Calculating the divorce rate

My Twitter (@benjamincaldwel) went all atwitter a couple of days ago with news that Russia’s divorce rate peaked in 2002 at more than 800 divorces for every 1000 marriages. Does this mean the country has a whopping 80% divorce rate?

In a word, no. While there are lots of ways to calculate the divorce rate, each of them flawed in some way, simply comparing one year’s number of divorces with the same year’s number of marriages is among the worst ways to do it. From a 2005 New York Times article on the topic, which also debunks the longstanding myth that half of US marriages end in divorce:

[Researchers note that] the people who are divorcing in any given year are not the same as those who are marrying, and that the statistic is virtually useless in understanding divorce rates. In fact, they say, studies find that the divorce rate in the United States has never reached one in every two marriages, and new research suggests that, with rates now declining, it probably never will.

Russia’s actual divorce rate is surely high, and does appear to be higher than the US. But I would ballpark Russia’s divorce rate in the 50-60% range for couples getting married this year. I’ll explain how I got there momentarily.

The difficulty in calculating the divorce rate is that it necessarily involves speculation. The only way to avoid some kind of speculating would be if you took a sample of people married in the same year (1930, let’s say) and then waited for everyone married that year to have their marriages end, either through death or divorce. You’d get a pretty accurate rate that way, you would just have to wait a long time to get it.

Most of us are interested in more current numbers. For example, how many of the couples getting married this year (or at least, some year in the not-too-distant past) can we expect to see end their marriages in divorce? Since not all of those couples have divorced yet, we’re into speculative territory.

What some researchers do is what they call a “life table” approach. They may take an estimate of the time frame in which half of divorces occur — usually between 0 and about 7 years of marriage, though the exact timeframe varies — and work from there. For example, let’s say we have a sample of 100 US couples married in 2002, and of those 21 have divorced as of today. If we have reason to believe that half of the couples married in 2002 who will divorce have now done so, we could estimate the divorce rate for couples married in 2002 to be around 42%. But that is an educated guess. We don’t really know where that midway point of divorces takes place, we just guess based on past history and currently identifiable trends. And if we want really current numbers, like an estimate for couples who are only now getting married, we need to be even more speculative: We now must also guess about where that midpoint in the distribution of divorces is going to be. Such an approach, even when done as well as possible at the time, runs an inherent risk of making you look foolish in retrospect.

Further complicating matters, divorce rates are influenced by a variety of factors, some more easily predictible than others. Demographic, economic, and other social changes are just three examples, and all of these have had major impacts on Russia in the past two decades.

Ultimately, no one knows precisely what the divorce rate for couples marrying this year will be, because it’s all based on speculation about possible future divorces that haven’t happened yet.

Now, back to Russia. As I said at the beginning of this post, even though they can document 800 or more divorces per 1000 marriages in 2002, that is absolutely, unequivocably not an 80% divorce rate. It is an inappropriate comparison of two very different cohorts. The population is different. That same article on Russia notes that from 1980 to 2005, the number of marriages decreased by one-fourth. So, relative to the population of couples available to be married, the population of couples available to be divorced has been growing significantly.

For the purposes of demonstration, I’m going to make up some numbers to show how flawed it is to compare a given year’s number of marriages with that same year’s number of divorces to try to calculate a divorce rate.

First, let’s assume an actual divorce rate of 60%, and that the rate breaks down to 10% per year in the 1st through 6th years of marriage. (This is wrong, of course, but used for demonstration purposes.) Second, let’s assume that the marriage rate declined 25% from 1988 to 2002, and declined evenly in that time. This is a small exaggeration, since the actual 1/4 decline took from 1980 to 2005. Finally, let’s assume the actual divorce rate had held constant at 60% since the dawn of time. If we use 1333.3 marriages in 1988 as our starting number (you can use any number there, since it’s the percentages that matter), what we would see would look something like this:

1995
Marriages: 1167
Divorces: 750
Apparent divorce rate: 64.29%
Actual divorce rate: 60%
Difference: 4.29%

2002
Marriages: 1000
Divorces: 650
Apparent divorce rate: 65%
Actual divorce rate: 60%
Difference: 5.00%

Three key points here: 1, notice how this exaggerates the “apparent” divorce rate for those simply comparing the number of marriages to the number of divorces in a specific year. 2, notice how the systematic exaggeration of the “apparent” divorce rate as compared with the actual divorce rate gets worse over time. This is always going to be true when the marriage rate is in decline. 3, our process here assumed that all divorces were done by the seventh year of marriage because it makes the math easier. Making this more real by assuming that half of divorces are done by the seventh year of marriage, and the other half take place at gradually dwindling frequency rates after that, would make the systematic exaggeration of the “apparent” divorce rate much worse.

We can demonstrate this with a different set of assumptions. Let’s again assume a 60% divorce rate since the dawn of time, but now let’s assume a more realistic distribution of those divorces. Let’s say that half of divorces take place in years one through six, and the other half are evenly distributed between years 7 and 16 of marriage. Let’s assume the same marriage rate decline as what’s actually scientifically justified — 25% from 1980 to 2005. Starting from a good-for-easy-math number of 2000 marriages in 1980, we then see numbers that look like this:

1996
Marriages: 1680
Divorces: 1096
Apparent divorce rate: 65.36%
Actual divorce rate: 60%
Difference: 5.36%

2002
Marriages: 1560
Divorces: 1026
Apparent divorce rate: 65.77%
Actual divorce rate: 60%
Difference: 5.77%

These show that the “apparent” and actual divorce rates are not the same thing, and they show how comparing one year’s number of marriages with the same year’s number of divorces creates worse comparisons over time. Admittedly, they do not account for the full scope of that 800-versus-1000 number. I say the actual current rate is in the 50-60% range because (1) by presuming an end point to divorces after a specific number of years, my examples here do more to deflate the difference in actual-vs-apparent divorce rates than to inflate them; the distinction becomes greater when you model the numbers in ways that more closely approximate reality. And (2) these statistical models do not account for other social and economic changes in Russia that may be throwing off the divorce curve, that is, how divorces are distributed over time among those couples who do divorce. With those in mind, I would ballpark the expected divorce rate for couples getting married in Russia this year in the 50-to-60 percent neighborhood, though again, social and economic conditions can influence the numbers greatly in either direction.

Thankfully, there are lots of people out there who do this kind of work for a living, and can do both the detail work and the explantion better than I can. Andrew Cherlin and David Popenoe are two worth reading. More information on the flaws inherent in estimating divorce rates is here.