Thread by @david_h_solomon

I’m excited to tell you about my new paper with @umitgurun. We document a striking new fact: Birth rates in the US are robustly lower in areas of higher local racial diversity, after controlling for a huge range of alternative factors. We then try to understand why this is.
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This links the two largest demographic changes of our age:
i) The large increase in racial diversity, and
ii) The large decrease in birth rates
There’s been a large and puzzling decline in US birth rates since 2007. The rise in diversity explains almost 89% of this drop.

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Our best guess for the reason is homophily – the preference to marry someone similar to you (here, the same race). When you’re surrounded by people of different races, you have fewer partners that meet your criteria, so either don’t marry, marry later, or get a worse match.

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Identifying causality is hard here. Our results are consistent with a causal channel, but this is open to interpretation. At a minimum, the most obvious non-causal versions have difficulty explaining all the facts we document. So what are those facts?

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First, we need to define some terms. For “race”, we measure it as the US Census does. This choice matters less than you might think, and lots of definitions give similar answers. “Local” means either city, county or metro area, depending on data availability.

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The big one is “diversity”. We focus on two aspects. The first we call “racial concentration” – being in an area with many different races in small proportions. Statistically, it’s a Herfindahl index, the sum of square of shares for race groups.

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The second we call “racial isolation” – being from a numerically smaller group in your area. We measure this as “race share”, the fraction of the local population of the same race as you. It can be thought of as a consequence of greater diversity at the individual level.

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In US Census/ACS data, higher diversity is associated with women aged 18-40 having fewer children. Conservatively, a one standard deviation increase in race share or decrease in race concentration is associated with 0.064 and 0.044 fewer children respectively. This is big!
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We control for lots of obvious confounders. We control for the woman’s state and year, so we’re just looking at differences within, say, Michigan in 2007.

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We control for lots of demographic factors explicitly. Race itself, education, income, citizenship, employment, and marital status. We also interact these demographic variables with state and year. Attributes of your local area, including mobility.

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The most important control is area by year fixed effects. You can’t do this for race concentration, as there’s only one value for all residents in an area and year. But race share has another source of variation – within the area, are you from a smaller or a larger group?

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Race share continues to positively predict birth rates even after controlling for area by year. So if you think that more racially concentrated cities are bigger, or denser, or have more job opportunities, or higher childcare costs, or anything else, this is controlled for.
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One way to think about the result is that if you take a city with a large black population, like Detroit, MI, black people there will have more children than expected, and white people will have fewer.

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But if you go to Ann Arbor, MI, which has more white people, whites will have more children, and blacks will have fewer. In both cases, we’re comparing to blacks and whites in Michigan generally, and blacks and whites in that year generally.

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Area-by-year fixed effects help control for unobserved factors that simultaneously influence both diversity and birth rates. E.g. individuals less inclined towards marriage may prefer living in diverse areas. These fixed effects can capture such unobserved characteristics.
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Having established the robustness of the base finding, we next turn to various sub-tests to try to understand the mechanism here. The first is time period. There are lots of important events in the history of US race relations. Is some major event responsible for the effect?
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We find that the effect holds in recent years, after the Civil Rights Act, before WW2, during the gilded age, and, astonishingly, even before the Civil War, in 1850 and 1860. In other words, the mechanism has to be something present in many different eras.

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The effect also exists for many different racial groups – in the tightest specification, it holds for whites, blacks, native Americans, Chinese, Japanese, other, and two races. The mechanism has to be present for many races, rather than just about white/black race relations.
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The effect is also present internationally, but less consistently. It is present in the UK and several African countries, while Central and South America show more mixed results. So while it’s not universal, the effect is also not limited to US-specific factors.

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Diversity is associated with other relationship outcomes, so it’s not just costs of raising children. A one standard deviation increase in race share is associated with a 1.2% higher chance of being married, and getting married 2.3 months earlier.

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These facts rule out many explanations you might think of for the main result. We need a factor that is present in many eras of history, applies to many races, isn’t just attributes of a given city, holds internationally, and is related to marriage outcomes. So what’s left?

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One explanation is homophily. People have a tendency to prefer to marry those of their own race. If these preferences exist on average, when you live in an area with fewer people “like you”, you may not find a match, or get a worse match (in your preference ordering).

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This has two implications we can test. First, preferences for homophily likely differ across races and across time. If you’re from a race where people marry outside their race more frequently, then it should matter less whether you’re living near your own race.

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Second, sex differences will matter too. If the women of a race “marry out” at a higher rate than the men, then being around those of the same race should matter more for men of that race than women (as the men are more dependent on the women than the reverse)

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Both predictions are born out in the data. These results are strongly related to homophily, and it’s hard to think of what other theories would generate these patterns.

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Homophily also holds for traits other than race. Consistent with this, we also find effects for income share that are about a third as large as race – living in an area with more people of your own income level is associated with more children.

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The second explanation for our effect is trust. Robert Putnam famously documented that in diverse areas, people feel more isolated and have less trust of others. This might reduce their chances of finding a spouse, or the number of children they want to have.

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The tests here aren’t nearly as tight as for homophily. But the main predictions are born out – higher trust areas have more children, and adding in measures of trust reduces the effect of race share by 20-37%.

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Finally, can the rise in diversity explain the overall decline in birth rates? Nearly all the evidence we look at is cross-sectional – comparing two people within the same area at the same time. Here, we want to look at the time series of births in general.

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It goes without saying that with overall time series changes, it’s very hard to get any identification. The results here are only credible, if at all, because of the much sharper cross-sectional tests. But still, does diversity have enough bite to explain what we see?

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We find that the increase in diversity explains 44% of the decline in birth rates since 1971, and 88% of the decline since 2006. This is a potentially very large effect. In particular, the recent declines are very hard to explain with standard drivers of fertility.

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One question we’ve gotten – what about countries like Japan and South Korea, where birth rates have declined a lot, but which are quite racially homogeneous? There’s a few answers here. The boring one is we don’t have race data for them, sadly.

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Second, remember that our main prediction is about the cross section, not the time series. That is, “Does a Japanese woman in a highly Japanese town have more children than a Japanese woman in a town with more immigrants?” Maybe! We would need to test.

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Third, the simplest answer is that Japan’s time series decline in birth rates is probably driven by other factors.

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Even for the time series (where our predictions are weaker and more circumstantial), the idea that “higher diversity is predicted to lower birth rates” is very different from “all declines in birth rates are due to higher diversity” (which is surely false).

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The strongest counterexample to our theory (that we can test) is actually not Japan, but Brazil. There, areas with higher diversity are robustly associated with *higher* birth rates. It’s worth noting that their definitions and ideas of race are quite different from the US.

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For instance, they have categories of “brown” and “indigenous”, and the question of who is in which category differs from US notions. But this is part of the point – if homophily is the driver, then how people think of themselves will change the effect.

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That said, the international results don’t tell a clear story of what’s driving the differences. El Salvador and Ecuador have patterns like the US, Uruguay and Brazil go the other way. South Africa has strong results in the US direction, Jamaica is mostly zero.

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There’s obviously a lot more work to be done, and open questions as to what all the drivers of the effect are, especially across countries. Homophily and social trust seem to be part of the story, but there are probably other drivers too.

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Our study also gives a new perspective on the prior finding that immigrants from high-fertility countries tend to converge to lower native fertility levels over time. While cultural transmission has been the primary explanation, our results suggest an alternative mechanism.
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Immigrants typically move from areas where they're part of the racial majority to places where they're a minority. This shift in racial share could explain the observed fertility decline across generations, independent of cultural assimilation.

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Overall, we think that these results are sufficiently strong to indicate that there is likely some fundamental tension between higher racial diversity and lower birth rates.
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Understanding what is driving the relations we document is of considerable social importance, as these are some of the biggest demographic changes of our era.

The full paper can be found here:

/Endpapers.ssrn.com/abstract=48819…