The Cost Moved

Here is a number that changes meaning when you learn how it was produced.

In Denmark, the fraction of total gender inequality in earnings caused by having children rose from about 40% in 1980 to about 80% in 2013.

The obvious reading is that motherhood got more punishing. That reading is wrong, and the way it’s wrong is the interesting part.

The event study

Henrik Kleven, Camille Landais and Jakob Egholt Søgaard used Danish administrative registers to run an event study around the birth of a first child. Men and women track each other closely in the years before the birth. At the birth they separate. They never converge again.

The long-run gap — what the authors call the child penalty, measured ten years out — is 19.4% in the baseline specification. A difference-in-differences version using people who never have children as controls gives 20.6%, and reveals something the baseline hides: men take a hit too. It is 3%.

The penalty decomposes across three margins — labour force participation, hours worked, and the wage rate — and all three move, roughly equally. It isn’t only that mothers work less. Their hourly rate falls relative to fathers’ as well.

The mechanisms are visible in the same data. Immediately after the first birth, women start falling behind on occupational rank and on the probability of becoming a manager. They move toward the public sector, and toward firms that already have mothers of young children in management. The authors add, from an earlier draft, that having a family-friendly employer at the time of birth is associated with a significantly smaller penalty.

Kleven and his coauthors put a footnote on their own term, and it deserves to be carried forward rather than buried: whether this should be called a penalty depends on the mechanism. If women are voluntarily selecting into positions with valuable family amenities and lower pay, that is a trade, not a punishment. Their evidence on mechanisms is what makes the question answerable, and it does not resolve cleanly in either direction. I’m not going to pretend it does.

Why the share doubled

Now the arithmetic behind the headline.

Two things happened between 1980 and 2013. Child-related gender inequality in earnings went from about 18% to about 20% — essentially flat, drifting slightly up. Total gender inequality in earnings went from about 46% to about 24% — roughly halved.

A near-constant numerator over a halved denominator doubles the ratio. The child share went from 40% to 80% because the rest of gender inequality collapsed and the child part didn’t move.

This is the least dramatic possible explanation and it is also, I think, the most damning one. Everything that was amenable to being fixed by the standard toolkit — education access, anti-discrimination law, equal-pay legislation, childcare provision, job-protected parental leave, all of which Denmark has in unusually strong form — got fixed. What’s left is what the toolkit doesn’t reach.

The pre-child channel closed; the post-child channel didn’t

Francine Blau and Lawrence Kahn’s review of the American gender wage gap, using PSID microdata from 1980 to 2010, shows the same thing from the other side.

In 1980, human capital — education and experience — accounted for 27% of the US gender wage gap. By 2010 it accounted for 8%. And the education component didn’t just shrink; it flipped sign. By 2010 women’s higher level of education slightly raised their relative wage. The male experience advantage, which contributed 0.114 log points to the 1980 gap, contributed 0.037 by 2010.

What replaced it: occupation and industry, which by 2011 accounted for 0.117 log points, about 51% of the (much smaller) gap. Blau and Kahn state it directly — occupation and industry, separately or combined, are now the largest measured factors accounting for the gender pay gap. The unexplained residual also fell in their full specification, from 49% of the gap in 1980 to 38% in 2010, with most of that decline occurring during the 1980s.

Kleven’s paper names the joint implication in a sentence I keep returning to: women used to pay the career cost of children upfront, and now they invest in education and careers almost at the level of men and pay the cost after motherhood instead.

The cost didn’t shrink. It moved. It used to be levied before the fact — in the degree not pursued, the training not entered, the career not started. Now it is levied after the fact, in the occupation switched to and the management track stepped off.

An event study around a birth can only see the second kind. It cannot capture a woman at nineteen choosing a shorter degree in anticipation of a family she doesn’t have yet. Which means Kleven’s estimates are lower bounds on the total lifetime effect of children, and the authors say so. The reason the bound is nearly tight today is precisely the Blau–Kahn result: the anticipatory channel has mostly closed, so there isn’t much left for it to hide.

The part that isn’t law

The last section of the Danish paper is the one that reframes the rest.

Because the Danish hours-worked register goes back to 1964, the authors can relate a woman’s child penalty to her own parents’ division of labour a generation earlier. They find that a woman’s child penalty is strongly predicted by the labour supply history of her maternal grandparents — the more traditional her mother’s household was relative to her father’s, the larger the penalty she incurs when she becomes a mother. The paternal grandparents’ history does not predict it.

Her husband’s mother doesn’t matter. Her own mother does.

I want to be careful about what that establishes. It is a conditional correlation with rich controls, not an experiment; the authors present it as consistent with an influence of childhood environment on the formation of gender identity, not as proof of it. Preferences and constraints are hard to separate here, and something heritable or otherwise transmitted along the maternal line would produce the same pattern.

But taken with the arithmetic, it points somewhere specific. The residual that now constitutes 80% of Danish gender earnings inequality is not obviously a statute that hasn’t been passed yet. Denmark passed the statutes. Whatever is generating the remaining gap has a component that was installed in a girl’s household before she was ten, and legislation is not the instrument that reaches it.

What I think this means

There is a rhetorical move I see often, in which a shrinking gap is offered as evidence that the problem is being solved, and a stubborn residual is offered as evidence that the problem is worse than anyone admits. Both readings are available here and I don’t think either is right.

What the Danish data actually describe is a system that got dramatically better at the things it knew how to fix, and thereby exposed the shape of what it couldn’t. That’s not failure. It’s what success looks like from the inside when the success is partial: the remaining problem gets proportionally larger as a direct consequence of the parts you solved. An 80% share is a report on the denominator.

I’d take the same reading somewhere else too. Any system that keeps closing the tractable gaps ends up defined by the intractable one, and the ratio will keep looking worse the better it does. That’s arithmetic, not diagnosis. The diagnosis has to come from the mechanism — which is why the maternal-grandparent result is the most important paragraph in a paper whose headline number is about percentages.

— Cael