Poverty, marriage, and single mother update

With the annual Census report on poverty out, here are two quick updates.

First, updating this post, the share of all poverty (using official rates) found in single-mother families remains lower than it was from 1974 to 2000. Since 1995, as the poverty rate has gone up and down between 10 and 15 percent, the share of poor people in single-mother families has fallen. As of 2015, 34% of poor people are found in single-mother families.

Marriage has declined, and single motherhood has increased, but that has not produced a poverty population more dominated by single-mother families. Of course these families are more likely to be poor than married-couple families, but they’re not the main poverty story.

Second, updating this post a little, it’s important to keep two major trends in the back of your mind when thinking about social change. The first is that marriage has declined precipitously since 1960. It’s unremitting decline is one of the major social facts of our time. The other trend to keep in mind is that poverty rates fell a lot after the 1960s, but since then have bounced around at an atrocious 10-15%. Now try to keep them both in mind at once: marriage falls, poverty goes up and down. This year’s update puts those together (sorry people who hate this kind of figure), as change in the percentage of women married, and change in the percentage of the population poor.

For a recent op-ed on poverty and marriage, here’s the unpaywalled version of my essay in the Washington Post‘s Post Everything.

On Asian-American earnings

In a previous post I showed that generalizations about Asian-American incomes often are misleading, as some groups have above-average incomes and some have below-average incomes (also, divorce rates) and that inequality within Asian-American groups was large as well. In this post I briefly expand that to show breakdowns in individual earnings by gender and national-origin group.

The point is basically the same: This category is usually not useful for economic statistics, and should usually be dropped for data on specific groups when possible.

Today’s news

What’s new is a Pew report by Eileen Patten showing trends in race and gender wage gaps. The report isn’t focused on Asian-American earnings, but they stand out in their charts. This led Charles Murray, who is fixated on what he believes is the genetic origin of Asian cognitive superiority, to tweet sarcastically, “Oppose Asian male privilege!” Here is one of Pew’s charts:

The figure, using the Current Population Survey (CPS), shows Asian men earning about 14.5% more per hour than White men, and Asian women earning 11% more than White women. This is not wrong, exactly, but it’s not good information either, as I’ll argue below.

First a note on data

The CPS data is better for some labor force questions (including wages) than the American Community Survey, which is much larger. However, it’s too small a sample to get into detail on Asian subgroups (notice the Pew report doesn’t mention American Indians, an even smaller group). To do that I will need to activate the ACS, which is better for race/ethnic detail.

As a reminder, this is the “race” question on the 2014 American Community Survey, which I use for this post:

There is no “Asian” or “Pacific Islander” box to check. So what do you do if you are thinking, “I’m Asian, what do I check?” The question is premised on that assumption that is not what you’re thinking. Instead, you choose from a list of national origins, which the Census Bureau then combines to make “Asian” (the first 7 boxes) and “Pacific Islander” (the last 3) categories. And you can check as many as you like, which is good because there’s a lot of intermarriage among Asians, and between Asians and other groups (mostly Whites). This is a lot like the Hispanic origin question, which also lists national origins — except that question is prefaced by the unifying phrase, “Is Person 1 of Hispanic, Latino, or Spanish origin?” before listing the options, each beginning with “Yes”, as in “Yes, Cuban.”

Although changes have not been announced, it is likely that future questions will combine the race and Hispanic-origin questions, and also preface the Asian categories with the umbrella term. This may mark the progress of getting Asian immigrants to internalize the American racial classification system, so that descendants from groups that in some cases have centuries-old cultural differentiation start to identify and label themselves as from the same racial group (who would have put Pakistanis and Japanese in the same “race” group 100 years ago?). It’s hard to make this progress, naturally, when so many people from these groups are immigrants — in my sample below, for example, 75% of the full-time, year-round workers are foreign-born.

Earnings

The problem with the earnings chart Pew posted, and which Charles Murray loved, is that it lumps all the different Asian-origin groups together. That is not crazy but it’s not really good. Of course every group has diversity within it, so any category masks differences, but in my opinion this Asian grouping is worse in that regard than most. If someone argued that all these groups see themselves as united under a common identity that would push me in the direction of dropping this complaint. In any event, the diversity is interesting even if you don’t object to the Pew/Census grouping.

Here are two breakouts. The first is immigration. As I noted, 75% of the full-time, year-round workers (excluding self-employed people, like Pew does) with an Asian/Pacific Islander (Asian for short) racial identification are foreign born. That ranges from less than 4% for Hawaiians, to around 20% for the White+Asian multiple-race people, to more than 90% for Asian Indian men. It turns out that the wage advantage is mostly concentrated among these immigrants. Here is a replication of the Pew chart using the ACS data (a little different because I had to use FTFY workers), using the same colors. On the left is their chart, on the right is the same data limited to US-born workers.

Among the US-born workers the Asian male advantage is reduced from 14.5% to 4.2% (the women’s advantage is not much changed; as in Pew’s chart, Hispanics are a mutually exclusive category.) There are some very high-earning Asian immigrants, especially Indians. Here are the breakdowns, by gender, comparing each of the larger Asian-American groups to Whites:

Seven groups of men and nine groups of women have hourly earnings higher than Whites’, while nine groups of men and seven groups have women have lower earnings. In fact, among Laotians, Hawaiians, and Hmong, even the men earn less than White women. (Note, in my old post, I showed that Asian household incomes are not as high as they look when they are compared instead with those of their local peers, because they are concentrated in expensive metropolitan markets.)

Sometimes when I have a situation like this I just drop the relatively small, complex group, which leads some people to accuse me of trying to skew results. (For example, I might show a chart that has Blacks in the worst position, even though American Indians have it even worse.)

But generalization has consequences, so we should use it judiciously. In most cases “Asian” doesn’t work well. It may make more sense to group people by regions, such as East-, South-, and Southeast Asia, and/or according to immigrant status.

Update: Adjusted divorce risk, 2008-2014

Quick update to yesterday’s post, which showed this declining refined divorce rate for the years 2008-2014:

On Twitter Kelly Raley suggested this could have to do with increasing education levels among married people. As I’ve reported using these data before, there is a much lower divorce risk for people with BA degrees or higher education.

Yesterday I quickly (but I hope accurately) replicated my basic model from that previous paper, so now I can show the trend as a marginal effect of year holding constant marital duration (from year of marriage), age, education, race/ethnicity, and nativity.*

This shows that there has been a decrease in the adjusted odds of divorce from 2008 to 2014. You could interpret this as a continuous decline with a major detour caused by the recession, but that case is weaker than it was yesterday, looking at just the unadjusted trend.

If it turns out that increase in 2010-2012 is related to the recession, it’s not so different from my original view — a recession drop followed by rebound, it’s just that the drop is less and the rebound is more, and took longer, than I thought.  In any event, this should undermine any effort to resuscitate the old idea that the recession caused a decline in divorce by causing families to pull together during troubled times.

This does not contradict the results from Kennedy and Ruggles that show age-adjusted divorce rising between 1980 and 2008, since I’m not trying to compare these ACS trends with the older data sources. For time beyond 2008, they wrote in that paper:

If current trends continue, overall age-standardized divorce rates could level off or even decline over the next few decades. We argue that the leveling of divorce among persons born since 1980 probably reflects the increasing selectivity of marriage.

That would fit the idea of a long-term decline with a stress-induced recession bounce (with real-estate delay).

Alternative interpretations welcome.

* This takes a really long time for Stata to compute on my sad little public-university computer because it’s a non-linear model with 4.8 million cases – so please don’t ask for a lot of different iterations of this figure. I don’t have my code and output cleaned up for sharing, but if you ask me I’ll happily send it to you.

Divorce rate plunge continues

When I analyzed divorce and the recession in this paper, I only had data from 2008 to 2011. Using a model based on the predictors of marriage in 2008, I thought there had been a drop in divorces associated with the recession in 2009, followed by a rebound back to the “expected level” by 2011. So, the recession reduced divorces, perhaps temporarily.

That was looking iffy when the 2013 data showed a big drop in the divorce rate, as I reported last year. With new data now out from the 2014 American Community Survey, that story is seeming less and less adequate. With another deep drop in 2014, now it looks like divorce rates are on a downward slide, but in the years after the recession there was a bump up — so maybe recession-related divorces (e.g., those related to job loss or housing market stressors) took a couple years to materialize, producing a lull in the ongoing plunge. Who knows.

So, here is the latest update, showing the refined divorce rate — that is, the number of divorces in each year per 1,000 married people in that year.*

Lots to figure out here. (As for why men and women have different divorce rates in the ACS, I still haven’t been able to figure that out; these are self-reported divorces, so there’s no rule that they have to match up [and same-sex divorces aren’t it, I think.])

For the whole series of posts, follow the divorce tag.

* I calculate this using the married population from table B12001, and divorces in the past year from table B12503, in the American Factfinder version of the ACS data.

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 Deva 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.

How we really can study divorce using just five questions and a giant sample

It would be great to know more about everything, but if you ask just these five questions of enough people, you can learn an awful lot about marriage and divorce.

Questions

First the questions, then some data. These are the question wordings from the 2013 American Community Survey (ACS).

1. What is Person X’s age?

We’ll just take the people who are ages 15 to 59, but that’s optional.

2. What is this person’s marital status?

Surprisingly, we don’t want to know if they’re divorced, just if they’re currently married (I include people are are separated and those who live apart from their spouses for other reasons). This is the denominator in your basic “refined divorce rate,” or divorces per 1000 married people.

3. In the past 12 months, did this person get divorced?

The number of people who got divorced in the last year is the numerator in your refined divorce rate. According to the ACS in 2013 (using population weights to scale the estimates up to the whole population), there were 127,571,069 married people, and 2,268,373 of them got divorced, so the refined divorce rate was 17.8 per 1,000 married people. When I analyze who got divorced, I’m going to mix all the currently-married and just-divorced people together, and then treat the divorces as an event, asking, who just got divorced?

4. In what year did this person last get married?

This is crucial for estimating divorce rates according to marriage duration. When you subtract this from the current year, that’s how long they are (or were) married. When you subtract the marriage duration from age, you get the age at marriage. (For example, a person who is 40 years old in 2013, who last got married in 2003, has a marriage duration of 10 years, and an age at marriage of 30.)

5. How many times has this person been married?

I use this to narrow our analysis down to women in their first marriages, which is a conventional way of simplifying the analysis, but that’s optional.

Data

I restrict the analysis below to women, which is just a sexist convention for simplifying things (since men and women do things at different ages).*

So here are the 375,249 women in the 2013 ACS public use file, ages 16-59, who were in their first marriages, or just divorced from their first marriages, by their age at marriage and marriage duration. Add the two numbers together and you get their current age. The colors let you see the basic distribution (click to enlarge):

The most populous cell on the table is 28-year-olds who got married three years ago, at age 25, with 1068 people. The least populous is 19-year-olds who got married at 15 (just 14 of them). The diagonal edge reflects my arbitrary cutoff at age 59.

Divorce results

Now, in each of these cells there are married people, and (in most of them) people who just got divorced. The ratio between those two frequencies is a divorce rate — one specific to the age at marriage and marriage duration. To make the next figure I used three years of ACS data (2011-2013) so the results would be smoother. (And then I smoothed it more by replacing each cell with an average of itself and the adjoining cells.) These are the divorce rates by age at marriage and years married (click to enlarge):

The overall pattern here is more green, or lower divorce rates, to the right (longer duration of marriage) and down (older age at marriage). So the big red patch is the first 12 years for marriages begun before the woman was age 25. And after about 25 years of marriage it’s pretty much green, for low divorce rates. The high contrast at the bottom left implies an interesting high risk but steep decline in the first few years after marriage for these late marriages. This matrix adds nuance to the pattern I reported the other day, which featured a little bump up in divorce odds for people who married in their late thirties. From this figure it looks like marriages that start after the woman is about 35 might have less of a honeymoon period than those beginning about age 24-33.

To learn more, I go beyond those five great questions, and use a regression model (same as the other day), with a (collapsed) marriage-age–by–marriage-duration matrix. So these are predicted divorce rates per 1000, holding education, race/ethnicity, and nativity constant (click to enlarge)**:

The controls cut down the late-thirties bump and isolate it mostly to the first year. This also shows that the punishing first year is an issue for all ages over 35. The late thirties just showed the bump because that group doesn’t have the big drop in divorce after the first year that the later years do. Interesting!

Sigh

Here’s where the awesome data let us down. This data is very powerful. It’s the best contemporary big data set we have for analyzing divorce. It has taken us this far, but it can’t explain a pattern like this.

We can control for education, but that’s just the education level at the time of the most recent survey. We can’t know when she got her education relative to the dates of her marriage. Further, from the ACS we can’t tell how many children a person has had, with whom, and when — we only know about children who happen to be living in the household in 2013, so a 50-year-old could be childfree or have raised and released four kids already. And about couples, although we can say things about the other spouse from looking around in the household (such as his age, race, and income), if someone has divorced the spouse is gone and there is no information about that person (even their sex). So we can’t use that information to build a model of divorce predictors.

Here’s an example of what we can only hint at. Remarriages are more likely to end in divorce, for a variety of reasons, which is why we simplify these things by only looking at first marriages. But what about the spouse? Some of these women are married to men who’ve been married before. I can’t how much that contributes to their likelihood of divorce, but it almost certainly does. Think about the bump up in the divorce rate for women who got married in their late thirties. On the way from high divorce rates for women who marry early to low rates for women who marry late, the overall downward slope reflects increasing maturity and independence for women, but it’s running against the pressure of their increasingly complicated relationship situations. That late-thirties bump may have to do with the likelihood that their husbands have been married before. Here’s the circumstantial evidence:

See that big jump from early-thirties to late-thirties? All of a sudden 37.5% of women marrying in their late-thirties are marrying men who are remarrying. That’s a substantial risk factor for divorce, and one I can’t account for in my analysis (because we don’t have spouse information for divorced women).

On method

Divorce is complicated and inherently longitudinal. Marriages arise out of specific contexts and thrive or decay in many different ways. Yesterday’s crucial influence may disappear today. So how can we say anything about divorce using a single, cross-sectional survey sample? The unsatisfying answer is that all analysis is partial. But these five questions give us a lot to go on, because knowing when a person got married allows us to develop a multidimensional image of the events, as I’ve demonstrated here.

But, you ask, what can we learn from, say, the divorce propensity of today’s 40-year-olds when we know that just last year a whole bunch of 39-year-olds divorced, skewing today’s sample? This is a real issue. And demography provides an answer that is at once partial and powerful: Simple, we use today’s 39-year-olds, too. In the purest form, this approach gives us the life table, in which one year’s mortality rates — at every age — lead to a projection of life expectancy. Another common application is the total fertility rate (watch the video!), which sums birth rates by age to project total births for a generation. In this case I have not produced a complete divorce life table (which I promised a while ago — it’s coming). But the approach is similar.

These are all synthetic cohort approaches (described nicely in the Week 6 lecture slides from this excellent Steven Ruggles course). In this case, the cohorts are age-at-marriage groups. Look at the table above and follow the row for, say, marriages that started at age 28, to see that synthetic cohort’s divorce experience from marriage until age 59. It’s neither a perfect depiction of the past, nor a foolproof prediction of the future. Rather, it tells us what’s happening now in cohort terms that are readily interpretable.

Conclusion

The ACS is the best thing we have for understanding the basic contours of divorce trends and patterns. Those five questions are invaluable.

---

* For this I also tossed the people who were reported to have married in the current year, because I wasn’t sure about the timing of their marriages and divorces, but I put them back in for the regressions.

** The codebook for my IPUMS data extraction is here, my Stata code is here. The heat-map model here isn’t in that code file, but this these are the commands (and the margins command took a very long time, so please don’t tell me there’s something wrong with it):

logistic divorce i.agemarc#i.mardurc i.degree i.race i.hispan i.citizen
margins i.agemarc#i.mardurc

The U.S. government asked 2 million Americans one simple question, and their answers will shock you

What is your age?

[SKIP TO THE END for a mystery-partly-solved addendum]

Normally when we teach demography we use population pyramids, which show how much of a population is found at each age. They’re great tools for visualizing population distributions and discussing projections of growth and decline. For example, consider this contrast between Niger and Japan, about as different as we get on earth these days (from this cool site):

It’s pretty easy to see the potential for population growth versus decline in these patterns. Finding good pyramids these days is easy, but it’s still good to make some yourself to get a feel for how they work.

So, thinking I might make a video lesson to follow up my blockbuster total fertility rate performance, I gathered some data from the U.S., using the 2013 American Community Survey (ACS) from IPUMS.org. I started with 10-year bins and the total population (not broken out by sex), which looks like this:

There’s the late Baby Boom, still bulging out at ages 50-59 (born 1954-1963), and their kids, ages 20-29. So far so good. But why not use single years of age and show something more precise? Here’s the same data, but showing single years of age:

That’s more fine-grained. Not as much as if you had data by months or days of birth, but still. Except, wait: is that just sample noise causing that ragged edge between 20 and about 70? The ACS sample is a few million people, with tens of thousands of people at each age (up age 75, at least), so you wouldn’t expect too much of that. No, it’s definitely age heaping, the tendency of people to skew their age reporting according to some collective cognitive scheme. The most common form is piling up on the ages ending with 0 and 5, but it could be anything. For example, some people might want to be 18, a socially significant milestone in this country. Here’s the same data, with suspect ages highlighted — 0’s and 5’s from 20 to 80, and 18:

You might think age heaping results from some old people not remembering how old they are. In the old days rounding off was more common at older ages. In 1900, for example, the most implausible number of people was found at age 60 — 1.6-times as many as you’d get by averaging the number of people at ages 59 and 61. Is that still the case? Here it is again, but with the red/green highlights just showing the difference between the number of people reported and the number you’d get by averaging the numbers just above and below:

Proportionately, the 70-year-olds are most suspicious, at 10.8% more than you’d expect. But 40 is next, at 9.2%. And that green line shows extra 18-year-olds at 8.6% more than expected.

Unfortunately, it’s pretty hard to correct. Interestingly, the American Community Survey apparently asks for both an age and a birth date:

If you’re the kind of person who rounds off to 70, or promotes yourself to 18, it might not be worth the trouble to actually enter a fake birth date. I’m sure the Census Bureau does something with that, like correct obvious errors, but I don’t think they attempt to correct age-heaping in the ACS (the birth dates aren’t on the public use files). Anyway, we can see a little of the social process by looking at different groups of people.

Up till now I’ve been using the full public use data, with population weights, and including those people who left age blank or entered something implausible enough that the Census Bureau gave them an age (an “allocated” value, in survey parlance). For this I just used the unweighted counts of people whose answers were accepted “as written” (or typed, or spoken over the phone, depending on how it was administered to them). Here are the patterns for people who didn’t finish high school versus those with a bachelor’s degree or higher, highlighting the 5’s and 0’s (click to enlarge):

Clearly, the age heaping is more common among those with less education. Whether it’s really people forgetting their age, rounding up or down for aspirational reasons, or having trouble with the survey administration, I don’t know.

Is this bad? As much as we all hate inaccuracy, this isn’t so bad. Fortunately, demographers have methods for assessing the damage caused by humans and their survey-taking foibles. In this case we can use Whipple’s index. This measure (defined in this handy United Nations slideshow) takes the number of people whose alleged ages end in 0 or 5 and multiplies that by 5, then compares it to the total population. Normally people use ages 23 to 62 (inclusive), for an even 40 years. The amount by which people reporting ages 25, 30, 35, 40, 45, 50, 55, and 60 are more than one-fifth of the population ages 23-62, that’s your Whipple’s index. A score of 100 is perfect, and a score of 500 means everyone’s heaped. The U.N. considers scores under 105 to be “very accurate data.” The 2013 ACS, using the public use file and the weights, gives me a score of 104.3. (Those unweighted distributions by education yield scores of 104.0 for high school dropouts and 101.7 for college graduates.) In contrast, the Decennial Census in 2010 had a score of just 101.5 by my calculation (using table QT-P2 from Summary File 1). With the size of the ACS, this difference shouldn’t have to do with sampling variation. Rather, it’s something about the administration of the survey.

Why don’t they just tell us how old they really are? There must be a reason.

Two asides:

• The age 18 pattern is interesting — I don’t find any research on desirable young-adult ages skewing sample surveys.
• This is all very different from birth timing issues, such as the Chinese affinity for births in dragon years (every twelfth year: 1976, 1988…). I don’t see anything in the U.S. pattern that fits fluctuations in birth rates.

Mystery-partly-solved addendum

I focused one education above, but another explanation was staring me in the face. I said “it’s something about the administration of the survey,” but didn’t think to check for the form of survey people took. The public use files for ACS include an indicator of whether the household respondent took the survey through the mail (28%), on the web (39%), through a bureaucrat at the institution where they live (group quarters; 5%), or in an interview with a Census worker (28%). This last method, which is either a computer-assisted telephone interview (CATI) or computer-assisted personal interview (CAPI), is used when people don’t respond to the mailed survey.

It turns out that the entire Whipple problem in the 2013 ACS is due to the CATI/CAPI interviews. The age distributions for all of the other three methods have Whipple index scores below 100, while the CATI/CAPI folks clock in at a whopping 108.3. Here is that distribution, again using unweighted cases:

There they are, your Whipple participants. Who are they, and why does this happen? Here is the Bureau’s description of the survey data collection:

The data collection operation for housing units (HUs) consists of four modes: Internet, mail, telephone, and personal visit. For most HUs, the first phase includes a mailed request to respond via Internet, followed later by an option to complete a paper questionnaire and return it by mail. If no response is received by mail or Internet, the Census Bureau follows up with computer assisted telephone interviewing (CATI) when a telephone number is available. If the Census Bureau is unable to reach an occupant using CATI, or if the household refuses to participate, the address may be selected for computer-assisted personal interviewing (CAPI).

So the CATI/CAPI people are those who were either difficult to reach or were uncooperative when contacted. This group, incidentally, has low average education, as 63% have high school education or less (compared with 55% of the total) — which may explain the association with education. Maybe they have less accurate recall, or maybe they are less cooperative, which makes sense if they didn’t want to do the survey in the first place (which they are legally mandated — i.e., coerced — to do). So when their date of birth and age conflict, and the Census worker tries to elicit a correction, maybe all hell breaks lose in the interview and they can’t work it out. Or maybe the CATI/CAPI households have more people who don’t know each other’s exact ages (one person answers for the household). I don’t know. But this narrows it down considerably.