Fertility rates and population

and why we need at least some immigration

In order to have a stable population, the fertility rate needs to be about 2.1 births per woman and a life expectancy that isn’t changing. The 0.1 is because not everyone makes it to adulthood to reproduce. The U.S. fertility rate dropped to a record low, 1.62, in 2023 (CDC 4/25/2024).

The provisional total fertility rate for the United States in 2023 was 1,616.5 births per 1,000 women, down 2% from the rate in 2022 (1,656.5);

In fact, the world fertility rate is barely above 2.1. Figure 1 provides data for selected countries over time.

Figure 1. Data from Our World in Data.

The U.S., along with many other countries, has been below replacement since the early 1970s. Increasing life expectancy can hide low fertility rates for awhile, but economically older adults consume less than young adults. Industries, such as education, are particularly impacted by a shrinking population of children.

I don’t think it is easy to relate fertility rates to population size. What does a fertility rate of 1.62 look like in terms of population size? To help get a sense of what happens, I made a simple model.

I assume everyone lives to age 80, in which case the replacement rate is 2. Everyone has children at age 30. The fertility rate doesn’t change for the 100 years of the model, and we start off with a population that has 1,000,000 people of each age. I ran the model for different fertility rates with the results in figure 2.

Figure 2. Simulated population size over time with a given fertility rate.

The black line across the top is the stable population scenario. One key thing to note is that over 100 years the population decrease isn’t linear in fertility rate. In other words, the drop from 0.75 to 0.5 is smaller than the drop from 1.75 to 1.5 at year 100. In particular, a 25% decrease in fertility rate from 2 to 1.75 has a more than 25% drop in population in 100 years.

If the fertility rate is cut in half to 1, roughly the China scenario right now, the population decreases by over 75% within 100 years. China has a real problem on its hands at the moment, and they currently aren’t open to immigration.\

Japan has had a low birth rate for years that is reaching a crisis. How is that working for them? BBC (1/23/2023).

Japan's prime minister says his country is on the brink of not being able to function as a society because of its falling birth rate.

The Harvard International Review (10/30/2025)

In response to this crisis, the Japanese government has tried incentivizing births by introducing “baby bonuses,” which pay expecting mothers 100,000 yen (US$670). Japan is also increasing the number of young immigrants allowed into the country to bolster the workforce and reduce the island nation’s dependence on older people in the economy.

In general, a shrinking population is an economic problem. In particular, you end up with fewer working-age people supporting an older population. Immigration is one “solution,” but the world overall is getting close to replacement fertility rates, in which case countries will be competing for those that want to leave their current country.

For the U.S., immigration is critical to maintaining or growing its population. The fact that people want to move to the U.S. is a huge advantage. How many and who the U.S. accepts should be a strategic decision, with how many being at least enough to maintain population. Who is likely to be a range of people based on the need for workers and talent. Unfortunately, immigration seems to be a political mess, ranging from no immigration to letting everyone in.

R Code

The R code for the simulation can be found at my new GitHub site. This is a direct link to the code.

Please share and like

Sharing and liking posts attracts new readers and boosts algorithm performance. I appreciate everything you do to support Briefed by Data.

Comments

Please let me know if you believe I expressed something incorrectly or misinterpreted the data. I'd rather know the truth and understand the world than be correct. I welcome comments and disagreement. We should all be forced to express our opinions and change our minds, but we should also know how to respectfully disagree and move on. Send me article ideas, feedback, or other thoughts at briefedbydata@substack.com.

Bio

I am a tenured mathematics professor at Ithaca College (PhD Math: Stochastic Processes, MS Applied Statistics, MS Math, BS Math, BS Exercise Science), and I consider myself an accidental academic (opinions are my own). I'm a gardener, drummer, rower, runner, inline skater, 46er, and R user. I’ve written the textbooks “R for College Mathematics and Statistics” and “Applied Calculus with R.” I welcome any collaborations.