Same-Sex Couples and Their Legalization in Europe: Laws and Numbers

We analyse same-sex partnership and family formation in Europe. We explore how the frequency of same-sex marriage or registered partnership can be associated to macro and micro factors and how parenting appears as a key determinant at both levels. We use the LawsAndFamilies Database, which includes both data on legal developments in family laws and statistical data on the legal recognition of same-sex couples, marriage and registered partnership for a large set of countries. We also use the French census and the Spanish household survey for specific purposes. We first determine crude rates of legal recognition for gay, lesbian and different-sex couples for nine European countries in the period 1980–2017. We second consider macro factors by measuring the impact of legal consequences attached to couples’ recognition on the frequency of same-sex marriage or registered partnering. We expect that the opening of parenting to same-sex couples will affect lesbian more than gay couples and result in more positive trends in women’s nuptiality. We finally explore micro factors related to the family structure expecting that the presence of children will work as an incentive to marry.


Introduction
There is an intimate and complex relationship between demography and law which has its roots in the very sources of population studies. Our discipline has indeed emerged from the act of compiling the two fundamental physiological events of birth and death in the civil or religious registers that attest to their legal and social recognition. We often even confuse the object of demography with what civil status allows us to study, thus including nuptiality, which is a purely social and legal phenomenon. Hence the recurrence of research on the relation between laws and numbers (or the evolution of laws and of numbers), which we briefly illustrate with elements borrowed from European social history.
Throughout the 1970s, a wave of divorce-law reform swept across Western Europe and was accompanied by an increase in the proportion of broken marriages, which was sometimes brutal from one year to the next and always more progressive over the wedding cohorts. These reforms "liberalized" access to divorce through a movement away from divorce-sanction, where marriage stability is an essential norm, in favour of a divorce-report, which only manages the consequences of the break decided by the spouses. The reduction in the ambition of the law makes it possible to keep the whole population in its reach. Statistical analysis showed that the increase in the number of divorces was the result of a complex process. A direct effect reflected distance, not between new and old laws, but between the practice of old laws and that of new laws. It was combined with a symbolic, indirect effect, where the change of reality reverberated with the change in representations of reality and could hardly distinguish broader cultural transformations related to the image of the couple and marriage (Commaille et al. 1983).
A quarter of a century later, the legal and statistical study of the forms of legalization offered to homosexual couples has confirmed both the complexity of the relationship between law and demography and the possibility of using it to reach the wellsprings of broad phenomena far beyond the behaviour of homosexuals alone with regard to marriage. In fact, the factors that encourage homosexual couples to legalize their union concern not only their own interests, measured by the extent of the rights opened by the new laws, but all forms of conjugality. More specifically, the factors that promote or discourage nuptiality, such as the respective weight given by the welfare state to the couple and the individual, or the legislator's desire to bring de facto situations closer to legal situations, are factors that affect all couples, whether homosexual or heterosexual (Festy 2006).
Both studies also showed the time needed to establish family institutions in the practice of populations. That is not new: according to Georges Duby, it took at least two centuries in the Middle Ages for the Catholic Church to impose marriage as a consecrated, clergy-controlled framework at the end of a long conflict in which the new order replaced an older one (Duby 1981).
In the Nordic countries, where the partnership laws offered an experience of several years in 2006, a gradual increase in the number of registered couples had begun to bring the behaviour of homosexual couples closer to that of heterosexuals. This increase was primarily the result of lesbians, whose registration frequency was lower in the first years of the law. With the passage of time, practices became established in the lives of couples without any change in the legislative framework (Festy 2006).
We resume the analysis of the marriage of same-sex couples in Europe, benefiting from 12 more years of statistical observation and an enriched analysis of the content of the laws. Over a prolonged period of time, we can now associate the evolution of the number of marriages with the dynamics of laws and not just a snapshot of them. The result is a deepening and questioning of the previous conclusions. The impressions we might have had initially will be submitted to a more systematic verification and measurement of the relationship between the consequences attached to same-sex legalization and the number of marriages or registered partnership.
However, the effect of the change in the legislative framework is only part of the explanation of marriage patterns of same-sex couples and the observed differences from opposite-sex couples. First, it is crucial to introduce a net measurement of nuptiality that relates the number of marriages to the actual number of couples in order to properly address the marriage propensity issue. We did it in 2006 for all the countries under study, but on the fragile basis of guessed estimates. We come back to the topic, focusing on a limited number of countries with sound, reliable data and we explore important elements that could explain marriage behaviour and the observed differences between same-sex and opposite sexcouples. On the one hand, there are the values that each couple attaches to the institution of marriage in a certain normative social framework. On the other hand, there are individual characteristics that are associated with a greater susceptibility to marriage. Finally, there are intermediate elements that could play on the first two and are, at the same time, variable throughout the life course. This is especially true of the relationship between the reproductive project and the project of the couple. The arrival of children, in relation to the existing kinship rights, can act as an encouragement for the marriage and consequently, couples without children would be less inclined to marriage. For this reason, we take into account the importance of the family dimension, and especially the presence of children, to better understand the different marriage rates between opposite-sex couples, gay couples and lesbian couples. Therefore, the comparative analysis of the crude marriage patterns across Europe in a context of legal change is complemented in this chapter by tentative efforts to disentangle two important drivers of marriage propensity. The French data, based on the annual rounds of census (2005)(2006)(2007)(2008)(2009)(2010)(2011)(2012)(2013)(2014)(2015)(2016)(2017), are introduced in the discussion of crude marriage rates; they exemplify how to switch from same-sex marriages to more meaningful and expressive nuptiality rates. In part IV, we introduce the presence of children as a driver of marriage to be controlled for when analysing partnership status. We then use the 2017 Spanish household survey data to explore the family determinants of marriage.

Trends in Marriage and Registered Partnership Frequency Throughout Europe
We use crude rates of marriage and/or registered partnership to compare levels and trends in union legalization in European countries that have opened possibilities of legal recognition to same-sex couples. We rely mostly on data collected and published by national statistical institutes.

Marriage Rates: Data and Indices
Traditionally, marriages are recorded administratively together with births and deaths and their statistics are generally published as "vital statistics". The extension to same-sex marriages hardly modifies the processing of statistical data, except for the details of tabulations, which are limited by small numbers (Festy 2007). It may take a couple of years before the process and publication of data on same-sex marriages become routine. Our collection of data was problematic only in Sweden, where the 2009 law characterized marriage as gender-neutral, thus abolishing any distinction between female, male and heterosexual marriages. Consequently, marriage statistics include the three types of marriages but do not identify them. Special requests had to be made to Statistics Sweden through our colleague Gunnar Andersson (Stockholm University).
The situation of registered partnership is much more diverse in the different countries. A few contrasting examples follow. In the Nordic region and the Netherlands, registered partnership was considered from the beginning as a near equivalent to marriage and the statistics were processed and published apart from those of marriage but along similar lines. In France, the procedure of "pacs" is very different from that of marriage, and so is the process followed by the data; the statistics are published by the Ministry of Justice instead of Insee and they do not benefit from the long tradition of vital statistics. In Germany, the conditions of registration vary from region to region and no statistics have ever been published at national level.
Apart from extreme cases like Germany, published data include minimum details with a distinction between male and female partnerships, which is enough for our purpose. Note that this form of registration in countries like France and the Netherlands also concerns heterosexual partners.
In some countries where marriage is open to same-sex couples, registered partnership is also an option for them. Our objective being the measurement of the frequency of union legalization, whatever its form, we should simultaneously consider data on marriage and registered partnership, with the risk of double-counting essentially couples who first registered their partnership and then transformed it into marriage. It would be necessary to identify these cases and subtract them from the total.
It is possible in France, where "pacs" that are dissolved in order to marry are counted yearly. Similarly, Statistics Sweden identifies among the married those who were previously registered. We could not obtain the same information for Belgium or the Netherlands and we had to restrict our measurement of legalization to marriage frequency, which probably underestimates legal recognition slightly.
One of our main objectives is not only the analysis of the frequency of homosexual marriage or registered partnership, but also the association of this frequency with the importance of legal consequences attached to marriage or registration. We will perform the measurement of this association through correlations between yearly statistical and juridical information for a group of countries where data are available in both domains. In other words, we retain for our analysis of frequencies the countries that also provide juridical data. We will detail the latter type of information later.
The question is apparently simple: among same-sex couples, what is the proportion of those who choose to legitimize their union through marriage or registered partnership? The answer implies numbers of marriages or registered partnerships as a numerator and numbers of gay and lesbian couples as a denominator. The former has been considered above; they are readily available, at least globally, without refined breakdowns. The latter are much more problematic, so that very few reliable estimates exist and still fewer time-series that would be necessary for the production of trends.
In most censuses or very large surveys, the number of same-sex couples is grossly overestimated due to errors in the declaration or coding of sex among the different-sex couples. Let us take this oversimplified example: homosexual couples are few while heterosexual couples are many, say 1000 against 100,000; errors about sex are rare, say that one of the partners makes an error in 1 p. 100 of couples. Among same-sex couples, 10 appear wrongly as heterosexual, which impacts very little the number of different-sex couples; among heterosexual couples, 1000 are wrongly classified as homosexual, which implies an overestimate of same-sex couples by a factor of 2 (Cortina and Festy 2014).
Amendments to the questionnaires or cross-checking sex with first names may eliminate the overestimate of same-sex couples. That has been the case in France where a series of reliable estimates have been provided yearly since 2010. We will use them at a later stage. Another solution is to rely on population registers instead of censuses or very large surveys; people are characterized by their civil status, including sex or gender, rather than being questioned about it; but similarly, they are not questioned about their relation to other persons in the household and the sexual nature of the relation must be guessed. That was done for the Netherlands once; it was not repeated, so no time-series can be calculated (Steenhof and Harmsen 2004).
For the geographical coverage to be wide and for the time-series to be as long as possible, we had to rely on simpler indices: crude rates that report numbers of marriages and/or registered partnerships to total population instead of the population directly exposed to risk (i.e., same-sex couples). More precisely, gay marriages and/ or registered partnerships are reported to total male population, and lesbian marriages and/or registered partnerships are reported to total female population.
The immediate meaning of crude rates is much more abstract than the meaning of refined rates, but we have good reasons to think that crude rates may provide a comparative view of levels and trends consistent with the comparative image that would be provided by refined rates. Countries we are dealing with are broadly similar in their demographic structure, for instance, in their degree of population aging, and we may suppose more generally that structural factors do not much affect comparisons based on crude rates. Nevertheless, we will develop the French case and will measure and compare trends in crude and refined rates for recent years below.
When the crude rates of a country are put on a graph for, say, 10 years, the first 2 or 3 years are generally much above any later trend. It is a classical "stock effect": couples who had been waiting for many years to legalize their union rush into the new law to get married or registered… at last! The overview of trends in Europe is much clearer when these early rates are omitted. This is the case with the graphs shown below.

Trends and Levels in Crude Marriage Rates
We have constructed graphs of yearly crude rates for male couples and for female couples; we have complemented our analysis by calculating sex ratios (crude rates for female couples/crude rates for male couples). Nine countries are considered; the Nordic countries are coloured in red (Finland, Norway, Sweden), the western countries in blue (Belgium, France, the Netherlands, the UK or rather England and Wales), the southern countries in green (Portugal, Slovenia). Note that the last group includes only two countries with short time-series; it will be difficult to draw firm conclusions.
Crude male rates are clearly lower in the north than in the west of Europe. Their increase-if any-is slow. Curves in the three countries are also remarkably intertwined, which points to regional homogeneity ( Fig. 3.1).
Rates are clearly higher in western countries and they are also much more diverse. In Belgium and the UK they are twice as high as the Nordic rates, while the Netherlands is in an intermediate position, which is closer to the Nordic group; in all these countries rates are stable. By contrast, crude male rates have risen a lot in France, they have more than doubled in a dozen of years, they are now much higher than anywhere else. In the most recent years, they are four times higher than in Norway or Sweden.
In southern Europe, rates are low: as low as in the north for Portugal, much lower in Slovenia. Time-series are too short to speak about stability (Portugal) or rise (Slovenia).
The graph for crude female rates differs neatly from the previous one for crude male rates ( Fig. 3.1).
In the Nordic countries, the rise is substantial and systematic. This is the case for the three countries, and the three curves are quite close: again, the region is homogeneous. The level is slightly lower than in Western Europe, but the distance between the two groups is much more limited for women than it is for men.  1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999  Among western countries, the relative homogeneity contrasts with the heterogeneity that characterized western male rates. France hardly differs from its neighbours, except for the most recent years, just after the introduction of marriage.
Crude female rates in the southern countries are clearly lower than anywhere else in Europe. The levels and shapes of the two curves for Portugal and Slovenia are quite similar.
The observations we considered counterintuitive for men are not visible for women: crude rates are increasing almost everywhere; rates in Nordic countries are hardly lower than those in Western Europe; France does not differ substantially from its neighbours.
The contrast between male and female crude rates is magnified by the calculation and graphical representation of sex ratios (crude female rate/crude male rate). The ratio is 1 when crude rates are equal for men and women; it is below 1 when female rates are inferior to male rates; it is over 1 when female rates are superior to male rates. There is a global movement of increase in sex ratios throughout Europe ( Fig. 3.2).
In Nordic countries, ratios move rapidly from below 1 (.6 in the late 1990s) to over 1 (more than 1.6 in the 2010s). The increase is spectacular: Finnish ratios are  1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999  In Western Europe, ratios have increased much more slowly; they are also more dispersed, over 1 in the Netherlands (1.2 in 2017), under 1 in France (.8 recently), around 1 in Belgium and the UK (in fact, England and Wales).
Ratios are still lower in Portugal, despite their increase. Numbers are so small in Slovenia for gays and lesbians that their ratios are erratic.
There are huge differentials through time in Nordic countries (multiplication by 3 in less than two decades) and large gaps between countries in north, west and south of Europe. Sex ratio is a factor associated to such a large heterogeneity in time and space.

Discussion
The progressive adoption of laws opening registration of partnership or marriage to same-sex couples in Nordic, and then western and southern countries (with a few exceptions like the early recognition of marriage in Spain) suggests similarities with the second demographic transition and the development of informal cohabitation as an alternative to marriage. The theory interprets the emergence of cohabitation as the consequence of a cultural reaction against traditional male breadwinner marriages (Lesthaeghe and van de Kaa 1986).
But instead of stability in a number of countries, one would have expected a gradual increase in the popularity of same-sex marriage or registered partnership everywhere, in conformity with processes of diffusion of social innovations, generally adopted first by a small minority of well-informed activists and then extended to larger circles by imitation (Nazio and Blossfeld 2003;Di Giulio and Rosina 2007). This process seems to have been, at best, unsystematic in terms of the adoption of marriage by gay and lesbian couples in each country.
More generally, it is somewhat paradoxical to compare trends and levels in samesex marriage to those in cohabitation, an alternative to different-sex marriage. It might be more appropriate to refer same-sex to different-sex marriages. The latter offer a longer time perspective than the former for obvious reasons. Our graph starts in 1980 and evidences a global decline of heterosexual nuptiality. It is one of the main symptoms of the second demographic transition.
The decline in nuptiality together with the introduction of same-sex registered partnership has pushed a polemist to announce the end of marriage as a consequence of the legalization of gay and lesbian unions (Stanley Kurtz). But differentsex marriage rates had started decreasing well before the legal formalisation of homosexual couples, a movement initiated by Denmark in 1989. We cannot even discern an acceleration in nuptiality decline. On the contrary, crude rates in Nordic countries have gone through a remarkable reversal of trend at the end of the twentieth century, so that an unexpected rise in heterosexual nuptiality parallels the slow increase in gay marriage rates and the more rapid movement in lesbian marriages. Some analysts interpret it as a spiritual revival that temporarily contradicts the theory behind the second demographic transition.
But this is only an exception. In general, same-sex and different-sex marriage evolve in opposite directions ( Fig. 3.3). The correlation with gay marriage rates is negative (r = −0,36); with lesbian marriage rates it is close to zero (r = −0,12). The absence of positive correlation between trends and levels in same-sex and differentsex marriage rates suggests that factors classically associated with the second demographic transition are not relevant for a contextual explanation of homosexual marriage rates in Europe. We will have a look at other contextual factors in the discussion of part 3.2.
France is the country with the largest increase in crude marriage rates for gays as well as lesbians. Male crude rates experience a rise from 0.1 p.1000 in 2005 to more than twice as much in 2017. Female rates follow the same pattern, but at lower levels, from 0.06 to 0.17. The gap between men and women is gradually reduced. The trend is steeper in France than anywhere else in Europe. Note a temporary decrease in 2011-2012, just  1 9 8 0 1 9 8 1 1 9 8 2 1 9 8 3 1 9 8 4 1 9 8 5 1 9 8 6 1 9 8 7 1 9 8 8 1 9 8 9 1 9 9 0 1 9 9 1 1 9 9 2 1 9 9 3 1 9 9 4 1 9 9 5 1 9 9 6 1 9 9 7 1 9 9 8 1 9 9 9 2 0 0 0 2 0 0 1 2 0 0 2 2 0 0 3 2 0 0 4 2 0 0 5 2 0 0 6 2 0 0 7 2 0 0 8 2 0 0 9 2 0 1 0 2 0 1 1 2 0 1 2 2 0 1 3 2 0 1 4 2 0 1 5 2 0 1 6 2 0 1 7 Fig. 3.3 Crude marriage rates, Europe 1980Europe -2017 Source: own calculation from marriage records and population statistics reflect a waiting behaviour of couples who preferred to run directly into marriage in 2013 rather than "pacsing" first in 2011-2012 and then switching to marriage. It may also result from a temporary deterioration of pacs registration when the procedure is partly transferred from courts to notaries. Trends in crude rates can be due to changes in the number of gay and lesbian couples or to changes in the frequency of "marriage" among these couples. E.g., a rise in crude MM rates may result from an intensification in the formation of gay couples or an increase in the proportion of couples who legitimize their union. The disentangling of the two dimensions is only possible if reliable estimates of the numbers of gay and lesbian couples are available periodically, in the best case on a yearly basis. It is the case in France thanks to the annual rounds of census, despite classical pitfalls in this kind of data, mainly faulty declarations of sex by heterosexual couples. The number of "true" couples has been reconstituted since 2010 through the use of first names. The comparison of "true" couples and "appar- Refined rates can be calculated and compared to crude rates. They tell a different story. From 2005 to 2017, there is hardly any rise in male rates, which went from .89 to .92, except for temporary ups and downs. The increase is slightly more important in female rates, which went from 0.89 to 1.10 and, more noticeably the frequency of lesbian marriages is continuously higher than that of gays and the gap increases between the two (Fig. 3.4).
In other words, the marked increase in French crude rates must be attributed to a rise in gay and lesbian couple formation, not to an intensification of nuptiality among these couples. Higher crude rates for men than women, sex ratios below 1, must be attributed to more numerous couples among gays than lesbians, not to the more intense nuptiality of gay couples. These conclusions, although limited to one country, will be on our mind when we interpret the association of trends and levels in crude rates with legal variables.
Referring marriages to couples opens the way to comparisons between same-sex and different-sex nuptiality. We concentrate on France in 2011, when a large survey was associated with the yearly census so as to give reliable information on couples, same-sex as well as different-sex; cohabiting and living apart partners are enumerated together (Buisson and Lapinte 2013).
A large majority of heterosexual couples were married or pacsed (77%), as compared with a minority of homosexual couples, only 47% of gay couples and 38% of lesbian couples were pacsed.
That may give the impression that different-sex couples legalize their union more frequently than same-sex. But this observation is misleading, essentially because heterosexuals have a longer history behind them, with more opportunities to marry or pacs than homosexuals.
A fair view of the propensity to pacs or marry is obtained by relating pacs or marriages in a given year (2011) to the number of unmarried and unpacsed couples, different-sex and same-sex being equally "exposed to the risk of legalization". In these circumstances, specific rates are higher for homosexuals than heterosexuals, although the latter have the possibility to pacs OR marry while homosexuals are only entitled to pacs. Specific rates are almost similar for unpacsed gay and lesbian couples (respectively .133 and .131) and somewhat above specific rates for unpacsed and unmarried heterosexual couples (.098).
The French case brings two elements into the discussion: couples' nuptiality plays little role in the development of same-sex crude marriage rates and it is much higher than heterosexual nuptiality. These observations cannot be extended to other countries-France is also characterized by very high crude marriage rates, especially among gays-but they do confirm that trends and levels in same-sex and different-sex marriage depend on different determinants and react independently of one another. In particular, the factors associated with the second demographic transition, which are closely related to Ron Inglehart's concept of "post-materialism", are relevant for heterosexual marriage decline, but are probably useless to explain homosexual nuptiality.

Trends in Legal Consequences Attached to Marriage or Registered Partnership
Legal recognition of same-sex couples opens up legal consequences inferior or equal to consequences opened up by heterosexual marriage. Here we measure positive legal consequences and establish their levels and trends in the same 9 countries to which we referred in the first part. We then try to answer this question: Is the frequency of same-sex legal recognition correlated with the level of legal consequences attached to recognition?

On Legal Scores
In the LawsAndFamilies Database 60 questions have been addressed to legal experts in each European country about possible consequences attached to each conjugal form (marriage, registered partnership or cohabitation, same-sex or different-sex). E.g., "Can a relationship of this type result in lower income tax than for two individuals without a partner?" or "Does a relationship of this type make it easier for a foreign partner to obtain citizenship?" Here we use the 25 questions about positive legal consequences that were selected by Waaldijk (2017). In the Database, the answers given by the legal experts were coded by them as "Yes", "Yes but with restrictions", "No except in some cases" or "No" (Waaldijk et al. 2017). Here these answer codes are numbered respectively 3, 2, 1 and 0. Global scores for several questions result from additions. Global scores for same-sex forms are compared with global scores for different-sex marriages. The index is 1 if homosexual couples get as high a score as married heterosexuals; it is below 1 if legal consequences attached to same-sex registered partnership or marriage are inferior to those attached to different-sex marriage. For each country, every year we retain the score obtained by the most positive same-sex status available at that moment. It implies switching from one status to the other when a new conjugal format is introduced, e.g., from registered partnership to marriage when same-sex marriage becomes possible and offers couples new advantages.

Trends and Levels of Legal Scores
In every country the global score increases over time: legal consequences attached to the best status offered to same-sex couples are gradually enlarged and look more and more like those attached to heterosexual marriage. For instance in Norway and Sweden, the early introduction of registered partnership offers homosexual couples at least 80% of rights associated with different-sex marriage; that score is later improved when the country moves to same-sex marriage (Norway 2009) or even before, through reform of registered partnership (Sweden). Very recently, the index culminates over 96% in Norway and over 98% in Sweden. Finland has experienced the same kind of trajectory but has reached "only" 89% ( Fig. 3.5).
Western countries are more dispersed. In the Netherlands, registered partnership and then marriage have immediately offered same-sex couples 95% of the rights granted to married heterosexuals and the percentage has even risen to 100% since 2014. At the other extreme, pacs in France opened to same-sex couples less than 60% of legal consequences attached to heterosexual marriage; only the opening of marriage to homosexual couples in 2013 brought that percentage to 90%. Belgium and the UK are in intermediate positions but have recently reached percentages that are very close (UK) or even equal (Belgium) to 1.
Southern countries lag well behind: their short histories culminate at relatively low levels (Portugal 80%; Slovenia 65%).
In brief, Nordic countries like Norway or Sweden open the way to a continuous enlargement of rights offered to same-sex couples; some western countries like the Netherlands accompany the movement while others, like France, follow it with a delay; southern countries lag far behind. Similarities between trends and levels in marriage rates on one hand and in legal indices on the other hand suggest the existence of a relationship between them. Dissimilarities point to no relationship.
Curves of male rates differ radically from those for legal consequences: stability in most curves instead of a systematic rise, a low level in Nordic countries compared to western countries instead of the reverse. By contrast, there are marked similarities between trends and levels in legal rights and sex ratios: all the curves increase, Nordic countries come first followed by western countries while southern Europe lags behind. There are also common traits for curves of lesbian rates, but these are less clear.
The calculation of coefficients of correlation through the ordinary least square (OLS) method confirms the visual impressions. Correlation is null with frequencies of gay marriage (.01), moderate with lesbian marriages (.34) and stronger with sex ratios (.49).
To better understand the meaning of any relationship between marriage rates and legal consequences attached to same-sex marriage, we have divided the latter into subgroups (material consequences, parenting, migration, other non-material consequences) and we have calculated scores following the same procedure as previously, with the consequences attached to heterosexual marriage as a reference. The first two subgroups offer the most illustrative results (Table 3.1).
The path followed by material consequences is very different from that previously described for all legal consequences. In all the Nordic countries but also in the Netherlands and Portugal, same-sex marriage or registered partnership offers the same material advantages as different-sex marriage as soon as union legalization becomes possible. Only Belgium, France, the UK and Slovenia evidence a progressive enlargement of material consequences opened to same-sex couples. For instance, in France, consequences attached to pacs were initially very restrictive; they were then enlarged and finally marriage put same-sex and different-sex couples on a par (Fig. 3.6).
This image of material consequences is also very different from those of rates and sex ratios. Coefficients of correlation are close to zero for women; they are negative for men (gay marriages are infrequent in the Nordic countries despite "generous" material rights); they are moderate for sex ratios.
On the contrary, parenting consequences have some similarities with all consequences. The major difference is the much lower initial level, even in pioneering countries like Norway or Sweden, but also in Belgium or France; it is followed by ample movements of aggiornamento that bring same-sex couples closer to heterosexual couples. Sweden's position in the forefront has been recently challenged by western countries like Belgium, the Netherlands and the UK, and, even more recently, by Portugal in the south. Coefficients of correlation are clearly higher than those previously measured on all legal consequences. They remain weak for men (.13), but substantial for women (.53) and sex ratios (.59). The distance between gays and lesbians is important once again and is well summarized by the association of parenting consequences and sex ratios.
The coefficients measure the distance between bunches of curves characterized by trends and levels of national rates and scores. We emphasize comparisons of levels by focusing on a short period of time: 2011-2015. The correlation between parenting and sex ratios is slightly reduced (.53 instead of .59). The emphasis is put on time trends if we focus on specific groups of countries, e.g. northern or western. This time, the correlation is markedly increased: it is .71 or .81 respectively.
The distance between frequencies of gay and lesbian marriages is associated with parenting issues more than with other dimensions of the law. The enlargement of consequences attached to marriage in each country plays a more decisive role than differences between countries in the openness of national laws. In other words, the dynamics of laws in various countries on aspects of parenting is associated with the dynamics of lesbian marriages, not with those of gay marriages. This is reflected in a common movement towards increased sex ratios at various levels.
Let us first remind the reader that our analysis relies on country-level information on the content and consequences of laws and the number and rates of marriages, not on individual-level data. The second reminder is that both variables-legal scores and rates-are dated, so that a dynamic process is captured, not a static snapshot. The results must be read this way: lesbian marriage rates are higher, and their rise is steeper in countries where the legal consequences attached to marriage are broader and their development more rapid. There is no such association for gays. Among the different domains covered by marriage laws, those concerning parenting are essentially responsible for this divergence between women and men. The other domains are not relevant.
In a context of continuous enlargement of legal consequences attached to gay and lesbian marriages, the divergent trends among men and women result in an increase of sex ratios, which tend towards the dominance of female over male marriages. As homosexual and heterosexual marriages gradually open to similar consequences, in particular for parenting, sex ratios will tend to a limit; they appear to do so in the most advanced countries, the Nordic ones. It will be important to check whether lesbian couples are far more numerous than gay couples or if women in couples legalize their union more often than gay couples.

Discussion
The results presented so far confirm and add precision to those we had obtained previously. They confirm that the impact of legislation on marriage rates has its origin in parenting dimensions of the laws and essentially concerns women. They are more precise because they rely on longer time-series of marriage rates associated with an innovative analysis of the dynamics of law content, which makes possible a correlation between two processes rather than between two snapshots: levels and trends in marriage rates together with levels and trends in law variables.
It has been possible to show that the impact of changes in laws was reflected with no delay in changes in marriage rates. This is true even after the very first years after the introduction of registered partnership or marriage were eliminated, when couples who were expecting that the law would be passed rushed into it. Further legal changes create a similar, though less spectacular movement.
However, the French case, which is developed above, suggests a caveat: an increase in crude marriage rates may be due not only to more marriages among existing same-sex couples, but also to an acceleration in the formation of new couples. An extension of consequences attached to registered partnership or marriage may incentivize same-sex partners to come out and live together, in particular lesbian partners.
The association of levels and trends in crude marriage rates and legal content in a number of countries is a direct application of Durkheim's "sociological method", which is based on (international) comparisons and the analysis of "variations concomitantes": "nous n'avons qu'un moyen de démontrer qu'un phénomène est cause d'un autre, c'est de comparer les cas où ils sont simultanément présents ou absents et de chercher si les variations qu'ils présentent dans ces différentes combinaisons de circonstances témoignent que l'un dépend de l'autre." (Durkheim 1894).
Here we have established that female marriage rates are higher in countries that grant more parental facilities, which is a relationship between macro data. It raises two questions: Can we take it for granted that the content of the law influences the number of marriages or do we need to identify a third variable that simultaneously impacts the extent of the laws concerning parenting? And if we fail on the latter issue, can we switch from a macro to a micro formulation and evidence that parents marry more frequently?
For instance, we may assume and can check whether women's empowerment could have contributed to the adoption of laws favouring homoparenting and if it can be associated with the increase in the female marriage rate. Some researchers have assumed that the societies which are the most advanced in their movement towards gender equality benefited from an increase in fertility that contradicted the fertility decline dimension of the second demographic transition. This movement has some similarities with the recent increase in crude different-sex marriage rate in the Nordic countries described above (Myrskylä et al. 2009(Myrskylä et al. , 2011. We measure gender equality through the Women's Political Empowerment Index (WPEI), which is based on yearly information concerning women's civil liberties, civil society participation and political participation, which offers long series of data for the 9 countries we examine. It was used recently to challenge Myrskylä's hypothesis (Kolk 2019;Sundström et al. 2017).
The coefficients of correlation do not confirm the assumption: WPEI is neither associated with the parenting index (r = −0,31) nor with female marriage crude rates (r = −19). We are left with the other assumption: in the next section, we will see whether higher rates in parent-friendly countries imply that same-sex parents do marry more frequently than non-parents.

Parenting and Same-Sex Nuptiality
The sociology of the family has done a good job of establishing the patterns and trends of non-marital cohabitation in Western societies (Kiernan 2001). The diffusion of unmarried couples and the normalization of having children outside marriage are related to the diversity of cohabitation typologies and to the complementarity of several profiles of cohabiters. These profiles range from young cohabiters who understand cohabitation as a trial period before marriage and exclude childbearing from their partnership project to older cohabiters who understand their partnership as a stable and committed relationship and whose fertility intentions do not differ significantly from those of married spouses (Hekel and Castro-Martín 2014). The differences in the stability and risk of union dissolution of marriages and cohabitations have also been explored (Axinn and Thornton 1992). Recent evidence has indicated that dissolution rates are higher for same-sex cohabitations than for different-sex cohabitations and marital unions but that the demographic determinants of union stability are rather similar among the different types of couples (Lau 2012;Manning et al. 2016).
Scholars have also more recently considered the reasons for getting married in contexts in which cohabitation is widespread and increasingly similar to marriage in terms of the rights accorded to the partners (Manning and Smock 1995). While some outline the importance of feelings (Billari and Liefbroer 2016), others refer to more material dimensions, such as class or socio-economic status (Manning and Smock 1995).
Interestingly enough, some researches based on qualitative evidence have tried to explore the specificities of the incentives for and barriers to same-sex marriage (Pichardo 2011). The list of potential factors operating as incentives includes: (i) considering marriage to be an act of activism; (ii) marriage as an asset protection; (iii) protection in case of the death of one of the members of the couple; (iv) adoption of children of one of the spouses by the other; (v) regularization of the immigrant spouse for social recognition for the couple relationship. In contrast, the barriers to marriage might be associated with (i) the social rejection that condemns discretion; (ii) the intent to adopt from abroad, where it is easier for a single person than for a homosexual couple; (iii) values that are antithetical to marriage, considering it a patriarchal and non-egalitarian institution with religious connotations.
The need to better understand the family-related attitudes and expectations of gays and lesbians emerges from this list of incentives and barriers. A recent study that uses German survey data shows that gays and lesbians expect fewer benefits and greater costs of being in a partnership than heterosexuals but at the same time they do not find differences in the expectations about parenthood according to sexual orientation. The authors think that same-sex parenthood attitudes might be affected by the fact that same-sex parenting is still not that common and that heteronormative values are more determinant than experience (Hank and Wetzel 2018).
Our main goal here is to do a nuptiality analysis and to explore the main individual and family determinants of marriage by comparing same-sex and oppositesex couples. Building on the assumption that fertility levels and family structure differ considerably between these two types of couples, we are specifically interested in analysing whether the higher or lower presence of children in the household (either the progeny of the two partners or children from previous relationships) is associated with the partnership status of the different types of couples.

Same-Sex and Opposite-Sex Nuptiality in Spain
In order to carry out a comparative analysis of the nuptiality of same-sex and opposite-sex couples, we selected the Spanish case and we use data from 2017, which means 12 years after same-sex marriage was legal in Spain in 2005. We think that such a period is long enough to address the issue of the impact of rights expansion such as marriage and parenting on demographic behaviours. In addition to this wide period of observation with the marital option available, the choice of the Spanish case is also related to the dramatic transformation of family dynamics and attitudes towards family change. Specifically, union formation patterns have changed in Spain through the diffusion of non-marital cohabitation as a regular path to family formation (Domínguez-Folgueras and Castro-Martín 2013).
Spain offers statistical sources of exceptional value for studying same-sex families, namely the last two population censuses, those of 2001 and 2011. These make it possible to identify and recount same-sex couples who live in the same household and who are self-identified as spouses. These sources are now updated through a large Household Survey (Encuesta Continua de Hogares) which has been implemented annually since 2014 by the Spanish Statistical Institute (INE). For 2017, which is the last year available, the total sample size of the survey was 259.628 individuals, out of which 806 have a partner of the same sex. Unfortunately, Spain does not have a unique and centralized register of partnerships, which implies that the analysis cannot be expanded to registered partnerships and has to be limited to unions formalized through marriage.
The primary variable of interest in our analysis is the type of couple based on the gender of the spouses: opposite sex, same sex male (two men), same sex female (two women); this information is obtained via reciprocal identification of the spouse or partner from the members of the household. This system is not free from problems, given that an incorrect declaration of the gender of the household members may affect the identification of the couples (O'Connell and Feliz 2011). The second relevant variable for the analysis is the partnership status: married or unmarried. An important characteristic of the household (family structure) is also considered: the presence of children. In our analysis, we also control for some individual demographic characteristics of the partners (age and educational level) and additional characteristics of the couples.
As shown in Table 3.2, the proportion of married couples clearly differs by type of union. In 2017 in Spain 14% of the total opposite-sex couples were cohabiting outside marriage while this proportion was around 45% for same-sex couples. These crude proportions are obviously affected by the socio-demographic composition and therefore we ran a logistic regression analysis to explore the probability of cohabiting outside marriage. One of the main reasons to do so is the remarkable difference in the family structures of each type of couple. As shown in Table 3.3, the large majority of opposite-sex couples of all ages have co-residing children (either common or not common, that is, coming from previous relationships and thus form-  (Andersson et al. 2006). The results of the logistic regression indicate that the probability of cohabiting outside marriage is 5 times greater for same-sex couples as opposed to opposite sex couples (Table 3.4). When controlling for the characteristics of the couples which have been found to be positively associated with marriage (especially the presence of children in the household), the relationship of the probability is reduced by more than half: 2 times greater for both men and women. These results are in line with previous analysis conducted with the 2011 census (Cortina 2016), where the probabilities of cohabitation were higher (around 4 in the bivariate and around 3-4 in the multivariate), which is to be expected because marriage had been an option for a shorter period at that time.
If we analyse the individual and family determinants in detail (Table 3.5. and Fig. 3.7), we observe that the probability of being married increases with age and is higher for those partners holding a university degree, while it decreases when the two spouses have different citizenships (Table 3.5). Once these individual and couple characteristics are taken into account, the effect of family composition (having children or not) in interaction with the type of couple emerges as a key factor. As the margins plot clearly shows (Fig. 3.7), when the couple does not have children, the likelihood of being married is clearly higher for opposite-sex couples than for samesex couples. However, when they have children there is no significant difference. The same predicted probabilities also indicate that there are no differences between gays and lesbians.
The analysis of the partnership status of the same-sex couples compared to the opposite-sex ones offers two major conclusions: (1) same-sex couples marry less due to a compositional issue: they have fewer children and couples without children are less likely to be married or more likely to cohabit; (2) when couples have chil- dren the probability of being married does not differ from same-sex and oppositesex couples. Even if these results refer only to the Spanish case, we can infer without risk that family structure matters when it comes to formalizing partnerships and that the compositional effect of having lower fertility rates partially explains the lower marriage/registration rates of same-sex couples. For the same reason, it could explain the recent increase of lesbian crude marriage rates across Europe observed in the previous sections.

Discussion
Nuptiality and fertility patterns have always been connected. Traditionally, marriage was the earlier step and the necessary condition for childbearing. As we have discussed above, the relationship between these events has been substantially altered in recent decades. We could even argue that now parenthood often works as a deter- This new reality of family sociology helps us to understand same-sex nuptiality. As long as the fertility patterns of same-sex couples are lower than those of opposite-sex couples, their nuptiality rates might also stay low. The fact that the proportion of parents is lower for lesbians and especially for gays might also imply that their attitudes and expectations about marriage are different and less favourable to marriage. In this direction, Hank and Wetzel (2018) argue that "accounting for individuals' expectations might contribute to better explaining why, for example, marriage-like partnerships and cohabitation are less frequent in gay and lesbian couples than in heterosexual couples".
Considering the role of parenthood raises new questions for the future: if samesex family formation changes and its fertility rates increase, having more couples living with common children (and not for the most part children who were born to previous couples) might incline these parent couples towards marriage and at the same time might also modify the attitudes towards marriage of childless same-sex couples.

Conclusion
The frequency of same-sex marriage or registered partnership can be associated through statistical analysis with macro as well as micro factors. At both levels parenting appears as one of the key determinants. At the societal level, we rely on international comparisons. In different countries, the content of the laws organizing access to marriage or registered partnership is associated with the frequency of union legalization, at least for women, not for men. In particular it is the case when countries enlarge the consequences attached to legal recognition in the domain of parenting. The result is an increase in the frequency of lesbian marriages while gay marriages tend to stagnate. The other consequences attached to legalization have no such impact.
At the micro level, we take advantage of the diversity of individual situations to compare nuptiality among homosexual and heterosexual couples, all other things being equal. We show that in Spain gay and lesbian couples marry less than differentsex couples but that this difference is substantially smaller when they have children. That confirms the importance of parenting in the decision of homosexuals to marry, but there are strict limits to the explanation given the low proportion of lesbian couples with children and the still lower proportion among gay couples.
For a more encompassing analytical framework it is tempting to treat the introduction of same-sex marriage as one of the various forms of union diversification that characterizes the second demographic transition, and to consider the factors associated with the latter as relevant for a global explanation of trends and levels in same-sex marriage. Our efforts in this direction have not been successful. That suggests to us that the second demographic transition does not constitute a comprehensive framework for the understanding of homosexual marriages.
Nevertheless, the comparison of attitudes, expectations and behaviours of samesex and different-sex couples regarding marriage and parenthood is the most promising avenue to investigate. Homosexual nuptiality is a recent innovation and the evidence accumulated is still scanty: we need more data to explore its determinants. Waaldijk, K. (2017). Introduction to the legal survey and its methods & Overview of the results from the legal survey & Conclusion. In K. Waaldijk (Ed.), More and more together: Legal family formats for same-sex and different-sex couples in European countries -Comparative analysis of data in the LawsAndFamilies database, (pp. 7-72, 151-181, FamiliesAndSocieties working paper 75 (2017)). Waaldijk, K., Digoix, M., Nikolina, N., Zago, G., Damonzé, D., Caporali, A., & Nait Abdellah, K. (Eds.). (2017). The LawsAndFamilies database -Aspects of legal family formats for same-sex and different-sex couples. Paris: INED. http://www.LawsAndFamilies.eu.
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