Four Variables About That Say a Lot About the USA Today (Name the Scale)

Now with a note about the “second demographic transition,” at the end.

It’s good to have an intuitive, descriptive sense of how key social indicators move together. That’s a different level of understanding than you get from building a foolproof causal model, like an election campaign might want to do.

Here are four things that go together at this stage of human history: Low birth rates, high women’s labor force participation, high education levels, and high average incomes. Since I’m thinking about birth rates these days, I could tell some stories about these four variables, like this:

When the economy provides opportunities for women, they decide to have fewer children to pursue careers instead, and because they have fewer children and more income, they invest more in each child’s education, so education levels — and incomes — rise.
Or: When birth rates are low, women have more time to do more productive things than raise children, so they spend more time in the labor force, making money they can spend on their children, who end up going to college more; as a result, the economy thrives.

Both stories reflect the fact that these four variables are correlated, but they sequence the scenarios differently. In real life, history is like that. We know these go together, reflecting a broad pattern of social, economic, and demographic development we associate with modernity, gender, and families. The details are complicated, but not always necessary.

You can visualize a set of relationships like this with a scatterplot matrix, which may be useful for just exploring the data even if you don’t use it in your final presentation. I made one using these four variables for U.S. states.* In the matrix below, you can see the correlations between variables drawn with each one as both x and y. You can scan along one row or column to see how different variables correlate with the same one, or look at the whole thing for particularly strong or weak relationships. At a glance, for example, the relationship between college graduation rates and both women’s labor force participation and GDP per capita seem especially strong. (I made the graph using the graph matrix command in Stata.**)

How well do all four variables hang together? If you happen to have had first-semester statistics with a professor who specialized in survey research, like I did, the way to check this that pops into your head is Cronbach’s alpha, which tells you how well a group of items might measure one or more latent variables you can’t measure directly. They call this the internal consistency of the scale. If your separate items are all well correlated with each other, you can combine them into a scale. Then, when you name the scale, you give the reader the impression that you know exactly what the latent variable driving them all is. In this case, I don’t have a name yet for what these four items together represent. But when you combine them all (by transforming each into a z-score and summing them), Cronbach’s alpha is .76, which is high. (If you check the correlations between them, weighted by population, they are all highly significant statistically. And each is highly correlated with the combined scale.)

But I can do better than that — I can show that it’s a meaningful scale by using it to predict something that matters, specifically the outcome of the 2024 presidential election. The states with higher scores on the scale — which means lower fertility, higher education, higher women’s labor force participation, and higher incomes — were more likely to vote Democratic in the 2024 election. Specifically, in 43 out of 50 states, the scale correctly picks the winner. Here’s the relationship between Trump vote share and the combined four-item scale.

The states in the bottom left, where Trump should have won but he didn’t, are just New Mexico and Hawaii. The states where he shouldn’t have won but did were Pennsylvania, Iowa, Nebraska, North Dakota, and also Wisconsin (where he got less than 50% of the vote but still won). The complete data table is below.

I’m not in charge of election strategy or predictions, so I don’t know if that’s a strong enough predictor to be useful, but for social science it’s pretty good. Look at it this way: A regression predicting Trump’s vote share with the four variables, weighted by population, has an adjusted R-squared of .79. With just the scale variable by itself the variance explained is .70.

If you’re focused on birth rates, like I am right now, you might consider that raising birth rates (as if you could) would lower women’s labor force participation, lower education levels, lower average incomes — and make people more MAGA. In other words, turn back the clock on social development. But pronatalists don’t usually advocate this outcome, and in fact they often claim we need more babies to save the economy and protect progress. Interesting speculation! It’s just totally counter to all of history.

Anyway, if you can name this scale you can explain something about America today — a set of social-development characteristics that divide the country pretty evenly down the middle, in line with our current political divide.

Ron Lethaeghe dropped a note to remind of two pieces he wrote with Lisa Neidert about the second demographic transition and its correlation with U.S. voting outcomes. They used a more sophisticated kind of index construction, with a lot more variables related to family demography, across counties, and found large and growing correlations with Republican vote share through 2016. You can see the paper archived here. Thanks!

* General fertility is the number of births per 1000 women ages 15-44, from CDC Wonder. Women’s labor force participation is for ages 25-59, and college graduate rates are for people ages 25-59, both from the 2019-2023 American Community Survey via IPUMS.org. State GDP per capita is from the Bureau of Economic Analysis for 2024, with population denominators for 2024 from the Census Bureau.

** Here’s the Stata code for the matrix command:

graph matrix gfr baplus wlfp gdpcap [w=pop], ///
mfc(brown%50) mlc(brown) mlw(vthin) msize(.3) ///
diagonal("General fertility" "College graduates" "Women's labor force participation" "GDP per capita", size(2.5)) ///
xlab(, labsize(2)) ylab(, labsize(2)) ///
diagopts(fc(none)) ///
xsize(10) ysize(10) ///
title("Correlation of select characteristics across US states", size(3)) ///
note("GFR, CDC for 2024; College grads ages 25-29, 2019-2023 ACS via IPUMS; Women's LFP ages 25-59, 2019-2023 ACS via IPUMS;" " " "GDP is 2024 $000s from BEA. Markers sized by population. PN Cohen figure.", size(1.5) span)

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Previously Published on familyinequality with Creative Commons License

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