Decadally-biased marriage recall in the American Community Survey

Do people forget when they got married?

In demography, there is a well-known phenomenon known as age-heaping, in which people round off their ages, or misremember them, and report them as numbers ending in 0 or 5. We have a measure, known as Whipple’s index, that estimates the extent to which this is occurring in a given dataset. To calculate this you take the number of people between ages 23 and 62 (inclusive), and compare it to five-times the number of those whose ages end in 0 or 5 (25, 30 … 60), so there are five-times as many total years as 0 and 5 years.

If the ratio of 0/5s to the total is less than 105, that’s “highly accurate” by the United Nations standard, a ratio 105 to 110 is “fairly accurate,” and in the range 110 to 125 age data should be considered “approximate.”

I previously showed that the American Community Survey’s (ACS) public use file has a Whipple index of 104, which is not so good for a major government survey in a rich country. The heaping in ACS apparently came from people who didn’t respond to email or mail questionnaires and had to be interviewed by Census Bureau staff by phone or in person. I’m not sure what you can do about that.

What about marriage?

The ACS has a great data on marriage and marital events, which I have used to analyze divorce trends, among other things. Key to the analysis of divorce patterns is the question, “When was this person last married?” (YRMARR) Recorded as a year date, this allows the analyst to take into account the duration of marriage preceding divorce or widowhood, the birth of children, and so on. It’s very important and useful information.

Unfortunately, it may also have an accuracy problem.

I used the ACS public use files made available by IPUMS.org, combining all years 2008-2017, the years they have included the variable YRMARR. The figure shows the number of people reported to have last married in each year from 1936 to 2015. The decadal years are highlighted in black. (The dropoff at the end is because I included surveys earlier than those years.)

Yikes! That looks like some decadal marriage year heaping. Note I didn’t highlight the years ending in 5, because those didn’t seem to be heaped upon.

To describe this phenomenon, I hereby invent the Decadally-Biased Marriage Recall index, or DBMR. This is 10-times the number of people married in years ending in 0, divided by the number of people married in all years (starting with a 6-year and ending with a 5-year). The ratio is multiplied by 100 to make it comparable to the Whipple index.

The DBMR for this figure (years 1936-2015) is 110.8. So there are 1.108-times as many people in those decadal years as you would expect from a continuous year function.

Maybe people really do get married more in decadal years. I was surprised to see a large heap at 2000, which is very recent so you might think there was good recall for those weddings. Maybe people got married that year because of the millennium hoopla. When you end the series at 1995, however, the DBMR is still 110.6. So maybe some people who would have gotten married at the end of 1999 waited till New Years day or something, or rushed to marry on New Year’s Eve 2000, but that’s not the issue.

Maybe this has to do with who is answering the survey. Do you know what year your parents got married? If you answered the survey for your household, and someone else lives with you, you might round off. This is worth pursuing. I restricted the sample to just those who were householders (the person in whose name the home is owned or rented), and still got a DBMR of 110.7. But that might not be the best test.

Another possibility is that people who started living together before they were married — which is most Americans these days — don’t answer YRMARR with their legal marriage date, but some rounded-off cohabitation date. I don’t know how to test that.

Anyway, something to think about.

The coming divorce decline

Unless something changes outside the demogosphere, the divorce rate is going to go down in the coming years.

Divorce represents a number of problems from a social science perspective.

• • Most people seem to assume “the divorce rate” is always going up, compared with the good old days, which are supposed to be the whole past but are actually represented by the anomalous 1950s.
  • On other hand, social scientists have known for a few decades that “the divorce rate” has actually been declining since the 1980s. That shows up in the official statistics, with the simple calculation — known as the refined divorce rate — of the number of divorces per 1,000 married women.
  • On the third hand, the official statistics are very flawed. The federal system, which relies on states voluntarily coughing up their divorce records, broke down in the 1990s and no one fixed it (hello, California doesn’t participate). In the debate over different ways of getting good answers, a key 2014 paper from Sheela Kennedy and Stephen Ruggles showed that the decline in divorce after 1980 was mostly because the whole married population was getting older, and older people get divorced less. That refined divorce rate doesn’t account for age patterns. When you remove the age patterns from the data, you see a continuously increasing divorce rate. Yikes!
  • On the fourth hand, Kennedy and Ruggles stopped in about 2010. Since then, the very divorce-prone, multi-marrying, multi-divorcing Baby Boomers have moved further out of their peak action years, and it’s increasingly clear that divorce rates really are falling for younger people.

In my new analysis, which I wrote up as a short paper for submission to the Population Association of America 2019 meetings, I argue that all signs point to a divorce decline in the coming years. Here is the paper on SocArXiv, where you will also find the data and code. And here is the story, in figures (click to enlarge).

1. The proportion of married women who divorce each year has fallen 18% in the decade after 2008. (There are reasons to do this for women — some neutral, some good, some bad — but one good thing nowadays is at least this includes women divorcing women.) And when you control for age, number of times married, years married, education, race/ethnicity, and nativity, it has still fallen 8%.

2. The pattern of increasing divorce at older ages, described by Susan Brown and I-Fen Lin as gray divorce, is no longer apparent. In the decade after 2008, the only apparent change in age effects is the decline at younger ages, holding other variables constant.

3. The longer term trends, identified by Kennedy and Ruggles, which I extend to 2016, show that the upward trajectory is all about older people. These are prevalences (divorced people in the population), not divorce rates, but they are good for illustrating this trend.

4. In fact, when you look just at the last decade, all of the decline in age-specific divorce rates is among people under age 45. This implies there will be more older people who have been married a long time, which means low divorce rates. Also, their kids won’t be as likely to have divorced parents, although more kids will have parents who aren’t married, which might work in the other direction. (You can ignore then under-20s, who are 0.2% of the total.)

5. Finally, to get a glimpse of the future, I looked at women who report getting married in the year before the survey, and how they have changed between 2008 and 2016 on traits associated with the risk of divorce. They clearly show a lower divorce-risk profile. They are more likely to be in their first marriage, to have college degrees, to be older, and to have no children in their households (race/ethnicity appears to be a wash, with fewer Whites but more Latinas).

6. Finally finally, I also looked at the spouses of the newly-married women, and made an arbitrary divorce-protection scale, with one point to each couple for each spouse who was: age 30 or more, White or Hispanic, BA or higher education, first marriage, and no own children. Since 2008 the high scale scores have become more common and the low scores have become rarer.

7. It’s interesting that the decline in divorce goes against the (non-expert) conventional wisdom. And it is happening at a time when public acceptance of divorce has reached record levels (which might be part of why people think it’s growing more common — less stigma). Here are the trends in attitudes from Pew and Gallup:

That’s my story — thanks for listening!

Visualizing family modernization, 1900-2016

After this post about small multiple graphs, and partly inspired by two news reports I was interviewed for — this Salt Lake Tribune story about teen marriage, and this New York Times report mapping age at first birth — I made some historical data figures.

These visualizations use decennial census data from 1900 to 1990, and then American Community Survey data for 2001, 2010, and 2016; all data from IPUMS.org. (I didn’t use the 2000 Census because marital status is messed up in that data, with a lot of people who should be never married coded as married, spouse absent; 2001 ACS gets it done.)

An important, simple way of illustrating the myth-making around the 1950s is with marriage age. Contrary to the myth that the 1950s was “traditional,” a long data series show the period to be unique. The two trends here, teen marriage and divorce, both show the modernization of family life, with increasing individual self-determination and less restricted family choices for women.

First, I show the proportion of teenage women married in each state, for each decade from 1900 to 2016. The measure I used for this is the proportion of 19- and 20-year-olds who have ever been married (that is, including those married, divorced, and widowed). It’s impossible to tell exactly how many people were married before their 20th birthday, which would be a technical definition of teen marriage, but the average of 19 and 20 should do it, since it includes some people are on the first day of their 19th year, and some people are on the last day of their 20th, for an average close to exact age 20.

I start with a small multiple graph of the trend on this measure in every state (click all figures to enlarge). Here the states are ordered by the level of teen marriage in 2016, from Maine lowest (<1%) to Utah (14%):

This is useful for seeing that the basic pattern is universal: starting the century lower and rising to a peak in 1960, then declining steeply to the present. But that similarity, and smaller range in the latest data, make it hard to see the large relative differences across states now. Here are the 2016 levels, showing those disparities clearly:

Neither the small multiples nor the bars help you see the regional patterns and variations. So here’s an animated map that shows both the scale of change and the pattern of variation.

This makes clear the stark South/non-South divide, and how the Northeast led the decline in early marriage. Also, you can see that Utah, which is such a standout now, did not have historically high teen marriage levels, the state just hasn’t matched the decline seen nationally. Their premodernism emerged only in relief.

Divorce

Here I again used a prevalence measure. This is just the number of people whose marital status is divorced, divided by the number of married people (including separated and divorced). It’s a little better than just the percentage divorced in the population, because it’s at least scaled by marriage prevalence. But it doesn’t count divorces happening, and it doesn’t count people who divorced and then remarried (so it will under-represent divorce to the extent that people remarry). Also, if divorced people die younger than married people, it could be messed up at older ages. Anyway, it’s the best thing I could think of for divorce rates by state all the way back to 1900.

So, here’s the small multiple graph, showing the trend in divorce prevalence for all states from 1900 to 2016:

That looks like impressive uniformity: gradual increase until 1970, then a steep upward turn to the present. These are again ordered by the 2016 value, from Utah at less than 20% to New Mexico at more than 30% — smaller variation than we saw in teen marriage. That steep increase looks dramatic in the animated map, which also reveals the regional patterns:

Technique

The strategy for both trends is to download microdata samples from all years, then collapse the files down to state averages by decade. The linear figures are Stata scatter plots by state. The animated maps use maptile in Stata (by Michael Stepner) to make separate image files for each map, which I then imported into Photoshop to make the animations (following this tutorial).

The downloaded data, codebooks, Stata code, and images, are all available in an Open Science Framework project here. Feel free to adapt and use. Happy to hear suggestions and alternative techniques in the comments.

Are middle children going extinct?

In The Cut, Adam Sternbergh has a piece called, “The Extinction of the Middle Child They’re becoming an American rarity, just when America could use them the most.”

This is good for me to read, because I’ve been asked to include more material about sibling relationships in the next edition of my textbook, The Family, and it’s not my expertise. Thinking about sibling relationships is good, but the demography here is off. Sternberg writes:

According to a study by the Pew Research Center in 1976, “the average mother at the end of her childbearing years had given birth to more than three children.” Read that again: In the ’70s, four kids (or more) was the most common family unit. Back then, 40 percent of mothers between 40 and 44 had four or more children. Twenty-five percent had three kids; 24 percent had two; and 11 percent had one. Today, those numbers have essentially reversed. Nearly two-thirds of women with children now have two or one — i.e., an oldest, a youngest, but no middle.

It is true there are a lot fewer U.S. families with more than two children today than there were in 1976. However, by my reckoning (see below), in the most recent data (2016), 38 percent of mothers age 40-44 who have had any children have had three or more. So, there’s a middle child in more than a third of families. And, crucially, that number hasn’t dropped in the last 25 years. I’ll explain.

The best regular national survey for this is the Current Population Survey’s June Fertility Supplement, which is administered to a national sample by the Census Bureau more or less every two years. They ask women, “Altogether how many children have you ever given birth to?” The traditional way to measure total number of children born for a cohort of women is to take the average of that number for women who are ages 40-44. (I would rather do it at ages 45-49, but they didn’t always ask it for women over 44.)

This is what you get for the surveys from 1976 to 2016 (remember these are the years the women reached the end of their childbearing years).

You can see how it’s a little tricky. First, the biggest changes were over by the 1990s, when the last of the Baby Boom parents reached their forties (their first kids were born 25 years earlier). The biggest changes after that were in the number of women having no children, which rose until 2006 but then fell, possibly as access to fertility treatments improved. (Note in all this we’re calling all the children one woman has a “family,” but really it’s a sibling set; some will be living with other people and some will have died, so it’s not a measure of family life in the household sense of family. And it’s all based on children women have, so if there are different fathers in these families we wouldn’t know it, and if these children have half-siblings with a different mother we wouldn’t know it, but that’s the way it goes.)

It’s hard to see what this means for the prevalence of middle children in the country, because the no-children women aren’t relevant. So if your question is, “what proportion of families with children have any middle children?” you would want to do it like this, which excludes the childfree women, and combines all those with three or more:

This shows the big drop in middle-child families that Sternbergh started with, but it puts it in perspective: the change was over by the 1990s, and since then it’s been basically flat at 35+ percent. So, things have changed a lot from the days of the Baby Boom, but the same article could have been written, demographically speaking, in 1992. (Note that the drop in total fertility rate since 2008 [see this] hasn’t yet shown up in completed fertility since it’s among younger women.)

It’s not clear whether the unit of analysis should be the family or the child, however. This says 38 percent of women produce middle-child families. But how many children have the experience of being a middle child (defined as a child with at least one older and one younger sibling)? That might make more sense if you’re interested, as Sternbergh is, in the effect of middle children on the culture. So just multiplying out the number of children per woman, and counting the number of middle children as the total minus two for all sibships of three or more (I think I did it right), you get this:

(Again, this assumes no one died before their mother turned 44, which did change over this period, especially as violent crime rates among young men fell. You could do something fancy to estimate that.)

So, it looks to me that, for the last 25 years, about 20-25 percent of children have been middle children.

On the other hand, looking in the longer run — much further back than Sternbergh’s starting point of 1976 — it’s clear that the proportion of children growing up as middle children has declined drastically. One quick and dirty way to show that is in children’s living arrangements. The final figure uses Census data (decennial till 2000, then American Community Survey) to show how many children are living as the only child, one of two, a middle child, or as the oldest/youngest in a three-plus family. This is messy because it’s just whoever is living together at the moment. So this is answering a question more like, “what proportion of children at any given time are living with an older and a younger sibling?” Here’s the trend:

(Note that, thanks to IPUMS.org coding, this does count people as having older siblings if the sibling is older than 18, as long as they’re living in the household. But I’m only including kids living in the household of at least one parent.)

Wow! In 1850 half of all U.S. children had an older and a younger sibling in the household with them. Now it’s below 20 percent. Still no drop since 1990, but the long-term change is impressive. So if all that personality stuff is true, then that’s a big difference between the olden days and nowadays. Definitely going to put this in the book.

Theology majors marry each other a lot, but business majors don’t (and other tales of BAs and marriage)

The American Community Survey collects data on the college majors of people who’ve graduated college. This excellent data has lots of untapped potential for family research, because it tells us something about people’s character and experience that we don’t have from any other variables in this massive annual dataset. (It even asks about a second major, but I’m not getting into that.)

To illustrate this, I did two data exercises that combine college major with marital events, in this case marriage. Looking at people who just married in the previous year, and college major, I ask: Which majors are most and least likely to marry each other, and which majors are most likely to marry people who aren’t college graduates?

I combined eight years of the ACS (2009-2016), which gave me a sample of 27,806 college graduates who got married in the year before they were surveyed (to someone of the other sex). Then I cross-tabbed the major of wife and major of husband, and produced a table of frequencies. To see how majors marry each other, I calculated a ratio of observed to expected frequencies in each cell on the table.

Example: With weights (rounding here), there were a total of 2,737,000 BA-BA marriages. I got 168,00 business majors marrying each other, out of 614,000 male and 462,000 female business majors marrying altogether. So I figured the expected number of business-business pairs was the proportion of all marrying men that were business majors (.22) times the number of women that were business majors (461,904), for an expected number of 103,677 pairs. Because there were 168,163 business-business pairs, the ratio is 1.6.  (When I got the same answer flipping the genders, I figured it was probably right, but if you’ve got a different or better way of doing it, I wouldn’t be surprised!)

It turns out business majors, which are the most numerous of all majors (sigh), have the lowest tendency to marry each other of any major pair. The most homophilous major is theology, where the ratio is a whopping 31. (You have to watch out for the very small cells though; I didn’t calculate confidence intervals.) You can compare them with the rest of the pairs along the diagonal in this heat map (generated with conditional formatting in Excel):

Of course, not all people with college degrees marry others with college degrees. In the old days it was more common for a man with higher education to marry a woman without than the reverse. Now that more women have BAs, I find in this sample that 35% of the women with BAs married men without BAs, compared to just 22% of BA-wielding men who married “down.” But the rates of down-marriage vary a lot depending on what kind of BA people have. So I made the next figure, which shows the proportion of male and female BAs, by major, marrying people without BAs (with markers scaled to the size of each major). At the extreme, almost 60% of the female criminal justice majors who married ended up with a man without a BA (quite a bit higher than the proportion of male crim majors who did the same). On the other hand, engineering had the lowest overall rate of down-marriage. Is that a good thing about engineering? Something people should look at!

We could do a lot with this, right? If you’re interested in this data, and the code I used, I put up data and Stata code zips for each of these analyses (including the spreadsheet): BA matching, BA’s down-marrying. Free to use!

Unequal marriage markets for Black and White women

Joanna Pepin and I have posted a new paper titled, “Unequal marriage markets: Sex ratios and first marriage among Black and White women.” In the paper, we find that the marriage markets of Black and White women are very different, with Black women living in metropolitan areas that have many fewer single men than White women do. And, in a regression model with other important predictors of marriage, this unmarried sex ratio is strongly associated with the odds of marrying.

We count this as evidence on the side of “structure” over “culture” in the debates over the decline in marriage. Here’s the main result, showing Black and White women in 172 metro areas (scaled for size), and the difference in sex ratios (the horizontal spread), the difference in marriage rates (the vertical spread), and the statistical effect of sex ratios on marriage (the slopes).

In a nutshell: As you move from left to right, there are more men, and higher odds of marriage. And almost all the White women are up and to the right compared with the Black women. One implication is that this could be one reason why marriage promotion programs in the welfare system aren’t working.

There are a couple of noteworthy innovations here. First, we used the American Community Survey marital events data, which is marriage happening (did you get married in the last year?) rather than just existing (are you married?). This is a better way to assess what might influence marriage. Second, young people, especially single young people who might be getting married, move around a lot. So what is their marriage market? It’s impossible to say exactly, but we define it as the metro area where they lived one year earlier, rather than just where they live now. (This is especially important because the people who move may move because they just got married.)

The paper is on SocArXiv, where if you follow the links you get to the project page, where we put most of the data and code. The paper is under review now, and we’d love to know if you find any mistakes or have any suggestions.

(This began with a blog post four years ago in which I critiqued a NYT Magazine piece by Anne Lowrie about using marriage to cure poverty. Then we presented a first pass at the American Sociological Association in 2014, and I put some of the descriptive statistics in my textbook, and we made a short video out of it, in which I said, “So, larger social forces — the economy, job discrimination, incarceration policies, and health disparities — all impinge on the ability of individuals to shape their own family lives.” Along the way, I presented some about it here and there, while thinking of new ways to measure marriage inequalities.)

2016 U.S. population pyramid, with Baby Boom

I’m finishing up revisions for the second edition of The Family, and that means it’s time to update the population pyramids.

Because it’s not so easy (for me) to find population by age and sex for single years of age for the current year, and because there is a little trick to making population pyramids in Excel, and because I’m happy to be nearing the end of the revision, I took a few minutes to make one to share.

The data for single year population estimates for July 1, 2016 are here, and more specifically in the file called NC-EST2016-AGESEX-RES.csv, here. To make the pyramid in Excel, you multiply one of the columns of data by -1 and then display the results as absolute values by setting the number to a custom format, like this: #,###;#,###. Then in the bar graph you set the two series to overlap 100%.*

In this figure I highlighted the Baby Boom so you can see the tsunami rolling into the 70s now. Unlike when I discuss cohorts previously, when I let it slide, here I actually adjusted this from what you would get applying the official Baby Boom years (1946-1964) with subtraction from 2016. That would give you ages 52 to 70, but the boom obviously starts ate age 69 and ends at age 51 here, so that’s what I highlighted. Maybe this has to do with the timing within years (nine months after the formal end of WWII would be May 2, 1946). Anyway, this is not the official Baby Boom, just the boom you see.

Click to enlarge:

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* I put the data file, the Census Bureau description, and the Excel file on the Open Science Framework here: https://osf.io/qanre/.