In the comments on my post about the paper when it originally came out (https://www.jefftk.com/p/three-car-seats) people pointed out that the methodology cannot determine whether there is a common cause, and a common cause is actually quite plausible. Posit that over time people are becoming more protective of children, for whatever reason. This (a) makes parenting substantially more work/money (closer supervision, more childcare hours), leading to people having fewer kids on the margin, and (b) makes people supportive of legislation to protect children (car seat laws). So while it looks that car seat laws are causing fewer children, they could actually both be caused by changing societal attitudes toward child protection.
In the comments on my post about the paper when it originally came out (https://www.jefftk.com/p/three-car-seats) people pointed out that the methodology cannot determine whether there is a common cause, and a common cause is actually quite plausible. Posit that over time people are becoming more protective of children, for whatever reason. This (a) makes parenting substantially more work/money (closer supervision, more childcare hours), leading to people having fewer kids on the margin, and (b) makes people supportive of legislation to protect children (car seat laws). So while it looks that car seat laws are causing fewer children, they could actually both be caused by changing societal attitudes toward child protection.