The Upshot Is Wrong: Completed Fertility Is Not Stable

Age, Period, and Cohort are a heckuva drug

This is a sponsored post paid for by fury at the stupidity of the internet. You’re welcome.

The NYT Upshot data blog wrote this over the weekend:

It contains many chart crimes others have critiqued.

I want to focus on this egregious deception:

That data was produced by Philip Cohen, i.e. @familyunequal on twitter. For the spectators, I want to note an issue here. The data says “Philip Cohen analysis of CDC data.” CDC does produce estimates of completed fertility from the National Survey of Family Growth, but that’s not what this data is. This data is synthetic childlessness calculated from a Lexis diagram. Basically for a given birth cohort you sum the share of women of that age who had a 1st birth in each year across some part of their life course, and that tells you the implied motherhood rate. But this value is inaccurate if mortality or migration altered the composition of the cohort over their life course. In principle what we want to do is get complete birth histories for all the women actually born, but in practice this is almost impossible to do. The method used here is reasonable enough, though in recent US cohorts it shows lower childlessness than direct surveys show.

But I flag this because collecting age-and-parity-specific-birth rates for women who were 45 in the years 1962-2024 is a bit of a chore. Maybe Cohen did it himself or had the data on hand from a prior project; well done if so! But I’m able to almost exactly reproduce it for 45-year-olds by just downloading the prefab data from the Human Fertility Database. If I gave data to the NYT which I downloaded from the Human Fertility Database, I would have had the NYT cite the Human Fertility Database since they did the real work. Perhaps Cohen re-invented the wheel and produced data extremely similar to HFD’s estimates. Or maybe the wheel built by the Vienna Institute of Demography got a rebrand. I do not not know. I hope he reconstructed the data himself, including scraping the old PDF files back to 1917, because claiming credit for HFD’s data would not be proper.

UPDATE: Cohen responded. He did indeed mislabel the source, the data was from HFD. I will note that the reason for the error is striking: incorrect attribution in order to bolster confidence in the data as “official.” But it’s not official! The population denominators there are not “official”! Even the birth counts are not “official” as HFD makes some modifications for ARDY/ACY preferences. So Cohen mislabeled the data specifically to give readers an incorrectly confident view of the data, both denying credit to the people who did the work, and misunderstanding and miss-stating what the data actually was. “I cited the wrong source to make it sound more impressive” is not a defense!

Anyways, here’s my reproduction of the graph using the HFD data:

This graph makes it look like even though births by age 30 are collapsing, later-life births are booming enough to make up for it and achieve stable fertility.

But of course, women who are 45 in 2024 are not the same women as those who are 30 in 2024! Aligning a chart like this by year is a classic error we ding students for in their first demographic methods class, because it creates the visual appearance of stability-by-period, when the actual variable you’re looking at is a cohort variable.

Now, here’s the same input data, but now the X axis will be birth cohorts of women instead of year of observation:

Here, you can see that while the gap between the age 30 and age 45 lines changes over time, the two lines are correlated.

Let’s focus on that gap. Here’s what it looks like:

I’ve marked both the actual observed 1st births between 30 and 45, as well as a dotted line for what a very straightforward linear extrapolation from recent trends might be.

You can contest that extrapolation, but it’s hardly crazy! It’s certainly a reasonable benchmark to say “1st birth rates between ages 30 and 45 will continue to increase, at a rate fairly similar to the increase we’ve seen in the last decade.” Maybe that won’t be true, but it’s at least a neutral starting point.

If we apply that extrapolation to our cohort graph, here’s what we get:

Only just over 70% of women born in 1994 can expect to be moms by age 45. Childlessness rates will soar from their current ~10-15% levels for women in their 40s now (born late-1970s) to ~30% for women born in the mid-to-late 1990s.

We can’t know what people said that wasn’t quoted in an interview. Given Cohen the benefit of the doubt, maybe right after this quote, he said something like, “But, at current ASFR1s, such a recovery would require a dramatic acceleration of 1st birth rates very very soon.”

If he gave that quote but didn’t make such a caveat, that would obviously be a case of an expert knowingly misleading a reporter. You cannot produce the figures I and Cohen produced without either 1) just copy-pasting them from someone else in which case there’s a citation issue here or 2) noticing and encountering the ASFRs and thus having it pass before your eyes that ASFR1(30-45) is not exactly going like gangbusters. I hope Cohen gave the appropriate caveat and the issue is the reporter chose to write the story instead of the facts.

But what if ASFR1 did go like gangbusters? Imagine this is what happens to 1st births at ages 30-45?

Basically, imagine the rate of late-in-life 1st births starts to rise again like it did for 1945-1970 cohorts.

What would that yield for overall motherhood rates?

We would still see that rates of childlessness would rise to about 22%, nearly double current levels. This would be similar to levels seen for the cohort of women born around 1910— women who came of age during the Great Depression, and at a time when early-life mortality was much higher than it is now (some women were childless because they died before ending their reproductive years— thankfully this is less common now).

I don’t think you should assume we are about to see a massive trend break. Provisional birth data for 2025 point to ASFR1 values virtually identical to 2024, meaning that any such break would come no earlier than 2026. But Jan-Feb 2026 also show no major difference in ASFR1 vs. Jan-Feb 2024 or Jan-Feb 2025, so really any major trend break must be happening right now.

But, are the vibes shifting that hard right now? I don’t think so. I don’t think we’re living through a dramatic pivot in the rate at which older women have 1st babies. If in the future data shows that April 2026 was such a hinge, I will be hilariously wrong, and nobody will enjoy dunking on this post as much as I will. But, I dunno guys, I just don’t think we’re seeing a baby boom right now.

As such, while the rapid-increase-in-older-1st-births take cannot be totally deprecated as an opinion… you should have a pretty strong prior on business-as-usual. You can forecast fertility usually with >90% and often >95% accuracy just by rolling prior years forward for sufficiently high-level variables. When somebody advocates for a major break in trend in such a high-momentum variable, they need a compelling reason why.

Nobody can offer such a compelling reason in this case.

As such, the NYT is (probably knowingly) promoting a view of fertility they know to be an error.

At this point, we’re rehashing old territory. I shredded Mike Konczal on almost this exact issue not long ago. Here’s the facts: fertility is falling very fast, and we are not seeing large recuperation at older ages as cohorts with delays hit those ages. Every single mathematical tool we have for projecting cohort fertility is flashing “DOWN” signs for eventual cohort fertility.

Every single demographer who touches ASFR data knows this. You can’t not see it. It’s obvious in all the tools we use.

If a demographer doesn’t say “Completed fertility seems to be declining,” you’re dealing with a demographer willing to obscure, hide, or mislead about facts in order to advance their preferred narrative.

Now, other points Cohen made are totally reasonable arguments: many demographers may see the decline but not worry about it because they are productivity optimists, or favor higher immigration, or think it comes from improvements in women’s autonomy. I disagree, but those are all disagreements we can have among people who basically all know how the math works. Those are hard problems.

But “Will completed fertility fall for recent cohorts to record-low levels?” has an easy answer, and the answer is “Yes.”

UPDATE: Cohen responded. His response is incoherent.

He says he’s not forecasting that 30-year-olds in 2024 will reach 88% ever-births by age 45, and true, he didn’t verbally say that. He simply published a graph with that as the obvious interpretation by any layperson, in an article headlined with that very claim as the thesis. He claims this makes the chart easier to understand— no, it makes it easier to misunderstand, which is why the discourse around it has been so grossly erroneous, with tons of commenters explicitly reading it to say that cohort fertility will be stable. Cohort trends are not that hard to explain! You can of course use cumulative fertility graphs as one approach, but if you want the whole time trend, the cohort-arranged method I took is bog-standard, I’m sure Cohen has taught his students to do it a thousand times. This is indeed a “perennial” problem, one with a settled solution: when showing cohort data, you arrange the data by cohorts, end of story. You do not show cohort data arranged by something other than cohort, because this leads to major misperceptions for virtually the entire lay audience, as literally everybody who’s ever made graphs of cohort fertility for laypeople is painfully aware.

He goes on:

WTF does this even mean? There’s no relationship between the idea that “completed fertility is known” and the idea of “replacement.” First of all, calculating replacement rate from the Lexis diagonal is a different beast since it requires a different set of mortality statistics: cohort mortality exposures instead of period ones, so the “replacement rate” as such is simply not identical for period fertility and cohort fertility. Again, this is like a week 5 of your first quant demo class homework problem Cohen is failing here. Second, he’s clearly making this up: the graph they chose didn’t introduce uncertainty, it created the appearance of certainty! To a layperson, it gave a strong sense that cohort fertility is and will be stable! My graph presentation communicates uncertainty, by having blank values for recent cohorts or using hashed values or you could even do something like simulated or Bayesian error ranges, that’s not hard to do. “Experts may disagree” yeah they probably will since you designed your chart in the way literally every expert knows is creates a maximal perception of “closed and complete” data! If you want to communicate uncertainty, show the uncertainty, not a graph that makes everything look tidy and complete.

Finally, a quick note: Cohen says “we” made the graph the way “we” did. Who is the “we” here? An unattributed research assistant? The journalist? To what extent is this Cohen sockpuppeting a journalist who didn’t know better? Is the Upshot responsible for any errors here, or is Cohen? Is this a Cohen op-ed, a Miller piece, or a Cohen-Miller double byline? What are we even looking at here?