Thread by @captgouda24

Fertility has fallen in the United States. At the same time, housing has gotten substantially more expensive. Are these related? How so? Benjamin Couillard attributes fully half of the fertility decline of the 2000s and 2010s to housing prices, a loss of 13 million children! 1/

The paper is a substantial improvement over the reduced form approach to estimating the effect of housing prices on fertility. Using local variation is not ideal, because housing supply changes somewhere affect prices everywhere. We're not really sure what we're measuring.

Instead, we're going to estimate demand for housing using BLP (1995) with micromoments, with some interesting modifications to deal with logs with zero, and adding a model of fertility choice. The next few tweets will explain what exactly this all means.

The fertility side is relatively straightforward. Parents maximize their utility over time, have preferences over both quantity and quality of children, and housing enters as a cost of kids. In each year, some percentage of people have kids as a function of characteristics below.

On the demand side, the starting point is Berry Levinsohn Pakes (1995). People have preferences over observed characteristics, price, and unobserved characteristics. These preferences are drawn from a distribution. We take a guess at the parameters for the variance

and then solve for the mean utility -- the sum of price and observed and unobserved characteristics -- which justify the market shares. (We then take more guesses at the variance, using instruments for the endogenous price -- characteristics are generally assumed exogenous).

Bayer, Ferreira, and McMillan (2007) skip over the distribution element, because they can directly observe detailed data on who lives in what place. Couillard does not have that data, but what he can do is use the partial and overlapping Census data to infer what he needs.

If he observes the joint distribution of tract, family status, and size (but not age or tenure), and tract and tenure and size (but not age or status), and so on, you can infer what is the most likely way to fill in the underlying details

Couillard also has some very interesting stuff in dealing with logs of zero. If you take ln(0), you get negative infinity. It breaks. You can rewrite things as a Poisson regression, which can handle such things, at the cost of your variances not being quite right.

Further, when we're simulating people's choices, Hotz-Miller requires using observed choices conditional upon some state to infer what people value. If there's noise and many states, sometimes zero people choose a thing. To get around this, he smooths things like number of children

For instruments for price, the basic logic is that places that are somewhat distant but not far away no longer offer amenities people go to, but they do offer things people could *move* to. Changes in those amenities affect rent cleanly.

When we do alter policy, it's a complicated general equilibrium system. We iterate until we get convergence.

So that's the model! But what of the results? They're both optimistic and pessimistic -- bad policy has had a terrible cost on fertility, but good policy can fix it. Returning rents to where they were in the 90s would put us back near replacement fertility rate.

We can also meaningfully increase fertility by pushing housing supply towards larger units -- people respond tremendously to having more space.

Benjamin Couillard, "Build, Baby, Build: How Housing Shapes Fertility" (2026)
ti.org/pdfs/BuildBaby…