# No, Not Having a Child Will Not Prevent Eleventy Billion Tons of Carbon Emissions

The Internet has been abuzz with discussion of an article in The Guardian asserting that the best way by far to fight climate change is to not have children. While this is not the first time this topic has been debated (nor even the first time it has appeared in The Guardian), this latest iteration features some particularly egregiously bad math, giving the argument the thin veneer of undeniable truth.

The story’s (sub-)headline number originates from a 2009 paper that purported to calculate how much carbon emitted by a person’s descendants should be blamed on that person. Half of the emissions of your children are your fault, a quarter of the emissions of your grandchildren, and so on. A new paper took that number and annualized it by dividing by the average lifetime, and put it in context of other sources of carbon emissions. Notably, it flipped the script: the new study frames things in terms of how much carbon you can avoid emitting by not having children.

According to the new study, you can save 58.2 metric tons of CO2-equivalent emissions per year by having one fewer child. This compares to a paltry 2.4 metric tons that you’d save by getting rid of your car, and progressively tinier numbers for other actions. Seems pretty clear, right? Cars don’t matter, just don’t have kids and you can feel superior to anyone who does!

Sirens should be blaring in your head right now. After all, on average, an American is responsible for 16 metric tons of emissions per year. And on average, an American will have 1.87 children. So by having just 0.87 children, you can be responsible for a negative amount of carbon emissions!

Now obviously, this is not what is meant by the study. So what is? Well, let’s go back to how that original number is calculated. We’ll assume a constant fertility rate of 1.87 children per woman and a constant amount of carbon emissions per lifetime. (Already, this latter assumption is very problematic — surely we will continue developing technologies to reduce our dependence on fossil fuels!)

So let’s say you have a child. This child will emit 16 tons annually, but you’re only responsible for half because the other parent is responsible for the other half. So that’s 16 × 1/2 = 8 additional tons annually. But we’re not done — your child will have 1.87 children. So as one of four grandparents, you’re responsible for an additional 1.87 × 16 × 1/4 = 7.5 additional tons. For your 1.87 × 1.87 great grandchildren, you’re responsible for 1.87 × 1.87 × 16 × 1/8 = 7 additional tons. And so on. Some high school algebra should convince you that this implies that you are responsible for 8 / (1 – 1.87 / 2) = 123 additional metric tons of carbon emissions per year for each child you have.

Now this is actually quite a bit higher than the 58.2 metric tons figure from the study. The reason for this is that the study uses a slightly more sophisticated model incorporating the expectation that fertility rates will drop. But the big disparity in these numbers should already tell you that something is up — fertility remaining as it is now vs. declining slightly already changes their number by more than a factor of two!

In fact, let’s see what happens as we vary the fertility rate. The function s = 8 / (1 – f / 2) gives the purported annual carbon savings s of having one fewer child assuming a constant fertility rate f. Here’s a plot of this function:

So we see that this number, which the study authors very precisely specify to three decimal places, is extremely sensitive to changes in fertility rate. And indeed, if the fertility rate were at least 2 (as it was for the vast majority of human history), their reasoning would say that having one fewer child would reduce your carbon footprint by an infinite amount.

Now let’s step back here and notice a few things. If people are reproducing at below a replacement rate (that is, the magical 2 from above), then barring any miraculous advances in life-extension technology, there will be fewer people in the future, and carbon emissions will be lower even if per capita emissions remain the same. So how can it be that having one child instead of zero can increase your carbon footprint from 16 tons per year to 16 + 58.2 tons per year?

The fundamental flaw in the paper is that it matters when carbon emissions are happening. Yes, your descendants will emit a lot of carbon, and indeed, if the human race never dies out (and we never find a technological replacement for respiration), our progeny will necessarily emit an infinite amount of carbon. But what matters for climate change is the atmospheric concentration of carbon dioxide, and what affects that is the rate at which carbon is emitted net of carbon absorption. A billion tons of carbon emitted over a billion years does not have the same environmental impact as a billion tons of carbon emitted in one year. At a bare minimum, the emissions of our descendants in hundreds of years need to be discounted compared to the emissions of our cars today. Otherwise, you’re comparing apples to oranges.

Ultimately, I find it incredibly harmful to tell people who are concerned about climate change that the best thing they can do is to not have children. In fact, the best thing they can do is to have children and to inculcate them with a sense of responsibility for the environment. Bring them up to be minimalist, car-free vegetarians. Nurture their interest in science. Combating climate change requires smart, motivated young people to create new technologies and to normalize low-carbon living. There’s lots of evidence that your biological children will grow up to be a lot like you. If only people who don’t care about climate change have children — well, you do the math.

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