Marriage makes Wilcox richer, how to lie with asterisks edition

Brad Wilcox wrote a blog post for the Atlantic the other day, in which he described the well-known pattern by which children of married parents on average grow up richer and more highly educated than those raised by single parents. (Follow Wilcox’s lies, errors, and shenanigans under this tag.)

It’s old news, but before I make today’s point, here are a few reasons this kind of thing is wrong and useless.

1. Although the headline says, “Marriage Makes Our Children Richer,” the data Wilcox shows does not approach a causal model. Comparing children who lived with married parents as adolescents to those who did not when they are young adults, he uses controls for mother’s education, race/ethnicity, and household income. Those married parents differ from the single parents in many more ways than that, and did before they got married. Wilcox and actual researchers know this. The Atlantic business editor apparently doesn’t.

2. Even to the extent that marriage helps married people, which it does, on average, this does not imply that mothers who are currently not getting married would get those benefits if they did get married. Because, who are they going to marry? If rich-prince-charming were there most of them would have married him already. So to consider the effects of them marrying you have to take into account that it’s not the right guy or the right relationship at the right time. So, good luck.

3. Finally, so,  you gonna promote marriage? We’ve seen how that works. On the other hand, we know we can mitigate a lot of the harm from difficult childhoods by throwing jobs and money at their food, healthcare, and education needs. If you care about poverty and inequality more than marriage, that’s the way to go.

Anyway, my complaint today is about a particular kind of deception that Wilcox likes do engage in, which Mark Regnerus also did in his infamous paper. The trick is to display unadjusted figures, but describe them as if they include statistical controls. First, how Wilcox did it this time, then an simple example of how wrong it is.

Wilcox shows this figure, among others:

WilcoxAtlanticScreenShotThis is supposedly how marriage makes children richer, because most of the blue bars (“intact family”) are taller than the red bars (“non-intact family”). Set aside what should be the obvious conclusion: having a mother who went to college matters much more than whether your parents were married (which we also already knew). I want to focus on the little symbols *^, which indicate a statistically significant difference with the different controls he used. This is his footnote:

An asterisk (*) indicates a statistically-significant difference (p < 0.05) between respondents who lived with both, married biological parents at Wave I compared with respondents from other family structures, controlling for respondent’s age and race/ethnicity. A hat (^) indicates that there was still a statistically-significant difference when Wave I household income was added as an additional control.

But the numbers shown in the figure are not adjusted for those controls. Presumably, the family structure differences would be smaller with the controls — and they’re already pretty small.

We don’t have his underlying numbers (and I wouldn’t expect to see them in a peer-reviewed journal anytime soon; Regnerus never reported his). So I made a simple example to show how misleading this is. I took the employed 25-55 year-old non-Hispanic White and Black men from the 2011 American Community Survey (excluding the richest 5%) and compared their earnings with and without controls for education, age, hours and weeks worked in the previous year, and marital status. The question is, how much more do White men earn? These are the simple regression results:


In the first model, the intercept is the mean earnings for White men, and the Black coefficient is the difference between the White and Black means. This is the unadjusted difference — $13,551 — which is the equivalent of what Wilcox plotted in the graph. But with the controls the difference is reduced to $5,498 — a big difference. The difference is illuminating because it shows how much of the overall gap is accounted for by the distribution of the control variables for Black versus White men.

If Wilcox did this exercise, however, he would produce a graph like this:


See how he did that? He’s selling a $5,498 difference with a $13,551 label. He did the same dishonest thing in his “Knot Yet” report, with Kay Hymowitz and others.

When your audience is ideological foundation bigwigs and credulous (at best) editors, these asterisks and footnotes just make you look smart. These people are apparently impervious to honest reasoning. For the rest of us, at least, it can be a lesson in how to not to do research.

ADDENDUM: How should you do it?

Conrad Hacket below asks what I suggest as a better way to represent the data. Sometimes the unadjusted difference is important even if it is statistically accounted for by some control variable. In the case of race differences in earnings, for example, the fact that there is a $13k+ gap is itself socially important. However, if you are going to make some argument about its importance net of the controls, this is how I would do it, given this very simple linear model, with no interactions or any fancy stuff (note I used non-transformed earnings and censored the top 5% — those at $150k+ — so that the coefficients would be easily interpretable in dollars without being too skewed by the richy-rich).

Using the regression coefficients and the grand means, you sum the products of the means and coefficients for each group, like this:


And then graph the results with a label like this:


Another reasonable strategy instead of using the grand means is to use a common scenario for the calculation, such as a married high school graduate, age 35, who works full-time year-round. Or various other methods of obtaining predicted values.


13 thoughts on “Marriage makes Wilcox richer, how to lie with asterisks edition

  1. Could you add an illustration of how you would recommend graphing the income differences in the ACS with controls included? It seems to me audiences could be potentially confused if you graphed only the hypothetical incomes or income differences based on a regression model with various controls. Many might mistakenly assume, in this example, that $5.5k is the full income gap rather than $13.5k. Also, how would you recommend communicating the sensitivity of the hypothetical differences to the particular set of controls in the models?


  2. I don’t understand the statistics, but I was interested that on the original bar graphs, the average income of young women raised in non-intact households with a college-educated mother was higher than for those raised in intact families. I can think of explanations (e.g., women making a good income are more able to divorce; single mothers are better role models in certain ways — maybe more independent, self-reliant). I s this difference valid?


      1. Thanks for this post, Philip. I thought of you when I first read the article and was hoping you’d address it.

        Do you know that the non-intact mothers are all single? In other words, where do non-married, cohabiting couples fit? Are they omitted, or classified as not intact?


    1. “So highly educated women who are actually in intact, but non-married, families”

      Exactly how many of these “highly-educated-women-in-non-married familes” exist?

      Basically, the news for the last 20 years whether you get it from Murray or ACS is that educated women do marriage and in-marriage childbirth like 80-90%; less than college educated women do marriage and in-marriage childbirth at 50% or lower. These are the main causes of income differences between married families and between races. Let us not mae up arbitrary Katie Roiphe families which are statistically insignificant.


      1. I was responding to Claudia’s comment with an additional reason that the college-educated, non-intact mothers’ children’s income might be higher (albeit insignificantly). Regardless of the size, it’s likely not really just single parents in that non-intact group (although I don’t know for sure, given the lack of detail I have about Wilcox’s study).

        In other words, my comment wasn’t about comparing the less-educated with the more-educated (the between group variation) but considering how the within-in group variation among college-educated non-married mothers could affect the mean, standard deviations, and significance, particularly in such a small group (as you note).


  3. I am still not getting the argument; what are you arguing:

    1. Total Income of married families is not much larger than women in unmarried (or non-intact families)?

    2. Total income of women when in married families is not substantially higher than women in married families?

    3. Women in unmarried families will not get an improvement in income if they were to get married.

    I am not saying what you are arguing is wrong; I have lost the plot in this “he said” , “I said” argument.

    Once again I am reverting to my old argument: we listen to what Wilcox, and Regnerus, and Kay Hymowitz and AEI say, but do not believe, because we know the baggage they carry. Whereas you have the burden to be correct.


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