Will Women Save More Than Men? A Theoretical Model of Savings and Marriage *


 Winfred Small
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1 Will Women Save Moe Than Men? A Theoetical Model of Saving and Maiage * Shohana Amya Gobad San Diego State niveity, niveidad de Zaagoza, IZA, CESifo Alfedo Mavão Peeia The College of William and May, CASEE, niveidade do Algave College of William and May Deatment of Economic Woking Pae Numbe 95 July 00 * We ould like to thank Chale Hoioka fo Hoioka fo vey ueful comment and uggetion a ell a fo oviding u ith vey ueful tatitical data baed on Jaan Family Income and Exenditue Suvey, Fance Woolley fo vey uefully comment, Rui M. Peeia fo vey ueful comment, uggetion and editoial aitance, and Hoad Youo fo editoial aitance
2 COLLEGE OF WILLIAM AND MARY DEPARTMENT OF ECONOMICS WORKING PAPER # 95 July 00 Will Women Save Moe Than Men? A Theoetical Model of Saving and Maiage Abtact Thi ae eent an intetemoal model of individual behavio ith uncetainty about maiage and divoce and hich accommodate the oible eence of economie o dieconomie of cale fom maiage. We ho that a cenaio of highe maiage ate and highe divoce ate ill be aociated ith highe aving ate in the eence of economie of maiage and ith loe aving ate in the eence of dieconomie of maiage. In the context of taditional gende ole, thi imlie highe aving ate by young men and loe aving ate by young omen than in le taditional countie, the ooite being the cae ith aving ate of maied omen elative to thoe of maied men. We etablih the elevance of taditional gende ole and maital tatu to undetanding cocounty vaiation in gende diffeential in aving behavio. JEL Code: Keyod: E, J aving behavio, maiage, divoce, economie of maiage, gende ole Shohana Amya Gobad Deatment of Economic,San Diego State niveity, San Diego, SA Deatment of Economic, niveidad de Zaagoza, Sain IZA, CESifo Alfedo Mavão Peeia Deatment of Economic, The College of William and May, Williambug, SA CASEE Cente fo Advanced Studie in Economic and Econometic, niveidade do Algave, Potugal
3 . Intoduction Peonal aving behavio i a vey imotant vaiable influencing economic goth. Conventional economic theoy, hoeve, doe not eem to ovide a good undetanding of the deteminant of eonal aving. Fo intance, thee ae cuently no good exlanation fo the conideable deceae in eonal aving ate obeved in the nited State ove the lat fe decade fom aound % in the middle 970 to the cuent.7% ee, fo examle, Auebach and Kotlikoff (990, Hungefod (006, and Guidolin and La Jeunee (007] o fo the lage diffeence in houehold aving taditionally obeved among indutialized countie on aveage ove the lat decade eonal aving ate ee, accoding to OECD (009, cloe to zeo fo Autalia, Denmak, and Finland, aound 5% fo Jaan and Koea, and ove 0% fo Fance and Gemany, fo examle]. Some of the mot commonly ued exlanation fo vaiation in houehold aving ae elated to demogahy and family deciionmaking. Demogahic chaacteitic ae exected to influence aving to the extent that the motive fo aving  uch a the deie to eae fo etiement, to bequet, o to fund education  vay ove the lifecycle. ing a lifecycle model of conumtion and aving, economit have eviouly elated aving to, fo examle, the age tuctue of the oulation, life exectancy, and labo foce aticiation ate of the aged ee, fo examle, Hoioka (989, 997, Hoioka and Wan (007, and Hoioka and TeadaHagiaa (00], etiement age, family ize, ecent of oking age oulation ee, fo examle, Smith (990], and ecent of omen in the labo foce (ee, fo examle, A and Ree (00]. The focu of thi ae i on a aticula demogahic chaacteitic: maital tatu. Economit have itten about the effect of maiage conideation on aving. Men eaing fo maiage aea to ave moe ee Hoioka (987 on the effect of maiageelated exene on aving and Du and Wei (00 on the effect of high ex atio on aving]. That maiage and divoce
4 ae elated to aving ha alo been etablihed, fo examle, by Auebach and Kotlikoff (990 and Luton and Smith (00. In thi ae e examine the ole of both maiage undetood a including cohabitation] and divoce undetood a including eaation and idohood]. Ou theoetical model tand out in that it imultaneouly model the maiage and aving deciion. It offe a novel eective by incooating in an intetemoal model of aving behavio unde uncetainty eveal facto elated to coule fomation: the likelihood of maiage, the likelihood of divoce, and the eence of economie o dieconomie fom maiage. The key ole of economie o dieconomie fom maiage in ou model i uggeted by the mixed evidence in the emiical liteatue on the gende diffeential in aving behavio. Women ave moe than men accoding to a numbe of tudie baed, fo examle, on data fom South Koea ee Kim (997 and Lee and Pocock (007], Kenya Andeon and Baland (00] and the S Hungefod (999]. Seguino and Floo (00 analyzed a anel data et fo emiindutialized countie and hoed that the highe omen income i elative to that of men, the highe i a county go dometic aving ate. Hoeve, hen Phi and Woolley (008 etimated midlife men and omen obability of eve having contibuted to a Regiteed Retiement Saving Plan (o RRSP, a Canadian couin of IRA ogam in the S they found that geate female contol a aociated ith a loe obability of having contibuted, a ell a loe contibution level. They alo found that an inceae in male eaning had a much lage effect on total aving into thi kind of etiement lan than an equivalent inceae in female eaning. It i alo the cae that accoding to the 008 Family Income and Exenditue Suvey (Statitic Bueau, Jaan, 008, ingle men ave moe than ingle omen in Jaan. Ou model attemt to econcile ome of thee aaent contadiction in the emiical liteatue. In the context of taditional gende ole, maiage entail economie of maiage fo omen and dieconomie of maiage fo men. Ou model incooate uch gende aymmety and theefoe
5 accommodate diffeent aving behavio by young ingle men, elative to thoe of young ingle omen, and diffeent aving behavio by maied omen elative to thoe of maied men. In cultue ith moe egalitaian gende ole e exect fee gende diffeence in aving ate at both youth and midlife. A a eult, cocultual vaiation in nom egading gende ole in the houehold could oibly exlain gende diffeence in aving ate. While e vie maiage like fim comoed of individual ho oduce togethe and/o conume togethe, in the tadition of the Ne Home Economic ioneeed by Becke (960, 965 and Mince (96, 96, ou model deciionmake ae individual ho can be eithe ingle, maied, o ingle again (via divoce o death. The income fom hich they ave i thei individual dioable income. Economie o dieconomie of maiage exand o educe the uchaing oe of individual income. Ou analyi build on Becke (97 ioneeing economic analye of maiage and on economic model analyzing intamaiage tanfe a comenation fo ok in maital houehold oduction, uch a GobadShechtman and Neuman (988. Thi ae i oganized a follo. In ection e eent the analytical model. In ection e eent the analytical eult on the imact of change in the obability of maiage on the aving ate of agent at diffeent tage of thei live. In ection 4 e do the ame ith change in the obability of divoce. Finally, in ection 5 e dicu ome of the emiical imlication of ou eult and ovide uggetion fo futue ok.. The Analytical Fameok We conide houehold a comoed of individual agent, even if maied. Ou tylized agent a male o a female  live fo thee eiod: youth, o eiod, midlife, o eiod, and old age, o eiod. The agent maximize an individual intetemoal utility function ( defined on conumtion c i ith i =,, and. Vaiou otential maital tate ae oible. In cae of maiage,
6 both ivate and houehold ublic good, i.e., good conumed jointly ith the oue, ae oibly conumed by the agent, but e don t fomally ditinguih beteen the to tye of good. The utility function i aumed to atify oitive maginal utility, deceaing maginal utility, and contant abolute ik aveion. Futue conumtion i dicounted by a facto δ that catue imatience. ( Max ( c δ ( c δ ( c ] Thi utility function i maximized ubject to budget containt fo each of the thee eiod. The agent can deive income fom to ouce: ok o inteet on at aving. It i aumed that the agent ean the ame age in evey one of the thee eiod, hich aume intetemoal moothing of eaning. Saving ean a etun. In the abence of integeneational altuim and/o uncetainty a to the time of death, thee ae no aving in eiod. The model conide that individual agent continue to make thei on conumtion and aving deciion hethe maied o ingle. Maiage i defined a beingincoule and include cohabitation, and accodingly, divoce include eaation hee individual did not tie the knot. We aume that the agent i unmaied in the fit eiod. Thee i a obability that the agent ill emain ingle in the econd eiod, the altenative being to may. Thee i a obability that the agent ill be ingle, idoed, o divoced in the thid eiod. Fo the ake of imlicity e ill efe to a the obability of divoce. It i aumed that and ae exogenou and indeendent, that the divoced tate i equivalent to the ingle tate, that agent can not may in eiod, and that divoce doe not entail eithe exta exene o exta income. In eiod and (midlife and old age, the budget containt deend on maital tatu of the agent. 4
7 Conumtion and aving ae eonal, not houehold baed. Fom a uchaing oe eective, an agent can benefit fom maiage to the extent that the agent ha acce to the oue income to buy good conumed by the agent. Ho much the agent benefit fom oual eaning i catued by an economie of maiage aamete, γ. In the cae of γ = maital tatu doe not affect the conumtion value of eaning. Thi could be a ituation hee the agent i ingle o a ituation hee maied eole eaning geneate neithe economie of maiage no dieconomie of maiage. If γ > thee ae economie of maiage in the ene that in the maied tate individual income can geneate moe conumtion and aving fo agent than if they ee to tay ingle. One oible eaon fo the economie of maiage i that the individual exect to obtain a highe dioable income afte maiage, via acce to hi o he oue income. Altenatively, the oue may uchae good benefiting thi individual ivate conumtion o hi conumtion of houehold ublic good. Such intamaiage tanfe of income may be the eult of that agent doing moe ok in houehold oduction and getting comenation fo uch ok fom the oue. In a context in hich leiue doe not ente the utility function, uch diviion of labo ithin the houehold i an economy of maiage to the eon doing the houehold oduction ok. In contat, if γ <, thee ae dieconomie of maiage in the ene that in the maied tate individual income ha a loe uchaing oe fo agent than if they ee to tay ingle. Thi could include a ituation hee the agent income i ued to ay the oue and the oue buy good that don t benefit the agent, o that the conumtion value of the agent' income i loe than hat it ould be if the agent ee ingle. Anothe oibility i the cae in hich the oue doe not aticiate in the labo foce and theefoe doe not have indeendent income. Given thee conideation, the budget containt fo the thee eiod can be itten a: ( = c 5
8 ( = c ith obability γ ( = c ith obability ( = ( c ith obability γ ( = c ith obability ( The otimal level of aving in the fit to eiod i obtained by maximizing ( ubject to ( and can be eented in geneal tem a: hee, (, = agmax V ( V = ( δ{ ( ] ( γ ( ]} δ { ( ] ( } γ ( ]} Given the oetie of the utility function, ae detemined by ( V (4 = ( δ ( { ( ] ( γ ( ]} = 0 (5 V = δ { ( ] ( γ ( ]} δ ( { ( ] ( γ ( ]} = 0 Let thee fit ode condition be denoted in an imlicit fom by 6
9 (4 F, ;, 0 ( = (5 F, ;, 0 ( = Function (4 (5 eeent aving ate imlicitly, hee i = i (, ;, = 0, ith i =,. The effect of the diffeent agument on aving behavio can be obtained by uing the imlicit function theoem and the elated infomation eented in the Aendix.. On the Effect of Change in the Pobability of Maiage on Saving Behavio We no conide the effect of change in the obability of maiage ( on aving in both youth and midlife and theeby on lifetime aving. Pooition Effect of change in the obability of maiage on aving at youth] Saving at youth deceae ith the obability of maiage if thee ae economie of maiage ( γ > and inceae ith the obability of maiage if thee ae no economie of maiage ( γ <. Poof: ing tandad technique e obtain (6 = ( / det( F It can be hon that ign( = ign{ /( ]} 7
10 hee the tem in the quae backet i oitive. Futhemoe, the eaon hy the ign i ambiguou i becaue ign ign egadle of the value of γ. No it can be hon that: ign ( ign ( = ign{( ign{( /( /( ]} if γ > and ]} if γ < Fom the deivative above and (A. it can be een that 0 < B < (numeato i loe in abolute value than the denominato. Accodingly, /( ] = ( B, hee > 0 if γ > < 0 if γ <. QED The intuition behind Pooition i clea. Economie of maiage ae inteeted a ituation hee maiage hel tetch the value of each dolla eaned by the agent. In thi cae, the agent ave le in youth in eaation fo maiage, ince they anticiate ith a highe obability a tate of the old ith a highe uchaing oe. The evee i tue in the eence of dieconomie of maiage. 8
11 Pooition Effect of change in the obability of maiage on aving in midlife] Saving in midlife inceae ith the obability of maiage if the agent exeience economie of maiage ( γ >. In contat, if maiage geneate dieconomie ( γ >, midlife aving deceae ith the obability of maiage. Poof: (7 = ( / det( F It can be hon that ign( = ign{ ( / ]} hee the tem in the quae backet i oitive. No, it can alo be hon that and ign ( = ign{( ( / ]} if γ > ign ( ign{( ( / ]} if γ <. Fom the deivative above and (A.6 it can be een that( / ] = ( C, hee C > 0 (numeato i loe in abolute value than the denominato. Accodingly, < 0 if γ > > 0 if γ <. QED 9
12 The edicted imact of a change in the obability of maiage on individual aving in midlife goe in a diection that i ooite to that of the edicted imact of a change in the obability of maiage on individual aving in youth. An agent ho exect maiage to be a cotly ooition due to dieconomie of maiage ill be aving moe in youth, befoe maiage, a he o he anticiate a dain on eaning afte maiage. Hoeve, once maied and actually exeiencing the dain on eaning, uch individual ill be aving le than a comaable ingle. In contat, the individual facing economie of maiage ill be aving le in youth, befoe maiage, and moe in midlife, afte maiage. Effectively, economie of maiage amount to a highe income to ave fom. We no tun to the effect of maiage on lifetime aving. A e have hon, a change in the obability of maiage ha ooite effect on aving at youth and midlife. Accodingly, a elevant quetion i hethe o not anything can be aid about the oveall effect of the obability of maiage on the eent value of lifetime aving, i.e., hat e can e ay about. The ign of the aggegate effect i, in geneal, ambiguou. It i oible, hoeve, to identify a definite ign in the folloing aticula, but athe inteeting, cae. Pooition Effect of change in the obability of maiage on lifetime aving] Conide an agent ith a elatively high ate of imatience (δ ufficiently loe than /(. Then, an inceae in the obability of maiage inceae the eent value of lifetime aving fo agent exeiencing economie of maiage and deceae that eent value if thee ae no economie of maiage unle both the obability of divoce and economie of maiage ae vey lo]. Poof: Fom (6, (7, (A., and (A.8 0
13 ign ] = ign  ( ] if γ >, ( if γ < In tun, uing (A. and (A.7 ign  ( ] = 4 ign ( δ ( { ( ] ( γ ( ]}] 4 Suoe no that the ate of time imatience i uch that δ ( = and a aumed that ( ( dilay contant elative ik aveion c, uch that = c. In thi cae ign  ( ] = ign ( ] ( γ ( ] ( ] Notice that < (, and fom concavity of (, fo a ufficiently high, the ign of the above exeion i negative. Moeove, if γ >, then the ign of the above equation i unambiguouly negative ince the fit to tem ae a convex combination of to tem each of hich i loe than the thid tem in abolute value. In thi cae the magnitude of the obability of divoce doe not matte. On the othe hand, if γ <, the ign of the equation ill alo be negative unle bothγ and ae vey lo. 4 It hould be noted that in eality one ould exectδ ( >. Fo the eult to hold it i ufficient that the dicount ate i ufficiently lo (the ate of time imatience i ufficiently high fo the above exeion not to be much lage than one. QED
14 Thi eult etablihe that fo a elatively imatient agent the eent value of lifetime aving inceae ith the obability of maiage in the eence of economie of maiage and deceae in the eence of dieconomie of maiage. Oveall, economie of maiage eeent highe lifetime uchaing oe fo a maied agent. Deite the fact that they ave le hen they ae young they end u aving ootionally moe hen they ae matue. Intuitively, a high degee of imatience guaantee that aving ae educed le at youth than ae inceaed at matuity. The ooite i tue fo agent ith dieconomie of maiage. An inteeting excetion, hoeve, i that even fo uch agent if the obability of divoce and dieconomie ae vey lo, an inceae in the obability of maiage ill alo inceae lifetime aving. Intuitively, the dieconomie of maiage ae damatic and the likelihood of etuning to a highe uchaing oe tate of the old i mall o oveall anticiated futue uchaing oe fom maiage i elatively lo and geate aving ae equied. 4. On the Effect of Change in the Pobability of Divoce on Saving Behavio Pooition 4 Effect of the obability of divoce on aving] Saving of agent thoughout thei lifetime deceae ith the obability of divoce if thee ae dieconomie of maiage ( γ <. If thee ae economie of maiage ( γ > a highe obability of divoce affect aving oitively. Futhemoe, the obability of divoce affect aving behavio (negatively o oitively the mot at midlife. Poof: (8 = ( / det( F (9 = ( / det( F
15 Notice that given the eult above, ign( = ign( = ign( hich i oitive if γ > and negative if γ <. Notice alo that fom (A. and (A., >, hich imlie that <, i.e., the obability of divoce affect aving behavio (negatively o oitively moe at midlife than in youth. QED. The intuition behind thi ooition i that agent execting dieconomie of maiage ill vie divoce a eeenting highe income. Theefoe, fo uch agent the moe likely divoce i, the le they have to ave to hedge againt futue tate of the old. In contat, individual execting economie fom maiage ill ave moe if they exect a highe obability of divoce in anticiation of a moe likely tate of the old ith a loe uchaing oe. 5. Concluding Remak and Diection fo Futue Wok In thi ae e eent an intetemoal model of individual behavio ith uncetainty about maiage and divoce in hich e accommodate the exitence of economie o dieconomie of cale fom maiage. We ho, in geneal, that a cenaio of highe maiage ate and highe divoce ate i aociated ith highe aving ate in the eence of economie of maiage and ith loe aving ate in the eence of dieconomie of maiage. Accodingly, the exitence of economie o dieconomie of maiage lay a cental ole in the detemination of aving behavio of diffeent agent at diffeent lifecycle tage.
16 Ou eult have imotant emiical imlication in tem of obeved gende diffeence in aving behavio. In a ociety ith taditional gende ole, being male o female ill affect hethe agent exect economie o dieconomie of maiage. In taditional ocietie, omen ae exected to efom mot of the home oduction in maiage, huband ean moe than ive, and men make moe of thei eaning available to thei oue than omen do. A a eult, taditional gende ole tanlate in ou model into men exeiencing dieconomie of maiage, and omen exeiencing economie of maiage. It follo fom ou eult that unde taditional gende ole at the emaiage tage, omen ill ave moe if they exect to tay ingle than if they exect to may, and men ill ave moe if they exect to may than if they exect to tay ingle. It alo follo that in taditional ocietie ingle men ill have highe aving ate than ingle omen. Conide the cae of Jaan. A hon, fo examle, by Hendy (985, Jaan ha a taditional cultue in hich mot houehold oduction eonibilitie fall on omen hile men ae exected to hae moe of thei income ith thei ive than the othe ay aound. A edicted by ou model, the aving ate of alaied ingle male oke aged 4 o younge a.9 ecent, comaed to.4 ecent fo ingle omen accoding to the Family Income and Exenditue Suvey (008. In contat, it alo follo fom ou eult that in taditional ocietie at midlife men ill ave le and omen ill ave moe the moe they ae likely to be maied. It i alo likely that maied omen oenity to ave ill exceed that of men. Thi hel exlain hy in South Koea, anothe taditional ociety, Lee and Pocock (007 found that the highe the faction of eaning eaned by omen, the moe coule aved and that among dualeane coule the individual aving of ive exceeded thoe of huband. Ou eult alo ugget that the ooite atten of aving behavio ill occu in oulation ith moe egalitaian gende ole. Fo intance, ou analyi hel exlain hy among a amle of 4
17 coule intevieed in Ottaa, Canada, in 995 (Phi and Woolley 008 omen aved le elative to thei huband than did maied omen in a nationally eeentative South Koean amle. Phi and Woolley (008 hoed that the moe Canadian omen eaned elative to thei mate, the le houehold aved in the fom of etiement account. Alo, accoding to that tudy, omen had malle amount of aving if they had financial contol than if that contol a in the hand of thei huband. Given that Ottaa i a govenment ton, thi Canadian amle a highly educated, and in Noth Ameica high education tend to be oitively aociated ith egalitaian gende ole. Inteetingly, an analyi by Hungefod (999 of individual contibution to 40(K enion lan in the nited State, alo efomed in 995, hoed that omen aticiant had ignificantly highe contibution ate to thei lan than men, oibly eflecting the fact that the amle of.s. houehold a boade and le educated  and theefoe moe taditional  than the Canadian amle. Alo, the.s. amle a not limited to coule and coveed a ide age ange, and e exect gende diffeential to vay ith lifecycle tage and maital tatu. While ou eult etablih the concetual elevance and otential emiical ignificance of maital tatu and economie and dieconomie of maiage in undetanding diffeence in aving behavio, the eult in thi ae hould be egaded a jut a fit look at the athe comlex inteaction of maiage and aving behavio. Fom a concetual eective, the theoetical undeinning of the model hould be efined to allo fo iche eult and moe detailed tetable imlication. Fo examle, e aume that the ate at hich agent hae thei income ith thei oue i given. Thi aumtion i elated to ou aumtion that utility i olely geneated by commecial conumtion good, and not by home oduced good. One hould theefoe conide a fulle model that lace homeoduced good in the utility function and take account of ho the economie of maiage ae elated to the incentive fo home oduction  fo intance, omen getting moe acce to thei huband income ae likely to oduce moe homeoduced good. In addition, 5
18 futhe eeach hould elax the aumtion of contant eaning ove the lifetime of the agent, hich exclude gende diffeence in eaning. Thi ould enich the oibility of gende comaion. Finally, e ignoe the cot of divoce. Clealy, it i not imly the divoce ate that influence aving, but alo hat the anticiated oety ettlement ae in cae of divoce. Futhe ok hould alo examine the oible connection beteen aving ate and egime of oety diviion. It could be extemely inteeting to detemine the extent to hich the ediction of thi model can hel exlain obeved diffeence in aving behavio along the life cycle, aco gende, and aco countie. In aticula, futue eeach hould include a full analyi of male/female diffeence in aving ate at youth and at midlife uing a cocounty amle. It follo fom ou model that uch analyi of gendeecific and oveall aving ate hould take account not only of maiage ate and divoce ate, but alo of degee of taditionalim in the definition of gende ole. It may be helful to ue a meaue of uch taditionalim of the tye incooated in the eeach of SevillaSanz (00. Finally, thi line of eeach ha the otential fo athe tong imlication fom a ublic olicy eective. It could etablih to hat degee moe tuctual atten of ocial behavio ae at the oot of the lack of effectivene of conventional olicy intument, uch a tax incentive, hen it come to omoting eonal aving ee, fo examle, Tanzi and Zee (998 and Hungefot (006]. 6
19 REFERENCES Andeon, Sian and JeanMaie Baland (00, The Economic of Roca and Intahouehold Reouce Allocation, Quately Jounal of Economic 7(: A, Paticia and Ray Ree (00, Family Labou Suly, Taxation and Saving in an Imefect Caital Maket», Revie of Economic of the Houehold 8 (, fothcoming. Auebach, Alan J. and Laence J. Kotlikoff (990, Demogahic, Fical Policy, and.s. Saving in the 980 and Beyond, in Laence H. Summe (ed.. Tax Policy and the Economy Vol 4, NBER, Cambidge: MIT Pe. Becke, Gay S. (960, "An Economic Analyi of Fetility." In Demogahic and Economic Change in Develoed Countie, a Confeence of the niveitienational Bueau Committee fo Economic Reeach. Pinceton, N.J.: Pinceton niveity Pe.. (965, "A Theoy of the Allocation of Time." Economic Jounal 75: (97, "A Theoy of Maiage: Pat I." Jounal of Political Economy 8: Guidolin, Maimo and Elizabeth A. La Jeunee (007, The Decline in the S Peonal Saving Rate: I It Real and I It a Puzzle? Fedeal Reeve Bank of St. Loui Revie 89 (6: GobadShechtman, Shohana A. and Shohana Neuman (988, "Labo Suly and Maital Choice." Jounal of Political Economy 96:940. Hendy, Joy (985, "Maiage in a Recently Indutialized Society: Jaan." In Contemoay Maiage: Comaative Peective on a Changing Intitution edited by Kingley Davi in aociation ith A. Gobad Shechtman. Ne Yok: Ruell Sage Publication. Hoioka, Chale Yuji (987, The Cot of Maiage and Maiageelated Saving in Jaan, Kyoto niveity Economic Revie 57 (: (989, Why I Jaan' Pivate Saving Rate So High? in Ryuzo Sato and Takahi Negihi, ed., Develoment in Jaanee Economic (Tokyo: Academic Pe/Hacout Bace Jovanovich, Publihe, (997, A Cointegation Analyi of the Imact of the Age Stuctue of the Poulation on the Houehold Saving Rate in Jaan, Revie of Economic and Statitic 79 (:556. and TeadaHagiaa, Akiko (00, Souce and Poect fo Aia Goth: Saving Rate, mimeo., Aian Develoment Bank, Manila, Philiine. and Wan, Junmin (007, The Deteminant of Houehold Saving in China: A Dynamic Panel Analyi of Povincial Data, Jounal of Money, Cedit and Banking 9 (8:
20 Hungefod, T. (999, Saving fo a ainy day: doe eetiement acce to etiement aving inceae etiement aving? Mimeo (Wahington, DC, Social Secuity Adminitation.. (006, Saving Incentive: What May Wok, What May Not. Congeional Reeach Sevice Reot. htt://.olicyachive.og/handle/007/bitteam/867.df Kim, S.K. (997, Cla Stuggle o Family Stuggle?: The live of omen factoy oke in South Koea. Cambidge : Cambidge niveity Pe. Lee, Jungmin and Mak L. Pocock (007, Intahouehold Allocation of Financial Reouce: Evidence fom South Koean Individual Bank Account. Revie of Economic of the Houehold 5(: Luton, Joeh P. and Jame P. Smith (00, Maiage, Aet, and Saving. In Shohana GobadShechtman (ed. Maiage and the Economy. Ne Yok: Cambidge niveity Pe. Mince, Jacob (96, "Labo Foce Paticiation of Maied Women: a Study of Labo Suly." In Aect of Labo Economic edited by H. Gegg Lei. Pinceton, N.J.: Pinceton niveity Pe. Reinted in Studie in Labo Suly, Collected Eay of Jacob Mince, Vol.. Aldehot.K.: Edad Elga (99. (96, "Maket Pice, Ootunity Cot, and Income Effect." In Meauement in Economic edited by C. Chit. Stanfod, CA: Stanfod niveity Pe. Reinted in Mince (99. OECD (009, Houehold Saving Rate, Annex, Table, Economic Outlook, 86, Novembe. Phi, Shelley and Fance Woolley (008, Contol ove money and the aving deciion of Canadian houehold, Jounal of SocioEconomic 7: Seguino, Stehanie and Maia S. Floo (00, Doe Gende Have Any Effect on Aggegate Saving? An Emiical Analyi, Intenational Revie of Alied Economic, 7(: Sevilla Sanz, Almudena (00, Houehold Diviion of Labo and CoCounty Diffeence in Houehold Fomation Rate, Jounal of Poulation Economic, Smith, Roge S. (990, Facto Affecting Saving, Policy Tool, and Tax Refom: A Revie. Intenational Monetay Fund Staff Pae 7(:70. Statitic Bueau, Jaan (008, Family Income and Exenditue Suvey. Tanzi, Vito and Hoell Zee (999, Taxation and the Houehold Saving Rate: Evidence fom OECD Countie, Intenational Monetay Fund Woking Pae 98/6. 8
21 APPENDIX To tudy the effect of change in the obabilitie of maiage and divoce on aving behavio e ue the imlicit function theoem. The deteminant of the Jacobian matix of the fit ode condition ith eect to and, that i (4 and (5, i oitive, i.e., Det ( F > 0. Thi i a diect equiement of the otimization oblem in that it elate to the tict concavity of the objective function ith eect to the deciion vaiable and. Futhemoe, ince Det ( F 0, the condition of the imlicit function theoem ae alo atified. To obtain the neceay infomation fo the identification of the effect on aving behavio e totally diffeentiate F and F a given by (4 and (5 to obtain: (A. = ( δ ( { ( ] ( γ ( ]} < 0 (A. = δ ( { ( ] ( γ ( ]} > 0 Fom (A. and (A. it follo that (A. = ( ( > (A. = δ ( { ( ] γ ( ]} > 0 if γ > ( < 0 if γ < (A.4 = 0 9
22 0 (A.5 0 ]} ( ( ] ( { ( > = = F F γ δ (A.6 ]} ( ( ] ( { F = γ δ ]} ( ( ] ( { ( γ δ 0 ]} ( ( ] ( { ( < = F γ δ Fom (A., (A., and (A.6 it follo that (A.6 ] ( ( F F = 0 ]} ( ( ] ( { ( < γ δ, hee given (A. the fit tem ha a negative ign. (A.7 0 ( 0 ]} ( ] ( { < > > < = γ γ γ δ if if F Fom (A. and (A.7 it follo that ( F F =. Accodingly thee to deivative ill alay have the ooite ign egadle ofγ. (A.8 0 ( 0 ]} ( ] ( { < < > > = γ γ γ δ if if F
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