Lifetime chance of marrying for Black and White women

I’m going to Princeton next week to give a talk at the Office of Population Research. It’s a world-class population center, with some of the best trainers and trainees in the business, so I figured I’d polish up a little formal demography for them. (I figure if I run through this really fast they won’t have time to figure any mistakes I made.)

The talk is about Black and White marriage markets, which I’ve written about quite a bit, including when I posted the figure below, showing the extremely low number of local same-race, employed, single men per women Black women experience relative to White women — especially when they have less than a BA degree.

This figure was the basis for a video we made for my book, titled “Why are there so many single Black women?” For years I’ve been supporting the strong (“Wilsonian“) case that low marriage rates for Black women are driven by the shortage of “marriageable” men — living, employed, single, free men. I promised last year that Joanna Pepin and I were working on a paper about this, and we still are. So I’ll present some of this at Princeton.

Predictions off

Five years ago I wrote about the famous 2001 paper by Joshua Goldstein and Catherine Kenney, which made lifetime marriage predictions for cohorts through the Baby Boom, the youngest of whom were only 30 in the 1995 data the paper used. That’s gutsy, predicting lifetime marriage at age 30, so there’s no shame that they missed. They were closer for White women. They predicted that 88.6% of White women born 1960-1964 would eventually marry, and by the age 49-53 (in the 2013 American Community Survey) they were at 90.2%, with another 2.3% likely to marry by my estimates (see below). For Black women they missed by more. For the 1960-1964 cohort, they predicted only 63.8% would ever marry, but 71.3% were already married by 2013, and I’m projecting another 7.5% will marry. (I also wrote about a similar prediction, here.) If they actually get to 79%, that will be very different from the prediction.

Their amazing paper has been cited another 100 times since I wrote about it in 2010, but it doesn’t look like anyone has tried to test or extend their predictions.

Mass incarceration

Interestingly, Goldstein and Kenney undershot Black women’s marriage rates even though incarceration rates continued to rise after they wrote — a trend strongly implicated in the Black-White marriage disparity. This issue has increased salience today, with the release of a powerful new piece by Ta-Nehisi Coates in the Atlantic (my old job), which exposes the long reach of mass incarceration into Black families in ways that go way beyond the simple statistics about “available” men. The large ripple effects implied by his analysis — drawing from his own reporting and research by Devah Pager, Bruce Western, and Robert Sampson — suggest that any statistical model attempting to identify the impact of incarceration on family structure is likely to miss a lot of the action. That’s because people who’ve been out of prison for years are still affected by it, as are their relationships, their communities — and their children in the next generation.

Some new projections

I should note that some readers unfamiliar with demographic analysis may find parts of what follows morbidly depressing.

To set up the marriage market analysis I’m doing with Joanna — which isn’t ready to show here yet — I’m going to introduce some marriage projections at the talk. These use a different method than Goldstein and Kenney, because I have a different kind of data. This is a lifetable approach, in which I use first-marriage rates at every age to calculate how many women would get married at least once before they die if they lived 2010 over and over again from birth to death. I can do this because, unlike Goldstein and Kenney in 2001, I now have the American Community Survey (ACS), which asks a giant sample of people if they have married in the previous year, and how many times they’ve been married before, so I can calculate a first-marriage rate at every age. To this I add in death rates — making what we call a multiple-decrement life table — so that there are two ways out of the birth cohort: marriage or death. (Give me marriage or give me death.)

The way this works is you start with 100,00 people, and each year some of them die and some of them get married — according to the rates you have measured at one point in time. For example, in my tables, of 100,000 Black women at the start of year 0, only 98.7% make it to age 15, the first year they can be counted as married in the data. By the time you get down to age 30, there are only 67,922 left, as 2,236 have died and 29,843 have married for the first time. And so on down to the bottom. In the last row of the table, when they are all dead, you calculate how many got married before dying.*

The bottom line: 85.3% of White women, and 78.4% of Black women born and stuck in 2010 forever are projected to marry before they die — a surprisingly small gap. The first figure shows you that basic result:

Note that my projections of 85.3% of White women and 78.4% of Black women ever marrying are lower than, for example, the roughly 96% of White women and 91% of Black that were actually ever-married at age 85+ in 2010 (reported here), for several reasons. First, I count dead people against the ever-married number (additionally, married people live longer, not necessarily because they’re married). Second, today’s 90+ year-olds mostly got married 70 years ago, when times were different; my estimates are a projection of nowadays.

A very interesting age pattern emerges here, which is relevant to the incarceration and “available men” question. If you look back at the figure, notice that the big difference in marriage opens up early — peaking at 28 points by age 33, before narrowing to 7 points at the end.The big difference in marriage is that White women marry earlier. In fact, as the next figure shows, after age 33 Black women are more likely to marry than are White women. I don’t think I knew that. Here are the number marrying at each age:

Specifically, although White women are twice as likely to marry in their mid-twenties, of our fictional 100,000 women stuck in 2010, just 15.6% of White women, compared with 36.8% of Black women end up marrying after age 33.

The other way of looking at this — and an answer to a common question about marriage rates — is to see the chances of marrying after a given age if you haven’t married yet. This figure shows, for example, that a White women who lives to age 45 without marrying has a 26% chance of someday marrying, compared with a whopping 49% for Black women.

It is surprising that Black women, with lower cumulative odds of marrying at every age in the cohort, are so much more likely to marry conditional on getting to their 40s without marrying. Maybe you’ve got a better interpretation of this, but this is mine. Black women are not against marriage, and they are not ineligible for marriage in some way (even though most of these single women are already mothers**). Rather, they have not married earlier because they couldn’t find someone to marry. That’s because of all the Black men who are themselves dead, incarcerated or unemployed (or scarred by those experiences in their past) — or married to someone else. So within their respective marriage markets (which remain very segregated), the 45-year-old single White woman is much more likely to be someone that either doesn’t want to marry or can’t marry for some reason, while the 45-year-old single Black woman is more active and eligible in the marriage market. This fits with the errors in the earlier predictions, which failed to pick up on the upward shift in marriage age for Black women — marriage delayed rather than foregone.

What do you think of that interpretation? If you have a better idea I’ll mention you at Princeton next week.

Note: I found so many mistakes as I was doing this that it seems impossible there are any more. Nevertheless, caveat emptor: This analysis hasn’t been peer reviewed yet, so consider it only as reliable the latest economist’s NBER paper you read about on the front page of the every newspaper and website on earth. (And if you’re a journalist feel free to refer to this as a new working paper.)

* Technical notes: I used death rates from 2010 (found here), and marriage rates from the five-year ACS file for 2008-2012 (which has 2010 as its midpoint), from IPUMS.org. I adjusted the death rates because never-married people are more likely to die than average (I told you this was depressing). I had to use a 2007 estimate of mortality by age and marital status for that (found here), which is not that precise because it was in 10-year increments, which I didn’t bother to smooth because they didn’t have much effect anyway. The details of how to do a multiple-decrement lifetable are nicely described (with a lot of math) by Sam Preston here (though if you really want to replicate this, note one of his formulas is missing a negative sign, so plan to spend an extra few days on it). To help, I’m sharing my spreadsheet here, which has the formulas. (Note that survival in the life table doesn’t refer to being alive, it refers to being both alive and never-married.) The mortality and marriage rates are for non-Hispanic women; the never-married adjustment is for all women. For the marriage rates I used all Black and White women regardless of what other races they also specified (very few are multiple-race when you exclude Hispanics).

** In 2010, 63% of never-married Black women who lived in their households had at least own of their own children living with them.