Different Measures of Fertility

There are various ways to measure fertility. The most common statistics are either the crude birth rate or what’s called the “Total Fertility Rate,” or TFR. TFR is a hypothetical figure. Basically, each year, you look at the share of women having babies for each year of age, estimating the “natality risk” for each age bracket. Then you look at today’s 15 year olds, and extrapolate out, if current age-specific natality rates remain constant, how many babies will that 15-year-old girl have over her whole life. It’s a neat stat because it controls for age differences, so the population getting older won’t cause the birth rate to fall, unlike the crude rate, where population composition changes can cause major changes.

So let’s compare TFR back to 1960, the longest time series I have on hand right now, to the crude birth rate.

Now, let me be clear, though these units are similarly scaled, they have different meanings. Crude birth rates are babies divided by population. TFR is the hypothetical number of babies that will be born by a woman who turns 15 in the specified year over her whole lifepsan.

As you can see, the two trends do have some co-movement, especially through the 1980s. Since then, TFR remained about stable as the crude rate fell, reflecting a larger and larger share of the population that wasn’t of reproductive age, either because they were too old (boomers) or too young (echo boomers, meaning Millennials). But as Millennials have come of age to have kids, TFR has fallen sharply.

But hold on. TFR is hypothetical. What if what we want to know isn’t hypothetical lifetime births, but actual lifetime births? This is my favorite measure of fertility, which we called Completed Fertility (CF). Until 2012, CF the Census Bureau surveyed women about CF, asking women aged 40–45 how many kids they’d had in their whole life. In 2012 and after, thanks to more late-in-life pregnancies, they bumped up to surveying women 45–50. My time series below uses the highest age definition available for each year, and fills in gap years with simple linear extrapolations.

Completed fertility looks different. It peaks way after the others, and its been more stable since. What’s going on?

Well, simple. Women who are 45 in, say, 1960, had, on average, 3.654 kids. But when did they have those kids? Not when they were 45! Probably in their late teens, 20s, and 30s. So the “completed” fertility reported in a given year should reflect TFR in years decades earlier. And crucially, because TFR reflects just “that year” figures, the timing of births can cause TFR to jump around more erratically. A recession can supress TFR, even if those women are just shifting a birth by a few years. So completed fertility helps us see what womens’ actual experience was.

But saying “women who hit middle-age in year X had Y babies” is kind of boring and hard to conceptualize. Let’s do this another way. Let’s approximate, using the 5-year windows specified by the Census data, birth-year-specific completed fertility rates, and then line up TFR with those cohorts’ plausible peak fertility years, and see how accurately TFR captured realized fertility. This is a hit-or-miss activity because I’m getting approximations of specific birth-cohort CF, and because don’t have direct measures of when those womens’ actual births occurred with respond to historic TFR. But this should give us a first approximation of how well TFR predicts CF. Also, note that because of how I compute my cohorts, some years at the beginning and end have incomplete coverage in the data, so I’m less confident about them. Additionally, I mark where Census Bureau changes in the top-year of completed fertility could impact results.

I also mark a very important factor: the replacement rate of fertility, or about 2.08 kids per woman. When fertility measures like TFR or CF are below 2.08, it means that, in the long run, mortality is likely to exceed natality, and thus, without immigration, the population will shrink through demographic decline.

As you can see, my TFR measure time-shifted and averaged out to coincide with expected peak fertility for each birth cohort roughly corresponds to their experienced fertility. However, TFR still overstates fertility of women born before 1940, and understates the fertility of women born from about 1940 to 1960. In other words, TFR failed to capture some important changes in when fertility occurred across these womens’ lifespans. For women born after 1960, TFR during their peak fertility years has tended to overstate experienced fertility.

But the most important takeaway from this chart is that no generation of women in America has birthed above-replacement-rate since the women born in the mid-1940s.

That is to say, declining fertility isn’t new. When TFR got close to replacement rate in the mid 2000s, it wasn’t necessarily because women were actually going to have more babies across their lifespan, but maybe was just time-shifting. However, we don’t have full completed fertility data from after the 1966 birth cohort, and I’ve got no data for those after 1971. Maybe completed fertility will show some divergence from what the estimated TFR in those birth cohorts’ peak fertility years would suggest. It doesn’t seem likely that completed fertility would exceed TFR by enough to get over replacement, but maybe!

Broadly speaking though, this raises an important point. American population growth has been driven by immigration and by lifespan-lengthening health improvements, not by above-replacement fertility. Women in America have been experiencing below-replacement fertility for at least two or three generations.

We can break down this data by some different categories. Here’s estimated completed fertility by birth cohort, broken out by lifetime marital status.

As you can see, there are several interesting trends here. Most obviously, never-married women have way lower lifetime completed fertility than ever-married women. But while the gap is large, fertility for never-married women is rising steadily. Unmarried childbirth is less stigmatized than in the past, abortion rates are declining since the 1980s highs, and women who might have been married in the past are opting out of marriage now, but not out of childbirth.

But the other very interesting trend is that married fertility has actually managed to get above replacement rate for some cohorts. Married women born from about 1963–1970 managed to reproduce at or above replacement rate. Kudos to you, women of Early Generation X!

But of course, despite rising fertility for never marrieds and near-or-above replacement rate fertility for ever marrieds, fertility has fallen. Why? Because the never-married share rose! If we chain the marital demographic composition to that experienced by the 1932-birth-cohort, we get substantially different realized completed fertility.

As you can see, the marriage-state-chained estimate is substantially nearer replacement rate than the actual completed fertility. The dotted line is total completed fertility estimated from the same sample from which I derive marital status; slightly different from my main sample. As you can see, the marital-status sample actually has slightly lower fertility in many years, so the marital adjustment is could be bigger than just the comparison to my headline figure may suggest.

Adjusting for changes in the marital status composition of the population accounts for more than half of the gap between completed fertility and the replacement rate.

Now, a caveat. It’s possible that whatever social phenomena could have kept people married would have caused married people to have fewer kids. That is, maybe if people who selected into the never-married category had remained married, they would have had fewer kids, more similar to the never-married group, anyways. That’s entirely possible. I’m willing to believe a pure marital status adjustment overstates the impact of the rise of never-marrieds. But it seems almost certain that higher incidence of marriage would create some significantly higher realized fertility.

I’d love to break this data out by native/foreign born as well, but CPS doesn’t make much of that data readily available. Completed fertility is only available by nativity status from 1994–2010.

As you can see, foreign-born women have above-replacement-rate fertility for all birth years, while native-born have below-replacement. Native-born are falling, foreign-born were rising at least as of those born in 1970.

Unfortunately, Census Bureau hasn’t updated native/foreign born completed fertility since 2010 and thus can’t give us comparable statistics reflecting completed fertility up to age 50, so we can’t make a time series to compare to our total realized fertility. But we can do a decomposition by components for native/foreign fertility completed as of age 45, showing how much of that difference in fertility is accounted for by nativity.

As you can see, without the increased foreign-born share of women since the 1949 birth cohort, completed fertility, the orange line, would have been appreciably lower. The effect is not as large as the effect of changed marital composition, but it’s still meaningful.

Without rising immigration, completed fertility likely would have been about 2% lower, which means about 8% further below replacement rate.

Now, a caution. My method here is two totally separate estimates. You can’t just add up marriage and immigration and say the combined effect was X%. I don’t know how immigration interacts with the marriage rate. It’s also possible that if the immigrant population had not risen that immigrant fertility would have followed a different trajectory, just as was the case for marriage. But that seems less likely.