davidsolomon

In terms of the general effects that some counties are richer than others, and some years people are richer than others, this will be captured by our fixed effects that control for overall birth rates for each combination of county, year, and number of children. So all effects are measured relative to other two child families in the same county and year. This captures the large majority of other regulatory and social changes that might be happening in that county and year.

Next, we also add income by year and income by county fixed effects. So if richer people in a given county have more children relative to the average of all two child families in that county and year, we'll also control for that. If richer people in a given year have more children compared to the average of all two child families in that county and year, we'll capture that too.

The point isn't that you need to add every one of these complicated fixed effects to find our result. It shows up in simpler tests too. It's just that you can control for a lot of potential confounding effects, and it still seems to be there.

At a minimum, one thing that we can hopefully convince you of is that our research methodology as designed is reasonably conceptually sound. If we're wrong in our research design, that's a problem regardless of anything else. But if our identification strategy is at least defensible if actually implemented correctly, that's a good start.

Having skeptical priors about research in general, whether incentives, error rates, or whatnot, is totally fair.

This is definitely possible - we've only looked at deaths.

One point to note about the 57 deaths number. There's also an argument to be made that you should apply the same burden of proof to claims that car seats reduce fertility, and that car seats reduce car crash fatalities. In other words, some people are skeptical of our methodology, which is totally fair. But if you subject the hypothesis that child car seats reduce car crash deaths to the same level of skeptical prior, the evidence in favor of saving lives is much, much weaker than the evidence on fertility, in our opinion.

The 57 deaths is our best point estimate from the regressions, but in the vast majority of specifications you can't rule out an effect of zero. By contrast, we find pretty strong evidence on the fertility reduction, that we think is fairly tightly identified compared with other competing explanations.

One of the interesting things about the feedback we've gotten on the paper has been the number of people who report that this problem is a pain for them, even if it doesn't rise as far as stopping them having another child. To us, this makes it more likely that this pain (if real) is actually deterring some people who are at the margin.

> That's just not how people make decisions at that level. If you want a kid you get a kid and you roll with it. You know it's gonna be expensive but you just deal.

The way I think about it as that these laws only need to affect some families that are on the margin. Are there some families that are just on the fence and tossing up whether to have a third child? It seems likely to me. As long as this cost is a significant one, it just needs to move the needle for these groups to show up in aggregate effects. Lots of people will make the same choice either way, whether it's to have a third child or not have a third child. Our predictions are for people right on the margin.

>Controlling for income is really really hard since basically everything about lifestyle has some relation to income.

We use county-by-year fixed effects to take out the average effect of birth rates in that county and year, whatever form that variation takes. So if it's just that Cook County in Illinois got richer one year and so had more children, this will be absorbed by the fixed effects, and our car seat impacts are considered relative to this baseline. We also control for birth rates for that number of children and age combination, so we're comparing essentially two families with a six year old and a three year old, but in one state/year they both have to be in car seats, and in the other one only one child has to.

Hi, I'm one of the paper authors here. Happy to answer questions.

Here's how I think about our methodology. Car seat laws generate an unusually sharp prediction for births that can be distinguished from a lot of competing effects (not perfectly, of course, but compared with a lot of other demographic effects)

We're not testing whether the state and years with more stringent car seat laws have lower birth rates. That could be due to tons of stuff going on in those states.

We're not even testing whether the states and years with more stringent car seat laws have lower birth rates just for third child births. That could be relatively fewer things, but still a lot.

Rather, we're testing whether states and years with more stringent car seat laws have lower third child birth rates specifically for families whose first two children are below the mandate for their state and year. And this mandate is itself changing over time for both states and years, so we're talking about different ages of children in question depending on which state and year it is.

This clearly doesn't rule out everything. But the set of candidate explanations for what else could be going on for those specific families in those years is a lot smaller than the broad demographic effects we started with.