Divorce and marriage patterns, some Danish data

I decided to follow up on this post and have a closer look at the Danish numbers. In the post I’ve used data from Statistics Denmark’s public database (Statistikbanken). First, let’s just have a look at the raw numbers (from: ‘SKI107: Skilsmisser fordelt efter parternes bopæl, alder og ægteskabets varighed’):

The above graph displays the total number of divorces as a function of the length of marriage for the divorces that happened in Denmark during the year 2010. To take an example, 911 couples divorced after 3 years of marriage. Divorce risk as a function of marriage duration is pretty much (though not completely) monotonically decreasing over time (yes, I know it’s problematic to extrapolate from cross-sectional data like this, but let’s just pretend for a moment that this makes sense anyway…) after the first decade of marriage. When looking only at the first 10-15 years the distribution looks a bit bimodal. Actually, I can’t help remarking here more specifically that when it comes to the 7th year, the divorce risk is actually lower than it is for any other marriage duration in the 0-9 year span except for the first two years of marriage – i.e. the 7 year mark is a local minimum. There were 148 divorces at the 25-year mark, but only 93 divorced after 27 years of marriage. This is not to say that the risk of divorce at the 25-year mark is high – it’s almost twice as high for marriages that have lasted exactly 20 years (291) – but the risk doesn’t really tail off there, rather it does it a couple years later (in terms of marriage duration). The total number of divorces in 2010 was 14292, or about 39 each day of the year. I found it interesting that whereas people are much more likely to marry during the summer, there does not seem to be much systematic variation in the divorce rate over the course of the year – but you can judge yourself, here are the data from 2010 (‘BEV3C: Vielser og skilsmisser på måneder’):

['2010M01' = First month of 2010 (and so on)]

Back to the other data set, if we once again assume that the age/duration profile of divorcees/divorces do not change much over time so that we can extrapolate from the data we have, and you then decide to condition on a divorce actually happening during a marriage, what is then the likelihood that a marriage that will fail will end at year X? (To make this absolutely clear: This is not the probability that a marriage that has lasted X years will end in divorce during that year.)

If you instead look at the cumulative distribution function, it looks like this:

I cut it off after 20 years – more than 85% of all divorces are accounted for by then and adding more numbers seemed counterproductive because it made it harder to see what was going on to the left of the graph – where the most important stuff’s going on – in detail. More than half of the marriages that ended in divorce in 2010 were marriages between partners who had been together for 9 years or less. 73% of them were between partners who’d been together for 15 years or less. Almost one fourth of them (24%) had only lasted 4 years or less.

Divorce data

From page 18 of this book, Divorce: causes and consequences. The book also mentions a 2002 CDC report which found that after three years, 12 % of all marriages had ended in divorce or separation; after 5 years, 20 % of all first-marriages had ended, after 10 years; 33 %. After 15 years the number is 43 %. Maybe there’s such a thing as a ’7-year-itch’, but the divorce likelihood is statistically much higher in the years before that and divorce risk in general is highly front-loaded. If 20 % of all marriages have ended in divorce after 5 years and the likelihood that a marriage will end in divorce after 50 years is 50%, that means that 40 % of all divorces that do happen (…at least within a 50 year time frame) take place during the first 5 years of marriage. In the US, first marriages that end in divorce last about eight years [on average].

US divorce patterns might not be similar to those found other places, so it makes sense to add some data from the UK (same link): “According to [a 2004] survey, husbands engaged in extramarital affairs in 75% of cases; wives in 25%. In cases of family strain, wives’ families were the primary source of strain in 78%, compared to 22% of husbands’ families. Emotional and physical abuse were more evenly split, with wives affected in 60% and husbands in 40% of cases. In 70% of workaholism-related divorces it was husbands who were the cause, and in 30%, wives. The 2004 survey found that 93% of divorce cases were petitioned by wives, very few of which were contested. 53% of divorces were of marriages that had lasted 10 to 15 years, with 40% ending after 5 to 10 years. The first 5 years are relatively divorce-free, and if a marriage survives more than 20 years it is unlikely to end in divorce.”

As should be clear from the above passages, divorce patterns are not the same across countries. In the US, people are more likely to divorce early on, whereas the Brits tend to wait longer before they split up. CDC probably has more US data here if Plamus or Gwern (or others?) are interested in taking a closer look, but I didn’t find what I was looking for and I didn’t want to spend a lot of time searching for that data.

If people marry young, the likelihood of divorce is much higher than if they do not. Here’s another graph from the book (p.36):

This link between age and divorce risk is not controversial, the wikipedia link has more:

“Success in marriage has been associated with higher education and higher age. 81% of college graduates, over 26 years of age, who wed in the 1980s, were still married 20 years later. 65% of college graduates under 26 who married in the 1980s, were still married 20 years later. 49% of high school graduates under 26 years old who married in the 1980s, were still married 20 years later.[28]” [...] In 2009, 2.9% of adults 35–39 without a college degree were divorced, compared with 1.6% with a college education.[30]“

The book notes (p.40) that: “Interracial marriages are more likely to disrupt than marriages in which both spouses are the same race and ethnicity.[36] Interracial marriages have a 10 percent higher chance of failure in the first 10 years than same-race marriages (41 percent versus 31 percent).”

Here’s another interesting tidbit from the wikipedia article:

“According to a study published in the American Law and Economics Review, women currently file slightly more than two-thirds of divorce cases in the United States.[67] There is some variation among states, and the numbers have also varied over time, with about 60% of filings by women in most of the 19th century, and over 70% by women in some states just after no-fault divorce was introduced, according to the paper. Evidence is given that among college-educated couples, the percentages of divorces initiated by women is approximately 90%.” [my emphasis - again, from the wikipedia link above. This 90% estimate is comparable to the British estimate above and maybe I should have emphasized that one as well. Anyway, it seems that females are much more likely to file for divorce than are males, and it seems that they are pretty much almost always the ones to file for divorce when both partners have a high education level. There's needless to say more than one model of marriage dynamics that fits those facts, but in order to get a good model, you probably need to include in such a model the fact that males are on average much more likely to cheat on their partner than are females.]

The figure below (the book, p.32) on household data is somewhat unrelated to the above, but worth posting:

Part iii of this previous post of mine has some related Danish household data. Danish readers might also want to reread this post if they want to know more about some related Danish numbers. Right now I’m considering having a closer look at Statistics Denmark’s data on marriage/divorce-patterns – I know they have data on this stuff – so I might write another post on this subject at a later point in time.

Reexamining the Case for Marriage: Union Formation and Changes in Well-being

“This article addresses open questions about the nature and meaning of the positive association between marriage and well-being, namely, the extent to which it is causal, shared with cohabitation, and stable over time. We relied on data from the National Survey of Families and Households (N = 2,737) and a modeling approach that controls for fixed differences between individuals by relating union transitions to changes in well-being. This study is unique in examining the persistence of changes in wellbeing as marriages and cohabitations progress (and potentially dissolve) over time. The effects of marriage and cohabitation are found to be similar across a range of measures tapping psychological well-being, health, and social ties. Where there are statistically significant differences, marriage is not always more advantageous. Overall, differences tend to be small and appear to dissipate over time, even when the greater instability of cohabitation is taken into account. [...]

Examined across a range of outcomes, we found the similarities between marriage and cohabitation to be more striking than the differences: Entering into any union improved psychological well-being and reduced contact with parents and friends. Direct marriage and marriage preceded by cohabitation were statistically indistinguishable in all outcomes examined, providing no evidence that premarital cohabitation has negative consequences for wellbeing or ties to family and friends. When union dissolutions were excluded from the analysis, there were no statistically significant differences between the married and cohabiting for depression, relationships with parents, contact with parents, or time with friends. [...] The married fared better in health than cohabitors, but the opposite was true of happiness and self-esteem. [...]

We found no evidence that marriage and cohabitation provide benefits over being single in the realm of social ties; indeed, entering into a union reduced contact with parents and social evenings with friends. In some ways, of course, it is not surprising that forming a coresidential relationship reduces time with others, as partners spend time together that cannot be spent elsewhere. These findings do not, however, support arguments in the literature that marriage expands social circles and does so to a greater extent than cohabitation (e.g., Nock, 1995). Our results are more consistent with Sarkisian and Gerstel’s (2008) assessment of marriage as a ‘‘greedy’’ institution — and suggest the same of cohabitation. [...] We found no change over time in the effects of marriage and cohabitation on ties with family and friends, suggesting that these ties do not rebound in the years following marriage or cohabitation.”

With as many as half of all marriages ending in divorce or separation (Goldstein, 1999; Raley & Bumpass, 2003), marriage is as likely to be temporary as it is to be a lifetime relationship.”

Here’s the link.

(More) random stuff

Can’t let the blog die so I sort of have to at least post something from time to time. So here goes…

1. Global sex ratios:

At birth: 1.07 male(s)/female
Under 15 years: 1.07 male(s)/female
15-64 years: 1.02 male(s)/female
65 years and over: 0.79 male(s)/female
Total population: 1.01 male(s)/female (2011 est.)

Link. Here’s an image of child sex ratios in India (via brownpundits:

Here’s one for the whole population, image credit: Wikipedia (much larger version at the link):

I’ve from time to time read about the Chinese gender ratio problem, I didn’t know there were much going on on that score in India. The clustering of gender ratio frequencies seems in my opinion sufficiently non-random to merit some explanation or other, especially when it comes to the northern provinces (Punjab, Haryana & Kashmir). Here’s a pic dealing with more countries:

Link.

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2. Gambler’s ruin. I remember having read about this before, but you forget that kind of stuff over time so worth rehashing. I think the version of the idea I’ve seen before is the first of the four in the article; ‘a gambler who raises his bet to a fixed fraction of bankroll when he wins, but does not reduce it when he loses, will eventually go broke, even if he has a positive expected value on each bet.’ I assume all readers of this blog already know about the Gambler’s fallacy but in case one or two of you don’t already do click the link (and go here afterwards, lots of good stuff at that link and I shall quote from it below as well) – that one is likely far more important in terms of ‘useful stuff to know’ because we’re so prone to committing this error; basically the important thing to note there is that random and independent events are actually random and independent.

A couple of statistics quotes from the tvtropes link:

“The Science Of Discworld books have an arguably accurate but somewhat twisted take on statistics: the chances of anything at all happening are so remote that it doesn’t make sense to be surprised at specific unlikely things.”

“There is something fascinating about science. One gets such wholesale returns of conjecture out of such a trifling investment of fact.” (Mark Twain. Maybe it’s more of a science quote really – or perhaps a ‘science’ quote?)

“People (especially TV or movie characters who are against the idea of marriage) often like to cite the “50 percent of marriages end in divorce” statistic as the reason they won’t risk getting hitched. That is actually a misleading statistic as it seems to imply that half of all people who get married will wind up divorced. What it doesn’t take into account is the fact that a single person could be married and divorced more than once in a single lifetime. Thus the number of marriages will exceed the number of people and skew the statistics. The likelihood that any one person chosen at random will be divorced during their lifetime is closer to 35 percent (the rate fluctuates wildly for males, females, educated and uneducated populations). It’s still a huge chunk of people, but not as high a failure rate for marriage for an individual as the oft-cited “50 percent of all marriages” statistic would leave you to believe.” (comment after this: “How can you give that setup and not deliver the punchline. “But the other half end in death!”")

A mathematics quote:

“Black Mage: 2 + 2 = 4
Fighter: You can’t transform numbers into other numbers like that. It’d just go on forever. That’s like Witchcraft! “

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3. Messier 87. Interesting stuff, ‘good article’, lots of links.

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4. Substitution cipher. I’d guess most people think of codes and codebreaking within this context:

“In cryptography, a substitution cipher is a method of encryption by which units of plaintext are replaced with ciphertext according to a regular system; the “units” may be single letters (the most common), pairs of letters, triplets of letters, mixtures of the above, and so forth. The receiver deciphers the text by performing an inverse substitution.

Substitution ciphers can be compared with transposition ciphers. In a transposition cipher, the units of the plaintext are rearranged in a different and usually quite complex order, but the units themselves are left unchanged. By contrast, in a substitution cipher, the units of the plaintext are retained in the same sequence in the ciphertext, but the units themselves are altered.

There are a number of different types of substitution cipher. If the cipher operates on single letters, it is termed a simple substitution cipher; a cipher that operates on larger groups of letters is termed polygraphic. A monoalphabetic cipher uses fixed substitution over the entire message, whereas a polyalphabetic cipher uses a number of substitutions at different times in the message, where a unit from the plaintext is mapped to one of several possibilities in the ciphertext and vice-versa.”

The one-time-pad stuff related is quite fascinating; that encryption mechanism is literally proven unbreakable if applied correctly (it has other shortcomings though..).

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5. Evolution may explain why baby comes early.

“there’s only so much a human female pelvis can increase in terms of width before serious functional problems in locomotion make change in that direction unfeasible. [...] If the pelvis was prevented from getting any wider due to biomechanics, and a large adult brain was a necessary condition of high fitness value for humans, then one had to accelerate the timing of childbirth so that the neonate exited while the cranium was manageable in circumference.”

Interesting stuff.

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6. Random walk. The article actually has some stuff related to the previous remarks on gambler’s ruin.

Quote of the day

If marriage was a manufactured product it would be promptly banned in many countries due to its outrageous failure rate and the damage caused by the failures.

‘Doug’, here.

Random fact of the day

Almost 40 percent of America’s children are born to unmarried parents.

A lot more here, HT: Tyler Cowen.