(Note: This post takes the perspective of strongly preferring higher American fertility to lower American fertility on anything close to current margins. I endorse this view and consider it very overdetermined, but this post does not defend or justify it.)

(Note: This post has been edited to include consideration of two studies arguing against the main study.)

It is often said that governments can do little to increase the birth rate.

I find this implausible. We do lots of things as the government that decrease the birth rate. We could Stop It. Or do the opposite.

A paper that came to my attention recently looks at a concrete example of such a policy: Car seat requirements.

You can see the various rules by state here. Some are relatively reasonable. Others, not so much.

Several commenters have disputed the conclusion that these seats have minimal effects beyond the age of two, including pointing to this study claiming 55% injury reduction in ages 4-8 (sci-hub), and this study claiming 29% reduction in injuries in ages 8-12. I examine them in an added area of the safety section. There are reasons to worry the controls are insufficient, in ways the main study examined does not need to worry about. Neither study has the usefully power to look at deaths, and the death data does not leave room for much effect there. There is still plausibly substantial benefit on preventing lesser injuries.

The first best solution to this particular issue is to eliminate all car seat requirements, or at least limit such requirements to children under the age of two.

Failing an age two limit, limiting to the first four years would confidently capture most of the safety benefits, while eliminating more than 80% (and likely more than 90%) of the negative effects.

Failing that, we could even exempt any child with two younger siblings (or even two younger children present in the car), for obvious practical reasons, and still most of the negative effects (at least on births) go away while most of the safety benefits clearly remain.

Car seat requirements also allow us to get an estimate of what impact a direct front-loaded economic subsidy might have on American fertility. I estimate that various incentives will generate or prevent one additional birth per ~$270,000 in effective size, with the note that front-loading likely increases this effect while spreading it out over a longer period will likely decrease it.

This happens to correspond almost exactly to the cost of raising a child to age 18.

To the extent that there are real safety benefits to car seats for older children, it means the true cost of the mandate is lower, which in turn would lower my estimate of the necessary incentives accordingly.

Overview

Here are the key findings and explanations, starting with the abstract. Anything [in brackets] throughout this post is me editing/clarifying based on other things from the paper. And I add paragraph breaks, because almost all papers need more of those.

Abstract: We show that laws mandating use of child car safety seats significantly reduce birth rates, as many cars cannot fit three child seats in the back seat. Women with two children younger than their state’s age mandate have a lower annual birth probability of 0.73 percentage points [a relative drop of 7.8%]. This effect is limited to third child births, households with access to a car, and households with a male present, where both front seats are likely to be occupied.
We estimate that these laws prevented [at most] 57 children’s car crash fatalities in 2017, but prevented 8,000 births that year, and 145,000 births since 1980.
[from later]: By contrast, if current laws had applied over the whole sample, we estimate there would have been a further 350,000 fewer births.
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Our prediction is that third child birth rates are reduced only when the first two children are younger than the state/year mandate, which is itself changing over time.
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We consider one unexpected cost – child car seat laws. Since 1977, U.S. states passed laws mandating that children be restrained in child safety seats. While initial laws typically applied to children ages one to three, since the mid-1990s mandated age limits have seen a huge ratcheting upwards. The median age at which children are allowed to ride in just a seat belt in U.S. states is now eight, and every single law change has increased the age, not reduced it (with the average state making 3.2 such age changes).
Enthusiasm for these laws has not been curbed by studies showing that child car seats are no more effective than seat belts in preventing death or serious injury for children above age two (e.g. Levitt 2008, Doyle and Levitt 2010). This may be due to the perception that such mandates are virtually costless, beyond that of the car seats themselves.
However, these laws can significantly raise the cost of another child for women who already have two young children. While the exact type of mandated restraining device varies, many cars cannot easily accommodate three child seats in the back row of seats, as would be needed if both front seats are occupied by adults
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We find that the estimated effects are driven entirely by households with access to a car, and where there is an adult male in the household, increasing the likelihood that both front seats are occupied by adults. Surprisingly, the effects are larger among higher income households. This suggests that the channel may not be just money, or that these groups bear a greater burden through higher compliance rates, greater knowledge of the law, or being more likely to plan their fertility.
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[Effect decomposition]: The first represents an intertemporal shift in birth rates, whereby child birth is delayed until existing children age out of car seats, offsetting some or all of the contemporaneous effect. The second component represents a permanent effect, whereby the additional cost dissuades some women from ever having a third child or more.
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Each additional year that the two eldest children are required to be in car seats results in a 0.60 percentage point reduction in the lifetime probability of having a third child.
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We estimate that switching from an eight-year-old mandate to a four-year-old mandate would result in the average woman having 0.0076 more children. [1 per 131 women who have two children.]
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Existing work such as Levitt (2008) and Levitt and Doyle (2010) shows no significant effects of the use of car seats on death or serious injury rates for children over age 2 relative to seat belt use, conditional on getting in a crash. This still leaves open the question of the impact of mandates themselves, whose effect may not map cleanly to actual usage. Using Federal data on fatal car crashes dating back to 1975, we estimate the effect of car seat laws on the number of child fatalities in car crashes to be very small. Our best point estimate corresponds to car seat mandates preventing only 57 fatalities of children below age eight in 2017, with the most favorable estimates being 140 fatalities prevented. In these and most specifications, we cannot reject a null hypothesis of zero lives saved.
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A surprising aspect of our results is that while the costs of upgrading to an SUV or minivan are non-trivial, they are relatively small compared with the lifetime costs of raising a child. This makes it puzzling that our effects are as large as they are. One possible interpretation here is that the people being influenced are very close to the margin of indifference, and there are a surprisingly large number of families in this situation. However, an alternative is that these costs are unusually salient relative to other considerations because of how immediate they are. If individuals engage in hyperbolic discounting (e.g. Laibson (1997), DellaVigna and Malmendier (2006)), immediate costs like buying a new car even before the child is born may end up weighing more heavily than much larger, far-off costs like paying for college. Another possibility is that the cost of a new car is not so much the actual reason, as much as a rationalization or polite excuse, especially if there is some disagreement between the parents (Voas 2003). The question of why car seats weigh as heavily as they do is an interesting one for future research.
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Finally [among other similar estimated effect sizes for other things], our estimate is similar to recent literature examining Russian maternity benefits (8.8% from Malkova (2018)) and mortgage deregulation (6% from Hacamo (2020)). From a policy point of view, car seat regulations are unusual in that increasing birth rates does not necessitate greater government expenditure, but simply removing a costly mandate.

Before diving into the details, what might the key takeaways be here, if true?

There are 145,000 births prevented, versus a population of 332 million.
About one American in 1,150 that would have been born since 1980, was never born due to this law. (source for overall births data).
Going forward, given current law, this will likely increase to 1 in ~500.
About one American in 2,500 that would have otherwise been alive today doesn’t exist because of this requirement.
That’s a lot.
A decline of 7.8% is quite a lot indeed.
Among those fully impacted it’s going to be quite a lot bigger than even that.
It is not clear these laws do anything to stop fatalities for children over 2.
For every fatality prevented, we prevent at least ~140 births.
We also prevent some number of other injuries.
We also impose a lot of costs on families in various forms.
Many people probably really hate minivans.
Many people care a lot more about immediate costs than long term costs.
These car seat laws that go out to 8 (!!!) years old are flat out nuts.

Allow me to emphasize that last point once again. These laws are completely, utterly nuts. They impose a real and substantial cost on families, which is so large that they forgo having additional children.

Even when that does not happen, it’s super annoying having to shuffle around car seats between vehicles or between trips. It means that one needs to have a background terror that if one took a taxi or otherwise tried to live life normally that one could somehow get in trouble. It insults the children. It is actively uncomfortable. At least the one car seat we have used was remarkably annoying to buckle and unbuckle, sufficiently so that I tried to avoid using the car even more than I would have otherwise. We now once again live in NYC so we have no car, yet for all three births worried before births if we would be allowed to take our son home without a car seat. The shame factor of having to purchase a minivan, should that arise for someone, is often not small.

I can totally see, as a father of three, how this could prevent births.

There is a claim to substantial safety benefits via older studies. I examine two of them in the Safety section. I don’t see anything large enough to plausibly justify such mandates in places where use is expensive, but it makes the decision to use a car seat for longer seem more reasonable when made by an individual who has that option.

The idea that most seven year olds require a car seat simply makes no physical sense. It is patently absurd. Nor is it a rule that one could remotely hope to enforce.

This can then serve as an example both of of an insane rule that still keeps getting ramped up to higher and higher levels of insanity, and also an example of an easy way to show that yes we can raise birth rates by improving the lives of families. And it can provide a point estimate of how much it might cost to do that with money, where we must do so with money, although this is complicated by people’s hatred of minivans.

Why Is Fertility Declining?

Before getting into the study’s true guts: What’s the core problem with the fertility rate? As the paper notes, we know about birth control, about female education and labor force participation rates, and about economic development, and other general factors, but none of those needles have moved in the United States for a while and yet the birth rate keeps declining.

No one is saying that car seats are the primary motivating factor here. Can economics explain it more generally?

The recent decline is also puzzling under standard economic theories of fertility. A recovering economy ought to have increased the budget set for available children, unless the costs of having children are rising faster than incomes.

Generally, I would propose five things here.

The dollar costs of having children definitely are rising much faster than incomes. Children disproportionally increase costs in education, housing and health care, which are exactly the sectors getting most expensive.
The lifestyle costs of having children are also rising. Burdens placed upon parents have increased. It is far easier to get into trouble. There are more things you are forced or expected to do that are expensive in various ways. The things most fun about children and childhood are more restricted. There are fewer other parents, especially of multiple children, to coordinate with.
Baseline career paths and expectations are increasingly incompatible with raising families, both in terms of real and imagined requirements. More time must be spent in school and then in jobs that do not pay enough, and there is more fear of being left behind, and young people are less able to meet, have sex and relationships and get into position to raise a family.
Meanwhile, we’ve set the expectation that marriage and kids are touchstones that you get after you make it, not something everyone gets to have and that then provides motivation to make it because you have something to protect. Which again plays into not being able to make it, because you’re not up against others with kids. Social rewards for children, especially those beyond the first or second, are greatly reduced, and media roll models hard to find.
A ‘recovering economy’ does not match the lived experience of most young people, who as far as I can tell are struggling economically.

Also: Recently, it seems a remarkably large number of people are being tricked into not having children by panic over climate change, and being made to feel bad about the idea of having children. Please do not fall into this trap.

Some people I know aren’t having children, or have even had vasectomies, due to AI risk. Please do not fall into that trap, either.

Or more bluntly:

Kids are more expensive now in dollars.
Kids are more expensive now in time and experiences and offer fewer rewards.
Kids interfere more with your ability to get dollars, and vice versa.
Young people are told to wait on kids until after they have it all figured out.
Young people have been screwed over and do not have it all figured out.
Young people are letting climate change drive them crazy.

This is mostly (but not entirely) a straightforward economic story. Higher prices, less willingness to pay, less pressure on people to buy. Quantity declines.

It is also an overdetermined story. Should this make us suspicious? In some ways yes, in some ways no. Certainly it raises the probability at least some of these are not major factors, but it also makes sense that such reasons would be mutually correlated and reinforcing.

This points to various different possible solutions.

The good news is that the essential goal is ‘make life better, more rewarding, easier and more affordable to live’ which are all great ideas anyway, so most of this is stuff already worth doing for other reasons.

Kids are expensive so give parents money, or reduce monetary costs. Presumably start with the big three: Health care, housing and education.
Burdens on parents are too large and rewards too small. Fix it. Reduce expectations and legal requirements of supervision and obsession with safety. Understand what risks are big and real and which ones are tiny and mostly fake, like kidnapping by strangers. This is where car seats come in. Don’t stick social services on people without a damn good reason. Allow kids to be kids and experience the chaos of youth, which is better for them anyway. Don’t teach the kids that they are something bad, or that they need to turn their backs on their parents and their traditions. Make it so a child’s future does not depend on an endless string of boxes being checked by discarding the boxes along the way. Let parents raise their children, to the extent feasible, as the parents best see fit. Ensure more places and events are kid friendly.
Kids interfere with long career and educational development, and a winner-or-long-term-commitment-takes-all working world. Reducing logistical requirements of children will help, as will lowering regulatory barriers to affordable child care. Reducing occupational licensing requirements and educational system gatekeeping, and changing college and graduate education to accommodate family formation, will help as well. So will general shifts from bullshit jobs towards actual production.
Cultural messaging can be hard to change especially by fiat, but we are not powerless here. The zeitgeist can be shifted. It can also shift when the underlying facts shift.
It is not so easy to ‘stop screwing kids over’ and this is essentially telling us to make a better country and get our house in order. So, fair, but the most likely key is to focus on defeating rent seeking by the old against the young. Zoning and other restrictions that drive up rent and house prices, tuition combined with price discrimination and educational job requirements that drives them into debt, and the barrier to letting people start their own small businesses, which are by default one’s best choice and more compatible with raising a family.
Give people hope for the future. Climate change takes away people’s hope, so solve climate change to give them their hope back. Do the same for some other issues. Help us celebrate what’s good and getting better, as many things are.

So, again, no one said this would be easy, but the situation is not entirely hopeless.

A weird dynamic to consider is that birth rates decline as economies develop, but also all the economic principles and observations of people’s choices say one’s willingness to have children declines as one’s economic situation worsens, once you control for someone’s social class and expectations.

Thus, I can notice this…

…and still expect that making a given person/couple’s financial life improve will in general will increase their birth rate, even if it’s not focused on things related to children, although that focus will certainly help. Part of this, of course, is that the graph does not represent one directional causation.

Data Sources

We obtain state car seat laws using Lexis Nexis StateCapital and NexisUni.
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We then identify the age at which point 50% of children can ride unrestrained using a seatbelt.

My guess is using straight age restrictions would have been better, because the weight exemptions don’t often bind and mostly are ignored, but they note that this would not have substantially changed the results.

Data on car crashes come from the Fatality Analysis Reporting System, from 1975 to 2018. This database contains information from vehicle crashes in which there is at least one fatality, and includes information on vehicle and passenger characteristics.

America is still very good about some kinds of data collection, which is handy.

Those are easy, fertility conditional on various other things is the tricky one that requires multiple data sources:

Our data on birth rates come from a compilation of assorted U.S. Census Bureau data products, aggregated and standardized by IPUMS USA, a service of the Minnesota Population Center. More specifically, our primary analysis is based on yearly vintages of the American Community Survey (ACS) conducted from 2000 through 2017, and 5% random samples from the 1990 and 2000 decennial census.
The result is a dataset comprised of repeated cross-sectional snapshots of U.S. households taken at different points in time. For each cross-section, we are able to observe key characteristics of all surveyed households, including the age and sex of the household head, all other adults (including spouses), and all children present in the household. Moreover, each survey includes other relevant characteristics, such as race/ethnicity, household income, car ownership, and geographic location (generally at the county level, though at the state level in earlier vintages).

This suggests that we have a bunch of other useful data that can provide color on the situation. Car ownership being included seems quite useful even if it doesn’t directly impact the headline answer.

Sorting everything gets a little odd.

We are interested in the decision of each woman to give birth, rather than each household. We exclude group homes, households with inmates or children-in-law, and households with no adult woman present (as households with only an adult male and children will lack information on the mother’s age). If a household has multiple women over 18 years of age, we split them into separate observations, assigning children to the corresponding mother, and noting the presence of any adult males. This unit, which we term a “household”, thus differs from the census definition.
We then take information from the survey year t for the age of the woman and any children, and infer ages and birth events for all prior years from t-1 back to the year in which the adult-age woman was 18 years of age.6 In doing so, we are only able to infer birth events for children that remain in the household until the time the snapshot is recorded.

In practice this is measuring the thing we care about. A child no longer in the household presumably won’t matter (or won’t matter much) for the purposes of car seats.

This is at least a minor issue:

We implicitly assume that a household has not moved across states from when the woman was adult-age until the year of the snapshot.

Moves that are for unrelated reasons will tend to scramble the data and make car seat impacts look smaller than they are - paper thinks the effect is unclear but that seems wrong to me. Moves that are party about car seat rules or other related rules would likely do the opposite. Moves intentionally towards permissive areas would be strong arguments for permissiveness. Moves intentionally towards restrictiveness would be the opposite but I am trying to imagine ‘I am going to move to where others have to use car seats for longer’ and my brain can’t do it. Paper mentions that strategic moving seems unlikely.

Result is a very large sample. It is missing substantial numbers of births…

In Panel B, the final panel has approximately 69.7M household-year observations with an average adult woman age of 25.3. The average woman in our sample has an annual probability of giving birth of 8.4%. In comparison, a back of the envelope estimate of publicly reported fertility rates for women aged 18 through 35 in 2010 is 9.1%.
One contributing factor to our lower estimated birth rate is the inability to observe births in which the child was subsequently separated from the mother (e.g., through adoption, divorce with fraternal custody, etc.). However, it is unlikely that this lower estimated birth rate poses a significant challenge to our empirical strategy, which is largely based on both state and year variation in car seat laws, and variation in the number and ages of children across households in a given state.

…but I agree with the paper that this should not impact the approach taken.

From Their Analysis

Non-linear effects from increasing ages, as you’d expect (italics in original):

For instance, mandating use of car seats until age 4 (as many early laws required) will affect relatively few women, and for a relatively short period of time. In particular, for a woman to be impacted, she would need to have given birth to two children who are both age 3 or less, and be looking to give birth to a third before the oldest reaches age 4. If each pregnancy takes roughly 9 months from conception to birth, three children require at least 27 months, even in the unlikely scenario of no gaps between birth and conception. With a 48-month mandate, and 27 months of pregnancy time, the only women affected would be those who wished to get pregnant again in less than 10.5 months on average after their first and second children (or those who had twins or other multiple birth events). In other words, the practical burden of low age mandates is likely to be very small.
At the other end of the scale, increasing ages to 6 or 8 is likely to have much bigger impacts. The likely spacing of births every couple of years will see a larger fraction of women already affected by the mandate, and extending it further will cut into periods when additional births might otherwise be likely.
To see this effect, in Figure 2 we plot the fraction of person/year observations in each year that are impacted by car seat laws under our definition– that is, women who have two children that are both legally required to be in a car seat. The graph shows that the impact was almost zero until 1983, around 1% of observations affected between 1984 and the early 1990s, increasing slightly to around 1.5% of observations in 2000. However, there was an enormous increase between 2000 and 2010, to over 6% of observations affected. In other words, while the existence of these laws is quite old, the period where they have had significant bite is relatively recent.
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In particular, what we require is that having a third child is discontinuously more difficult if both existing children are mandated to be in car seats.

Bingo, and a big reason the policymakers did not understand what they were doing. I am guessing they never thought about the situation where there were three children that all required car seats and that they would not physically fit in the same regular car, whereas three children can otherwise sit in the back without problems. All right, not with zero problems (have you met children?) but nothing you can’t handle.

Also, note that this table shows how the number of years the laws bind impacts the probability of ever having a third child (ignoring effects on fourth and later births, and it is clear as day.

(The numbers in parenthesis are t-values.)

Eight years bound meant twins, which shows a huge jump. The effect here is highly non-linear, on top of the non-linear impact on years bound from the laws. It seems clear that a four-year law has less than 10% of the impact of an eight-year law - compare one year to five, and two to six.

The paper also notes that the presumed mechanism whereby car seat requirements prevent births sometimes will not apply. Not every existing car will be able to fit three children in the back with two car seats. Many will be able to fit three car seats already, without upsizing:

But notably we do not require that it is impossible to fit three car seats in the back of all cars, nor that it is straightforward to fit in two car seats and a third older child in between in all cars. There may be some small cars whereby fitting in an older child in the middle may still be a struggle, which would make the law less binding at older ages (because the same cost of a bigger car is imposed even if the oldest child has aged out of the law).
In addition, there will be some women with larger cars who have access to modern smaller booster seats for older children, who will be able to have a third child without needing a bigger car, even if all three are bound by the law. For our tests to work, there only has to be some significant fraction of people who are affected in a discontinuous manner by these changes, which we feel is likely.
If these discontinuous costs mean that some sizable fraction of the populace will need a larger car for a third child, this is predicted to reduce third child birth rates.

They frame this as ‘the effect only needs to apply sometimes’ but it is worth noting that this means that when the effect does show up, its impact will be proportionally larger than measured by the whole group. If half of parents already have a minivan or other sufficiently large car, or would have to upgrade anyway, or don’t own a car at all - hello, New York City - then they presumably aren’t being impacted by such laws, which would mean that the other half is seeing twice the decline that the overall average shows.

What do the people tell you?

Anecdotally, it is rare to find people who will openly state that car seats concretely stopped them having a third child. But it is quite common to find people who cite car seats as being a pain and a hassle that they had to deal with, especially in the context of having a third child.

That’s why we check the stats and revealed preferences. If a family did decide to not have a third child due to a car seat requirement, I would not expect them to tell you this when asked, even if they consciously knew it themselves. There are lots of good reasons to have or not have another child, so it is easy to come up with an answer that plays better on all levels than ‘I didn’t want to buy or couldn’t afford a minivan.’

Methodology

To identify the effect of car seat laws on fertility rates, using our panel of female-year birth outcomes we estimate OLS regressions of the following form:

Which is a lot of Greek symbols that one does not need to worry about, it’s another way of saying ‘we did a regression on a bunch of factors.’ It effectively results in:

I am not checking their math and regressions, but in terms of methodology this all seems fine and standard.

Results on Near Term Fertility

What was found? They describe Panel A.

Women with exactly two children both under the state-year car seat mandate age have a probability of giving birth that is lower by 0.422 percentage points (t-statistic of -2.79). In terms of economic magnitude, by way of comparison over the whole sample (years from 1973 to 2017), the likelihood of giving birth in a given year for women that have exactly two children is 12.14% for 25-year-olds, 8.55% for 30-year-olds, and 5.20% for 35- year-olds.
Column 2 adds controls for the woman’s age and race, and the effect increases to -0.554, with a t-statistic of -4.09.
Column 3 adds ex-post demographic controls measured in the survey year, namely household income, education, and male type (i.e. husband, permanent partner / other adult male, or none). The effect increases slightly to -0.620, with a t-statistic of -4.80. Columns 4 through 6 allow all demographic controls to vary by year, county, and both county and year respectively.
The effect increases in the full controls specification to -0.732, with a t-statistic of -5.69.

The full effect size comes after putting in these various controls. I do not have a good intuition for why the controls should increase the effect size this much, but the majority of the effect is present without any controls.

The above covers women up to age 35. They then extend this analysis to ages 36, 38 and 40, which they note increases measurement error, and get -0.756, -0.699 and -0.688 respectively, which shows the cutoff at 35 wasn’t important. Women ages 36-40 have fewer third kids so the overall size dropping there is expected.

This test does seem to have potentially turned up something:

Finally, column 5 includes only observations from the 2000 ACS onwards. This sample ensures that at every date we have the full sample of female ages from 18- 35, albeit at the cost of examining a considering shorter time period. The effect of Two Children, Both Bound is -0.476, with a t-statistic of -3.42.

Panel B shows the effect size seeming to decrease somewhat over time.

That’s a substantially smaller effect for the later time period. There is some possibility that impact of similar laws is declining over time. Possible hypothesis is this happens over time as cars become relatively better and more affordable and people’s wealth increases. Also fertility declined in the later period, which will make the effect look smaller, and accounts for a decent chunk of this.

The conservative thing to do is plausibly to stick to this later-stage point estimate of -0.476 percentage points per year, rather than -0.732, if one wanted to know what size effect one could count on going forwards.

They then consider some other possible error sources, none of which seem to me to be worth worrying about given the full context, and dismiss them.

Next the paper finds strong confirmation of the causal theory. In cases where the car seat constraint binds less - either no car is owned, or no male is present so the front seat is free - the decline in fertility vanishes.

They then find the effect modestly increases with household income. They speculate, as I would, that this is a combination of more value on class signals and more reluctance to defy stupid state mandates, but that is only speculation.

Urban density also modestly increases the effect, for unclear reasons.

In terms of showing that births were reduced, conditional on the data and math checking out, I find this very convincing. This looks and feels real.

Permanent versus Temporary Fertility

The paper then considers the possibility that children are sometimes postponed until conditions change, but that the permanent effect size could be smaller.

Their conclusion is that there is some of this effect, and this reduces the temporary net effect from 0.72% to a permanent effect of 0.6% per year.

If we look back at the chart labeled Panel B above, we see that going from a four-year law with a newborn and a two-year old to an eight-year law changes the impact of the law from 0.32% reduced lifetime probability of a child to a full 4.48% reduction. So there is over a 4% chance that this changes final family size from three or more children down to two. That includes households that would never have had a third child anyway, and in many cases a family might still have a third child but be shut out of a fourth or fifth because they run out of time, so this is a huge reduction in future births.

It seems right to care more about permanent births than temporary births, but the difference between 0.72% and 0.6% could easily be made up for by the decline in fourth births in the future. Very few of these births effectively get ‘made back up’ later.

This checks with the many observations that families often want more children than they end up having, and the many cases where biology refuses to cooperate. Also, once you have a large gap in time, it is more tempting to stop and ‘get your life back.’ The clock, in many ways, is always ticking.

When they do a simulation of the entire population, they get this result for all women:

Figure 3 Panel A shows that the average woman in the sample would have a higher probability of giving birth of 0.012% per year for uniform mandates at age two, and 0.0096% for a four-year uniform mandate. The effect on birth rates is fairly similar within this range.
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However, as mandates increase to age five and upwards, the estimated average birth probability decreases considerably. A uniform eight-year-old mandate would result in a lower annual birth probability per woman of -0.033%, and a uniform nine-year-old mandate would result in lower annual birth probabilities of -0.046%.
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The difference between a uniform four-year-old mandate (0.0096% relative to existing laws) and a uniform eight-year-old mandate (-0.0325% relative effect) is a 0.042% per year difference in average birth rates.

This is why I can say with confidence (as I do in the overview) only that more than 80% of the negative effects can be eliminated, rather than the 90% that seemed to follow from other numbers elsewhere.

We estimate that uniform age mandates of two, three and four years old if applied throughout the sample would have led the U.S. to have had 145,000, 143,000 and 117,000 more births, respectively. By contrast, seven- and eight-year-old mandates would have resulted in 235,000 fewer and 392,000 fewer births respectively. In other words, a switch from a uniform three-year mandates to uniform eight-year mandates would have been associated with 536,000 more births.
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Another useful counterfactual is to estimate how many fewer births would have occurred if the heterogeneous laws in 2019 had been enacted across states in 1980 and not changed since. This would have resulted in 350,000 fewer births.
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A uniform four-year-old mandate in 2017 would have resulted in 7,700 more births in 2017, and a three-year-old mandate would have resulted in 8,000 more births.

Next, a quick survey to confirm that yes, children impact and force car purchases:

Multiplying the 51% of parents changing cars around the birth of children, and the 38% of them citing car seats as being important in this decision, gives 20% of surveyed parents changing their car around the birth of a child with car seats being a large or a very large factor in their choice. These results support the viewpoint that fitting in child car seats can pose a significant potential cost when having more children.

Theory Versus Practice

A common argument for minimizing the impact of such rules is to point out that there technically exist ways to cope with them. This post on LessWrong suggests sufficiently small boosters exist. This would still be highly annoying, and intuition says that this is going to be a very tight squeeze if the kids are approaching eight years old even in the best case.

If you are in this spot, I do think it is worth checking if such solutions work for you.

What is important to the policy question, however, is that, even if such a possibility exists, it does not negate the practical impact of the rules on fertility. If someone does not consider an option, then for the purposes of their decisions it does not exist.

Safety

Do car seats, and car seat requirements, improve safety?

Existing work on the intensive margin of using a car seat (e.g. Levitt 2008) finds minimal effects. However, these papers largely examine the impact of using a car seat, whereas the impact of mandating safety seats is plausibly even lower.

How polite. The impact of mandating them is going to be far lower, because some parents will use them anyway and others will ignore the mandate.

If car seats are worth using, mostly we should expect to see them in use, because parents care about the safety of their children. If anything, modern parents care too much about improving the marginal safety of their children versus other things children need. I would expect overuse of car seats even without a mandate.

What did Levitt find? From the abstract:

We find no apparent difference in the two most serious injury categories for children in child safety seats versus lap-and-shoulder belts.
Child safety seats provide a statistically significant 25% reduction in the least serious injury category.
Lap belts are somewhat less effective than the two other types of restraints but far superior to riding unrestrained. (JEL I18)

It seems physically plausible to me that the seats could prevent some minor injuries while not substantially impacting serious injuries and fatalities.

The new paper does a new analysis, and finds this:

Overall, the most reliable effects are observed for restrictions on four-year-olds and five-year-olds, in terms of being consistently negative point estimates across specifications, and showing some marginally significant effects with the full set of controls. These estimates indicate a reduction of -0.695 deaths per 100,000 for four-year olds (t-statistic of -1.79), and a reduction of -0.762 deaths for five-year olds (t-statistic of -1.84) (-0.598 deaths and -0.871 deaths respectively in column 8 with only eight-year olds and below included). Meanwhile, there are some ages (such as one-year olds) that show significantly positive effects on death rates from car seat restrictions, an effect for which we do not have a clear explanation.

The whole thing is a mess. I think we are meant to focus on the fourth column in each group. It seems non-obvious that car seats are doing net-positive things. The most generous interpretation here has the seats being net safer up through year five.

But what does this look like most? The null hypothesis, where the seats are doing nothing and the whole thing is random. Which was what Levitt found as well.

The paper still asks, what if they are as real as they could plausibly be?

While the evidence for car seat laws reducing death rates is weak and inconsistent, our main interest is in the economic magnitude implied by the point estimates. We multiply the coefficients in Panel B by the total number of children who are restricted in all U.S. states in 2017 (the year with the most stringent laws in our sample).
In the full specification of fixed effects (column 4 and 8), the number of children’s lives saved nationwide is estimated to be 40 in column 4 and 57 in column 8. Under the most charitable interpretation where we take the maximum effects and treat all negative point estimates as being genuine but all positive point estimates as being zero, the total number of lives saved is estimated to be 122 and 140 respectively.
To give context, it is worth noting how many children’s car crash fatalities there are in the first place in the U.S. In 1978, the number of fatalities for children age 0-8 was 2,392. By 2017, this had declined 73% to 654 total.
However, this is almost exactly the same as the 72% decline in fatalities for children ages 9-12 over the same period from 975 to 273 (who were largely unaffected by these laws).
In other words, back of the envelope approximations are consistent with the small numbers we document.

If fatalities declined the same amount for both age groups, that once again strongly implies the null hypothesis. At minimum, most of the gains here are clearly from other sources, and any benefits from safety seats has declined by ~70%.

What about the study that claims that there is a reduction in injuries up to age 12 here?

Before I looked, I had a simple hypothesis that this would be driven by common cause. If you choose to use a booster seat for your ten year old, you are not taking a normal attitude to safety. You are going to be driving slower and safer, and in safer roads, in safer cars, and so on.

Thus, the first thing I looked for was, did the study control for those factors?

There was control for model year of car, and general car type, and positioning within the car, and conditions of the accident like precipitation, weekend (?) and so on.

Since we care most about incapacitating or fatal injuries I looked there first. They found no effect unadjusted, a large effect adjusted (which is an absurd claim if taken seriously) and error bars here are absurd to the point where we can safely ignore the results entirely rather than pick them apart more.

For any injury at all, they have unadjusted risk ratio 0.709 and adjusted of 0.814 [0.749,0.884], so the adjustments are now in the intuitive direction. They have ages 8-9 with a ratio of 0.869 [0.818,0.923] and the 10-12 year olds at 0.675 [0.505,0.902].

The 10-12 year old CI is presumably super wide because very few kids still wore car seats at those ages.

That means that the combined group’s result, where the ratio should be closer to 1 and which they claim is their main result, is outside (barely) the 95% confidence interval for the 8-9 year old group.

They mention that child height and weight are factors in whether to use a booster seat and are not considered. If I am understanding the dynamics correctly this should reduce effect size some amount, but my guess is the real factor is ‘am I obsessed with safety or not?’ Which, again, means those parents are most likely to use them correctly, and to take hard to observe other safety precautions.

I am willing to believe that the effect here constitutes a reduction in minor injuries, but the size here is at best a very hard upper bound on the effect size, and the other studies show that car seats in another group had a larger than this effect on minor injury with no detectable effect on major injury. So I don’t see how the effect on incapacitating or deadly injury, which are the only place where the economic effect could be big enough to matter, could be large. Of course, that’s for the 8-12 age group, so that result is no surprise.

The other study is in ages 4-8, so more on point. It rhetorically assumes its conclusion. It says previous research demonstrates reduction in injury in ages 4-7 by 59%. This is the kind of research that makes claims about ages 4-7 ‘based primarily on children who were ages 4 and 5.’ This was then used to impose such rules on children up to age 8. Clever trick.

The data controlled for a few things, similar to the other study, but seems to be less thorough about it. That is confirmed by a smaller adjust, here from a 49% odds ratio to 55%. This could also be explained by the drivers here being far less weird, since many were only obeying a legal requirement and making a more plausible choice aside from that. Injury was defined as AIS score of 2+.

There is no question that this result looks substantial and robust as far as it goes. It does not include any measures of death, presumably because deaths were too rare.

Another intuition pump: The CDC says seat belts reduce deaths in adults by 45% and injuries by 50%. The booster seats are used in order to mimic the ‘proper’ effects of such safety belts. A ‘belt positioning booster seat’ having a larger effect than this when compared to an adult safety belt seems, shall we say, like a highly implausible result.

The population-wide mandate-dependent statistics seem to me to be more robust on several levels, especially in terms of the dangers of potential confounders.

Another population-wide check that makes sense: Look at children and compare to the general population.

Since 1975, fatality rates dropped 77 percent for infants, 75 percent for children ages 1-3, 52 percent for children ages 4-8, and 49 percent for children ages 9-12.
For passenger occupied vehicles and kids younger than 13, we see a steady decline from 1,384 deaths in 1975 to 612 deaths in 2019. We see a much larger decline in pedestrians and bicyclists killed.

Population sizes were similar throughout.

If child seat use increased safety by a lot in ages 4-8, you’d expect to see it show up here when compared to ages 9-12, for whom use of such seats remains rare and mostly not recommended. Looking at the chart, you can see that nothing much changed here in the 4-8 vs. 9-12 comparison, but for the 0-3 year old groups things did improve in relative terms.

This again strongly suggests that the benefits are concentrated in the 0-3 age range, and the rest of the gain is coming from other sources.

(We see a decline in motor vehicle deaths overall, but it is smaller. I am guessing this is mostly due to demographic shift - Americans are getting older, and older people die more often in crashes.)

The bottom line is thus: In a counterfactual world, where the mandates end at age 4, what would you expect the 4-8 year old column to look like instead? There simply isn’t any room left for there to be a big safety impact that could possibly make these laws make sense, even if maximal estimates are used.

If we make reasonable assumptions of declining marginal safety as kids age and that parents will use the seats the first two years regardless, and then look at how much impact you can mathematically fit in here, the answer is very little.

Why?

A question left unanswered is why such policies have been adopted almost universally across states and grown steadily more stringent, even without Federal mandates (Bae et al. 2014).
The answer that seems most compelling, but perhaps surprising under public choice economics, is that regulators are simply unaware of the magnitude (or maybe even the existence) of costs being imposed on family formation. At a minimum, the relative lack of public discussion of this tradeoff suggests that it may not be foremost in the minds of policymakers. It is nonetheless difficult to imagine the compelling social interest in existing policy arrangements.

Hahahahahaha. Yes. I am sure the regulators involved are merely unaware of the issue and that they will come around as soon as it is pointed out to them.

No.

To be clear, I don’t think that the regulators had any idea whatsoever about this effect.

That’s because they don’t care.

Such costs are not their problem in any way. Their goals and cares lie elsewhere. They don’t do a cost-benefit analysis.

They don’t think about or talk to a normal human in the situation they are regulating. Or consider the physical layout of the car of that normal human and whether the things in question will fit into that car and how much that might cost that human.

They also choose not to notice that no one has ever run a proper control for the crash test dummy experiments used to justify car seats, except that one time that they found the same results for those dummies that didn’t use a car seat. You see, when you ask to do such tests, the testing companies refuse, because they don’t want to piss off their customers.

This is not an innocent mistake. The magnitude of the damage was likely unintentional, but the idea that all of this was the result of well-intentioned folks all around? No.

This is not complicated. It is a clear case of ‘who benefits?’ with a clear answer: The regulators and lawmakers get more authority and power and get to use it and look like they care. The car seat makers get to sell more officially approved car seats. The gas companies get to sell more gas because the new vehicles are less fuel efficient. The automobile manufacturers get to sell more minivans.

Meanwhile, the usual Public Health Concerns get trotted out, to make it clear that an imagined possible improvement of any size justifies any amount of cost and any number of other consequences. There are so many hot takes. The first comment on the podcast link above is that children are bad. The second is that the dummy tests aren’t representative (and presumably somehow neither are the accident statistics).

The fourth literally says this:

I'm a pediatrician
…
Decreasing severe head trauma even by 0.001% is more than enough to justify the "cost" of the car seat or inconvenience. The economists act like a small reduction in head trauma is not worth the cost of having to install the car seat, but anybody who has treated pediatric victims with brain trauma from car accidents would tell you that's insane!

For those who are curious about the offering here: Google says there are about 50,000 such traumas each year, from all sources, so 0.001% even from all sources means one such injury prevented every two years.

The sixth comment once again calls upon us to celebrate the lack of births.

The seventh confirms that the minivan issue was a factor in a couple’s decision.

After that, it gets worse.

The better question than asking ‘why’ here is, ‘why not?’ Who is going to stop and reverse this? And then hopefully open the door to targeting other child-unfriendly, family-unfriendly needless regulation, ‘for our own safety’ or otherwise?

How Expensive?

To bring it all home, we must ask what the true cost of the car seat policy is.

Consider the car seat requirement as decomposing into a few different consequences.

The need to buy a new car, presumably a minivan ($$$).
The need to fill up that minivan ($$$), since it’s going to be less fuel efficient.
The need to use car seats that aren’t needed, since they’re annoying.
The need to drive that new minivan, including social downsides.

If you buy a new minivan, MSRP is likely about $33,000.

If you buy a used minivan, it will be cheaper. A very quick survey said maybe $15,000.

Let’s say on average this net costs $15,000 after your trade-in.

For gas mileage, you’re likely talking about an average of a few miles a gallon, something like 20 instead of 25. The average American drives about 15,000 miles per year, so this is about 125 gallons a year, historically let’s say $3/gallon so $425/year for a few years, so this cost is relatively small, a few extra thousand.

How much direct disutility from using the car seats? If you assume the average child on the margin is going to school and camp, one can guess something like two trips per day, which means getting in and out of the car 730 times a year. How much would you pay each time to not have to deal with that stupid car seat? How much would you pay to not deal with the middle car seat, in particular? This is arguably a bigger cost than the gasoline for some, but mostly let’s assume it’s not so bad.

How much worse is it to be forced to drive a minivan? I did a quick unscientific poll.

This seems to safely say the dollars are a bigger deal, but 41% thought the non-dollar concerns were larger, so they don’t dominate by much. If we interpret almost all as 100/0 and majority as 66/33, we get about a third of costs from non-$ factors. That seems sane.

So let’s say that it costs $18,000 all-in for the van and extra gas, and another $9,000 in various anguish for the minivan. If we round up for the actual car seats themselves, we can say roughly $30,000 all-in for those in this situation.

Obviously, the true costs will vary a lot. Some will already own such a car, or not need one, or have been planning to upgrade anyway, and thus will be down $0. Some will kind of like getting a new bigger vehicle. Others will really, really loathe their new minivans.

91.5% of all households own a car. Let’s guess that 80% of households in this position would need to change the car they drive, with 11.5% already owning a sufficient car (or that would have upgraded anyway) and 8.5% who don’t have a car period.

Those in this the situation ‘have two children who require car seats and no other children’ reduce their yearly chance of birth by 0.73 points, or a relative drop of 7.8%, when this cost is imposed on them on the margin.

That means that of those where the constraint binds, there is a relative yearly drop of 9.75%, or an absolute decline of 0.91 points.

So approximately we find that a tax of $30,000 cuts fertility by 10%. If this was purely an actual tax, then we would be collecting $270,000 in taxes for every birth prevented.

It is worth noticing that the bulk of this tax is due immediately at birth. This is about 2/3rds an up front cost. Up front costs likely have a lot more impact than longer term costs, even factoring in a reasonable discount rate.

We don’t know that a subsidy would have the same effect, as it might be viewed differently, but a reduction in costs in other ways likely would. And some people would greatly benefit from a large subsidy, so it isn’t totally clear the net impact would be smaller. It’s hard to know for sure.

If this were a matter of ‘the money you spend to induce births results in that much real value being destroyed in a pit and the money will be gone for no benefit’ then $270,000 is a lot of money.

As an interesting point of comparison: How much does it cost to have a baby and raise them? A 2015 study done by the USDA found that it cost an estimated $233,610 to raise each of two children from birth to age 17 in a middle-income family with two parents. That figure, adjusted for inflation, is just over a quarter of a million dollars at $286,000 in 2022.

In other words, the cost to get families to have another child is almost exactly the same as the cost to raise a child to age 18. That’s a coincidence, but it creates quite the intuition pump: You pay the costs of raising the child, and in exchange the parents agree to have it.

A second point of comparison: The average American will pay $480,407 in taxes throughout their lifetime. That's an average of 34.49% of all lifetime earnings spent on taxes. So you’d be spending ~60% of the expected tax revenue up front, and only getting it back over time, and people require a lot of services on the margin. Not obviously a great deal.

Another less serious but more fun potential comparison point: Aella put her proposal of ‘have and raise your child’ at $1 million per baby. Offer likely still open.

In another sense of expensive, whenever there is an obviously crazy and stupid legal requirement, it reduces respect for the law and trust in our government and authorities generally. This is usually considered a cost, but can also be a benefit. In general, teaching people to resent and whenever possible ignore the law, and that the law should not be expected to make sense, should be considered a cost when considering what to do, even if this is often the sane reaction to current conditions.

Child Tax Credit

The good news is, that’s not how any of this works. The money is not destroyed, as it is when families are forced to suffer for no reason. This would effectively be a shift of the tax burden away from families to households and individuals without children. The money is transferred, and can be used by families to buy goods and services like food and housing and childcare.

There are plenty of good existing reasons to want to do this transfer and provide a child tax credit. The child tax credit enacted by Congress during the pandemic severely reduced child poverty, generally making kids importantly better off, and still didn’t come close to covering the costs of raising children. It was good policy all around, even without a birth rate impact, and if anything should have been longer term and larger, and more front-loaded because the costs of children are front-loaded and also front-loaded payments have more impact on decisions than spread out payments.

I am guessing that is a lot of why previous attempts at subsidy in various places didn’t have as much impact as their proponents were hoping to get. The payments have been too spread out. Doing things like Hungary’s ‘have enough children and you are then permanently immune from income tax’ is a very long-term proposition, among its other problems.

Paths Forward

The obvious direct step is to eliminate any and all car seat requirements beyond two years of age, or at least within three or four years of age. The vast majority of the damage done by car seat mandates happens after age four and almost all of it happens after age three, whereas the vast majority of the safety benefits (or, more likely, all of them) happen by age two and certainly by age four.

While we’re at it, let’s end this equally absurd rule that minors are not allowed to ride in the front seat. On a recent trip, a friend of mine was pulled over and her thirteen year old daughter, who is taller than she is, was told she had to move to the back seat because minors cannot ride in the front seat. I am going to go ahead and not explain why this rule is absurd, although I will take joy in pointing out that there is consensus we should let some minors drive cars despite them being statistically terrible at doing so, and knowing they will thereby get into a lot of accidents.

More broadly, we can extend the logic of the car seat mandates, in two ways.

We can ask what other rules impose large effective costs on families without much benefit, especially those that come out of an obsession with safety. And especially those that interfere with the logistics of life. Making parents unable to be confident letting their children stay home on their own, or run errands or go to the playground, until in many cases they are in high school, is a severe cost that compounds with larger family size. It is expensive in dollars, in time, in stress and experiences and in the joys of childhood. A startlingly large number of comedians routines include a nostalgia for such childhood experiences, and other ways in which we were previously allowed to handle adversity and risk.

By removing those restrictions, we can greatly reduce the burden on parents, increase the resilience and joy of our children, at only very small ‘safety’ risk.

The more ways we find to make modern life compatible with family life and general human existence, the more willing parents will be to have more children, and the better off everyone involved will be on all levels.

The second way we can build upon these results is that we now have a point estimate for the cost of raising fertility via direct adjustment of taxes or subsidies - for every $270,000 or so, about the 18-year cost of raising a child, we induce or prevent one additional birth. This is an additional benefit of transfers to families, which already have many other benefits.

It also provides an argument for front-loading as many of those payments as possible. This is not studied directly here but it is highly likely that fertility effects are larger on up-front (at-birth) payments than longer term payments, including for reasons of certainty and liquidity and tangibility. One can certainly take this too far, but given the large up-front costs of a child, we are not doing enough to front-load benefits.

Don't Worry About the Vase

On Car Seats as Contraception