The changing household age range, U.S. 1900-2017

One way to understand daily interaction, and intergenerational resource exchange, is just to look at the structure of households. This doesn’t tell you everything that goes on in households, but it gives some strong clues. And we can measure it going back more than a century, thanks to IPUMS.org’s collection of Census microdata.

In 1900, the most common situation for an American was to live in a household where the age difference between the oldest and youngest person was about 38 years. Now the most common situation is an age range of 0 — either living alone, or with someone of the exact same age. And there are a lot more people living in households with only similar-aged adults, with age ranges of less than 10.

In between 1900 and 2017, life expectancy increased, the age at first birth increased, and the tendency to live in multigenerational households fell and then rose again. So the household structure story is complicated, and this is just one perspective.

But it’s one indicator of how life has changed. Line up your household from youngest to oldest, look to your left and look to your right — how far can you see?

 

Data and Stata code (for all decades 1900-2000, then individual years to 2017) are available on the Open Science Framework, here.

White children are 2.7-times more likely than Black children to live with a parent who has a PhD

For a reflection Amy Harmon was working on, a followup to her article on the experience of Black mathematicians in American academia, I took a shot at the question: How many children have parents with PhDs?

The result was the highlighted passage (17 words and a link!) in her piece:

[all the racial biases that contribute to Black underrepresentation include] the well-documented racial disparities in public-school resources, the selection of students for gifted programs — and the fact that having a parent with a Ph.D. is helpful to getting one in math, while black children are less than half as likely as white children to live with such a parent.

To get there: I used data from the U.S. Census Bureau via IPUMS.org: The 1990 5% Public Use Microdata Sample (decennial census); and the 2000, 2010, and 2017 American Community Surveys.

I coded race/ethnicity into four mutually-exclusive categories: Single-race White, Black, and Asian/Pacific Islander (API); and Hispanic (including those of any race). I dropped from the analysis non-Hispanic children with multiple races reported, and American Indian / Alaska Natives (for whom about 0.5 percent lived with a PhD parent in 2017).

IPUMS made a tool that attaches values of parents’ variables to children with whom they share a household. I used that to calculate the highest level of education of each child’s coresident parents. In the Census data, children may have up to two parents present (which may be of the same sex in 2010 and 2017). Children living with no parent in the household were not included.

This let me calculate the percentage of children living (at the moment of the survey) with one or more parents who had a PhD. For each of the four groups the percentage of children living with a parent who has a PhD roughly doubled between 1990 and 2017. API children had the highest chance of living with a PhD parent, reaching 6.8 percent in 2017. The percentages for the other groups were: Whites, 2.7 percent; Blacks, 1.0 percent; and Hispanics, 0.7 percent:

The 2.7% for White children, versus, 1.0% for Black children, is the basis for her statement above.

Details (including the whole parents’ education distribution), data, codebook, and code, are available on the Open Science Framework at: https://osf.io/ry3zt/ under CC-BY 4.0 license.

Math bias

Both of Amy’s pieces are important reading for academics in many disciplines, including sociology, to reflect on the experience of Black colleagues in the environments we inherit and reproduce.

With regard to math, Amy points out that Black exclusion is not just about denying economic opportunity, it’s also about denying the public the benefits of all the lost Black math talents — and about denying Black potential mathematicians the joy and satisfaction of a passion for math realized.

As Daniel Zaharopol, the director of a program for mathematically talented low-income middle-school students, put it when I interviewed him for a 2017 article: “Math is beautiful, and being a part of that should not be limited to just some people.”

And Amy makes a good case that math bias and its outcomes contribute directly to racism much more broadly:

Some misguided people claim that there are not many black research mathematicians because African-Americans are not as intelligent as other races. These people, whom I have reported on for other stories in recent months, almost invariably use mathematical accomplishment as their yardstick for intelligence. They note that no individuals of African descent have won the Fields Medal, math’s equivalent of the Nobel Prize. They lack any genetic evidence to explain the gap in average I.Q. scores between white and black Americans that they cite as the basis of their belief, or reason to think that a genetic trait would be impervious to social or educational intervention, or that high I.Q. is key to math ability, which Timothy Gowers, a 1998 Fields medalist, has attributed largely to “the capacity to become obsessed with a math problem.”

But I have been reporting on these topics for several years, and I am acutely aware that math prowess factors heavily into the popular conception of intelligence. There’s a vicious cycle at work: The lack of African-American representation in math can end up feeding pernicious biases, which in turn add to the many obstacles mathematically talented minorities face. Which was one more reason it seemed especially important to hold up to the light all the racial biases that contribute to that underrepresentation.

The rise of Jewish boys’ names in the US

Names are cultural as the personal is political for marginalized groups.

I’ve had these numbers sitting around for a while, since I noticed Nazis on Twitter calling me “Shlomo” as an insult, and was just spurred to write them up by a fascinating Twitter thread from someone who goes by Benjamin (בנימן טבלוב). He writes in response to criticism of Jews who change their names from their “real” European names to Hebrew names, specifically Israeli Prime Minister Benjamin Netanyahu, whose father changed the family name from Mileikowsky after they moved from Europe to Palestine in 1920. (Netanyahu is terrible in every way, that’s not the point.)

Benjamin explained that the Jews of northern and eastern Europe historically practiced patronymic naming exclusively, naming children after their fathers, as in: Jacob, son of Isaac, son of Abraham. (The most famous contemporary patronymic society is Iceland, although they sometimes use matronyms now, too.) It was only with the bureaucratization of modern citizenship in eighteenth and nineteenth century Austria, Prussia, Russia, France, and Bavaria, that Jews were forced to take permanent surnames, and these were often not of their choosing, based things like on places, occupations, or even insults. Besides being generally dehumanizing, this system of Jewish surnames also eventually made it easy to round Jews up for the Holocaust (see the Kaplan and Bernays’ The Language of Names, and this paper, for some history). An exception, incidentally, is the use of the priestly honorific terms Cohen and Levy, which were already in place (e.g., Philip, son of Marshall the Cohen) and then became permanent surnames. I assume Israeli politicians aren’t ditching the name Cohen for something more Hebrew sounding.

So when Jews went to Palestine, they often took new Hebrew names; but when they came to America they took more English names, and then gave their kids mainstream American names. The history of coercive naming in Europe makes it easier to see why this might not have been so objectionable to the Jewish immigrants in the early twentieth century. Kaplan and Bernays quote an immigrant to New York who said, “Nothing good ever came to us while we bore them [old names]; possibly we’ll have more luck with the new names.” (My grandmother was born Tzivya (צִבְיָה), which became Cywja when she boarded a ship from Poland in 1921, and then eventually Sylvia.)

Jewish names today

Today it’s probably safe to say most Jewish children in the U.S. don’t have Jewish first names per se (although they sometimes have a Hebrew name they use just for religious occasions). Here I look at the trends for seven Jewish boys’ names I found on various naming websites: Shlomo, Chaim, Eliezer, Mordechai, Moshe, Yosef, and Zev. These were the most popular ones I could think of (feel free to suggest others).

First a little data on Yiddish and Hebrew in America. This is all from the Decennial Census and then, after 2000, the American Community Survey, which asked about “mother tongue” (language spoken at home as a child) from 1910 to 1970 (except 1950), and language spoken at home after that. The Census doesn’t ask about religion.

Yiddish was the language spoken by the big wave of Jewish immigrants in the early twentieth century. Hebrew is the primary official language of Israel, and the religious language of Judaism. This shows the percentage of people in the U.S. who spoke Yiddish or Hebrew from 1910 to 2017.* The peak in 1930 is 1.1 percent, during the immigration boom. The 1970 peak reflects the only year “mother tongue” was asked of non-immigrants as well as immigrants. By 1980 only one-in-500 Americans spoke Yiddish or Hebrew at home.

The second thing about Yiddish and Hebrew is children. There are a declining number of old immigrants speaking Yiddish, and no new immigrants speaking Yiddish. So most people speaking Yiddish as their language today are probably the descendants of those immigrants, orthodox Jews participating in ethnic revival or preservation. The same goes for people speaking Hebrew at home, except by now some of these could be immigrants from Israel and their children. (By 2000 Hebrew speakers outnumbered those speaking Yiddish.) Here’s the percentage of Yiddish and Hebrew speakers that were under 18 for the same years.

It was low in 1930, when they were mostly working-age immigrants, and then in 1960 when their kids were grown. The percentage under age 18 increased after 1960, and now 40 percent of Yiddish speakers are children (which is not the case for Hebrew). And, this is key: the proportion of all U.S. children speaking Yiddish at home has more than doubled since 1980, from 5 to 11 per 10,000. If these numbers are to be believed.

Names

The sample numbers here are small, but the ACS sample is also picking up about 150 Yiddish or Hebrew speaking women per year having babies, which implies that population is having about 10,000 babies per year, or about 26 out of every 10,000 babies born in the country.

So, who’s naming their sons Shlomo, Chaim, Eliezer, Mordechai, Moshe, Yosef, and Zev? Now switching to the Social Security names database, I find that these names together accounted for 1,943 boys born in 2017 (that’s 9.9 out of every 10,000 US boys born). What’s interesting is that none of these boys’ names reached the threshold for reporting in the database — five children — until 1942. This is remarkable given that Yiddish was in decline by then. And they’ve all been growing more common since that time. So all those Yiddish immigrants in 1920 weren’t naming their sons Moshe, or at least not legally, but now a growing (though small) proportion of their descendants are.

I can’t tell if Yiddish or Hebrew speakers are giving their sons these names. But there must be some connection between the rise of these names and the increase in the proportion of children speaking Yiddish at home. It might not be same people teaching their kids Yiddish, but they may be part of the same (highly localized) revival.

I’ve put the Social Security names data, and my SAS code for extracting name trends, on the Open Science Framework here.

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* An earlier version had much higher prevalence of Yiddish and Hebrew before 1980 because I was accidentally just showing the percentages among immigrants.

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.