IF SHAKIRA, a Colombian pop star, marries her boyfriend, the Spanish national footballer Gerard Piqué, the only unusual things about it would be that she is even more famous than he is and ten years older. Otherwise, theirs would be just a celebrity example of one of the world's biggest social trends: the rise of international marriages—that is, involving couples of different nationalities.

A hundred years ago, such alliances were confined to the elite of the elite. When Randolph Churchill married Jennie Jerome of New York, it seemed as if they had stepped from the pages of a Henry James novel: brash, spirited American heiress peps up the declining fortunes of Britain's aristocracy. Now, such alliances have become almost commonplace. To confine examples to politicians only: the French president Nicolas Sarkozy is married to the Italian-born Carla Bruni and his prime minister François Fillon has a Welsh wife, Penelope Clarke. Nelson Mandela is married to Graça Machel (from Mozambique). Denmark's new prime minister Helle Thorning-Schmidt is married to a Briton, Stephen Kinnock. And two leading ladies of Asian countries, Aung San Suu Kyi of Myanmar and India's Sonia Gandhi, are both widows from international marriages. In rich countries alone such unions number at least 10m.

International marriages matter partly because they reflect—and result from—globalisation. As people holiday or study abroad, or migrate to live and work, the visitors meet and marry locals. Their unions are symbols of cultural integration, and battlefields for conflicts over integration. Few things help immigrants come to terms with their new country more than becoming part of a local family. Though the offspring of such unions may struggle with the barriers of prejudice, at their best international marriages reduce intolerance directly themselves, and indirectly through their progeny.

The mists over marriage

So it is all the more disappointing that until recently so little has been known about these unions. Records are patchy. Some countries do not collect annual information about the citizenship of couples. Official figures may say nothing about a marriage if it takes place abroad (for example in the country of the immigrant spouse).

Defining what counts as international is tricky too. A wedding of a local man and a foreign-born bride is easy. But the marriage of two foreigners in a third country sometimes counts and sometimes doesn't. Trickiest of all is how to treat the marriage of a second-generation immigrant who has citizenship of a host country (say, the child of a Moroccan in France or a Mexican in America). If such a person marries a native Frenchwoman or an American, that usually does not count as international, even though it is an alliance across ethnic lines. Perversely, if he marries a girl from his parents' country of origin, that does count as international—but this is not a marriage across an ethnic divide and may indicate isolation not assimilation.

Belatedly, answers to these questions of scale and definition are coming, chiefly thanks to the efforts of the International Union for the Scientific Study of Population (IUSSP), a professional association of demographers, and, especially, of Doo-Sub Kim, a professor at Hanyang University in Seoul who chairs its panel on cross-border marriages. Global figures remain sketchy, but marriage patterns in Asia and Europe, at least, are becoming clearer. Some tentative, often surprising, conclusions are emerging.

Asia is the part of the world where cross-border marriages have been rising most consistently. According to Gavin Jones of the National University of Singapore, 5% of marriages in Japan in 2008-09 included a foreign spouse (with four times as many foreign wives as husbands). Before 1980, the share had been below 1%. In South Korea, over 10% of marriages included a foreigner in 2010, up from 3.5% in 2000. In both countries, the share of cross-border marriages seems to have stabilised lately, perhaps as a result of the global economic slowdown. The country with the biggest share of such unions is Taiwan, where 13% of wives in 2009 were foreigners, about the same level as in 1998, but a big fall from the peak in 2003, when 28% of all weddings involved a foreign-born wife. Chinese citizens are not considered foreigners in Taiwan and if you include marriages in which they are one of the spouses, the proportion is still higher. International marriages have played a significant role in modifying the ethnic homogeneity of all these East Asian countries.

International marriages are common in much of Europe, too. Calculations by Giampaolo Lanzieri, an Italian demographer, show that in France the proportion of international marriage rose from about 10% in 1996 to 16% in 2009. In Germany, the rise is a little lower, from 11.3% in 1990 to 13.7% in 2010. Some smaller countries have much higher levels. Nearly half the marriages in Switzerland are international ones, up from a third in 1990. Around one in five marriages in Sweden, Belgium and Austria involves a foreign partner.

The Mamma Mia factor

The rate seems to be rising fastest in Mediterranean countries: in Spain and Italy, cross-border marriages accounted for less than 5% of the total in 1995; by 2009, the share had reached 14% in Italy and 22% in Spain. Cyprus is a special case: no less than three-quarters of marriages there in 2009 were international (up from half in 1995). But that is because Venus's birthplace has a thriving wedding-and-honeymoon market. Many couples from abroad wed there. Such figures are based on wedding records. Another way of getting at the trends is census micro-data (ie, from detailed samples collected as part of the census). These have a wider coverage, are extremely precise, and go back decades, which is helpful. On the other hand, many countries do not provide them. Researchers from the Centre for Demographic Studies (Barcelona) and the Minnesota Population Centre have for the first time trawled through the censuses of more than 50 countries in every continent for people aged 25-39. In general, they find that cross-border marriages are rising in most places, but the most significant fact is the big difference between levels in rich and developing ones. In most developing countries, the share of men married to foreign women was less than 2% in 2000 (0.7% in Ghana and Bolivia; 0.2% in Colombia and the Philippines; 3.3% in South Africa). In contrast, three rich countries—America, Britain and France—account for half the total in the sample. America alone has a third. Because it is so large, though, the share of international marriage remains low: only 4.6% of Americans were married to a foreigner in 2010, up from 2.4% in 1970. Albert Esteve of the Autonomous University of Barcelona reckons that the total number of cross-border marriages among 25-39-year-olds in his sample was about 12m in 2000. The sample excludes several countries with large numbers of such unions—Japan, Taiwan, Australia and Canada—so the grand total is certainly higher, probably 15m, possibly more. Compared with the very roughly 500m marriages within that age group round the world, 15m may not seem like much. But it is more than it used to be and, in some countries—senders and recipients of foreign spouses alike—the growth in cross-border marriages is having a significant social impact.

Everywhere, cross-border marriage rises with migration, but more slowly. According to Mr Esteve's figures, the correlation is roughly one international marriage for every two new migrants. That would seem to mean that half of new migrants are marrying into their host society and the other half (presumably) into their own communities. So a surge in immigration usually leads to only a more modest rise in cross-border marriages; the process is slower and more complex.

Research into four European countries by Suzana Koelet of the Free University of Brussels and others confirms that international marriages have not risen as much as one might have expected in Europe. On her calculations, rates of marriages with a person from another European Union country have been flat in Belgium and the Netherlands since 2000 and shown only a modest rise in Spain. Marriage rates between Swiss and EU citizens have also not budged. True, marriages with foreigners have increased sharply in Spain—but that was because of a spurt of marriages with non-EU citizens: Spain had huge immigration flows from Latin America during the 1990s and 2000s. By implication, the closer integration that the EU is supposed to be bringing about seems to be having no discernible impact on the marriage choices of Dutch, Belgian and Spanish citizens.

Why not? For part of the explanation, Ms Koelet points to the intriguing marriage patterns of the Swiss. The country has one of the highest rates of international marriage in the world (surpassed only by Liechtenstein, Luxembourg and Cyprus). But the Swiss “marry out” in particular ways. The German-speaking Swiss marry largely neighbouring Germans; the Francophone Swiss marry the French; Italian-speakers marry Italians. It is the same with Belgians: Flemish-speakers tend to marry Dutch partners, Walloons marry French people. Language, it appears, remains a persistent barrier to international marriage in Europe and the spread of English as a second language does not seem to have changed that.

Asia is different. In Europe and America, marriage tends to follow migration. In Asia, people marry to migrate. Marriages in South Korea, for example, are often arranged by a broker in an unromantic process that takes two or three days and costs the Korean groom $20,000-30,000. Similarly, Taiwan has many marriages between its male citizens and Vietnamese women. The growth began when Taiwanese companies started investing in Vietnam.

Local men in such countries, Mr Jones argues from Singapore, look for foreign brides for two reasons. First because of the so-called “marriage strike” affecting some East Asian societies. In the richer countries of East and South-East Asia, like Japan, Singapore, South Korea and Taiwan, a third or more of local women are not marrying; and those who do wed late, at 31 or 32. This is causing some men to look to foreign shores for potential mates. The other reason—specific to a few Asian societies—is because a combination of traditional preference for sons and the availability of sex-selective abortion skewed the sex ratio at birth 20 years ago, leaving too few native-born women now. South Korea is an example. In 1990, it had 117 boys born for every 100 girls. Men are looking abroad to plug the gap in their local marriage market.

Hard noses, not soft hearts

For their part, the young women, often from poor areas of China and Vietnam, are looking for economic opportunities. Marriage with a man from a richer country is seen as a means of advancement and a way of helping their families at home. In Asia, it seems, cross-border unions are products of distorted local marriage markets; in Europe, they are results of gaps in labour markets that encourage migration. In both parts of the world, diasporas play a role: as immigrants settle down they encourage friends and family from back home to follow in their footsteps.

Many Asian men also seem to be looking abroad for wives in the hope that immigrant women will bear them more children. This indeed happens in Europe and America: the fertility rate of new immigrants is higher than average, though it reverts to the local mean within a few years. So at first, migration adds to the birth rate. Strangely, this higher initial fertility does not seem to happen in Asia, or at least not in South Korea. According to Kwang-hee Jun of Chungnam National University, non-naturalised immigrant women have on average just 1.08 children—even fewer than native Koreans, whose average is 1.79.

This finding was a shock and a puzzle. Why are immigrants in South Korea behaving so differently from those in Europe and America? One explanation may be that the age gaps between husbands and much younger wives discourage large families. Another is that in the past decade, about 60% of foreign brides have come from China, where the fertility rate is also low, especially among Chinese of Korean ethnicity. Jungho Kim of Ajou University also suggests poverty. Both spouses will usually work and may be unable to afford to bring up a child in a society where half of the cost of pre-school education comes from the household budget. Evidence for this comes from families with a Vietnamese-born bride: when they do have children, says Danièle Bélanger of the University of Western Ontario, they send some of them back to be raised for a few years by grandparents in Vietnam, where schooling is cheaper.

Victims or opportunists?

Marriage between girls from poor countries and older men from rich ones are controversial. As Sang-lim Lee of the International Organisation of Migration centre in Goyang says, when men pay the brides' family “they tend to think they have bought a good. If it has a defect, they think they can send it back.”

It is certainly true that the men tend to be older, often much older. Doo-Sub Kim finds that Korean husbands are on average 17 years older than their Vietnamese-born brides. They usually have around three years' more education as well. One fifth of Korean husbands have been married before. All this is very different from the typical pattern in native Korean marriages.

It is also true that some young women are victims of cruelty, neglect, physical abuse and trafficking. Women in strange countries are almost always vulnerable. A Vietnamese interpreter married to a Korean man complains that “if I run away here, my parents will be embarrassed in Vietnam.” That, she explains, would leave her unable to return home, but with “no place to go here”. The media in Vietnam tend to portray migrant brides either as victims of trafficking or people driven by desperate poverty to migrate. Children of international marriages in South Korea have more health problems than average. In Taiwan, they do less well at school—something that occurs in European countries, too.

Yet this is not the dominant pattern, still less the sole one. International marriages often seem to work for the couple involved—at least if the longevity of their union is any guide. And they seem to have social benefits, as well as costs, for both receiving and sending countries.

Though the gap in background, age and education between spouses in international marriages is greater than in those between compatriots, it does not seem to affect these unions' durability. Doo-Sub Kim plotted the time that cross-border marriages have lasted in South Korea against the couples' ages and educational backgrounds. Amazingly, the bigger the difference, the longer the marriage. It is hard to know why this should be. Maybe those who marry foreigners invest more in their marriages. Or maybe younger, poorer wives find it harder to leave.

Vietnamese girls are seen in much of Asia as the paradigm of the submissive foreign bride. But a study of their role in Taiwan by Ms Bélanger shows that many are married to men whose companies trade with Vietnam—and they are vital to the companies' future. As one man told her, revealingly: “I have six trusted subordinates. One is my wife. One is her younger sister. They will not betray me.” Remittances to their families help keep the practice alive in Vietnam, even though many young men there dislike it and say they have been driven out of their villages by the shortage of brides and forced to migrate to Hanoi and Ho Chi Minh City. Similarly, marriage abroad is seen as so desirable by the Punjabi diaspora that the press in Punjab is full of advertisements offering to arrange marriages abroad.

Not all international marriages in Asia are those of poor brides in rich lands. In a “reverse migration” Japanese women from rich Tokyo have married into poor peasant families in South-East Asia—especially in Bali and Thailand—and settled down to live a more “authentic” rural life, perhaps as a way of escaping the strictness of Japanese family life. That same impulse may well be behind the surprising growth in the numbers of Japanese women married to Africans in Japan (probably as many as 3,300 in all). As one wife told Djamila Schans of Maastricht University, “I had doubts marrying a foreigner but he waited for me at the station every day. Sometimes even with flowers! A Japanese man would never do such a thing.”