The Fertility, Marriage, and Gender Equality Quandary

Anson Zhou (University of Hong Kong) — “The Fertility, Marriage, and Gender Equality Quandary,” presented at the NBER Summer Institute, Gender in the Economy, on 29 July 2026. No discussant; the room asked questions throughout, and one of them nearly derailed the talk. Written from the July 2026 draft.

Suppose you run a country. You would like three things, and you would like them for reasons you can defend in public.

You want more babies, because the pension system is a chain letter and it needs new members. You want children raised by two parents, because the evidence on single parenthood and children’s outcomes is not encouraging and because a chunk of your electorate cares about this for reasons that predate the evidence. And you want women to earn as much as men, partly on principle and partly because a large literature says the misallocation of talent is expensive.

These are three separate ministries with three separate budgets, and each has its own instruments. Nobody has asked whether they can all succeed at once. Zhou asks, and the answer is no, and the interesting part is why the no is a three-way no rather than three pairwise ones.

The fact, which is a Venn diagram

Take four datasets — an OECD panel of 37 countries from 1970 to 2014, a global panel of 95 countries from 1990 to 2015, the fifty US states plus DC in 2023, and 656 US commuting zones in 2000. For each observation, code three dummies at the sample median: high fertility (F), low single parenthood (M), gender income equality (G). Median splits, so each circle contains exactly half the sample, so under statistical independence the middle of the Venn diagram should hold 12.5 percent.

It holds 2.5 percent in the OECD panel. 4.3 percent in the world sample. 5.9 percent across US states, 7.6 percent across commuting zones. Every one of them below the dartboard.

The median-split choice drew fire from the floor immediately — why not absolute, policy-relevant thresholds? Zhou’s answer was partly presentational (the 12.5 percent benchmark is a clean thing to be below) and partly that the paper does the absolute version anyway: in the world sample, requiring fertility above 2.1, dual parenthood above 75 percent and a female income share above 35 percent produces joint attainment at about a quarter of the rate the marginals imply, and tightening the thresholds pushes the ratio below 0.10.

What makes this a genuinely new fact rather than three old ones is the next step. Zhou runs a mutual-information decomposition and finds synergy: the interaction information is negative in every sample, meaning the dependence between any two of the three outcomes gets stronger once you condition on the third. In the OECD panel, pooling gender-equal and gender-unequal countries blurs the fertility–marriage relationship; separate them and it sharpens. So the structure genuinely cannot be recovered from pairwise analysis, which is a decent explanation for why a literature that has diligently worked through the pairs never saw it.

The model, which is a marriage market with two prices

Now the mechanism. Zhou builds the smallest marriage market that can generate this. People draw idiosyncratic taste shocks for marriage and match competitively. Marriage is not a piece of paper; it is a contract in which the husband transfers a share $\alpha$ of his income to the wife and in exchange gets access to fertility $n_m$. Both $\alpha$ and $n_m$ are equilibrium prices — a two-dimensional price vector that clears the marriage market. Wives bear more of the childcare time cost than husbands, and consumption and children are substitutes ($\rho > 1$), so a higher female wage lowers fertility while a higher male wage raises it.

Everything then collapses to three equations, two of which are pure accounting:

Equations 16–18 in the paper. $M$ is the marriage rate, $\lambda$ the psychic benefit of marriage, $\alpha$ the transfer share, $\Gamma_w$ the gender wage gap, $\Gamma_y$ the gender income gap, $l_{\text{f}}$ female labor supply, $\chi$ the time cost per child, and $n$ fertility.

Read them in order and the quandary is right there. A high marriage rate needs a large economic surplus $\alpha\Gamma_w$, which needs either a generous transfer or a big wage gap. A big wage gap widens the income gap unless female labor supply is high. And high female labor supply requires low fertility. Pick any two and the third is the one that gives.

The reason women marry, in this model, is entirely economic: her gain is $\lambda \cdot (1+\alpha\Gamma_w)$, and $\alpha\Gamma_w$ is just how much marriage expands her budget set — how rich he is relative to her, times the fraction of it he hands over. Which produces the sentence that closes the loop: if women’s wages are high enough to deliver income equality, then there is no point in marrying men.

Three ministries, three failures

Run the comparative statics and every conventional instrument breaks something.

Pro-marriage policy raises $\lambda$, which lifts the marriage rate; since married couples have more children than single women, average fertility rises mechanically; higher fertility cuts female labor supply and widens the income gap. Gender-equality policy raises $w_{\text{f}}$, which cuts fertility through substitution, which cuts the equilibrium transfer, which shrinks the surplus from marriage, which cuts the marriage rate. And subsidized childcare — reducing the time cost $\chi$ — raises fertility and marriage, and here is the counterintuitive one: female labor supply falls, because the income effect through higher fertility beats the direct effect of the cheaper hour.

There is a fiscal observation buried in this section that deserves more than the paragraph it gets. The cost of subsidizing childcare rises with $w_{\text{f}}$. So as gender wage gaps close, pro-fertility policy gets progressively more expensive — you are subsidizing a non-market sector with no productivity growth while the opportunity cost of the time it consumes keeps rising. Baumol, in the nursery.

The way out, and the constraint that binds

The three instruments share a limitation: they all move wage levels or cost levels, and leave the allocation of childcare between spouses untouched. Zhou’s fourth instrument moves the allocation — reserved paternity leave, or a government propaganda campaign telling fathers to do more — shifting $\delta$ of the childcare burden from wife to husband, holding the total fixed.

This can, in principle, deliver all three. But only under two conditions, and the second one is the paper.

The first is easy: the wife has to be better off, which requires

Condition 21 in the paper: the transfer share must be smaller than her wage relative to his — i.e. her own earnings must loom larger in her budget than the transfer she receives. Otherwise shifting time off her own labor income isn’t worth much to her. Development makes this easier, since it moves $w_{\text{f}}/w_{\text{m}}$ up.

The second is that the husband has to be better off. He is now doing childcare and still transferring income, and the only thing he gets in return is more children. So he consents only if the fertility response is big enough to compensate him:

Condition 22 in the paper: the marginal utility of the extra child on the left against the marginal utility of forgone consumption on the right. It holds more easily when men weight children heavily ($\beta$ large), when fathers start from a low childcare base ($\chi_{\text{m}}$ small), and when fertility responds strongly to the policy.

That is the real content of the “magic bullet.” Not that redistributing childcare works, but that it works only when both spouses are made better off — and that whether they are is an empirical question about the fertility response, which is why the model needs a calibration.

Mexico, and a stable alpha

The calibration is to Mexico, 1990–2015: fertility falls from about 3.5 to 2.1, dual parenthood falls almost entirely because single motherhood rises about ten points, the female income share climbs from under a quarter toward a third, and the schooling gap reverses. Zhou decomposes wages into a gender-neutral TFP term, a human capital gap read off years of schooling, and a residual he labels gender-biased TFP, then calibrates period by period holding all other parameters fixed.

Two results. First, the imputed transfer share $\alpha$ barely moves — it sits around 13 to 14 percent through a period when fertility falls by a third. Women’s wages rose so much that men had to keep transferring at the same rate just to sustain a falling fertility rate. The gains from marriage, for men, are shrinking. Second, gender-neutral TFP growth alone accounts for roughly half the fertility decline and roughly half the marriage decline. The fertility half is partly assumption — substitutability does that — but the marriage half is the model earning its keep: marriage falls because the thing men are buying got scarce.

The exchange

The sharpest moment came about thirteen minutes in, and it wasn’t about the data. A senior questioner — the speaker later addressed her by name as Claudia, and Claudia Goldin appears in the acknowledgments, though captions mangle names and I’d hedge — interrupted the transition to the model to say she could write a simpler one that delivers all three, with two assumptions: linearity in pay per hour, which removes the convexity that drives specialization in the first place, and something she described as getting rid of “what we women call men’s learned helplessness.” Her point was methodological: rather than watch a model with a lot of machinery in it fail to produce the trinity, tell us which of two simple assumptions fails in the world.

Zhou’s reply was “I never thought about that” and an offer to talk afterwards, which is the honest answer. But the objection has real teeth, because the paper’s two fundamental asymmetries are exactly the two she named — the biological one (single mothers exist, single fathers mostly don’t, in the model entirely don’t) and the one where wives do the childcare. The second is not a primitive of the world; it is what the paper’s own preferred policy is designed to change. So the model assumes the friction whose removal is the answer, and the theorem is about the conditions under which the assumption can be relaxed. That is defensible, and Zhou says as much — the results go through “as long as woman is doing more” — but the room’s instinct that you could learn as much by dropping the convexity is not obviously wrong.

Two other objections landed and were conceded rather than answered. There is no bargaining power in the model, so a higher female wage cannot buy a woman more of her husband’s time — it can only buy her out of the marriage. And single women in the model choose fertility knowing they will get no transfer, when in reality a quarter of them do get one, and many more expect to. As one questioner put it, the model has commitment without contracting, which is a strange place to end up in a paper about marriage as a contract.

(Somewhere in a ministry, three officials are each hitting their target and being told by the other two that this is precisely the problem. The paper’s contribution is to show that they are all correct, and that the only instrument that helps is the one none of them controls, because it is about who does the dishes.)