Here’s a fun example of a quasi-experiment. A team of behavioral economists has analyzed U.S. data on fertility rates. Demographers have known for decades that fertility in most of the world’s most prosperous countries has been decreasing.

In this new report, two economists have concluded that the introduction of the iPhone played a part in our fertility decline.

Here’s how People magazine summarized the result:

New research conducted by economists at Middlebury College …theorized that the United States’ “plummeting” birth rate can be attributed in large part to the introduction of the iPhone.

The working paper theorizes that the introduction of the iPhone accounts for somewhere between 33% and 52% of the decline in the U.S. fertility rate among women aged 15-44.

Authors Caitlin K. Myers and Ezekiel Hooper examined iPhone users from 2007 to 2011, when the phone was only sold at AT&T. “Taken together, these cohort effects imply that the diffusion of the iPhone deepened the decline in births among women under 30 while suppressing the rise in births among older women,” the working paper reads.

In an NPR story the journalist described the research team’s technique:

[The study] makes clever use of an accident of history that creates a kind of natural experiment. When iPhones first came out, they worked only with AT&T.

“In some areas of the country, AT&T had broadband coverage and you could get an iPhone, and in other areas, including where I live in Vermont, that coverage was much more limited,” Myers recalls. “And what you can see in this simplest of comparisons, births start to fall in the places where you can get one, and they’re not falling nearly as much in the places where you can’t.”

This is a quasi-experiment. In fact, I love the journalist’s wording here, when they write “accident of history.” A quasi experiment often takes advantage of such an “accident” to test a hypothesis that would be impossible to test with a true experiment.

1. In this quasi-experiment, what are the levels of the quasi-independent variable?
   
2. What makes it quasi-independent variable, and not a true independent variable?
   
3. What is the dependent variable?
   
4. What might be some confounds, or internal validity problems? That is, what other qualities might vary along with access to the AT&T iPhone network? Here’s an example of an internal validity problem: It might be that counties with more early access to iPhones contained more urban neighborhoods, compared to counties without early iPhone access.
   
5. Now your turn: Think of at least two other potential confounds.

Here’s what NPR said about these confounds, by the way:

One might argue the results are skewed because smartphones spread faster in urban areas or wealthier communities. But the results hold up even when Myers controlled for variables like population density and local economics.

• f. Was your proposed third variable controlled for?

• g. Reflect on how a quasi experiment differs from a true experiment. Could the researchers have conducted a true experiment at the county level to test this question? What would that have needed to look like?

The researchers proposed two reasons for the decline in fertility after the introduction of the iPhone. As NPR summarized:

Myers suggests smartphones … placed access to information about contraceptives and abortion in the palm of users’ hands. The devices also might have depressed birth rates by making it easier for people to find pornography.

• h. The two explanations above are mediators (Chapter 9). If you’re feeling ambitious, you could sketch them using three boxes and three arrows, following the models at the end of Chapter 9.  

The original empirical working paper is in the National Bureau of Economic Research .