Carole Bonnet

Fanny Godet

Anne Solaz

Décembre

Lionel Wilner

Sébastien Roux

Gendered economic determinants of couple formation over 50 in France

Keywords: Formation de couple, seniors retraités, revenu, état matrimonial genre, mariage, Pacs, cohabitation Gendered economic determinants of couple formation over 50 in France Union formation, elderly, retired, economic resources, socioeconomic characteristics, gender, marital status, repartnering, mariage, Pacs, cohabitation Classification JEL : J12, J14, J16

documents de travail ne reflètent pas la position de l'Insee et n'engagent que leurs auteurs.

Introduction

The prospects of forming or reforming a union are no longer restricted to younger generations. Forming a couple after 50 is an increasingly common event for several reasons. First, as divorce at older ages is more frequent, being alone and thus at risk of reforming a couple is more likely. Second, the social norms about partnership at older age have changed. They became more permissive lowering societal barriers for older individuals interested in new relationships and allowing people to form new partnerships later in life. Thus forming or reforming a couple at older ages is also less stigmatizing than it used to be, especially after the partner's death. Third, with the increase in life expectancy, people expect to live longer and longer in good health. It may thus change their decisions about partnering on their remaining lifespan.

The very large generations of baby-boomers are now reaching retirement age. Their marital histories have been much more diverse than those of previous cohorts. They experienced an increase in divorces [START_REF] Prioux | L'évolution démographique récente en france: une mortalité relativement faible aux grands âges[END_REF] and separations, in cohabitation with respect to marriage, in re-partnering and remarriage chances over last decades [START_REF] Brown | The gray divorce revolution: Rising divorce among middle-aged and older adults, 1990-2010[END_REF]. When they reach age 60, the baby-boomers are less in a relationship than the previous cohorts, and when in a relationship, they are less often married. They are also more likely to have experienced several marriages or partnerships or to have formed step-families. The individuals in their fifties and sixties have also different views about families with a rejection or redefinition of traditional family values [START_REF] Bonvalet | Réinventer la famille : l'histoire des baby-boomers[END_REF]. For all these reasons, couple formation at older ages is now more common.

In spite of these ongoing deep changes, living arrangements at older ages and their determinants [START_REF] Kalogirou | Marital status of people aged 75 and over in nine eu countries in the period 2000-2030[END_REF][START_REF] Tomassini | Living arrangements among older people: an overview of trends in europe and the usa[END_REF]Delbès andGaymu, 2003, 2005) have been much less studied than at young or prime age. Union formation after 50 may share some common characteristics with union formation at younger ages but also presents some specific aspects. First, children are no longer a common prospect of the new couple. However, many of the new partners already have children, and have been already in couple or married. Second, health problems are more frequent. Third, as living conditions depend less on working status with the prospect of the end of working life, the "marriage gains" -such as the insurance aspects or economies of scale that couple formation provides-could play a larger role at these ages. These economic determinants of couple formation at late age have surprisingly received even less attention with the recent exception of [START_REF] Vespa | Union formation in later life: Economic determinants of cohabitation and remarriage among older adults[END_REF] and [START_REF] Brown | Later life marital dissolution and repartnership status: A national portrait[END_REF]. Finally, forming a couple involves finding an adequate partner, but the marriage market at older ages differ from those at younger ages. One characteristic of the marriage market at older ages is that the pool of potential partners is particularly imbalanced in sex: at each age, many more women are living alone than men and the gap is increasing with age.

From dating to marriage, forming a new union may take different forms, involving or not a co-residential partnership, or a contract (civil partnership or marriage contract). The choice of marital status might depend on different factors at older ages than at younger ages. As the desire to marry is often associated to parenthood, the desire for marriage may be less pronounced at these non-reproductive ages (Brown et al., 2012). However, marriage provides undeniably insurance patterns that people can look for when they are getting older. For instance, in some European countries, only married couple are eligible to a survivor's pension1 . Marriage is also associated to inheritance rights, and different rules of taxation. Civil partnership generally could provide some of these advantages but not all.

Studying couple formation at older ages is particularly important in the European context, where unmarried cohabitation began to widespread very early from the 1970's and became more and more massive hereafter. The changing European context with the arrival of the large and particular generation of babyboomers is particularly interesting, whereas the previous literature on the topic has mainly focused on the US context. Would the rejection of marriage by the babyboomers during their parenthood age continue at older ages, or would some economic necessities urge people to marry when they are getting older?

Our study provides recent original empirical evidence on the economic determinants of coresidential union formation among seniors in France, whether they differ by sex, how they evolve with age. As couple formation sharply diminishes in age and can be considered as a rare event for the elderly, we use an administrative and exhaustive data source: the French fiscal tax returns of 2015 and 2016. This database allow us to observe almost 120 000 people over 50 who form a couple in 2015. Economic situation is studied through individual resources but is also highly linked to current marital status since the potential benefits associated could moderate marital choices. A second contribution is to look at the union type, whether seniors would decide to remain cohabitants, to enter a civil partnership or to marry. Finally, we also analyse assortative mating of old couples in terms of income and age.

2 Union formation in later life : theoretical aspects

Expected returns from partnership formation

When forming an union, individuals expect positive returns from partnership formation, especially economic ones [START_REF] Weiss | The formation and dissolution of families: Why marry? who marries whom? and what happens upon divorce[END_REF]. The economic literature emphasized several mechanisms.

First, the couple formation provides economies of scale. Thus sharing a dwelling is associated with higher living standards at least for the partner with the lowest income but possibly for both partners who can benefit from the economics of scale.

Second, it is well-known that the couple may constitute an insurance against several risks such as income or health shocks. The health deterioration and long-term care exposure in later life is one of them. This is particularly true at older ages, the probability of these events increasing with age. Couple is associated to better health [START_REF] Lee | Effects of marital 718 transitions on changes in dietary and other health behaviours in us women[END_REF][START_REF] Hank | Families and health: A review[END_REF] in general, resulting from healthy and less risky behaviours, social support from the spouse, increased well-being by lower loneliness feelings. Besides, the partner is also often the first and main caregiver when health problems and disability occur. Resulting from their higher life expectancy and the gender age gap between partners, women are more often the caregiver of her partner than the reverse. Women are more likely than men to take care of a disabled spouse before his death. Widows might be less interested in meeting a new partner [START_REF] Carr | The desire to date and remarry among older widows and widowers[END_REF] or being a caregiver again [START_REF] Brown | Later life marital dissolution and repartnership status: A national portrait[END_REF] compared to widowers, who may search for social support given by their former spouse. As concerns insurance against income shocks [START_REF] Kotlikoff | The family as an incomplete annuities market[END_REF], let us mention that a significant proportion of 55 years and older exit paid employment for a reason other than retirement that can lead to an income shock : transitions to unemployment, withdrawals from the labour force or disability 2 . Finally, the income loss associated to the transition from employment to retirement could be also attenuated for couples compared to singles. Third, couple is also a way to maximize the complementarities between spouses and increase the home production function. However, we should note that after retirement age, there is no longer (or less) possibility of investing in paid work to increase complementarities at the couple level. The division of labour can be based on the past experience acquired in the field of domestic production however because one partner has become more efficient than the other. As the division of work was particularly imbalanced between men and women in these generations, we could anticipate that men and women may not benefit in the same way of couple formation at old ages. As women participated more to home production during their life, their housework skills may be valued and searched by men when forming a couple at old ages, while women may be more reluctant to repartner because it may mean reassuming the domestic tasks.

2.2

The importance of legal framework and the case of France

Legal rules (welfare states policies or laws) associated to different marital statuses differ across countries. However, in most countries married couples have more rights but also more obligations than unmarried couples while couples in a civil partnership are in an intermediate position. These rules were generally implemented to "protect" the married spouse who invests the most in the unpaid work (still the woman in most cases), particularly following union dissolution with the objective to offset the potential negative economic consequences [START_REF] Kandil | The sexual divison of labour within couples in france according to their marital status a study based on time-use surveys from 1985-1986[END_REF]. By consequence, previously married such as widowed or divorced benefit from some rights (and obligations) associated to their former marriage, compared to previously separated from non marital unions. These rights (and obligations) associated to marital status may affect the decision to form an union whether the new couple formation keep or not former rights, or give access to new ones. This results in different levels of protection for the surviving or divorced/separated spouse depending on the type of union. With the assumption that forming a new union or marriage may be a way to compensate the negative economic consequences of the previous one, the law may moderate the protection by stipulating that some benefits associated to the previous status may be lost in case of a new union. At older ages, Social Security rules, which differ according to the marital status may play a big role.

Let us consider the case of France. Marriage offers more protection but also some obligations3 In case of disruption by partner's death or after a break-up, being married is more protective than being unmarried. In the case of death of a married spouse, a part of the pension of the deceased spouse, called the survivor's pension, is paid to the surviving spouse. Widow's pensions can only be claimed by the surviving married spouse, which excludes those who were in a civil partnership or in a cohabiting union. All pension schemes pay widow's pensions, but at different rates and subject to specific conditions that may induce different incentives to form an union and once this union formed, to enter into a Pacs4 or to remarry. 5 In the event of marital break-up, the law sets up private transfers between spouses for married partners. One spouse may pay the other a "spousal alimony", by decision of the family judge if she considers that the marital investments during marital life are responsible for the gender gap in income or pension rights.

As concern inheritance, both marriage and Pacs (associated to a testimony) give inheritance rights whereas it is not the case for unmarried union. These determinants may play a different role for men and women, regarding their differences in their respective economic situation and life expectancy.

Finally, the French legal framework regarding income tax policies is also different for married, Pacsed and unmarried couples. In short, marriage remains the most protective legal marital status for the spouses, Pacs being a kind of intermediate between cohabiting and married unions as it progressively extended some protections associated to marriage -in terms of taxation for instance making this Civil partnership (associated to a reciprocal testimony) attractive for wealth sharing. Because the legal framework allows specific rights to individuals according to their marital status, people may have more or less incentives to form new partnership and to choose one specific marital status for this new union.

3 Constraints and main determinants of couple formation after 50

3.1 Marriage market : an imbalanced sex-ratio of potential partners

The marriage market at older ages offers different opportunities for men and for women [START_REF] Schimmele | Repartnering after union dissolution in later life[END_REF]. The number of available women (not currently living in a relationship) per men of the same age living alone increases in age as shown in figure 1. The marriage market is becoming strongly imbalanced to the disadvantage of women as they are getting older. At age 50, there is almost one available woman per man, while at age 70, there are more than two women per man. Then, it increases reaching 5 women available per one man at age 88. It sharply increases from this age. While 65% of men of 90 still live as a couple, only 15% of the same-age women are in this situation (figure 2). This gender imbalance is due to the higher risk of widowhood that women encounters because of their longer life expectancy and the average age gap between partners with the men being generally the oldest [START_REF] Daguet | De plus en plus de couples dans lesquels l'homme est plus jeune que la femme[END_REF]. Moreover, women are less likely to form a new couple than men after a separation or after the partner's death whatever the age [START_REF] Wu | Repartnering after first union disruption[END_REF]. This is both a determinant and a consequence of the unbalanced sex-ratio. It is a determinant because the lower likelihood of forming or reforming a couple amplifies the unbalanced sex ratio. It is a consequence because as long as the availability of potential partners is reduced, the more difficult it is for women to form a couple. The women's "repartnering penalty" or the men's "repartnering premium" may thus be amplified at older ages by the imbalanced sex-ratio of potential partners that advantage more men's repartnering than women's one. The women's penalty is intensified because elderly men tend to prefer women who are younger [START_REF] Kunkel | Aging. The Social Context[END_REF].

For all these reasons, single men are in a better situation to form a new partnership than single women, and it should be all the more the case as they are getting older. Overall, we expect that: H1: Given that the ratio of available women per men living alone increase in age, the gender gap in repartnering chances should be even more pronounced at older ages.

The role of individual economic resources

The theoretical effect of economic resources on union formation is mixed.

Following the needs hypothesis [START_REF] Ivanova | The effect of children on men's and women's chances of re-partnering in a european context[END_REF], couple formation may constitute a way of improving living standards for the more disadvantaged singles. Concerning poverty, it has been shown that repartnering is one way to overcome the financial consequences of divorce for prime-age divorcees [START_REF] Dewilde | Remarriage as a way to overcome the financial consequences of divorce -a test of the economic need hypothesis for european women[END_REF]. This particularity may be even more pronounced for older divorcees because the alternative ways of increasing living standards are scarcer. For older people indeed, job opportunities are limited after 50 and almost non-existent during retirement. Since the individual economic situation on the labour market is less likely to sharply improve, forming a partnership may thus constitute the unique way of improving the economic situation for people living alone. So, we may expect people with lower incomes to be more likely to form a new union in later life.

Economic resources may also refer to attractiveness theories [START_REF] Ivanova | The effect of children on men's and women's chances of re-partnering in a european context[END_REF]. They may reflect human capital, current income and wealth, that are generally positively associated to the likelihood of forming a partnership because they determine future financial resources that will be shared within spouses6 . So, we may expect people with (lower) higher incomes to be (less) more likely to form a new union in later life. Following attractiveness theory, as soon as they wish to form a couple, we might expect high-income singles to be more likely to form a couple. For low-income singles, the two theories predict opposite expectations. While the needs hypothesis would urge low-income to form couple by necessity, the attractiveness theory would not favour them on the (re)marriage market. Thus, the income effect direction will depend of the balance between the need and the attractiveness forces. We may thus formulate the following hypothesis :

H2: (H2A) if needs dominate, we expect a decreasing income gradient along income distribution (H2B): if attractiveness dominates, we rather expect an increasing gradient

The shape of the income effect on couple formation may also differ by gender however. Because of the traditional division of gender norms, men are more "socially" expected to be the main provider of resource and could be searched for their breadwinner role, while women's resource would reduce the likelihood to form a couple, according to the independence hypothesis or marital specialisation approaches [START_REF] Becker | A Treatise on the Family[END_REF]. The labour market participation of women increases the opportunity cost of marriage and decreases marriage gains linked to the specialization. In Oppenheimer's theory of marriage timing, however, women's economic resources and education make them more attractive on the marriage market in modern society, but could also extend the timing of search for the right partner, and delay marriage formation anyway. In these generations, indeed, it is empirically observed that high-educated women (it is no more the case now) were those less likely to form an union. This "marriage penalty" for high-income women could remain at older ages. Thus : H3: We expect the positive income effect on union formation for higher incomes to be less strong for women than men.

As concerns the choice of the type of union chosen, we expect a positive effect of income on marriage rather than on cohabitation. Marriage could be more desired by wealthy people that could afford it and because of the long-term commitment and security that marriage provides relatively to cohabitation. However, in France, the socio-economic status (SES) gradient in cohabitants is less marked than elsewhere (cohabitants are not as disadvantaged than in US for instance) and this effect is not necessary strong. However, tax rules differ according to the type of union. Married couple and Pacs partners are required to file joint tax returns while joint taxation is not possible for cohabiting partners. Because income taxation is progressive, filing jointly rather than separately leads to paying less tax in almost all cases where one partner earns substantially more than the other. Marrying or contracting a Pacs would be more financially interesting for couples with a difference in individual incomes. So, we expect that : H4: We expect couples with a difference in individual incomes to contractualize more often their union.

The role of current marital status

Individuals living alone may face a trade-off between the gain of forming a new union and the potential loss of the benefits associated to their current marital situation. As previously shown, depending on the legal framework, marital status may be associated to different types of benefits and obligations. The legal framework is thus going to have a role both on union formation [START_REF] Schimmele | Repartnering after union dissolution in later life[END_REF] and on the type of union chosen. Individuals may lose some advantages associated to their current status and then will be less likely to form a couple or will adopt a living arrangement in which they can keep their advantages [START_REF] Chevan | As cheaply as one: Cohabitation in the older population[END_REF][START_REF] Baker | The married widow: Marriage penalties matter![END_REF].

The advantages of forming a couple may differ by current marital status. People living alone could be legally single, divorced or widow/er. For the widowed elderly, forming a new union could be penalizing in some cases as the benefit of the survivor's pension in some retirement schemes may be conditioned on remaining alone (or at least not married). For instance, widows who decide to remarry may lose their survivor's pension and may prefer to remain in an unmarried partnership [START_REF] Caradec | Les formes de vie conjugale des "jeunes" couples "âgés[END_REF]. Divorcees who benefit from a spousal alimony could also lose it if they perceived it by annuities (it is still the case for these generations in some case). On the contrary, singles will not lose any benefits potentially associated to their previous marital status.

On the contrary, forming a couple (and all the more in case of marriage) could provide a security for later life, and provide an access to these rights for those who do not benefit from them already such as cohabitants. As the risk of partner's death is increasing in age, so does the financial incentive to marry, compared to enter a civil partnership (Pacs) or to remain in a consensual union. So people may balance between their current and future rights. From a gender point of view, it is quite clear that women's resources are more likely to be linked to previous marital history than men's one.

H5: Thus, we expect being a widow to be more decisive than being a widower on both the decision to cohabit and to marry Beyond economic aspects, this gendered effect could be reinforced by differentiated disincentives and norms. Widows (and divorcees) could face more disincentives to form a new partnership than men. First they may not want to be involved in caregiver tasks, especially widows, who may have already been involved in such tasks before the husband's death. Remind that married spouses, contrary to cohabiting partners, have the obligation/right to mutual support ("devoir d'assistance"). It may then be possible that cohabiting reflects the reluctance to provide as much care as married spouses would do when disability occurs. Social barriers to remarriage are also stronger for women than men: a woman should not remarry while it might be better accepted for men.

Finally, regarding inheritances, the choice of marital status is important. In case of death of one the spouse, the widow (and not the surviving spouse in a cohabiting union) will inherit from at least 1/4 of the wealth of the deceased spouse and, and it may be particularly important at older ages. The widow is entitled to remain in the common dwelling whoever was the owner. Marrying the new partner is a way to protect her. But we may also expect the opposite if someone prefers not to diminish the inheritance of children born from a previous union. Vespa (2012) shows that wealth is not associated with the risk of remarrying compared to cohabiting. We do not have information on wealth in our data (with the exception of being owner of his/her housing) but if we assume income and wealth are positively correlated, we may formulate the following hypothesis : H6: High-income individuals may be more likely to marry than to cohabit if the intention to protect the new spouse's inheritance is high 4 Data, variables and methods

Data and sample

We use an exhaustive administrative database resulting from a matching (made by the national Institute of Economic Studies, Insee) of different tax databases (mainly income and housing tax returns)7 . It covers the whole French population. This database includes demographic information on individuals (sex, age, marital status, date and place of birth, place of residence), household structure (existence of a couple8 , number of children and other co-resident people), housing tenure status (owner, renter in the private sector of in the social housing sector), individual incomes (wages, self-employment income, unemployment allowance, pension and survivor's pension 9 ), incomes at the household level (alimony, property incomes, financial assets income) 10 and also the amounts of social benefits received by households 11 . This database is a panel over two years. It is the possible to analyze marital status transitions between two years. We use the 2015-2016 waves.

Our sample is composed of the entire population of 50 and over in 2015 12 . To analyze union formation, we select for the analysis the individuals who are not in a co-resident partnership at the beginning of 201513 , i.e. around 7.26 million of individuals: 2.42 million men and 4.84 million women. Beyond the large sample size, this database provides reliable and precise information on income and family structure (careful checking of kinship). Since the fiscal administration follows people even in case of geographical move to collect their resources, the risk of attrition is almost null (see figure 3).

We dropped people identified as living in a nursing home, assuming they are not at risk of forming a co-resident union.

Variables of interest

Our variables of interest are previous marital status and income. Regarding legal marital status we know whether people were married in case of divorce (divorced status) or death of the married husband or wife (widow or widower status). Unfortunately, when people are still legally single, we do not know whether they have been in an unmarried partnership before or they have never lived with someone. This lack of information on previous unmarried partnership is a minor issue for the older generations for which marriage was the dominant form of partnership. In that case, legally singles are likely to have never been in a relationship. However, it is clearly a drawback for the younger cohorts born in the 1960's, for which unmarried unions were more frequent. In that case, being single could mean both that the person has never been in a relationship or never been married but could have been in an unmarried relationship. In this younger generation however, the proportion still having children at home is quite large and could constitute a good proxy for previous unions.

Regarding income, we computed deciles of the sum of individual incomes perceived the year before : wages, self-employment income, unemployment allowance, alimony, pension and survivor's pension. In fiscal data of year t, the demographic situation considered is that of the 1st January of year t (in other terms the end of year t-1), while income reported refer to income perceived during (t-1). This time lag avoids the risk of reverse causality issue.

Control variables

We control for a set of socio-demographic variables. First of all, we control for the household structure of respondent: the presence of offspring, distinguishing those under 18 from already adult children (either student or disabled child)14 , and the presence of at least one parent living in the same household. Previous works have shown that the presence of children explains a large part of the gender gap in repartnering after divorce [START_REF] Ivanova | The effect of children on men's and women's chances of re-partnering in a european context[END_REF]. The legal marital status provided partial information on past partnerships.

We control for age, repartnering being negatively associated to age.

We control for country of birth, preferences for being in an union or a type of union may differ.

We also introduce the detailed employment situation defined by the main source of previously mentioned incomes. Indeed, in the income tax file, occupational status is not reported directly but the diverse types of income are declared. We can then deduce the main occupational status, those associated to the highest amount15 .

We also consider the housing status, whether the individual is owner, renter in the private sector of in social housing sector, could affect the likelihood to move and form new couple (or could affect the incentives for the new partner to join). Moreover, the ownership status is a good proxy for wealth.

Models

We first perform a logistic regression on the probability to form a new partnership in 2016 for those who are aged more than 50 and who live alone in 2015. The timing of marital status choice could differ. While some couples may decide to contractualize their union at the beginning of their partnership, others may decide to do it later. Then, for the type of union chosen, we distinguish those who have just formed a coresidential union in 2016, from those who formed a coresidential union earlier (and who are already in a cohabiting union in 2015). For each of these two samples, we run a multinomial logistic regression on the type of union chosen in 2016 : it may be (or remain for already cohabiting couples) a consensual relationship, it may be a Pacs (French civil partnership) or it may be a marriage.

For instance, we run the following regression on the probability to form a new partnership: = place of residence by size of urban area 5 Results

Logit(union i |X i ) = α + βGender i + 3 j=1 ε j 1 M statusi=Mj + 10 j=1 ζ j 1 Incomei∈Dj + 5 j=1 η j 1 Agei∈Clj + 4 i=j µ j 1 Estatusi∈Cj + 3 j=1 ν j 1 T HT enurei∈Hj + 3 j=1 π j 1 Fi∈F amj + 4 j=1 κ j 1 BCi∈Cj + 4 j=1 λ j 1 Si∈SU

Couple formation after 50 16

At all ages, the probability of forming a new cohabiting relationship for men is higher than that of women (figure 4). On average, 2.7% of single men aged 50 and over are forming a couple yearly against 1.2% of single women. This may be related to the marriage market being more favorable to men at these ages, in line with our first hypothesis (H1). The probability to form a partnership sharply decreases with age for both men and women.

Men are always more likely to form a new partnership than women at all ages, and this gender gap increases in age (figure 5). For instance, while men at 50 are 1.3 (5.5/4.2) more likely to form a co-residential couple than women of the same age, this ratio increases to 2 at age 68 and continues to increase hereafter. The male re-partnering premium is increasing in line with the sex ratio imbalance, supporting our first expectation H1.

Determinants of couple formation over 50

We confirm that the probability of forming a union is higher for men that for women all other things being equal (Table 1). We also performed the same regression separately by sex. the probability of forming a new union is sharply decreasing in age for both men and women, and even strongly for women. On the whole population, we observe a rather flat income gradient, except at the two extremes of the distribution. At the bottom of the distribution, for the first decile, in line with our H2A hypothesis, needs dominate and the probability to form an union is higher than for the second decile. At the upper part of the distribution, attractiveness seems to play a bigger role, richer individuals being more likely to form a union. This relatively flat profile for the income effect over the main part of the income distribution masks diverse and interesting effects by gender. For illustration, the marginal effects of income deciles on couple formation chances raw (without controls) and adjusted (including all previously commented controls) are drawn in figure 6, in a model interacting income and sex variables on the whole population. The graph showing the raw income marginal effects exhibits a U-curve, more or less marked at the bottom or top of the distribution according to the sex. The H2A Needs hypothesis seems to be more pronounced for women as shown by the decreasing gradient of income at the bottom of the distribution, while the H2B Attractiveness hypothesis (increasing income gradient) seems more pronounced at the upper part of the distribution for men. After controlling for age and other controls (adjusted marginal effects), the different results by gender are even more pronounced. For men, we observe an increasing income gradient on the probability to form an union. Richer men are more likely to form a couple, especially when belonging to the last deciles, in line with our H2B Attractiveness hypothesis. At the bottom of the distribution, the slighty higher probability of forming a couple for first decile relatively to second decile could be interpreted as a way to escape poverty for poorer men, in line with our H2A Needs hypothesis.

For women, we observe a totally different pattern for the income effect. The probability to form an union is decreasing with income, in a very pronounced way on the second part of the income distribution. The highest-income women have the lowest probability to form an union, going beyond our H3 hypothesis, which stipulates that the expected positive income effect on union formation for higher incomes may be less pronounced for women. A higher income enables women to remain single following the Becker independence hypothesis. This results also reflects a marriage market pattern: highly educated women were those most likely to remain singles in these generations (even it is not true anymore). Besides, a branch of literature on seniors also point that the desire for a new partnership might be less strong for women, because they would be less likely to bear again the domestic tasks burden. They would have a preference for Living Apart Together relationship (LAT)17 [START_REF] Régnier-Loilier | Neither single, nor in a couple. a study of living apart together in france[END_REF][START_REF] Liefbroer | Why do intimate partners live apart? evidence on lat relationships across europe[END_REF][START_REF] Régnier-Loilier | Faire couple à distance. prévalence et caractéristiques[END_REF] or remaining alone. The opposite income gradient for men and women is confirmed whatever the age (introducing the interaction between age and the income individual deciles in the regression), but largely less pronounced for older ages for women (figure 7). The effect does not stop with retirement. For men, the curves are almost parallel between retired and not yet retired (figure 8). The effects remain however at even old ages: beyond 80, the advantage of the highest decile is still significant. For women, the negative income gradient of the likelihood to form a couple is more pronounced for never married and divorcees whereas the income gradient is more limited for widowers (figure 9), as already observed. The fact that the effect is less pronounced for widows might be associated to the perception of a survivor pension that guaranties current and future earnings for previously married women.

Figure 9. Income gradient effect on couple formation after 50, according to marital status

The role of previous marital status

Previously divorced are more likely to repartner than never married [START_REF] Gierveld | The dilemma of repartnering: Considerations of older men and women entering new intimate relationships in later life[END_REF]. One reason could be that ever married senior may have some characteristics making them more attractive compared to never married. Among never married, some have never been in a partnership before, particularly for oldest generations for which cohabitation was still rare. Being widowed is associated with lower chances of repartnering than divorced status. But this covers interesting opposite effects for men and women when comparing with never-married, in line with our second hypothesis. Widowers are more likely to form a new union than never married men while the opposite result stands for widows who are less likely to form a new partnership. This result supports our H5 assumption according to which widows are less likely to form a couple. These latter may have some financial incentives not to repartner, benefiting from a survivor's pension from the previous marriage. The survivor's pension is indeed lost in case of repartnering in the public sector and might be reduced or suppressed when the household financial resources (including those of new partner) overtake a threshold18 . Some different gender norms on repartnering for widows and widowers or different attractiveness may also play a role.

5.2.3

The role of other socio-demographic variables

Having a child under 18 is a positive determinant of forming a new couple, both for men and women, but of much larger magnitude for men. It is in line with patterns of repartnering chances for men, who might look for a partner and social mother (stepmother) when they are the main custodial parent [START_REF] Ivanova | The effect of children on men's and women's chances of re-partnering in a european context[END_REF]. However, for women, though the positive effect is less strong, the result is the opposite of what has been shown for younger ages. At younger ages, the presence of children within the household is generally an obstacle for woman's repartnering chances [START_REF] Ivanova | The effect of children on men's and women's chances of re-partnering in a european context[END_REF]. One reason of this difference may come from the age of the children who may be already quite old on average, mostly teenagers, and do not need so much care than younger ones. This time freed up can be devoted by the mothers to their new partner. Having older children (including for instance a student or a disabled child) plays negatively. It could be related to the wish to wait until the child leaves home before forming a new co-residential couple. The direction of the relationship can also be reversed. The presence of an adult child may be a source of social support for older mother or father cohabiting with one of their child for health-related reasons, as pointed by [START_REF] Schimmele | Repartnering after union dissolution in later life[END_REF]. Having at least an old parent in the dwelling, who is likely to have health problems, plays expectedly strongly negatively on his or her couple formation chances.

Regarding occupational status, results show that working people, both women and men, are always more likely to repartner than retired. As already observed for younger ages (Ekert-Jaffe and Solaz, 2001; [START_REF] Kalmijn | The influence of men's income and employment on marriage and cohabitation: Testing oppenheimer's theory in europe[END_REF], unemployment continues to constitute a penalty on the marriage market at older ages relatively to working people, either wage-earner or self-employed. Male self-employed are more likely to repartner than wage-earner, perhaps because they need a collaborating partner.

To the exception of women born in Africa, foreign-born women and men, are more likely to form a couple whatever the geographical origin. This could be due to a selection effect: those who stay or just came on the French territory are more likely to have the desire to form a partnership soon, while other singles at older age would prefer to emigrate. Living alone might be perceived differently according to the culture of origin.

Being owner of the dwelling plays negatively on the chances of forming a new couple relatively to being renter. Considering being owner as a proxy of wealth, this result is in contradiction to what has been observed by [START_REF] Vespa | Union formation in later life: Economic determinants of cohabitation and remarriage among older adults[END_REF] on US data, who found a wealth positive gradient of later age partnerships formation. One explanation may come from the wish of staying in the same place, when you are owner. Some senior might prefer to keep their dwelling and begin rather a LAT relationship rather than a co-residential union such as been observed by Régnier-Loilier et al. ( 2009) and assumed by [START_REF] Lewin | Intentions to live together among couples living apart: Differences by age and gender[END_REF] even if not supported by the empirical evidence. The negative effect on union formation is also observed for social housing. We may assume that the risk of loosing the financial advantage of living in a social housing (lower rent price) could be a disincentive to quit it. Finally, we check the impact of the place of residence. We observe that both living in rural and a big urban area are associated to a higher probability of forming an union. Two different reasons may be put forward. A big urban area may be linked to more social contacts and opportunities of meeting potential partners. Regarding rural areas, it may be more difficult to live alone in such places.

Which type of union is chosen?

Union contractualization at the time of couple formation

Among men aged 50 and older who enter a new union, around 13% opt for a marriage the same year and 7% for the French civil partnership called Pacs19 . Among women, the proportions are respectively 11% and 6%20 .

Among couple formation after 50, the proportion of men who marry directly is relatively stable from 50 to 80 (direct marriages represent roughly 15% of couple formations), then decreases. This effect might be a cohort effect. For the oldest generations, marriage is still the main way of forming a couple. It is also possible that these late marriages are related to the awareness of the existence of survivor's pension when people reach older ages. Civil partnerships are rather constant with age and represent 5% of these new couples (figure 10). The proportion of women who contractualize their new union through marriage follows the same pattern but at a lower level. The difference at each age between men and women may be explained by the gender age gap between partners, men marry younger partners than women do. 2 shows the probability to opt for a contractual union, respectively married or pacs partnership relative to non-contractual union (the reference category). To make the interpretation easier, some covariates are built at the household level such as the couple mean age and the age gap between partners.

The marital legal status plays a big role on the decision to marry. We observe interestingly opposite effects by gender. Previously married men, either divorced or widowed, are more likely to remarry. We also observe this phenomenon for divorced women. Previously married people may have some preferences for marriage or may be willing to protect the new partner compared to the previous one. The exception is widows, who are less likely to remarry. This is in line with our H5 hypothesis (the perception of a survivor's pension or the existence of norms are disincentives to remarry). The probability of opting for a Pacs is less associated to the previous marital status, with the exception of widowed who are less likely to opt for a Pacs than never married and of divorced women who are more likely to contractualize their union in a Pacs (even if a lower magnitude than in a marriage).

There is a positive income gradient for men to opt for a contractual union compared to a non contractual one (table 2); either marriage or Pacs, in line with our H6 hypothesis. Many reasons might explain this choice: inheritance rules or the wish to insure his partner in case of death by giving her the possibility to perceive a high survivor pension. The income gradient is more pronounced for marriage than for Pacs, income only playing a role beyond the 6th decile. But once playing a role, the effect of income is more pronounced for opting for a Pacs than for marriage. It may also reflect an education effect, people opting for a Pacs being more educated. The pattern is different for women. The Pacs is an option for women with the highest individual incomes, beyond the 8th decile. Below, there is no significant difference in choosing a Pacs or an informal union. Most noticeably, the effect of income on the choice of marriage follows a U-shaped pattern. Women in the first part of the income distribution and in the highest decile are more likely to opt for a marriage. For the poorest, it is a way to escape income poverty, in the long-run, marriage being a long-term commitment. For the richest, as for men, fiscal, inheritance rights or the wish to insure the partner in case of death might drive this choice.

Owners, women as men, are more likely to contractualize their union. The advantage in terms of inheritance, especially regarding the possibility for the married spouse or the registered partner to remain in the house after the death of the other spouse may be a strong incentive.

The regression also shows a slight effect of the younger ages (calculated as the mean age between partners) on the probability to contract a civil partnership but none effect of age for marriage. But the results show a huge effect of the age gap introduced in 7 classes. For marriage, there is an increasing and strong gradient of age gap: the oldest is the man relatively the woman, the higher are the chances of marrying. This can result from some bargaining within couple and "the price to pay" to form a couple with a young woman. As youth is valued on the marriage market, young women would be able to bargain a marital status that protects them, such as marriage or Pacs. A younger partner may also mean a potentially higher period of widowhood that should be covered through legal arrangements. The pattern is almost similar when considering the probability to enter a Pacs but of lesser magnitude, with the exception of the strong effect on the probability to opt for a Pacs of women being much older than the man. It is in line with the results showing that couples who opt for Pacs have less traditional values than couples who opt for marriage [START_REF] Kandil | The sexual divison of labour within couples in france according to their marital status a study based on time-use surveys from 1985-1986[END_REF].

In table 3, we introduce some other covariates at the household level: household total income, the share of woman's income within household income (three items, woman's income represents less than 40% of total household income, between 40 and 60%, and more than 60% of total income). We introduce this covaiate to test our H4 hypothesis regarding the potential fiscal optimization through marriage or Pacs in case of large income gap among couples. We also introduce the interaction between man's and woman's previous marital status to investigate a possible marital status homogamy.

We observe that for both marriages and Pacs, there is a clear positive income effect observed for both women and men. The couples who decide to marry or Pacs at later ages are wealthier couples. The coefficient of ownership is also positive, reaching the same conclusion. These wealthier couples may also be the most aware of the rights involved by contracting such formal unions. In line with [START_REF] Vespa | Union formation in later life: Economic determinants of cohabitation and remarriage among older adults[END_REF], cohabiting is more likely for less socioeconomically privileged individuals. In line with our H4 hypothesis regarding fiscal optimization, marriage and Pacs are more likely in more traditional couples, with the man being the main provider of resources (woman's share of income lower than 40% of total household's income). Pacs is also more likely (with a weaker effect than marriage) when the woman is the main provider of resources. Beyond the tax benefit, this may reflect less traditional values couples (this type of couple's configuration is rarer). We confirmed the important effect of the previous marital status, especially widowhood. Widows are less likely to marry, whatever the marital status of their new spouse, while being divorced or widower for a man was associated to a higher probability of marrying. The probability to marry is the highest when the man is widowed and the woman never married. It may reflect the search of a new spouse to get social support for the man and the slightest reluctance of women who never experienced marriage. Odds ratios are reported in the table * p < 0.10, * * p < 0.05, * * * p < 0.01 Note: The mean age of partners, the difference of age, men's and women's coresident family, men's and women's employment status, men's and women's housing tenure, men's and women's birth country and women's size of urban area are included as control variables in the regression. The entire regression table is given in table 6

Union contractualization among individuals already in a cohabiting partnership

Here, we analyze the probability to marry or to enter into a civil partnership (compared to remaining in the cohabiting union) for couples already in a cohabiting union. Among those in a cohabiting partnership, 2.9% of men and 2.6% of women over 50 marry and 1.7% of men and 1.6% of women opt for a Pacs in 2016. All these couples have begun in a cohabiting union, but might decide to contractualize it for different reasons. They are probably more likely to be formed recently, compared to married counterparts. Unfortunately, we do not have information on the duration of the current partnership.

The effect of marital status and age gap between partners are in line with our previous findings for newly formed couples (table 4). There is a steady decreasing effect in age for marriages, also observable for Pacs, but with a slight rebound for Pacs for very old couples. This effect, if confirmed by the data, might come from very late decisions to contract a union as an insurance when one partner is on the verge of dying21 . Marriage would be also an option but is longer and more complicated to implement. Marrying or contracting a Pacs is more common among still active respondents with a penalty when the man is unemployed. Self-employed are less likely to marry compared to wage-earners as previously observed by [START_REF] Frémeaux | Plus ou moins mariés : l'évolution du mariage et des régimes matrimoniaux en France[END_REF], but are more likely to contract a Pacs. This may reflect their preference for union contract in which professional properties are separated.

Household income level variables confirm that contracting a Pacs or a marriage is positively associated with income. The income gradient is more pronounced for Pacs than for marriage. This model also shows that larger income gaps are a strong motivation to contract a pacs or marriage, in line with fiscal optimization or the will to protect the new spouse. But as previously observed, whereas Pacs concerns couples with higher income differences whatever the direction (the man or the woman may be richer), marriage is more chosen by more traditional couples in which the man earns much more than the woman. Thus both contracts are used to protect the spouse who earns less, but the least traditional couples might have a preference for the Pacs.

Who repartners whom?

When choosing a partner, individuals may take different characteristics into account, which reflect common backgrounds [START_REF] Haandrikman | Explaining the flight of cupid's arrow: A spatial random utility model of partner choice[END_REF]). Partner's choice may be based on cultural aspects or on demographic aspects (Demographic homogamy): age, stage in the life course [START_REF] Haandrikman | Explaining the flight of cupid's arrow: A spatial random utility model of partner choice[END_REF] or marital histories and current marital status. [START_REF] Ono | Homogamy among the divorced and the never married on marital history in recent decades: Evidence from vital statistics data[END_REF] finds that the never married and the divorced persons tend to marry within their own marital history group. Partner's choice may also be based on socioeconomic aspects. Income, education, social class homogamy have been largely studied. Understanding income assortative mating among the elderly is particularly important as it will help to understand the evolution of inequalities among the retired population. If we observe Income homogamy, this may increase inequalities while if richer men form a new partnership with low income women, this may reduce inequalities.

Contrary to women who have a smaller pool of eligible partners and discouraging social norms to match with younger men (Brown et al., 2012), men are in an advantageous position on the marriage market. They can choose more freely their future partner. It is not clear to what extent they prefer to match with someone of roughly the same age or younger since youth and probably health, largely associated to age, are valued attributes on the marriage market. Thus it is not clear how men may benefit from their advantageous position. Their advantageous position on the marriage market may make them more likely to find suitable partners and thus to marry-up, that is to say with a partner having positive attributes on the marriage market such as a younger partner.

Demographic homogamy

Figure 11 shows the distribution of the age gap between partners of the new unions formed after 50 according to man's (left column) and woman's age (right column). For comparison, we also reported the distribution of all others unions of people of the same age category. The first striking point is that the age gap distribution of new unions is spread out more evenly, it means that the variance is higher. Partners who recently formed an union are less frequently of roughly the same age than when we consider all unions. This is generally observed for second union and this corresponds also to a more constrained marriage market. We also observe a preference for younger partners. Men aged 50 to 59 are more likely to form an union with women who are more than 5 or more than 10 years younger than them. It is also the case for women, 50-59 women are more likely to match with a younger men, but the distribution is largely less unbalanced than for their male's counterparts. For older men and women, the distribution concords with the potential available partners: men and women who form a couple choose more and more someone younger since available partners of the same age or of older age are less and less numerous.

Figure 12 presents the marital status of both partners in new couples. As we could expect, the never married men (and women respectively) are more likely to form a couple with an unmarried partner. Divorced are also more likely to form a new union with a divorced partner. This could be due to a cohort effect because of age similarity, there are more unmarried partners available of your age. However this could be due to a preference effect: people who do not marry at prime age may have unobserved characteristics (less traditional values) and look for a partner with the same unobserved characteristics, leading to serial cohabitation [START_REF] Lichter | National estimates of the rise in serial cohabitation[END_REF]. However, widowers and widows are more likely to form a couple with a divorcee than a widow, probably because of the preference for younger partners. Income homogamy We observe that when in the first decile (figure 13), the probability to form an union with someone belonging to the first decile is the most frequent. It is line with social (or educational) homogamy when the man or woman belongs to lowest deciles. Income homogamy is less pronounced in the third and fifth deciles. We observe however that contrary to women, men in these deciles are more likely to form an union with women with at most the same income situation. Women are more likely to be income hypergame, choosing a partner better positioned in the income distribution. From the 7th decile, we observe an increasing gradient of income homogamy for women, while it arrives later for men. It could be that men who decide to form an union may look more for housework complementaries and that income or human capital of the new partner play less, whereas for richer women, this is a criteria. More than 40% of women of the highest decile who form an union choose a partner in the same decile. Forming a couple for people over the age of 50 is practically the only way to improve their standard of living, since career opportunities diminish in age and especially during retirement. At the bottom of the distribution, probability to form a new union for men and women is close. But then, the pattern of the income effect is totally different. For men, we observe an increasing income gradient on the probability to form an union. Richer men are more likely to form a couple, especially when belonging to the last deciles. Having high incomes is valued on the marital market for men. For women, on the contrary, the probability to form an union is decreasing with income, in a very pronounced way on the second part of the income distribution. The highest-income women have the lowest probability to form an union. High incomes may also be valued on the marital market for women, but it is likely that women's intention to form a new couple at these ages is less pronounced. The persistence of an unequal division of domestic work and the potential for future informal caregiving may discourage them from doing so. They may then prefer to remain alone or in a non-resident couple relationship, especially when their individual income allows them to have an adequate standard of living. Indeed, [START_REF] Lewin | Intentions to live together among couples living apart: Differences by age and gender[END_REF] indicates that older women in LAT have lower intentions to live together than older men. A higher income enables women to remain single. The form of union chosen is crucial and potentially linked to different legal protection for the new partner. On the one hand, marrying may make the surviving spouse eligible for a survivor's pension. On the other hand, marrying may lead to lose the benefit of the survivor's pension for those already widows. This article shows that people aged 50 or over are sensitive to these financial aspects in their marital choices and we observed both effects. The level of income is positively correlated with the choice of contractualizing the union (immediately or after cohabitation). Marriage is particularly likely when the man has more resources than his partner. Widows are also less likely to remarry, probably to keep their survivor pension or because of they are opposed to remarriage [START_REF] Talbott | Older widows' attitudes towards men and remarriage[END_REF]. We also observe that marriage and Pacs are more likely in couples with differences in individual incomes, reflecting the advantage of having a jointly income taxation in these type of unions.

These results, focused on economic aspects, do not rule out that many other patterns are probably playing in the process of partnering or repartnering at old ages, such as norms, the reproving gaze of children (De Jong [START_REF] Jong Gierveld | Parents' partnership decision making after divorce or widowhood: The role of (step) children[END_REF], the wish to keep its residence and social network, health.... In that sense, the data used are not sufficient enough and this work appeals for richer data to study marital behaviours at old age. However the results emphasize that the monetary aspects are an important determinant in couple formation after 50.

A Descriptive statistics of people living alone at the beginning of 2015

Figure 1 .

 1 Figure 1. Sex-ratio at different ages

Figure 2 .

 2 Figure 2. Proportion of people by living arrangements, by age and sexe

Figure 3 .

 3 Figure 3. Population pyramid on January 1st, 2016 of Metropolitan France

Figure 4 .

 4 Figure 4. Probability of forming a union after age 50 according to gender

Figure 5 .

 5 Figure 5. Gender gap in repartnering chances in a more and more imbalanced marriage market

Figure 6 .

 6 Figure 6. Income gradient effect per sex on couple formation after 50

Figure 7 .

 7 Figure 7. Income gradient effect on couple formation after 50, according to age

Figure 10 .

 10 Figure 10. Proportion of contractual unions among new couple formation after 50 by age and sex

Figure 11 .

 11 Figure 11. Age disparity in the new couples and in the existing couples, by sex and age Men Women

Figure 12 .

 12 Figure 12. Marital status of the new partner, by sex and marital status Men Women

Figure 13 .

 13 Figure 13. Income decile of the new partner, by sex and income decile Men Women

Table 1 .

 1 Logit model of forming a union, all 50 and +, men and women Odds ratios are reported in the table. * p < 0.10, * * p < 0.05, * * * p < 0.01

			All		Men	Women
		OR	se	OR	se	OR	se
	Gender
	Men	1.623 * * * 0.009
	Women	1.000	.
	Marital status
	Never Married	1.000	.	1.000	.	1.000	.
	Divorced	1.539 * * * 0.009	1.591 * * * 0.013	1.359 * * * 0.012
	Widow(er)	0.840 * * * 0.009	1.048 * * * 0.018	0.708 * * * 0.010
	Income decile
	D1	0.936 * * * 0.013	0.856 * * * 0.017	1.050 * * 0.020
	D2	0.869 * * * 0.012	0.828 * * * 0.016	0.922 * * * 0.017
	D3	0.940 * * * 0.013	0.892 * * * 0.018	0.985	0.017
	D4	0.992	0.013	0.984	0.019	0.999	0.017
	D5	1.000	.	1.000	.	1.000	.
	D6	0.997	0.012	1.031 * 0.018	0.963 * * 0.016
	D7	0.975 * * 0.012	1.061 * * * 0.018	0.894 * * * 0.016
	D8	0.990	0.012	1.136 * * * 0.020	0.835 * * * 0.015
	D9	0.984	0.012	1.157 * * * 0.020	0.791 * * * 0.014
	D10	1.076 * * * 0.013	1.311 * * * 0.022	0.737 * * * 0.014
	Age
	50-59	1.585 * * * 0.013	1.382 * * * 0.016	1.918 * * * 0.023
	60-69	1.000	.	1.000	.	1.000	.
	70-79	0.510 * * * 0.006	0.590 * * * 0.010	0.443 * * * 0.008
	80-89	0.189 * * * 0.004	0.285 * * * 0.008	0.137 * * * 0.004
	90 and +	0.082 * * * 0.005	0.135 * * * 0.011	0.059 * * * 0.005
	Employment situation
	Wage earner	1.408 * * * 0.013	1.363 * * * 0.018	1.437 * * * 0.019
	Self-employed	1.443 * * * 0.021	1.503 * * * 0.028	1.447 * * * 0.036
	Unemployed	1.361 * * * 0.019	1.310 * * * 0.025	1.451 * * * 0.028
	Retired and others	1.000	.	1.000	.	1.000	.
	Housing tenure
	Owner	1.000	.	1.000	.	1.000	.
	Renter	1.468 * * * 0.009	1.435 * * * 0.013	1.487 * * * 0.014
	Social housing	0.885 * * * 0.007	0.962 * * * 0.011	0.809 * * * 0.009
	Family
	1 child 0-18	1.683 * * * 0.012	2.165 * * * 0.021	1.215 * * * 0.013
	1 dependent 18 and +	0.798 * * * 0.006	0.819 * * * 0.009	0.780 * * * 0.009
	1 parent	0.663 * * * 0.017	0.634 * * * 0.022	0.683 * * * 0.027
	Birth country
	France	1.000	.	1.000	.	1.000	.
	Europe	1.239 * * * 0.016	1.299 * * * 0.023	1.168 * * * 0.022
	Africa	1.047 * * * 0.011	1.213 * * * 0.016	0.860 * * * 0.014
	Others	1.112 * * * 0.022	1.146 * * * 0.031	1.049 * 0.029

Table 2 .

 2 Multinomial logit of union chosen the year of couple formation (individual income)

	(reference: cohabiting union)
				Men			Women
			Pacs	Marriage		Pacs	Marriage
		OR	se	OR	se	OR	se	OR	se
	Men's income decile
	D1	0.953	0.116	0.888	0.068	1.072	0.142	0.934	0.082
	D2	0.994	0.121	0.822 * * 0.064	0.899	0.125	0.894	0.077
	D3	1.047	0.130	0.867 * 0.070	1.128	0.148	0.804 * * 0.072
	D4	0.961	0.115	0.869 * 0.065	0.924	0.120	0.902	0.074
	D5	1.000	.	1.000	.	1.000	.	1.000	.
	D6	1.247 * * 0.130	1.042	0.070	1.312 * * 0.144	0.993	0.074
	D7	1.461 * * * 0.145	1.117 * 0.073	1.552 * * * 0.164	1.094	0.079
	D8	1.478 * * * 0.143	1.147 * * 0.073	1.486 * * * 0.155	1.152 * * 0.081
	D9	2.088 * * * 0.194	1.346 * * * 0.084	1.960 * * * 0.197	1.366 * * * 0.095
	D10	3.408 * * * 0.306	1.951 * * * 0.117	3.013 * * * 0.295	1.958 * * * 0.132
	Women's income decile
	D1	1.110	0.114	1.694 * * * 0.116	1.014	0.114	1.668 * * * 0.128
	D2	1.223 * * 0.112	1.626 * * * 0.101	1.042	0.106	1.600 * * * 0.113
	D3	1.140	0.104	1.393 * * * 0.088	0.908	0.092	1.347 * * * 0.096
	D4	1.057	0.093	1.140 * * 0.071	0.908	0.088	1.138 * 0.080
	D5	1.000	.	1.000	.	1.000	.	1.000	.
	D6	1.215 * * 0.098	1.002	0.062	1.129	0.099	1.026	0.072
	D7	1.282 * * * 0.104	1.065	0.066	1.078	0.096	1.035	0.073
	D8	1.386 * * * 0.110	1.029	0.064	1.236 * * 0.107	1.017	0.072
	D9	1.491 * * * 0.117	1.057	0.066	1.260 * * * 0.108	1.018	0.072
	D10	1.560 * * * 0.129	1.322 * * * 0.085	1.436 * * * 0.131	1.338 * * * 0.099
	Mean age of the partners
	<55	1.395 * * * 0.099	0.963	0.050	1.403 * * * 0.107	1.025	0.058
	55-59	1.058	0.073	1.019	0.050	1.120	0.080	1.003	0.051
	60-64	1.000	.	1.000	.	1.000	.	1.000	.
	65-69	0.995	0.087	1.068	0.066	1.083	0.096	1.091	0.069
	70-74	1.150	0.132	1.240 * * * 0.101	1.252 * 0.145	1.246 * * * 0.103
	75-79	1.112	0.167	1.265 * * 0.133	1.230	0.181	1.271 * * 0.133
	80-84	1.325	0.242	1.014	0.148	1.233	0.228	0.898	0.133
	>=85	0.982	0.286	0.646 * 0.165	0.862	0.241	0.417 * * * 0.114
	Difference of age
	W. older >10 years	1.179	0.168	0.918	0.102	1.278 * * * 0.111	0.948	0.068
	W. older 5-10 years	0.764 * * 0.081	0.697 * * * 0.055	0.806 * * * 0.062	0.674 * * * 0.042
	W. older 2-5 years	0.860 * 0.069	0.735 * * * 0.047	0.961	0.065	0.800 * * * 0.044
	Same age	1.000	.	1.000	.	1.000	.	1.000	.
	Men older 2-5 years	1.060	0.057	1.061	0.044	1.023	0.063	1.084 * 0.050
	Men older 5-10 years	1.098 * 0.059	1.243 * * * 0.050	1.011	0.071	1.270 * * * 0.063
	Men older >10 years	2.271 * * * 0.126	2.467 * * * 0.104	1.943 * * * 0.170	2.284 * * * 0.141
	Men's marital status
	Never Married	1.000	.	1.000	.	1.000	.	1.000	.
	Divorced	0.998	0.043	1.262 * * * 0.042	0.987	0.048	1.269 * * * 0.049
	Widower	0.798 * * * 0.064	1.281 * * * 0.072	0.798 * * * 0.068	1.214 * * * 0.075
	Women's marital status
	Never Married	1.000	.	1.000	.	1.000	.	1.000	.
	Divorced	1.164 * * * 0.049	1.287 * * * 0.041	1.190 * * * 0.059	1.327 * * * 0.051
	Widow	0.704 * * * 0.056	0.607 * * * 0.037	0.673 * * * 0.055	0.613 * * * 0.039

Odds ratios are reported in the table. * p < 0.10, * * p < 0.05, * * * p < 0.01

Table 3 .

 3 Multinomial logit of union chosen the year of couple formation with household's income and interaction between marital status (reference: cohabiting union)

				Men			Women
			Pacs	Marriage		Pacs	Marriage
		OR	se	OR	se	OR	se	OR	se
	Household's income
	decile
	D1	0.551 * * * 0.065	0.921	0.063	0.590 * * * 0.076	0.978	0.075
	D2	0.822	0.098	1.027	0.074	0.798 * 0.105	1.070	0.087
	D3	0.993	0.114	1.081	0.077	0.881	0.112	1.062	0.085
	D4	1.143	0.123	1.076	0.075	1.078	0.125	1.009	0.079
	D5	1.000	.	1.000	.	1.000	.	1.000	.
	D6	1.255 * * 0.123	1.012	0.066	1.290 * * 0.134	1.055	0.076
	D7	1.655 * * * 0.154	1.113 * 0.071	1.584 * * * 0.157	1.032	0.074
	D8	2.044 * * * 0.183	1.183 * * * 0.074	1.806 * * * 0.176	1.169 * * 0.082
	D9	2.745 * * * 0.239	1.367 * * * 0.084	2.485 * * * 0.234	1.364 * * * 0.094
	D10	3.930 * * * 0.338	1.888 * * * 0.113	3.287 * * * 0.311	1.863 * * * 0.127
	Women's share of income
	<40%	1.403 * * * 0.058	1.452 * * * 0.046	1.345 * * * 0.063	1.456 * * * 0.052
	40% to 60%	1.000	.	1.000	.	1.000	.	1.000	.
	>60%	1.218 * * * 0.067	0.991	0.042	1.188 * * * 0.072	0.971	0.047
	Men's marital status ×
	women's marital status
	Never Married-Never Married 1.000	.	1.000	.	1.000	.	1.000	.
	Never Married-Divorced	1.387 * * * 0.096	1.358 * * * 0.074	1.387 * * * 0.104	1.541 * * * 0.095
	Never Married-Widow	1.087	0.151	0.870	0.101	0.954	0.131	0.944	0.106
	Divorced-Never Married	1.191 * * * 0.076	1.308 * * * 0.065	1.257 * * * 0.104	1.520 * * * 0.101
	Divorced-Divorced	1.219 * * * 0.068	1.682 * * * 0.071	1.240 * * * 0.081	1.846 * * * 0.097
	Divorced-Widow	0.620 * * * 0.066	0.691 * * * 0.056	0.590 * * * 0.066	0.694 * * * 0.062
	Widower-Never Married	1.062	0.169	2.198 * * * 0.223	0.836	0.170	2.044 * * * 0.249
	Widower-Divorced	0.908	0.093	1.440 * * * 0.104	0.977	0.107	1.529 * * * 0.123
	Widower-Widow	0.618 * * * 0.089	0.737 * * * 0.080	0.622 * * * 0.091	0.848	0.095
	Number of observations		53,490			46,610
	Number of events	3,587	6,819	2,735	5,019

Table 4 .

 4 Multinomial logits on the type of union chosen among individuals already in a cohabiting partnership (reference: remaining in a cohabiting union)Odds ratios are reported in the table. * p < 0.10, * * p < 0.05, * * * p < 0.01

				Men			Women
			Pacs	Marriage		Pacs	Marriage
		OR	se	OR	se	OR	se	OR	se
	Household's income
	D1	0.512 * * * 0.033	0.776 * * * 0.032	0.604 * * * 0.042	0.830 * * * 0.039
	D2	0.840 * * * 0.051	0.908 * * 0.039	0.916	0.061	0.944	0.046
	D3	0.955	0.056	0.980	0.040	1.030	0.065	1.010	0.047
	D4	0.991	0.055	0.951	0.037	1.059	0.063	1.018	0.044
	D5	1.000	.	1.000	.	1.000	.	1.000	.
	D6	1.147 * * * 0.057	1.077 * * 0.038	1.175 * * * 0.064	1.127 * * * 0.044
	D7	1.385 * * * 0.066	1.134 * * * 0.039	1.424 * * * 0.074	1.172 * * * 0.045
	D8	1.657 * * * 0.077	1.236 * * * 0.042	1.679 * * * 0.086	1.274 * * * 0.049
	D9	2.097 * * * 0.095	1.287 * * * 0.044	2.167 * * * 0.108	1.296 * * * 0.050
	D10	2.504 * * * 0.114	1.424 * * * 0.050	2.461 * * * 0.126	1.435 * * * 0.057
	Women's share of income
	<40%	1.381 * * * 0.032	1.359 * * * 0.024	1.393 * * * 0.036	1.412 * * * 0.029
	40% to 60%	1.000	.	1.000	.	1.000	.	1.000	.
	>60%	1.328 * * * 0.041	0.993	0.025	1.264 * * * 0.043	0.994	0.028

Table 6 .

 6 Multinomial logit of union chosen the year of couple formation (additional effects of table 3 )(reference: cohabiting union)Odds ratios are reported in the table.

		Men Women
	Marital status
	Never Married	38.9	19.3
	Divorced	40.8	31.6		Men	Women
	Widow(er)	20.3	49.1	Housing tenure
	Income decile			Owner	60.5	61.3
	D1	10.1	6.6	Renter	23.5	18.2
	D2	8.3	8.6	Social housing	16.0	20.6
	D3	8.3	11.6	Coresident family
	D4	9.3	13.9	1 child 0-18	7.7	7.2
	D5	9.9	13.1	1 dependent 18 and +	14.9	14.0
	D6	10.9	11.4	1 parent	2.1	2.6
	D7	10.9	10.5	Birth country
	D8	10.6	9.5	France	87.4	87.0
	D9	10.8	8.9	Europe	4.3	4.7
	D10	11.0	5.9	Africa	7.0	6.9
	Age			Others	1.4	1.4
	50-59	40.8	25.0	Size or urban area
	60-69	30.0	25.2	Rural	19.0	14.7
	70-79	15.1	20.1	<15,000	6.3	6.2
	80-89	11.0	22.7	15,000-49,999	7.9	8.0
	90 and +	3.1	6.9	50,000-499,999	33.3	34.9
	Employment status			+500,000	33.5	36.3
	Wage-earner	32.5	22.7	Observations	2,669,139 5,333,362
	Self-employed	4.2	1.4
	Unemployed	5.1	2.6
	Retired and others	58.2	73.4

* p < 0.10, * * p < 0.05, * * * p < 0.01

At the implementation of survivor's pensions, only married couples were eligible to this benefit. Then, depending on the country, this benefit has been gradually extended to couples in a civil union. In

2018, survivor's pension is still reserved for married couples in Belgium, France, Greece, Ireland, Poland for instance(OECD, 2018)

In 2013, according to OECD (2016), among people in the 55-64 age range leaving paid employment, 41% of men (45% of women) retire, 10% (9% of women) apply for disability benefits, 26% (18%) become unemployed and 23% (28%) withdraw from the labour force.

For instance, married spouses, contrary to cohabiting partners, have the obligation/right to mutual support ("devoir d'assistance"). This obligation to support is extended to parents-in-law.

Pacs (Pacte civil de solidarité) is the French civil partnership created in 1999

In the private sector scheme and the self-employed scheme, widow's pensions are paid to surviving spouses or surviving former spouses aged at least 55, whose income is below a given threshold. The income taken into consideration is the survivor's personal income or that of the new household, whatever the type of the new union. For private sector employees, survivor's pensions from the compulsory complementary schemes Arrco (blue and white collar) and Agirc (white collar) are abolished in the case of remarriage of the widowed. The widowed has to be aged at least 55 for Arrco and

for Agirc. In the public sector, there is no age or income level condition. The survivor pension is suspended in case of forming a new household.

A high income level is also positively correlated with high life expectancy even for older people[START_REF] Blanpain | L'espérance de vie par niveau de vie : chez les hommes, 13 ans d'écart entre les plus aisés et les plus modestes[END_REF]). Oppenheimer's theory[START_REF] Oppenheimer | American marriage formation in the 1980s: How important was womens economic independence[END_REF] suggests that higher economic resources increase the likelihood of union formation. Furthermore, a partnership with someone with a high income level is expected to last longer and is therefore more appealing.

This database is named Fideli -Fichier Démographique des Individus et des Logements

Unmarried (or not pacsed) couples are not easy to identify in such administrative data due to the lack of precision on the family relationship between household members. For heterosexual couples, partners of the couples have been identified by the National Institute of Statistics and Economic Studies[START_REF] Insee | L'union libre et la variable LIEN FAMILIAL des données fiscales[END_REF] under some assumptions: two non married people living in the same dwelling are considered as a couple as long as they are of different sex, with a reasonable age gap and not with the same last name (to exclude coresidential siblings).

We exclude the French overseas territories

We could also have included those who were in couple at the beginning of 2015 but break-up a partnership either by dissolution or widowhood during 2015.

They can not be distinguished unfortunately. Some student can choose to be registered on parent's tax return during their studies period. Disabled or dependent co-resident adult children are in the same category.

We also performed alternative definitions of professional statuses allowing multi-status item (such as wage-earner and unemployed) taking into account up to three different types of income perceived during the year, and results remains the same but the risk of correlation with the income amount deciles is higher and the message was less clear.

To check the robustness of our results to the 50 years old threshold, we ran our regressions on two sub-populations selected on receiving labour income or not (this population is mainly composed of retirees). Our main results hold. Results are available upon request from the authors.

"LAT is more common among young people, those enrolled in higher education, people with liberal attitudes, highly educated people, and those who have previously cohabited or been married. Older people and divorced or widowed persons are more likely to choose LAT to maintain independence",[START_REF] Liefbroer | Why do intimate partners live apart? evidence on lat relationships across europe[END_REF]

These financial incentives are stronger for women than for men as the survivor's pension is more often a source of income for widows. Indeed, women have more interrupted careers and lower wages resulting in lower pensions at retirement. So the level of potential survivor's pension for men is reduced. Besides, in some retirement schemes, survivor's pension is means-tested and men have more often higher resources than women.

We can not completely rule out however that a type of cohabitation used to exist before being observed in the fiscal data (but was not visible in housing tax because each partner has still its own dwelling), but appears the year when contracting the marital or Pacs contract because partners are then obliged to pool their resources on a fiscal point of view.

In the initial sample, 73,272 men and 64,948 women form an union (Table1). Here, we consider people forming an union and with no missing information on income and occupational status for them and their partner. It reduces the sample size to respectively 53,490 men and 46,610 women

To test this hypothesis, we plan to analyze whether the risk of death is higher for those contracting a Pacs at very old age relatively to those not contracting.