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 Population 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/.

African American marital status by age, Du Bois replication edition

At the 1900 Paris Exposition, sociologist W. E. B. Du Bois presented some the work of his students. In The Scholar Denied: W. E. B. Du Bois and the Birth of Modern Sociology, Aldon Morris writes:

Du Bois’s meticulousness as a teacher is apparent in the charts and graphs that he prepared with his students. For example, as part of his gold medal-winning exhibit for the 1900 Paris Exposition, Du Bois and his students produced detailed hand-drawn artistically colored graphs and charts that depicted the journey of black Georgians from slavery to freedom.

Some of collection is shown in this post at the Public Domain Review (shared by Tressie McMillan Cottom yesterday); the full collection is online at the Library of Congress (LOC).

The one that caught my eye was this, showing marital status (“conjugal condition”) by age and sex for the Black population. I can’t find the source details in the LOC record, so I don’t know if it’s Georgia or national, but I presume it’s from tabulations of 1890 decennial census or earlier:

It’s artistic and meticulous and clearly informative, beautiful. So I tried to make a 2015 update to complement it. I used data from the 2015 American Community Survey via IPUMS.org, and did it a little differently.* Most importantly, I added two more conjugal conditions, cohabiting and separated/divorced. Second, I used five-year age groupings all the way up, instead of ten. Third, I detailed the age groups up to age 85. Here’s what I got:

Some very big differences: Much smaller proportions of African Americans married now. Also, much later marriage. In the 1900 figure more than 30% of men and 60% of women have been married by age 25; those numbers are 5-6% now. I don’t know how they counted separated/divorced people in 1900, but those numbers are high now at 31% for women and 24% for men at age 60-64. Widowhood is later now, as 42% of women were widowed before age 65 in 1900, compared with only 13% now (of course, that’s off a lower marriage rate, and remarried people are just counted as married). And of course cohabitation, which the chart doesn’t show for 1900. Note I included people in same-sex as well as different-sex couples.

So, thanks for indulging me. I hope you don’t think it’s frivolous. I just love staring at the old charts, and going through the (very different) steps of replicating it was really satisfying. (I also just love that in another 100 years someone might look back on this and say, “Wait, which one was Earth again?”)

Note: If you want to compare them side-by-side, here’s a go at that. The age ranges don’t line up perfectly but you can get the idea (click to enlarge):

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* SAS code, ACS data, images, and the spreadsheet used for this post are shared as an Open Science Framework project, here.

Is there sex selection among Asian immigrants in the US?

There is a 2008 paper reported in the New York Times in 2009, which found skewed sex ratios among children of immigrants from China, Korea, and India, if their older siblings were girls, using the 2000 Census. The implication was that some parents were using IVF or abortion to select boy children if their first two were girls — as is the case in their home countries. There has been some other research on this from the early 2000s, but I haven’t seen it updated since then.

I took a quick stab at it, but don’t have time right now to pursue it more thoroughly. So here’s the quick answer I got, and I shared my data, code, and results in an Open Science Framework project, here. I hope someone will be interested and pursue it further (using my approach or not). The files there include all different ethnic/racial groups.

This is preliminary.

Using the American Community Survey data from 2010-2015, from IPUMS.org, I took U.S.-born children ages 0-5, whose parents were both born in China, Korea, or India and both were present in the household. I counted the sex of any present siblings under age 15 (excluding step- and adopted children). Then I restricted the data to those with 2 older siblings, and compared the sex ratios among those who had 0 or 1 older sister to those who had 2 older sisters. I did this in a logistic regression controlling for individual years of age, and using ACS person weights. There are judgment calls to make about age, siblings, data and other issues. The older you get the more likely you are to have kids moving out in a way that is not sex-neutral (for example, if parents with girls are more or less likely to divorce), and so on. Should parents be matched on immigration status, siblings born abroad included, why the years 2010-2015, and so on. This is what I mean by preliminary. But these results are interesting enough to prompt me to post them and encourage discussion and more analysis.

Here’s what I got:

The sex differences between those with 0/1 older sister and 2 older sisters are not statistically significant at p.<.05 in each of the three groups, but they are for the combined set (.046). These comparison involve a few hundred cases. Here are the unweighted, unadjusted results:

As you can see, just a few families intervening to choose boys — or some other force rearranging the living arrangements, or survival, of children and families, and the difference would not hold. Still, I think it’s worth pursuing. Maybe someone already has. If you decide to get into it, feel free to use this stuff, and let me know what you come up with!