November 30, 2012

Population Momentum

There's a lot of discussion today about fertility and population growth, but much of it reflects the common presumption that when the Total Fertility Rate drops down the replacement level of about 2.1, then the population stops growing.

Even leaving aside immigration, this is wrong because of the phenomenon of Population Momentum. As I wrote in in 2006
"A population will typically grow for 50-60 years after reaching replacement level fertility, 
"Population momentum" is a little complicated to explain, but try thinking of it from a grandparent's perspective. Imagine two neighbors comparing notes on who has more grandchildren. The one who lives on the north side of the street says, "My children each have two children in their families." 
The neighbor who lives on the south side of the street replies, "So do mine." 
The northern neighbor says, "Then you must have four grandchildren, just like me." 
The southern neighbor laughs, "No, I have eight grandchildren! See, you only had two children, so you have four grandchildren. But I had four children, so I have eight grandchildren."


Anonymous said...

Something else to ponder:

- Interval between generations. For example, suppose group A and group B both have a birth rate of 2/mother, but group A gets pregnant at 18 on average and group B gets pregnant at 30 on average. Now suppose group A has a birth rate of only 1/mother, and group B has a birth rate of 3/mother. If group A and group B are the same size, the total population has a birth rate of 2/mother, yet the population increases (quite dramatically). How is this happening? Group A has a wide spacing between generations, so for a given birth rate, there are relatively few of group A alive at any given moment. The opposite holds for group B, and group B comes to replace group A with its tightly-packed generations.

And of course there is immigration, both legal and illegal, and then the relatives of these immigrants and their citizen children come over, etc.

jody said...

this is where south korea is today. lowest birth rate in the world for a few years, but the population is still growing.

however germany and japan have passed this time period. the absolute number of germans on earth is now going down every year. same with japan. each year there are less japanese humans on earth than there were the year before.

within the next decade the same thing will happen to other nations in europe and to south korea as well. there are already a few nations in europe where they might be, right now, entering absolute population decline. russia was for a few years, then, miraculously, the birth rate went up enough again to reverse the decline very slightly.

the US economy is a fraud at this point, and "grows" strictly because the US government spends 1 trillion dollars more per year than it has, and because the US population goes up 1% per year due to immigration, which increases the number of consumers (but not necessarily the number of producers).

and despite this the economy is still expanding slower than the debt. what if the US entered actual population stasis, so that the population wasn't growing even 1% per year due to immigration and that new, extra 1% increase in number of consumers wasn't being added every year? wow. the economy would begin contracting steadily every year.

germany and japan can actually grow their economies, albeit in increments between 1% and 3%, despite literally having less consumers every year - because germany and japan are filled with germans and japanese.

but what will the US do by 2020 when all the cards come crashing down, and it cannot borrow another trillion dollars every year, and the euro americans are dying off, and being replaced with less productive mexicans and other random third worlders via immigration?

Matthew said...

This fertility decline will be used to justify even more immigration.

Several European countries are now granting residence to anyone who buys the homes foolishly overbuilt by real estate developers and their bankers. Spain is considering doing so. Citizens are giving away their countries to pay for the criminal misbehavior of the finance industry. I predicted this (for the US) back when the housing market collapsed. Shocked it hasn't actually happened, though I still wouldn't count it out.

People don't give a shit about their progeny, or their country, so long as they can keep living the good life. We don't breed, we finance the present on the backs of the future, and aren't willing to accept even a little sacrifice in order to preserve a decent country for our descendants.

Anonymous said...

The big fraud is when native populations are told "in order to grow the economy, we need immigration." Along with Western countries, that is what South Koreans are told today by their government and big business.

Doesn't it occur to native populations that nominal growth in the economy is less important that per capita growth?

Native populations in all countries, in particular in Europe and East Asia, could use the extra elbow room afforded it by a declining population.

Anonymous said...

Martin Peretz comes out for heavy immigration restrictions via a series of politically incorrect rhetorical questions:

So said...

Its why China kept growing even after the 1 child policy was implemented

Indira said...

"Something else to ponder:

- Interval between generations."

Yes this is part of the breed like rabbits aspect of hispanics that causes raw counts like 3.5 kids/generation (or whatever it is)to fail to capture the true growth.

If for example hispanic women start pumping out kids at 15, and white women start at 30, even if they have the same # of kids, the hispanic woman is working on grandkids by the same time the white woman is just starting.

Anonymous said...

OT: Dan Mogulof interviews the newly-appointed UC Berkeley chancellor Nicholas Dirks, who was Franz Boas Professor of Anthropology at Columbia.

"I think diversity is important at every level. And it’s something about which one can never actually say, 'Okay, we’ve done this. We’ve had a diversity initiative. We have these statistics in terms of our student body. We have this kind of representation in terms of our faculty,' and think that’s enough. It’s not. At Columbia, we have engaged in a number of different diversity initiatives. We now have more students of color than any other institution in the Ivy League. And we have more under-represented minorities. We did so in terms of the faculty after 2004, when I began my role as executive vice president; the president and the provost and the trustees made available certain resources, and we were able within three to four years to double the number of under-represented minorities on the faculty."

The question about diversity came up right after a question about Dirks' rumored support for an Israel divestment initiative at Columbia back in 2002, which he of course denied. Dirks' wife Janaki Bakhle, professor of South Asian history at Columbia, is an outspoken critic of Israel. this has ruffled some important Berkeley administrators' feathers, who are otherwise quite pleased with Dirks' pedigree.

Link to interview:


He also seems to have gotten rid of his once-prominent unibrow.

JayMan said...

Just in time, both of today's blog posts:

Why sub-replacement fertility is not necessarily all that bad « JayMan's Blog

Expectations and reality: a window into the liberal-conservative baby gap « JayMan's Blog

Anonymous said...

The problem is not population decline, but ethnic or racial REPLACEMENT of the declining population. Take Japan for example where we hear much noise (mainly from the UN and other leftist sources) about its "demographic disaster". Japan's current population is 127 million, which is well over TRIPLE that of similarly-sized California's. According to the Chicken Little's, Japan's population could "crash" to 95 million by 2050. I would think the very crowded Japanese might like a little more elbow room (and less traffic, pollution and cheaper real estate). In any case this is 22 million MORE then Japan's population in 1941 when it felt vigourous enough to be at war with China, the USA and the British empire. So long as the only population of Japan remains ethnically Japanese, I see no trouble. But if millions of people visibly and culturally alien to them began arriving, that is a whole different story.

AllanF said...

The first poster beat me to the punch on generation length, and nicely too, congrats.

But another interesting aspect, which is especially timely as this week Oregon's Senior Senator's wife gave birth to their third baby, is multiple generations from the same father. Because as one would expect from a Senior Senator, he's no spring chicken. Not that Congressmen would ever subject themselves to the indignity, but Senator Wyden will qualify for Social Security in a couple years.

From the birth announcement:
"Nancy Bass Wyden is co-owner of New York's Strand Bookstore. She and the senator married in September 2005. She gave birth to twins in October 2007.

Wyden has two adult children from a previous marriage.

The 63-year-old Democrat was first elected to the U.S. Senate in 1996."

And for the gawkers, no, Nancy's no spring chicken either. She was 51 in May when the pregnancy was announced. I don't know when her birthday is. I reckon that makes it about even odds whether she is still 51 or now 52.

Anonymous said...

It is as if Western leaders are either too stupid to comprehend what their immigration policies are bound to lead to, or, if they do understand, they must be evil enough to want the inevitable outcome.


Anonymous said...

This is mere hypothesis, suspicion but...immigration is a driver of population growth not just because immigrants have higher fertility rates, but because immigrants are disproportionately of childbearing age. Whether a Mexican illegal or an Indian here on an H-1B, the profile of the average immigrant is skewed towards someone getting ready to have a family. Immigrants' share of the breeding pool is much higher than their share of the overall population.

If the immigrants coming here looked like America, in terms of their profile, their impact on America's racial makeup would be far less profound.

People look at the number of immigrants America takes in annually - over a million - and think it small because annually it's only about 0.4% of our population. But since people grow in generations, not years, and since those generations are getting longer, now reaching almost three decades - the impact per generation is huge.

High immigration + longer generations + skewed age profile of immigrants + declining white fertility (at least in part because of too much immigration) = massive race replacement.

Reg Cæsar said...

Citizens are giving away their countries to pay for the criminal misbehavior of the finance industry. I predicted this (for the US) back when the housing market collapsed. Shocked it hasn't actually happened... --Matthew

"Giving away the country" happened long before the housing bubble popped, or even began. That's why you didn't see any change after that. Spain actually had some standards left to drop.

It's like the claim that "letting gays marry won't affect your marriage at all". No, because once you reach that level of idiocy, it's clear that marital law and custom have already been shot to hell for a long, long time.

Reg Cæsar said...

By coïncidence, I got an appeal letter today from the somewhat alarmist World Population Balance. (They used to say 'stop at two'. Now it's 'stop at one'.)

The president of the organization tells how, after he gave a presentation at a local college, a young, married mother of one, born in an Asian refugee camp, approached him:

After chatting several minutes she asked, 'Why does the video say we should have only one child per couple? I thought we could have two.' As I went to the whiteboard I hoped I could figure out a clear way of answering her. But, all of a sudden she said, 'I get it. The reason we should have only one child is because we have waited too long. We have become far too overpopulated.'

In that moment, she taught me.

Silver said...

Population momentum extends out to some fifty years in even in the totally unrealistic case of going from a total fertility rate of, say, 5.5 to a TFR of 1.5 over the space of one year. In this totally unrealistic scenario the total population will still increase over 50% from the first year of TFR 1.5 to the last year of population growth.

The TFR of sub-Saharan Africa is about 5.0 today. If it manages to decrease to replacement level over the next forty years, from that point (so, from about 2050 on) the population may grow another 25%-50%over the following fifty years depending on whether it stays at replacement or dips significantly under it over that period.

Silver said...


this is where south korea is today. lowest birth rate in the world for a few years, but the population is still growing.

Yes, but Korea's population growth has slowed to a crawl the last five years. It's completely possible (rather likely, even) that the population growth could be attributed solely to immigration.

Silver said...

I think diversity is important at every level.

Voodoo sociology, basically.

Reg Cæsar said...

So long as the only population of Japan remains ethnically Japanese, I see no trouble. --anon.

Homogeneity is great, but it doesn't solve the dependency-ratio problem. It's one thing to go down to 1.9 or 1.8 TFR for a few generations; it's something else entirely to go right to 1.2. It's the difference between tapping the brakes when you see the yellow light, versus slamming them and getting the airbag in your face.

Japan is actually the most forested country on earth, proportionally. A lot of the 'overcrowding' is a matter of choice.

Anonymous said...

the curious case of blair hornstine

and curiouser

jody said...

i volunteer to help south korea and japan with their low fertility problem.

as soon as they create the new Sx-69 visa for, er, reproductive immigrants, i'm there.

Anonymous said...

For those who are interested, the demographer, Nathan Keyfitz, modeled the momentum of population growth and provided exact formulas for the ultimate size of a population whose rate of natural increase declined to zero. The paper was written in the 1970s I believe and published in the journal Demography.

Renaldo V. said...

" Anonymous jody said...

i volunteer to help south korea and japan with their low fertility problem.

as soon as they create the new Sx-69 visa for, er, reproductive immigrants, i'm there."

-Why bother to go there when you can help out locally? I go out of my way here in the US to help new female Asian grad students on campus with this very issue- or at least to go through the motions.

Sideways said...

Does more really have to be said than "china had about 450 million fewer people when it instituted its one child policy?

Anonymous said...

I am always amused when I suggest to liberals that reducing immigration to industrialized nations is the way to reduce pollution - i even had one liberal flat out tell me that immigration did not effect land usage in any meaningful way, at the same time he supports cap and trade.. .what can you do?? ..

Sword said...

Reg Cæsar said...
Japan is actually the most forested country on earth, proportionally. A lot of the 'overcrowding' is a matter of choice.

Er, no.

A simple googling shows that it is the country that is #15 in relative forest cover.

Maya said...

Jody, such a visa already exists in S Korea. It's called the E-2. They just want you to watch some kids a few hours per day, as long as you are there. All you need is a bachelor's, and they''ll pay for your flight, visa and lodgings.

Maya said...

Granted I dealt only with the upper middle class in Korea, but most of my students came from families with 3 kids. More interestingly, a lot of the times the 1st or 2nd born was a boy, so it's not like these families were chasing that elusive male heir. I got the impression that the successful, urban Koreans like having large-ish families. Perhaps it's the economy that slowed down the birth rate

Anonymous said...

Granted I dealt only with the upper middle class in Korea, but most of my students came from families with 3 kids.

This is a well-known statistical anomaly, and it threw me for a loop when I first encountered it.

If you let:

F0 = the number of families with no children

F1 = the number of families with exactly one child

F2 = the number of families with exactly two children

F3 = the number of families with exactly three children

F4 = the number of families with exactly four children

etc etc etc

Then the population of all children is

0*(F0) + 1*(F1) + 2*(F2) + 3*(F3) + 4*(F4) + 5*(F5) + ...

In particular, the number of children who come from families with three or more children is the tail of that sum:

[3*(F3) + 4*(F4) + 5*(F5) + ...]

And because the "head" coefficients {0, 1, 2} are so much smaller than the "tail" coefficients {3, 4, 5, 6, ...}, it doesn't take very large numbers for the "tail" to just swamp the "head".

For instance, suppose you have 100 families, and suppose the children-per-family distribution looks like the following:

F0 = 15
F1 = 25
F2 = 30
F3 = 20
F4 = 5
F5 = 3
F6 = 2

Note that that distribution is HEAVILY weighted towards the lower values:

F0 + F1 + F2 = 15 + 25 + 30 = 70

of the 100 families have two or fewer children.

And yet

0*15 + 1*25 + 2*30 = 0 + 25 + 60 = 85

children come from 0-child or 1-child or 2-child families, whereas

3*20 + 4*5 + 5*3 + 2*6 = 60 + 20 + 15 + 12 = 107

children come from families with 3 or more children.

Bottom Line: From the point of view of everything we know about biology and ecosystems and evolution and everything else, FERTILITY TRUMPS INFERTILITY EVERY TIME IT'S TRIED!!!!!

Silver said...


Korea's TFR has been well under 2.0 for nearly thirty years. Over the last ten years it has been less than 1.2. The Korean economy was booming throughout this entire period, and is not any kind of trouble today.