 1.746** 1.697* (0.590) (0.604) (0.676) (0.767) (0.752) (0.811) JC*Medum no. of kds<14 2.254*** 1.815*** 1.818*** 2.185*** 1.737*** 1.739*** (0.401) (0.447) (0.440) (0.413) (0.421) (0.402) JC*Hgh no. of kds<14 2.536** 2.209** 2.145** 2.318** 2.012** 1.921** (0.846) (0.816) (0.879) (0.917) (0.754) (0.791) Medum no. of kds<14-0.098-0.124-0.126 0.529 0.483 0.464 (0.501) (0.460) (0.468) (0.705) (0.574) (0.599) Hgh no. of kds<14 0.425 0.318 0.358 1.043 0.888 0.912 (0.889) (0.662) (0.695) (1.298) (0.948) (0.969) Constant 88.403*** 91.665*** 92.627*** 85.169*** 88.456*** 89.325*** (0.591) (0.514) (2.037) (1.142) (1.046) (2.017) Controllng for: State dummes Yes Yes Yes Yes Yes Yes Trend Yes Yes Yes Yes Yes Yes Trend*State dummes Yes Yes Yes Dvorce law reform Yes Yes Yes Yes Dvorces per 1,000 resdents Yes Yes R-squared 0.412 0.500 0.501 0.495 0.582 0.584 a The dependent varable s the percentage of dvorces by mutual consent n state s n year t, where s = 1,..., 9 and t = 1991,..., 2006. The number of observatons s n each estmaton equal to 144. Estmated usng state populaton weghts. Robust standard errors n parentheses. *, ** and *** ndcate statstcal sgnfcance at the 10-percent level, 5-percent level, and 1-percent level. 28
Table 8: Descrptve statstcs of court record data. a Before the reform After the reform N = 2, 203 N = 1, 039 Mean S.D. Mean S.D. Chld s female 0.50 0.48 Chld s age 9.95 10.25 Mother s housewfe 0.18 0.39 0.16 0.37 Mother s ncome n e 100 6.40 3.43 6.64 3.24 Father s ncome n e 100 14.68 6.20 15.76 6.78 Mother s educaton 1.03 0.19 1.04 0.24 Father s educaton 1.06 0.31 1.07 0.33 Nether parent has a lawyer 0.76 0.74 Only the mother has a lawyer 0.05 0.06 Only the father has a lawyer 0.04 0.03 Both parents have a lawyer each 0.10 0.10 Parents have a jont lawyer 0.05 0.07 Mother s age at dvorce 35.00 6.24 36.18 6.25 Age dfference 2.95 4.84 2.67 4.89 No. of jont chldren 1.58 0.70 1.66 0.70 Length of marrage n years 10.65 6.12 11.04 5.94 Mother s no. of marrages 1.12 0.35 1.09 0.31 Father s no. of marrages 1.14 0.40 1.12 0.36 Judge s female 0.28 0.37 29
Table 9: The allocaton of custody. a Overall Before the reform After the reform Method of estmaton Probt Probt Bvarate probt Dependent varable Father s custodan/resdent Father s custodan Father s custodan/resdent Jont custody Coeff. S.E. MFX Coeff. S.E. MFX Coeff. S.E. MFX Coeff. S.E. MFX Jont custody reform 0.344 0.237 0.020 Outsde opton Chld s female -0.264*** 0.085-0.013-0.332*** 0.102-0.019-0.088 0.169-0.001-0.143* 0.085-0.056 Chld s age 0.093*** 0.016 0.005 0.095*** 0.019 0.005 0.111*** 0.032 0.001 0.003 0.016 0.001 Mother s housewfe -0.662*** 0.158-0.022-0.695*** 0.184-0.026-0.739** 0.361-0.005 0.014 0.208 0.005 Income & educaton Mothers s ncome n e 100 0.050*** 0.014 0.002 0.049*** 0.017 0.003 0.050 0.035 0.001 0.044** 0.022 0.017 Fathers s ncome n e 100-0.011 0.008-0.001-0.009 0.010 0.000-0.017 0.021 0.000 0.029*** 0.007 0.011 Mother s educaton -0.084 0.222-0.004-0.054 0.267-0.003-0.026 0.454 0.000-0.059 0.196-0.023 Father s educaton 0.145 0.130 0.007 0.192 0.151 0.011-0.020 0.317 0.000 0.152 0.151 0.060 Lawyers Only the mother has a lawyer -0.692*** 0.253-0.019-0.532** 0.269-0.019-6.513 25182-0.011-0.534*** 0.191-0.196 Only the father has a lawyer 0.296 0.194 0.020 0.576*** 0.217 0.054-1.036 0.718-0.004-0.434* 0.238-0.162 Parents have a lawyer each -0.312** 0.140-0.012-0.230 0.170-0.011-0.598** 0.268-0.004-0.610*** 0.152-0.223 Parents have a jont lawyer 0.176 0.155 0.010 0.210 0.199 0.014 0.026 0.270 0.000-0.615*** 0.168-0.222 Further control varables Mother s age at dvorce -0.019 0.012-0.001-0.030** 0.015-0.002 0.008 0.024 0.000 0.025** 0.012 0.010 Age dfference 0.015 0.010 0.001 0.018 0.012 0.001 0.023 0.021 0.000 0.006 0.011 0.003 No. of jont chldren 0.099 0.061 0.005 0.063 0.073 0.003 0.135 0.121 0.002-0.080 0.068-0.032 Length of marrage n years 0.011 0.013 0.001 0.016 0.015 0.001-0.004 0.027 0.000-0.019 0.014-0.007 Mother s no of marrages 0.259* 0.139 0.013 0.384** 0.162 0.021-0.030 0.303 0.000-0.062 0.146-0.024 Father s no of marrages -0.164 0.129-0.009-0.158 0.144-0.009-0.467 0.339-0.005-0.263* 0.137-0.104 Judge s female -0.174* 0.106-0.008-0.185 0.127-0.009-0.406 0.247-0.004-0.187* 0.110-0.073 Constant 1.854*** 0.420-1.770*** 0.498-1.314 1.090-1.566** 0.626 No. of observatons χ 2 (1) = 0.097 3,242 2,203 1,039 Log-lkelhood 569.144 395.152 776.553 McFadden Pseudo R-squared 0.441 0.437 ρ(s.e.) 0.171 (0.101) Lkelhood-rato test of ρ = 0 2.756, P-value= a In each estmaton we further control wth bnary varables for the court, for the month and the year of dvorce of dvorce. *, ** and *** ndcate statstcal sgnfcance at the 10-percent level, 5-percent level, and 1-percent level. b The margnal effect s the change n the probablty of the dependent varable caused by an nfntesmal change of each ndependent contnuous varable or, the dscrete change n the probablty for a changng bnary varable wth all the other varables fxed at ther means. 30
Table 10: The allocaton of custody controllng for almony payments. a Overall Before the reform After the reform Method of estmaton Probt Probt Bvarate probt Dependent varable Father s custodan/resdent Father s custodan Father s custodan/resdent Jont custody Coeff. S.E. MFX Coeff. S.E. MFX Coeff. S.E. MFX Coeff. S.E. MFX Almony payment n e 100-0.041*** 0.014-0.002-0.058*** 0.020-0.003-0.020 0.026-0.0002-0.042*** 0.014-0.017 Jont custody reform 0.406* 0.246 0.023 0.000 Outsde opton Chld s female -0.269*** 0.085-0.013-0.341*** 0.104-0.018-0.092 0.171-0.001-0.148* 0.085-0.058 Chld s age 0.087*** 0.016 0.004 0.088*** 0.019 0.005 0.109*** 0.032 0.001-0.003 0.016-0.001 Mother s housewfe -0.651*** 0.160-0.022-0.681*** 0.188-0.024-0.740** 0.362-0.005 0.015 0.211 0.006 Income & educaton Mother s ncome n e 100 0.045*** 0.015 0.002 0.045*** 0.017 0.002 0.046 0.035 0.001 0.033 0.022 0.013 Father s ncome n e 100-0.006 0.009 0.000-0.003 0.010 0.000-0.012 0.021-0.0001 0.040*** 0.008 0.016 Mother s educaton -0.114 0.224-0.006-0.059 0.270-0.003-0.054 0.458-0.001-0.069 0.200-0.027 Father s educaton 0.141 0.135 0.007 0.161 0.160 0.008-0.001 0.314-0.00001 0.189 0.158 0.075 Lawyers Only the mother has a lawyer -0.837*** 0.279-0.020-0.699** 0.298-0.020-6.492 25133-0.011-0.566*** 0.193-0.206 Only the father has a lawyer 0.339* 0.196 0.023 0.622*** 0.219 0.058-1.105 0.744-0.004-0.484** 0.246-0.178 Parents have a lawyer each -0.267* 0.142-0.010-0.165 0.172-0.008-0.571** 0.272-0.004-0.561*** 0.156-0.206 Parents have a jont lawyer 0.208 0.157 0.012 0.267 0.203 0.018 0.032 0.271 0.0004-0.582*** 0.169-0.212 Further control varables Mother s age at dvorce -0.013 0.013-0.001-0.023 0.016-0.001 0.010 0.024 0.0001 0.027** 0.012 0.011 Age dfference 0.015 0.010 0.001 0.016 0.012 0.001 0.026 0.022 0.0003 0.005 0.011 0.002 No. of jont chldren 0.103* 0.062 0.005 0.067 0.075 0.004 0.131 0.123 0.002-0.083 0.069-0.033 Length of marrage n years 0.011 0.013 0.001 0.016 0.015 0.001-0.002 0.027-0.00002-0.018 0.014-0.007 Mother s no. of marrages 0.237* 0.139 0.012 0.365** 0.162 0.019-0.009 0.311-0.0001-0.136 0.149-0.053 Father s no. of marrages -0.182 0.130-0.009-0.169 0.146-0.009-0.494 0.340-0.006-0.254* 0.138-0.100 Judge s female -0.185* 0.107-0.008-0.195 0.129-0.009-0.413* 0.249-0.004-0.200* 0.112-0.078 Constant -1.885*** 0.423-1.830*** 0.505-1.359 1.095-1.504** 0.637 No. of observatons χ 2 (1) = 0.097 3,211 2,184 1,027 Log-lkelhood 556.773 383.449 761.778 McFadden Pseudo R-squared 0.448 0.447 - ρ(s.e.) - - 0.174 (0.103) Lkelhood-rato test of ρ = 0 - - 2.752, P-value= a In each estmaton we further control wth bnary varables for the court, for the month and the year of dvorce of dvorce. *, ** and *** ndcate statstcal sgnfcance at the 10-percent level, 5-percent level, and 1-percent level. b The margnal effect s the change n the probablty of the dependent varable caused by an nfntesmal change of each ndependent contnuous varable or, the dscrete change n the probablty for a changng bnary varable wth all the other varables fxed at ther means. 31