## Abstract

It has long been debated how legalizing same-sex marriage would affect (different-sex) family formation. In this article, I use data on OECD member countries for the period 1980–2009 to examine the effects of the legal recognition of same-sex couples (through marriage or an alternative institution) on different-sex marriage, divorce, and extramarital births. Estimates from difference-in-difference models indicate that the introduction of same-sex marriage or of alternative institutions has no negative effects on family formation. These findings are robust to a multitude of specification checks, including the construction of counterfactuals using the synthetic control method. In addition, the country-by-country case studies provide evidence of homogeneity of the estimated effects.

## Introduction

An issue often discussed in the debates on the legal recognition of same-sex couples, either via same-sex marriage or civil unions, is whether there would be an effect on the value of marriage and generally on family formation. One concern is that same-sex marriage and possibly any other form of legal recognition of same-sex couples (such as domestic partnerships or civil unions) would encourage alternative family forms, such as cohabitation or single parenthood. This in turn would lead to fewer marriages, more extramarital births, and possibly more divorces. Several recent laws were at least partly justified using this argument, the most prominent ones being state constitution amendments such as Proposition 8 in California or the Defense of Marriage Acts, both representing legislation preventing federal or state governments from recognizing same-sex marriages.1

However, the effect of legalizing same-sex marriage (SSM) or same-sex civil unions or registered partnerships (SSRP) on family formation is theoretically unclear. On the one hand, SSM and SSRP laws could lead to “less traditional” family forms if they change social norms toward a “deinstitutionalization of marriage,” effectively reducing the social stigma associated with cohabitation and other alternative family forms (Cherlin 2004; Kurtz 2004). On the other hand, legal recognition of same-sex couples could induce the formation of more “traditional” families if it reignites the interest in marriage or if it reduces the pressure on government and employers to provide benefits to cohabiting couples (Lauer and Yodanis 2010; Rauch 2004; Safire 2003).2 In this article, I attempt to provide causal estimates of the effects of the introduction of SSM and of SSRP on family formation.

Recently, a small but growing body of academic research aims to assess some of the presumed consequences of legally recognizing same-sex couples, including claims made in the same-sex marriage debate. For instance, Alm et al. (2000) estimated the increase in federal income tax revenue due to legalizing same-sex marriage. A few studies have examined the welfare of children raised by same-sex couples compared with children raised by heterosexual couples. Rosenfeld (2010) found similar progress in school for both types of family structures, but Allen and colleagues (Allen 2013; Allen et al. 2013) argued that children in same-sex families fare worse. Most related to the current research, there have been only three attempts to estimate the causal effects of SSM or SSRP laws on family formation.

Langbein and Yost (2009) used state-level data from 1990, 2000, and 2004 on several indicators of family formation: the marriage rate, the divorce rate, the abortion rate, the extramarital birth rate, and the percentage of female-headed households. In all cases, they found no negative effects of granting marriage-like rights for same-sex couples on family formation and no positive effects of SSM bans. A limitation of this study is that the effects are identified by a small number of observations because of the lack of variation in SSM and SSRP laws during this period. In addition, the small number of SSM and SSRP laws also prevents the authors from separating the effects of SSM from the effects of SSRP.

In a previous study, I used the synthetic control method to construct a counterfactual marriage rate for the Netherlands, the first country to legalize SSM (Trandafir 2014). I found no significant differences between the actual and the synthetic marriage rates after the introduction of SSRP or after the legalization of SSM. However, I found some heterogeneity in the marriage behavior of various groups, depending on their degree of religiosity or conservatism. This suggests that different countries could experience different responses to the legalization of SSM or SSRP based on their demographics. Moreover, the close spacing of the SSRP and SSM laws made it difficult to separately identify the effects of each law.

Finally, Dillender (2014) examined the effect of legalizing SSRP or SSM on U.S. national- and state-level marriage rates between 1995–2010. Estimates from difference-in-difference models showed that the legal recognition of same-sex couples does not have negative effects on overall marriage rates, on different-sex marriage rates, or on the stock of married people.

The current study contributes to the extant literature on several dimensions. First, it includes almost all the countries that enacted an SSM or SSRP law. In addition, there are more countries legalizing SSRP and SSM in my sample (14 and 4, respectively) than U.S. states (8 and 5, respectively) over the study period. Taken together, these lend more credibility to the external validity of my results compared with previous studies, all of which focus on the experience of only one country (either the United States or the Netherlands). Second, many of these countries enacted SSRP or SSM laws much earlier than U.S. states (e.g., eight countries had introduced SSRP, and two had introduced SSM by the time the first U.S. state enacted a corresponding law), allowing me to examine long-term effects. Third, I consider the separate impact of SSRP and SSM laws on several indicators of family formation, yielding a more complete picture of the effects on family formation. Finally, I consider several scenarios under which the legalization of SSRP or SSM could affect family formation without an observable (short-term) change in the indicators considered.

I use data for the period 1980–2009 on 28 OECD member countries, 14 of which introduced some form of same-sex registered partnership (SSRP-adopters) and 3 same-sex marriage (SSM-adopters) during the sample period. I focus on three indicators of family formation: the different-sex marriage rate, the divorce rate, and the extramarital birth rate. The results from difference-in-difference models that allow for country-specific trends indicate no significant negative effects on family formation following either SSRP laws or SSM laws. Indeed, although imprecisely estimated, the estimated effects are generally small and insignificant; and in most cases, point to slightly more marriages, fewer divorces, and lower rates of extramarital births. These results are robust to several sensitivity checks, including the use of the synthetic control method to construct counterfactuals for each of the three indicators and for each adopting country. Finally, I investigate a number of potential scenarios under which the estimated effects could be confounded by concurrent changes in behavior, at least in the short run. In all cases, I find no evidence of any offsetting behavior, suggesting that SSRP and SSM laws are unlikely to have any negative effects on family formation.

## Background

### Short History of SSM and SSRP Laws in the OECD

Several developed countries currently grant same-sex couples marriage-like rights. The first country to do so was Denmark in 1989 with the introduction of registered partnership. This institution was designed to be a close equivalent to marriage but open only to same-sex couples.3 The Danish registered partnership was used as a model by several other countries, starting with the other Nordic countries: Norway in 1993, Sweden in 1995, and Iceland in 1996. The next country to introduce registered partnership was the Netherlands in 1998, but in a departure from the Danish model, this institution is open to both same-sex and different-sex couples. In another departure from the Danish model, France introduced in 1999 a different type of partnership: pacte civil de solidarité or pacs. This contract is open to both same-sex and different-sex couples but offers significantly fewer benefits or obligations than marriage.4 Belgium and Germany followed more closely the French example and introduced “weaker” institutions than the Danish-style partnership in 2000 and 2001, respectively.5 In the following years, several other countries adopted either Danish-style “strong” versions of registered partnership, such as Finland (2002), New Zealand (2005), the United Kingdom (2005), and Switzerland (2007); others adopted “weaker” versions, such as Luxembourg (2004) and the Czech Republic (2006).6

Far fewer countries allow same-sex marriage. In 2001, the Netherlands became the first country to officially open the institution of marriage to same-sex couples, and Belgium followed in 2003. In both countries, the decision was made by the legislature. In contrast, the judicial branch in Canada ruled against discrimination against same-sex couples in marriage and forced several provinces to legalize same-sex marriage starting from 2003, leading to recognition at the federal level in 2005 (Wright 2006). Finally, the newly elected socialist government of Spain pushed for and obtained the opening of marriage to same-sex couples in 2005, again by means of the legislature.7 However, the Spanish government also liberalized divorce at the same time, making it significantly easier for couples to divorce. Given the potential two-way relationship between divorce and marriage (Allen et al. 2006; Rasul 2006), the main analyses exclude Spain and focus on the other three countries that legalized SSM.

All the SSRP and SSM laws were subject to relatively heated debates (Merin 2002). In most cases, it was unclear whether the final result would be the status quo, the opening of marriage, or the introduction of an alternative institution. For example, the Netherlands and Belgium enacted an SSRP law only to have the debate flare up again and lead to the legalization of SSM several years later. In other cases, the fate of the legislation hinged on election results or on court decisions. In conclusion, the laws and their timing can be interpreted as plausibly exogenous.8

### Theoretical Background

In the standard economic marriage model (Becker 1973, 1974), individuals choose between two states: being in a marriage and not being in a relationship. The evolution of family structure over the past few decades suggests that the model has to be extended to include alternative family forms, such as cohabitation and/or registered partnerships. In such a model, any change in the value of marriage could affect family formation in the sense of shifting the preference of some couples from marriage to an alternative arrangement. If the different-sex and same-sex marriage markets are completely segregated, then the legalization of SSM or SSRP would not have any effects on different-sex family formation. However, there would be effects in the presence of any kind of spillovers between the two marriage markets.

The two types of laws may have different effects on family formation because of their specific features. SSRP laws introduce a separate institution, effectively segregating the market for legal unions: marriage for different-sex couples and civil union/registered partnership for same-sex couples.9 In contrast, SSM laws change the definition of marriage to include same-sex couples.

Legal recognition of same-sex couples through SSM could affect family formation through several channels. First, a line of research in sociology argues that the Western world experienced a “deinstitutionalization of marriage” starting with the later part of the twentieth century (e.g., Cherlin 2004). This development is characterized by changing social norms toward an increased acceptance of alternative family forms, such as cohabitation, single parenthood, divorced couples, and so on. In particular, Cherlin (2004) identified SSM as an indicator of the change in social norms, which suggests that the legalization of SSM could accelerate this trend of shifting preferences away from marriage. As a result, some couples on the margin could choose alternative family forms, leading to fewer (different-sex) marriages. To the extent that preferences for offspring do not change, this would also lead to more extramarital births (Kurtz 2004). The effect on divorce is less clear because the response of already married couples to changes in the value of marriage is theoretically and empirically ambiguous; see, for example, the discussion in Stevenson and Wolfers (2007).

Second, some individuals might be on the margin between a same-sex and a different-sex relationship. The legalization of SSM could induce these individuals to choose an SSM instead of a (different-sex) marriage. This would cause fewer different-sex marriages and potentially more divorces (if these individuals are currently in a different-sex marriage), but it would have no effect on extramarital births. Third, some individuals may hold strong beliefs about the exclusive access of different-sex couples to marriage. Akerlof and Kranton’s (2000) identity theory suggests that SSM laws could lead to a loss of identity for these individuals. In response, they may act in ways to support the “traditional view” of marriage, which could result in more different-sex marriage, fewer divorces, and fewer extramarital births. Fourth, the legalization of SSM could be interpreted as a move toward the institutionalization of same-sex relationships (Lauer and Yodanis 2010), which could reignite the interest of different-sex couples in marriage (Cahill 2004; Mello 2004; Safire 2003), resulting in more different-sex marriages, fewer divorces, and fewer out-of-wedlock births. Finally, when same-sex couples are granted benefits associated with marriage via SSM, gay rights organizations would presumably reduce the pressure on governments and employers to provide these rights to cohabiting couples (Rauch 2004). The decline in the value of marriage relative to cohabitation for different-sex couples could then slow down, leading to relatively more different-sex marriages and less extramarital births. For the same reasons mentioned earlier, the response of divorces would be theoretically uncertain.

The introduction of SSRP can affect family formation through some of the same channels, albeit with potentially different results. First, SSRP can also be seen as accelerating the trend in the deinstitutionalization of marriage, causing a decline in (different-sex) marriage, a potential rise in extramarital births, and no clear response in divorce. Second, individuals on the margin between same-sex and different-sex relationships could choose SSRP after it becomes legal, leading again to fewer different-sex marriages, potentially more divorces, and no effects on extramarital births. Third, there is less pressure to have marriage-like rights granted to cohabiting couples when same-sex couples can have these rights through SSRP. This would slow the decline in the value of marriage relative to cohabitation and spur more (different-sex) marriages and fewer out-of-wedlock births, with an uncertain change in divorce. Finally, the fact that SSRP and (different-sex) marriage are distinct institutions can make marriage a “purer” institution and encourage more family formation among different-sex couples.

In conclusion, the effect of SSRP or SSM laws on family formation is theoretically ambiguous and remains an empirical question. In addition, the theories discussed earlier imply that the enactment of these laws changes the value of marriage regardless of the number of couples entering either type of institution.10

## Empirical Strategy

The main approach is based on a difference-in-difference model exploiting the cross-country variation both in the type of legal recognition of same-sex couples introduced and in the timing of the law. The estimating equation can be written as:
$lnyit=β0+β1SSRPit+β2SSMit+fit+μi+vt+εit,$
(1)
where yit is an indicator of family formation in country i during year t, SSRPit is a variable equal to the fraction of the year t during which country i had an SSRP law in effect, and SSMit is a similar variable for SSM laws.11

Country fixed effects μi are used to capture time-invariant factors that may affect family formation in distinct ways in each country i. In addition, Eq. (1) includes country-specific time trends fi(t) that account for general trends in family formation separately for each country. It is important to include these terms because attitudes toward “traditional” family forms may evolve differently across countries. I also control for temporary shocks to family formation that are common across countries (e.g., global economic conditions, the discovery of new contraceptives or fertility treatments) through year fixed effects vt. Some specifications also include a set of covariates Xit that can influence family formation. To the extent that the SSM/SSRP laws are exogenous, the inclusion of these observable characteristics should not alter significantly the value of the estimates, but it should improve their precision. Finally, the standard errors are clustered at the country level to allow for within-country correlations.

The parameters of interest, β1 and β2, capture the percentage change in the indicators of family formation following the introduction of SSRP and SSM, respectively, interpreted as an “intercept shift” around the long-term trend.12 Their sign indicates the direction of the effect on family formation depending on the indicator analyzed. For instance, a negative sign indicates negative effects on family formation if the dependent variable is an indicator of “traditional” family forms (such as the marriage rate) and positive effects if the dependent variable is related to alternative family forms (e.g., the extramarital birth rate). These effects can be interpreted as causal if two identification assumptions are satisfied: (1) the only factor that influences family formation after the legalization of SSRP or SSM is the law itself, and (2) the countries that did not introduce a particular type of institution for same-sex couples provide a good counterfactual for the countries that did. I investigate several scenarios leading to violations of these assumptions in the Results section.

## Data

To obtain a more homogeneous sample, I restrict the analysis to OECD member countries, which are presumably more similar to each other. I use data for the period 1980–2009 and exclude Israel, Mexico, Slovenia, and the Slovak Republic because of data availability, and also Spain because the legalization of SSM coincides with the liberalization of divorce (see the Background section). The countries in the sample can be divided into four mutually exclusive groups. The first group is the “SSM-adopters” and includes the three countries that enacted an SSM law during this period: Belgium, Canada, and the Netherlands. The second group, “strong SSRP-adopters,” comprises the countries that enacted a Danish-type SSRP law: Denmark, Finland, Iceland, New Zealand, Norway, Sweden, Switzerland, and the United Kingdom. The third group, “weak SSRP-adopters,” counts the countries that legalized weaker versions of SSRP: the Czech Republic, France, Germany, and Luxembourg. In most of the analysis, the last two groups are combined into “SSRP-adopters.” Finally, “never-adopters” are the countries that did not adopt a SSM or a SSRP law during the study period: Australia, Austria, Greece, Hungary, Ireland, Italy, Japan, Korea, Poland, Portugal, Turkey, and the United States.13

I examine three indicators commonly used in both the economic and the sociological literature on family formation: the marriage rate, the divorce rate, and the extramarital birth rate (in economics, see the review article of Lundberg and Pollak (2007); in sociology, see Cherlin (2004) or Coontz (2004)). Because most of the debate in the media and in the political arena focuses on different-sex family formation, I use the different-sex marriage rate defined as the number of different-sex marriages per 1,000 individuals.14 The divorce rate is calculated as the number of divorces per 1,000 individuals. Although there is no distinction between same-sex and different-sex divorces in the data from SSM-adopting countries, the short time since the introduction of SSM and the relatively small number of same-sex marriages ensures that nearly all divorces are by different-sex couples. Finally, the extramarital birth rate is calculated as the fraction of births to unmarried mothers among all live births, without any distinction between same-sex and different-sex couples. The data sources for all the variables and the date of enactment of the SSM and SSRP laws for each country are listed in Online Resource 1, Table S1.

Figure 1 plots the evolution of the three indicators.15 To emphasize pre-intervention trends, the year when SSM or SSRP were introduced is normalized to 0. For never-adopters, year 0 corresponds to 2000, the median year of adoption among adopting countries. Panels a and b of Fig. 1 show that the marriage rate and the divorce rate are rather stable for the two SSRP-adopting groups prior to the enactment of the laws. On the other hand, these two indicators are almost parallel for SSM-adopters and never-adopters. Finally, panel c shows that all groups experienced an increase in extramarital births prior to the legalization of SSM/SSRP. These graphs underline the importance of controlling for country-specific trends in the regression analysis, and they suggest that linear trends should generally be appropriate.

As I mention in the Empirical Strategy section, some specifications include a set of country-year controls. These variables represent factors that can influence family formation and can be classified into three groups. The first group includes variables measuring the thickness of the partner market and includes the share of the population in the 25–44 age group and the sex ratio (the ratio of men to women in the population). The second group of variables describes the attractiveness of potential partners: the labor force participation rate and the unemployment rate in the 25- to 34-year-old age group, separately by gender. These variables are similar to those used in previous studies of marriage behavior (see, e.g., Gould and Paserman 2003). The last group describes the general state of the economy and comprises the overall labor force participation rate and unemployment rate, both separately by gender, and the real GDP per capita, given that previous studies have found that marriage, divorce, and fertility vary over the business cycle (e.g., for results on marriage and divorce, see Hellerstein and Morrill (2011) and Schaller (2013); for results on fertility, see Adsera (2005) and Mocan (1990)). Finally, total population is used to weigh observations in some specifications.16

## Results

### Baseline Results

Table 1 presents the main results. The estimates in the first column, obtained from a specification including only country and year fixed effects in addition to the two law indicators, indicate that SSM laws are followed by significant declines in different-sex marriage and significant increases in extramarital births. On the other hand, SSRP laws seem to have been followed by more family formation (more different-sex marriages, fewer divorces, and fewer births outside marriage). For instance, the estimate in the first column of panel A suggests that the different-sex marriage rate increased by approximately 10.5 % (exp(0.100) − 1) after the introduction of SSRP, and fell by a statistically significant 17.1 % (exp(0.158) − 1) after the enactment of an SSM law.

As mentioned in the previous section, one potential concern is that these estimates might be driven by diverging long-term trends in the indicators. For example, a potential drop in the marriage rate in SSRP-adopting countries after the enactment of the SSRP law would be underestimated because the marriage rate is declining in never-adopting countries but is relatively stable in SSRP-adopting countries. The specification in the second column of Table 1 adds country-specific linear trends to eliminate this potential bias. Although the precision of the estimates is vastly improved, the results are much smaller in absolute value and almost always insignificant. For comparison, the numbers in panel A in Table 1 now suggest that the different-sex marriage rate increased by approximately 2.8 % after the introduction of SSRP and fell by 5.1 % after the introduction of SSM, both relative to the long-term trend. Interestingly, the only coefficient that changes sign is that of the effect of SSM laws on extramarital births, which now indicates a reduction in the fraction of births outside marriage. Overall, the results from the specification including country-specific linear trends point to no significant negative effects of SSRP or SSM laws on family formation.

These estimates represent the average change in the indicators of family formation over the entire period after the introduction of SSRP or SSM. This average can mask anticipatory responses or lagged effects. For example, the estimated post-/pre-intervention difference in the marriage rate may be underestimated in absolute value if marriage rates decline before the enactment of the SSM/SSRP law. The same holds if a negative effect of the laws is felt only several years after enactment because of already planned marriages, divorces, or pregnancies. To examine this issue in more detail, I replace the law indicators with a set of dummy variables for each of the 10 years prior and nine years after the enactment of the corresponding law.17

The estimated coefficients and their 95 % confidence intervals are plotted in Fig. 2, separately for each indicator of family formation and for each law type. Despite the relatively large confidence intervals, several lessons can be gleaned from these graphs. First, the coefficient estimates vary closely around 0 in the period before the SSRP/SSM laws, suggesting that the identifying assumption of similar pre-treatment trends is satisfied (the case of extramarital births is one exception, which I discuss in the section, A Synthetic Control Approach). Second, the coefficients exhibit similar patterns before and after the date of enactment, confirming the lack of anticipatory reactions to the laws as well as the lack of a significant impact on family formation. Finally, the confidence intervals become wider over time, particularly in the case of SSM, suggesting that the lack of precision in the estimates is due to the lower number of observations given the recent enactment of these laws and not to features in the data. Overall, the figure confirms the previous finding of no significant negative effects on family formation.

### Robustness Checks

As mentioned in the Empirical Strategy section, difference-in-difference models are based on two identifying assumptions: (1) conditional on the control variables included, the only factor determining the outcome variable is the intervention; and (2) the control observations provide an appropriate counterfactual for the treated observations. In the next two sections, I examine the validity of these two assumptions.

I start by providing evidence on the exogeneity of the two law dummy variables. As discussed earlier in the Background section, anecdotal evidence suggests that the introduction of SSRP/SSM and the timing of the laws were not related to the evolution of family formation in adopting countries. However, this is not the only source of endogeneity. For example, migration from adopting to nonadopting countries could compensate for changes in family formation in adopting countries. In order for the coefficients to be biased upward in the case of different-sex marriage and biased downward in the case of divorce and extramarital births, individuals with lower preference for “traditional” family forms would need to migrate from adopting to nonadopting countries and/or individuals with strong preference for “traditional” family forms would need to migrate the other way. Both of these patterns are counterintuitive if the real effect of the SSRP/SSM laws is to lower the value of marriage.18

A related concern is that the results might be driven by omitted variables that are correlated both with the two law dummy variables and with the trends in family formation. I examine several such scenarios. First, it could be that the estimates are driven by the evolution of other determinants of family formation. For example, the estimates would be biased if these determinants are correlated with the adoption of an SSRP/SSM law or with the timing of the enactment. Column 3 of Table 1 shows estimates from a specification including country-year controls. The results are very similar to those in column 2, with all the coefficients indicating insignificant deviations from the long-term trends in family formation following the introduction of SSRP or SSM. Moreover, the signs of all the coefficients point to positive effects of the two laws on family formation. Given the drop in sample size and the similarity of the results when including the control variables, in what follows, I consider the specification in column 2 as the baseline.

Second, it is possible that nonlinearities in the long-term country-specific trends mask the true effects of the legalization of SSRP or of SSM. Column 4 of Table 1 presents the results from a specification including country-specific quadratic trends. A comparison with the baseline results reveals that the estimates are generally similar: small, insignificant, and pointing to no negative effects on family formation. The only exception is again a marginally significant increase in extramarital births after an SSM law, an issue to which I return in the next section.

Next, I examine in more detail the assumption that the “control” observations provide a good counterfactual for the “treated” observations, which could be partly or completely invalidated in several situations. Because all countries receive equal weights, it is possible that the results are driven by the evolution of family formation in smaller control countries. If these countries are “more liberal” and thus have a more similar evolution to adopting countries, they might push the overall average in the control group closer to that of the treated group and bias the results toward 0. To test for this possibility, I reestimate the baseline specification while weighting each country by its total population in that particular year. The results, listed in column 5 of Table 1, show little change compared with the baseline results and point again to the absence of negative effects on family formation.

Second, I consider the possibility that excluding Spain from the sample could bias the results toward finding no negative effects on family formation. Column 6 of Table 1 reports the results from the baseline specification when Spain is included in the sample. Not surprisingly, SSM laws are now followed by slightly more divorces and extramarital births and by slightly fewer marriages, but the effects are still relatively small and insignificant.

### A Synthetic Control Approach

Although the analysis in the previous section revealed little sensitivity of the results to the choice of treated and control observations, one might be concerned that none of the samples used provides in its entirety a valid counterfactual for adopting countries. In situations when an obvious control group is not available, Abadie and Gardeazabal (2003) and Abadie et al. (2010) have suggested creating an artificial one called “synthetic control.”20

The synthetic control is constructed for each indicator of family formation in each adopting country, using never-adopting countries as potential “donors.” The synthetic control is the set of weights assigned to the donors such that the weighted average of the outcome analyzed and of a given set of determining variables closely match the corresponding values for the adopting country during the period before the introduction of SSRP or SSM (the “intervention”).

Formally, let X be a vector of variables influencing family formation, y be the outcome studied, subscript 1 represent the particular adopting country, subscript 0 represent the set of never-adopting countries, and $Z1=X¯1y¯1′$ and $Z0=X¯0′y¯0′$, where the overline represents means over the pre-intervention period. The synthetic control is the set of weights W that minimize the weighted distance between pre-intervention averages of the variables in Z for the adopting country and its synthetic control:
$W*V=argminZ1−Z0W′VZ1−Z0W,$
where V is an arbitrary diagonal matrix of variable loadings. Abadie et al. (2010) suggested choosing the loading matrix that minimizes the root mean squared predicted error of the synthetic outcome in the pre-intervention period:
$V*=argminy1−y0W*V′y1−y0W*V=argmin1T0∑t=1T0yit*−y1t21/2,$

where yit* = y0W*(V) is the synthetic outcome in period t. The weights are restricted to lie in the unit interval and to sum to 1 to avoid out-of-sample inference, resulting in synthetic controls that are unlikely to match perfectly the pre-intervention trend in the outcome. In practice, these weights are calculated using a two-step maximization procedure. In the first step, each variable is assigned a loading, and the set of country weights that minimizes the weighted distance between the synthetic control and the adopting country is calculated as a function of these loadings. In the second step, the variable loadings are chosen such that the synthetic outcome matches the actual outcome in the adopting country as closely as possible, and the two steps are repeated until convergence is achieved. Abadie et al. (2010) showed that the synthetic control takes into account both the observable and the unobservable determinants of the dependent variable, producing an appropriate counterfactual for the evolution of the outcome in the absence of the SSRP or SSM law.

The data used are similar to those used in the previous section. I also include Spain given that there is no “tainting” of the results for the other countries. For each country, the pre-intervention period consists of the 10 years before the enactment of the SSRP or SSM law.22 The outcomes analyzed are the same as in the previous sections: the marriage rate (separately for different-sex couples and also overall, where possible), the divorce rate, and the fraction of births outside marriage. The variables included in the vector of determinants X are similar to those in the previous sections: the share of the population in the 25–44 age group, the unemployment rate of men and of women in the 25–34 age group, the sex ratio, and the real GDP per capita. In addition, because the procedure uses averages over the pre-intervention period, I can also make use of several variables for which only a few years of data are available: the share of women in tertiary education (from the World Bank Education Statistics) and several variables from the World Values Survey that capture attitudes toward divorce, marriage, single parenthood, religion, and abortion.23

Figures 3, 4, and 5 plot the corresponding actual-synthetic gaps for each adopting country (solid black line) and placebo tests (gray lines). The vertical lines indicate the date of enactment of SSRP and/or SSM laws. (Figures S1, S2, and S3 in Online Resource 1 plot the synthetic and actual indicators of family formation for all adopting countries, with the solid line representing the actual and the dotted line the synthetic indicator.)24

The figures show that the marriage rate and the divorce rate in adopting countries have similar evolutions to the counterfactual after the introduction of SSRP or SSM. In many cases, the actual–synthetic differences indicate positive effects on family formation (i.e., higher marriage rates and lower divorce rates), same as in the difference-in-difference approach. In the case of extramarital births, never-adopting countries do not always seem to provide a good counterfactual because the actual rate of births outside marriage is consistently higher than the synthetic rate during the entire pre-intervention period for several countries (France, Iceland, New Zealand, Sweden, and the United Kingdom). This can also explain the sensitivity of the difference-in-difference results pertaining to extramarital births. However, for the countries where a reasonably good synthetic control can be constructed, the actual extramarital birth rate is largely within the cloud of the placebo tests, even if marginally so in some cases (e.g., Belgium and the Netherlands).

This exercise also provides evidence on effect homogeneity. The difference-in-difference estimates in the previous section represent average effects over the entire post-intervention period and over all the adopting countries. This could potentially mask heterogeneity in the results, with some countries experiencing negative effects and others experiencing positive effects that cancel each other out. The comparative case studies conducted in this section show that the finding of no significant negative effects of SSRP/SSM laws on family formation apply to each of the adopting countries and not just on average.

The results in the previous sections show no evidence that the introduction of SSRP or SSM had negative effects on the three indicators analyzed. However, previous research has argued that these indicators might not perfectly capture individual behavior in response to changes in norms or in their environment (Lauer and Yodanis 2010). For example, it is possible that preferences for marriage are indeed negatively affected by the enactment of an SSRP or SSM law but that the marriage rate is almost unchanged (at least in the short run) because of a concurrent offsetting change in behavior. In this section, I study several scenarios under which changes in individual preferences for “traditional” family forms brought on by SSRP or SSM laws may be counteracted by some other behavior.

First, suppose that the legalization of SSRP/SSM makes people less likely to marry but also makes them prefer to marry younger. In this case, individuals older than the new desired age at (first) marriage would choose to marry, potentially leading to an unchanged marriage rate in the short run and a decline only in the longer run.25 If fertility decisions are related to the timing of marriage, the observed effect of the laws on extramarital marriages could also be affected, and a similar argument could be made in the case of divorces. Panels A and B of Table 3 provide the estimates from the baseline specification using age at first marriage of men and of women as the dependent variable, respectively (column 1). Several specification tests similar to the ones in the Baseline Results and Robustness Checks sections are shown in columns 2–5 (see the discussion of the tests in the previous sections). Regardless of the specification, the results are always small and rather precisely estimated, providing no evidence of any significant change in the timing of first marriages after the legalization of SSRP or SSM.

An alternative scenario is that SSRP/SSM laws change individual preferences toward offspring. If people decide to have more children and if fertility and marriage/divorce decisions are tied, then any negative effect of SSRP/SSM laws on marriage and divorce could be counteracted by an increase in marriages and a decline in divorces as a result of the higher fertility. This scenario could also explain the positive effects seen on extramarital births. Panel C of Table 3 shows the estimates when the dependent variable is the crude birth rate, defined as the total number of births per 1,000 individuals. Although there is some relatively weak evidence of an increase in fertility following SSM laws, the estimates are generally small and insignificant.26 In conclusion, I do not find any strong evidence that the main results are driven by a shift in preferences for children.

Finally, the main results might not capture the effect of SSRP/SSM laws if the laws are associated with changes in the economic environment that also affected family formation. For example, previous research has found that marriage, divorce, and fertility all seem to fluctuate with the state of the economy as measured by unemployment rates or real GDP (Adsera 2005; Hellerstein and Morrill 2011; Mocan 1990; Schaller 2013). Some evidence against this scenario is already provided in the Robustness Checks section, which shows that the main estimates are robust to the inclusion of country-year controls. In addition, in panels D–F of Table 3, I present results from models where the dependent variable is the unemployment rate of young men and women or the real GDP per capita. In general, the estimates are relatively small and insignificant. One exception is that SSM laws seem to be countercyclical (positively correlated with unemployment and negatively correlated with real GDP per capita). However, downturns are generally associated with lower marriage and divorce rates (Hellerstein and Morrill 2011; Schaller 2013), which could explain the main results for the divorce rate but not for the different-sex marriage rate. In addition, the estimates in panels D and E of Table 3 suggest that the unemployment rate of women increases more than that of men following an SSM law, and previous research has found that an increase in women’s unemployment (relative to men’s) leads to a decline in fertility (Adsera 2005; Mocan 1990) in contrast with the previous results in panel C. Therefore, these results do not support the idea that the economic environment dampened a potentially negative effect of SSRP and SSM laws on family formation.27

## Discussion

The results in the previous sections suggest that the legalization of both SSM and SSRP is followed by small and generally insignificant fluctuations in different-sex marriages, divorces, and extramarital births. These results are not consistent with any of the theories predicting that SSM or SSRP affect the value of marriage (see the earlier Theoretical Background section), suggesting the absence of spillovers of any kind between the same-sex and the different-sex partner markets.

There are several caveats to my findings. First, some aspects of family formation might not be well represented by the three indicators used in this study. For example, some researchers question whether these indicators capture the weakening of social norms and the deinstitutionalization of marriage (Lauer and Yodanis 2010). However, their evolution is still informative to the extent that they represent measures of revealed preference for family types. Second, only 14 of the 28 countries in the sample adopted SSRP, and even fewer (three) legalized SSM. As such, generalizations to other contexts should be performed with caution. Finally, the number of years after the introduction of SSM (and, to some extent, SSRP) is relatively short as most laws were enacted only recently. Although it is possible that some of the effects of these laws may be observed with a lag longer than what is available in current data, previous studies have found that public policies that change the value of marriage can affect family formation over time spans similar to or even shorter than those in the current study (see, e.g., Allen 1992; Bitler et al. 2004).

Despite these limitations, this study adds to the literature by being the first to provide causal estimates of the effects of legalizing SSM and SSRP on family formation in almost all the countries that introduced these arrangements. The results provide a starting point for an evidence-based debate on the legalization of SSM or SSRP and contribute to our understanding of marriage and fertility behavior in general.

## Conclusions

The same-sex marriage debate has seen starkly different claims with respect to what effects the legalization of SSRP or SSM could have on the institution of marriage and on family formation in general. In this article, I provide empirical evidence on this issue. My estimates suggest that both the introduction of SSRP and the legalization of SSM are not followed by significant negative effects on family formation. In fact, in many cases, the effects on the three indicators analyzed (different-sex marriage rate, divorce rate, and extramarital birth rate) indicate more family formation. These results are inconsistent with theories arguing that SSM or SSRP laws reduce the value of marriage compared with alternative arrangements. Given the prevalence of these arguments in the debate on the legal recognition of same-sex couples, these findings provide much needed foundation for evidence-based public policies.

## Acknowledgments

I am grateful to Meltem Daysal, Dan Hamermesh, Judy Hellerstein, and multiple anonymous referees for their helpful comments and suggestions. All remaining errors are my own.

## Notes

1

For more on Proposition 8, see document 678 from case number 09-CV-2292, or the transcript of David Blankenhorn’s testimony, available online (http://www.afer.org/our-work/hearing-transcripts/perry-trial-day-11-transcript/). For the Federal Defense of Marriage Act, see Rep. Henry Hyde’s intervention in House of Representatives Report 104-664, 1996. Finally, according to the National Conference of State Legislatures, as of January 2014, there were 33 U.S. states with constitutional or statutory provisions that effectively prohibit same-sex marriage (see http://www.ncsl.org/issues-research/human-services/same-sex-marriage-overview.aspx).

2

Throughout the article, “traditional family form” refers to different-sex married couples and to children born in these marriages.

3

Waaldijk (2004) compared the rights and obligations stemming from the two institutions and found that 84 % of the rights of different-sex marriage are offered by the Danish registered partnership.

4

Using the same type of evaluation as before, Waaldijk (2004) estimated that “pacs”-ed couples have only 55 % to 63 % of the benefits offered to married couples.

5

German partnership is only open to same-sex couples and was extended in October 2009 to cover all the rights and obligations of marriage.

6

Several other countries adopted weak or strong versions of registered partnership in recent years, but they are considered “nonadopters” in this article due to their late enactment of the laws: Hungary (weak version in July 2009), Austria (strong version, January 2010), and Ireland (strong, January 2011). The United States is also considered “nonadopter,” although a few states introduced same-sex marriage or civil unions, because these states represent a minority and because marriages and civil unions conducted in these states are not granted the federal rights and obligations of marriage.

7

Same-sex marriage has also been legal in South Africa since 2006; in Norway and Sweden since 2009; in Argentina, Iceland, and Portugal since 2010; and in a few U.S. states, starting with Massachusetts in 2005. South Africa and Argentina are not included in the analysis, and the other countries are considered “nonadopters” because of the period under study (see the Data section).

8

9

As mentioned earlier, some of the registered partnership laws allow for both same-sex and different-sex partnerships. In this case, the law could have an effect on (different-sex) family formation just by creating a competing institution to marriage. I do not explicitly consider this effect because it is not directly related to the legal recognition of same-sex couples, but the estimated effects from models controlling for this feature (available upon request) are virtually identical to the main results reported in the article.

10

The number of couples entering SSM or SSRP is much smaller than the number of different-sex couples who marry. Over the study period, on average, same-sex marriages and same-sex registered partnerships were equivalent to about 2 % and 1.6 % of different-sex marriages, respectively.

11

Results with variables that take the value of 1 if there was an SSM/SSRP law in effect for any fraction of the year (available upon request) are virtually identical.

12

It is possible that what matters is whether a law recognizing same-sex couples is enacted, regardless of whether it introduces SSRP or SSM. A specification replacing the two law dummy variables with an indicator for any type of law produces qualitatively identical results (available upon request).

13

Norway legalized same-sex marriage in January 2009. Given that the law was introduced at the very end of the sample period, I consider Norway a strong SSRP-adopter. In addition, as mentioned earlier, I abstract from the fact that a small number of U.S. states legalized same-sex marriage or civil unions/domestic partnerships.

14

Canada does not provide separate information on same-sex and different-sex marriages. The data from the three SSM-adopting countries that distinguish between same-sex and different-sex marriages (the Netherlands, Belgium, and Spain) show very small differences between the two marriage rates. This is not surprising because the two measures are identical by construction before the introduction of SSM, and same-sex marriages represent a very small fraction in all marriages (less than 3 %). Therefore, the results using the overall marriage rate (available upon request) are virtually identical.

15

The Swedish National Widow’s Pension Scheme extended certain pension benefits to married couples on January 1, 1990. This led to an abnormally large number of weddings in Sweden in 1989 (Hoem 1991). In the rest of the analysis, I replace this observation with the average of the Swedish marriage rate in 1988 and 1990.

16

The data are obtained from the World Development Indicators (sex ratio and total population) and from OECD (all other control variables). Note that some control variables are not available for the entire period, leading to some variation in sample size depending on the specification.

17

In order to further improve the precision of the estimates, I also include country-year controls. Figures plotting coefficient estimates from the specification without controls (available upon request) are qualitatively similar (see also the discussion on the similarity between the model with and without controls in the next section on Robustness Checks). This strategy can also be interpreted as a test of the underlying identification assumption of similar pre-intervention trends in adopting and never-adopting countries.

18

One scenario in which this could occur is if couples in nonadopting countries would want to “reclaim” the institution of marriage in adopting countries. This would imply that the benefits from reclaiming the institution in a different country are high enough to offset the relocation costs, which is unlikely: for example, because of the linguistic heterogeneity among OECD countries.

19

The effect of SSRP laws in this case is identified from the years that Belgium and the Netherlands had only an SSRP law—approximately three years each.

20

Other studies using the synthetic control method in a cross-country framework include Billmeier and Nannicini (2013), Cavallo et al. (2013), Lee (2011), and Nannicini and Billmeier (2011).

21

A second type of test plots the distribution of the ratio of post- to pre-intervention MSPE for all the placebo tests and places the MSPE for the adopting country in this distribution. An MSPE ratio at the right tail of the distribution can be interpreted as evidence toward “significance,” and an MSPE ratio at the lower tail of the distribution implies “insignificance.” The two approaches lead to the same conclusion (figures available upon request).

22

Unfortunately, there are not enough data on the vector of determinants to construct a counterfactual for Denmark and Norway, the earliest SSRP-adopting countries. Because the first ruling against discrimination in marriage in Canada was made in 2001 and several provinces started offering SSM as early as 2003, I consider the period 1992–2001 as the pre-intervention period for Canada. In the case of Spain, several provinces introduced domestic partnerships starting from 1998, so the pre-intervention period is 1988–1997. In both cases, the figures include vertical lines at both dates.

23

These variables are: the fraction of respondents who agreed with the statement “marriage is an outdated institution,” the average score provided to the question asking when divorce is justifiable (1 = never, 10 = always), the fraction of respondents approving of the situation “A woman wants to have a child as a single parent, but she doesn’t want to have a stable relationship with a man,” the average score provided to the question asking when abortion is justifiable (1 = never, 10 = always), and the fraction of respondents answering “not at all important” or “not very important” to the question “How important is religion in your life?” The first three variables are used when the outcome is the marriage rate or the divorce rate, and the last three are used when the outcome is the fraction of extramarital births.

24

As mentioned earlier, Belgium, the Netherlands, and Spain provide data on same-sex and different-sex marriages separately. The corresponding graphs in Online Resource 1, Fig. S1, include both the overall and the different-sex marriage rate. In addition, the Netherlands provides information on different-sex registered partnerships, and its graphs also include the difference-sex union rate (i.e., marriages and partnerships).

25

For example, suppose people can be of only two types: those who prefer to marry young and those who prefer to marry late. The introduction of SSRP or SSM could push the second type to the extreme of wanting to never marry. In this case, some of these individuals will indeed never marry, whereas others will switch to marrying young. In the short run, this will lead to more marriages until all the “switchers” have married. After that, the marriage rate will be lower because the only people who marry are those who want to marry young.

26

I find similar results using the fertility rate (the predicted number of children a women will have over her lifetime) instead of the crude birth rate.

27

I find similar results when using as dependent variable other measures of the state of the economy: the overall unemployment rate of men and of women, the labor force participation rate of young men and young women, and the overall labor force participation rate of men and women (results available upon request).

## References

Abadie, A., Diamond, A., & Hainmueller, J. (
2010
).
Synthetic control methods for comparative case studies: Estimating the effect of California’s tobacco control program
.
Journal of the American Statistical Association
,
105
,
493
505
. 10.1198/jasa.2009.ap08746
Abadie, A., & Gardeazabal, J. (
2003
).
The economic costs of conflict: A case study of the Basque country
.
American Economic Review
,
93
,
113
132
. 10.1257/000282803321455188
2005
).
Vanishing children: From high unemployment to low fertility in developed countries
.
American Economic Review
,
95
,
189
193
. 10.1257/000282805774669763
Akerlof, G., & Kranton, R. (
2000
).
Economics and identity
.
Quarterly Journal of Economics
,
115
,
715
753
. 10.1162/003355300554881
Allen, D. W. (
1992
).
Marriage and divorce: Comment
.
American Economic Review
,
82
,
679
685
.
Allen, D. W. (
2013
).
High school graduation rates among children of same-sex households
.
Review of Economics of the Household
,
11
,
635
658
. 10.1007/s11150-013-9220-y
Allen, D. W., Pakaluk, C., & Price, J. (
2013
).
Nontraditional families and childhood progress through school: A comment on Rosenfeld
.
Demography
,
50
,
955
961
. 10.1007/s13524-012-0169-x
Allen, D. W., Pendakur, K., & Suen, W. (
2006
).
No-fault divorce and the compression of marriage ages
.
Economic Inquiry
,
44
,
547
558
. 10.1093/ei/cbj030
Alm, J., Badgett, M. V. L., & Whittington, L. A. (
2000
).
Wedding bell blues: The income tax consequences of legalizing same-sex marriage
.
National Tax Journal
,
53
,
201
215
.
Becker, G. S. (
1973
).
A theory of marriage: Part I
.
Journal of Political Economy
,
81
,
813
846
. 10.1086/260084
Becker, G. S. (
1974
).
A theory of marriage: Part II
.
Journal of Political Economy
,
82
,
S11
S26
. 10.1086/260287
Billmeier, A., & Nannicini, T. (
2013
).
Assessing economic liberalization episodes: A synthetic control approach
.
Review of Economics and Statistics
,
95
,
983
1001
.
Bitler, M., Gelbach, J., Hoynes, H., & Zavodny, M. (
2004
).
The impact of welfare reform on marriage and divorce
.
Demography
,
41
,
213
236
. 10.1353/dem.2004.0011
Cahill, S. (
2004
).
Same-sex marriage in the United States: Focus on the facts
.
Lanham, MD
:
Lexington Books
.
Cavallo, E., Galiani, S., Noy, I., & Pantano, J. (
2013
).
Catastrophic natural disasters and economic growth
.
Review of Economics and Statistics
,
95
,
1549
1561
. 10.1162/REST_a_00413
Cherlin, A. (
2004
).
The deinstitutionalization of American marriage
.
Journal of Marriage and Family
,
66
,
848
861
. 10.1111/j.0022-2445.2004.00058.x
Coontz, S. (
2004
).
The world historical transformation of marriage
.
Journal of Marriage and Family
,
66
,
974
979
. 10.1111/j.0022-2445.2004.00067.x
Dee, T. (
2008
).
Forsaking all others? The effects of same-sex partnership laws on risky sex
.
Economic Journal
,
118
,
1055
1078
. 10.1111/j.1468-0297.2008.02160.x
Dillender, M. (
2014
).
The death of marriage? The effects of new forms of legal recognition on marriage rates in the United States
.
Demography
,
51
,
563
585
. 10.1007/s13524-013-0277-2
Gould, E., & Paserman, D. (
2003
). Waiting for Mr. Right: Rising inequality and declining marriage rates.
Journal of Urban Economics
,
53
,
257
281
.
Hellerstein, J., & Morrill, M. S. (
2011
).
Booms, busts, and divorce
.
B.E. Journal of Economic Analysis & Policy
,
11
,
1
26
.
Hoem, J. (
1991
).
To marry, just in case … : The Swedish widow’s-pension reform and the peak in marriages in December 1989
.
Acta Sociologica
,
34
,
127
135
. 10.1177/000169939103400205
Kurtz, S. (
2004
).
The end of marriage in Scandinavia
.
The Weekly Standard
,
9
(
20
),
26
.
Langbein, L., & Yost, M. (
2009
).
Same-sex marriage and negative externalities
.
Social Science Quarterly
,
90
,
292
308
. 10.1111/j.1540-6237.2009.00618.x
Lauer, S., & Yodanis, C. (
2010
).
The deinstitutionalization of marriage revisited: A new institutional approach to marriage
.
Journal of Family Theory & Review
,
2
(
1
),
58
72
. 10.1111/j.1756-2589.2010.00039.x
Lee, W-S (
2011
).
Comparative case studies of the effects of inflation targeting in emerging economies
.
Oxford Economic Papers
,
63
,
375
397
. 10.1093/oep/gpq025
Lundberg, S., & Pollak, R. A. (
2007
).
The American family and family economics
.
Journal of Economic Perspectives
,
21
(
2
),
3
26
. 10.1257/jep.21.2.3
Mello, M. (
2004
).
Legalizing gay marriage
.
:
Temple University Press
.
Merin, Y. (
2002
).
Equality for same-sex couples: The legal recognition of gay partnerships in Europe and the United States
.
Chicago, IL
:
The University of Chicago Press
.
Mocan, N. (
1990
).
Business cycles and fertility dynamics in the United States: A vector autoregressive model
.
Journal of Population Economics
,
3
,
125
146
. 10.1007/BF00187288
Nannicini, T., & Billmeier, A. (
2011
).
Economies in transition: How important is trade openness for growth?
.
Oxford Bulletin of Economics and Statistics
,
73
,
287
314
. 10.1111/j.1468-0084.2010.00626.x
Rasul, I. (
2006
).
Marriage markets and divorce laws
.
Journal of Law, Economics, and Organization
,
22
,
30
69
. 10.1093/jleo/ewj008
Rauch, J. (
2004
).
Gay marriage: Why it is good for gays, good for straights, and good for America
.
New York, NY
:
Times Books
.
Rosenfeld, M. (
2010
).
Nontraditional families and childhood progress through school
.
Demography
,
47
,
755
775
. 10.1353/dem.0.0112
Safire, W. (
2003
, June 30). The bedroom door.
The New York Times
Schaller, J. (
2013
).
For richer, if not for poorer? Marriage and divorce over the business cycle
.
Journal of Population Economics
,
26
,
1007
1033
. 10.1007/s00148-012-0413-0
Stevenson, B., & Wolfers, J. (
2007
).
Marriage and divorce: Changes and their driving forces
.
Journal of Economic Perspectives
,
21
,
27
52
. 10.1257/jep.21.2.27
Trandafir, M. (
2014
).
The effect of same-sex marriage laws on different-sex marriage: Evidence from the Netherlands
.
Demography
,
51
,
317
340
. 10.1007/s13524-013-0248-7
Waaldijk, K. (
2004
).
Levels of legal consequences of marriage, cohabitation and registered partnership for different-sex and same-sex partners: Comparative overview
. In K. Waaldijk (Ed.),
More or less together: Levels of legal consequences of marriage, cohabitation and registered partnerships for different-sex and same-sex partners. A comparative study of nine European countries
(pp.
137
153
).
Paris, France
:
Institut National d’Études
.
Wright, W. (
2006
).
The tide in favour of equality: Same-sex marriage in Canada and England and Wales
.
International Journal of Law, Policy & the Family
,
20
,
249
285
. 10.1093/lawfam/ebl008