## 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.

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