Divorce Rate math question

This one has made me wonder for some time. Since the early 1980s it has been said that half of all marriges end in divorce. That rose from 1/3 in the 1960s and 70s and then leveled off there for the most part. This figure is gotten by taking all the divorces and all the marriges then divifing the former by the later.

1,000 marriges this year, 500 divorces, rate is 50%.

But is it that simple? Since you do not usually get divorced the same year you get married those 500 divorces are from a pool of marriges from years past. Over time this should even out, or should it?

Question for the group is this: is this simple way of calculation overstating the rate?

You might be interested in these pages, assuming you haven't seen them already:

http://www.nytimes.com/2005/04/19/health/19divo.html

http://www.nytimes.com/1990/05/27/weekinreview/l-how-to-calculate-the-us-divorce-rate-correctly-707290.html

http://digitalcitizen.ca/2009/06/02/50-divorce-rate-is-a-myth-its-more-like-33-or-one-third/

Half the marriages end in divorce.

More than one half of the children born in America are born out of wedlock.

More than one half of the children born in America are not caucasian.

A changing world ...

Quote: EdCollins

You might be interested in these pages, assuming you haven't seen them already:

http://www.nytimes.com/2005/04/19/health/19divo.html

http://www.nytimes.com/1990/05/27/weekinreview/l-how-to-calculate-the-us-divorce-rate-correctly-707290.html

http://digitalcitizen.ca/2009/06/02/50-divorce-rate-is-a-myth-its-more-like-33-or-one-third/

Thanks for the links. This kind of helps, though I am still working to get mind into how the numbers totally work. I get that they do, but trying to visualize it some way.

It would seem to me that only a constitutional amendment banning divorce is the only way to protect the sanctity of marriage.

Quote: WongBo

It would seem to me that only a constitutional amendment banning divorce is the only way to protect the sanctity of marriage.

Divorce should be harder, but what does this have to do with the math question?

If for some reason the number of marriages per year dropped while the number of divorces held steady, then this metric would somewhat artificially "increase." I suppose conversely, if a whole new group of people were to suddenly be allowed to marry, there may be a temporary drop in the divorce rate during the period before the marriages of the new group began to fail. I guess what I'm saying is that there's a significant trailing effect, with divorces necessarily following marriages by some average period of time.

If the population were constant then we would expect to see one divorce per two marriages in any given year assuming a 50% probability of divorce.

However, the population of the US is increasing by about 1% per year. Assuming a uniform age distribution (which isn't the case), then a ratio of one divorce per two marriages per year would suggest a greater than a 50% probability of divorce, because people are generally younger when they get married than divorced, and the divorces are coming from a smaller population cohort.

The waters really get muddy when you consider the uneven age distribution and that some ages have higher marriage rates than others. All things considered, I think it is still safe to say that the probability of any given new marriage ending in divorce is about 50%, perhaps a little higher.

This is the same problem as the actuarial calculations for life expectancy.

They compute the age of death of people who die in the present time. But these are people born previously; many of them *very* previously.
What they compute is the average age of death of old people.

If you are looking for the life expectancy of a newborn baby, basically what you do is "future guessing", since you have no statistical data yet on their age of death.

The most advanced models try to extrapolate to the future the data from past generations. But this assumes that the trends will maintain ; however, trends have changed form several times during the last century. So this model is also flawed.

Conclusion: the future is not predictible (in these demographic cases). Neither for life expectancy, nor for divorce. Nor for population growth.
Only wise guesses.

From what I remember from a Demographics course I took at university a very long time ago there are 2 basic type of demographic statistics:
Cohort statistic: Following a particylar cohort (ie people born in a particular year)
Period Statistics: Statictic for a paricular year (I think that's the name but it could be some other name)
Almost all demographics statistics published (birth rates, death rates, life expetancy etc) are period statistics.
Cohort statistics are rarely published and when published are estimates. (since all people in the cohort must have died to calculate accurately)
BUT the interpretation of the period statistic on the average person (including most journalists and politician) relates to the cohort statistic.

A question to the Wizzard as Actuary about Life expectancy rates and tables.
Do the actuarist make assumptions about future life expectancy rates and tables when calculating Life Insurance Premiums based on the increase of life expectancy in the past?

I may be wrong, but I recall that the 50% divorce rate applies to the marriages in the current year. For example, of the marriages that are started in 2012, half of them will not survive the lifespan of the partners. Some celebrity ones may last a few hours, others may last 50 years, but half will split before one of the partners passes away.

Quote: AceTwo

A question to the Wizzard as Actuary about Life expectancy rates and tables.
Do the actuarist make assumptions about future life expectancy rates and tables when calculating Life Insurance Premiums based on the increase of life expectancy in the past?

You mean actuary, not actuarist. A cohort life table, or future period life table, should take into consideration future increases in life expectancy. I never had to do this, but in just overhearing coversations at SSA I think they mainly just look at trends in how long people are living now compared to the past. Such assumptions had huge impacts in how long the trust funds were expected to last, so these decisions were made at very high levels.

Some marriages last 18 hours. If one gets married 5 times and divorced 5 times during the year, does that count 5 times?

Quote: s2dbaker

Some marriages last 18 hours. If one gets married 5 times and divorced 5 times during the year, does that count 5 times?

Yes.