If you've been reading the news over the last week, you may have seen talk about new research linking fertility decline in the US to the release of the iPhone. For example, the New Zealand Herald reported that:
Middlebury College economist Caitlin Myers and her student Ezekiel Hooper tested a hypothesis that smartphones - which emerged with the arrival of the first iPhone in 2007 - might have something to do with it.
Until 2011, iPhones were available from a single US cellular network, AT&T, so they compared US counties that had near-universal AT&T coverage with those that had little or none during those years.
And they found that access to the iPhone correlated with reductions in births by 4.5% to 8% at ages between 15 and 19, and by 3.2% to 6.6% at ages between 20 and 24.
There were also statistically significant but smaller declines among older women.
Other news sources picked up that the research attributed 33 to 52 percent of the decline in fertility to the iPhone's release (see here and here, for example). That result made me sceptical, and my concerns really echo those of Tyler Cowen here:
In 2008, 1.9% is the share of the mobile-subscribing population with an iPhone wireless subscription. As a percent of all adults that is 1.6%.
In 2009, it is 4.3%. 3.6% of all adults.
In 2010, 6.8%. 5.5% of all adults...
So when the authors talk about diffusion explaining 33–52% of the decline in the general fertility rate among American women 15–44, I still do not get how that is supposed to operate.
If less than six percent of all adults have an iPhone by 2010, how could iPhones reduce fertility by between one-third and half? This requires very large spillovers from a small group of early adopters, and I am not convinced the paper has made those spillovers quantitatively plausible (we'll get to the authors' views on that later).
The research is reported in this NBER Working Paper by Caitlin Myers and Ezekiel Hooper (both Middlebury College). They use data on national wireless broadband coverage at the census block level to categorise US counties into those where less than 10 percent of the population have coverage by AT&T ('control' counties) and those where more than 90 percent of the population have coverage by AT&T ('treated' counties). Their sample includes 1399 'control' counties, and 914 'treated' counties (with 794 counties excluded from the sample). The reason that Myers and Hooper chose AT&T is because AT&T had an exclusive arrangement with Apple for almost the first four years after it was first launched in June 2007. The first Android phones didn't become available until October 2008, and didn't become widespread in the 'control' counties until a year later. So, there was a period where AT&T coverage is a reasonable proxy for the prevalence of iPhones.
Myers and Hooper then compare control counties with treated counties in terms of annual age-specific fertility rates (in five-year age groups). However, they recognise a key problem, which is that the treated and control counties differ in meaningful ways, the most obvious of which is that the treated counties are more urban than the control counties. This is a problem for their analysis because fertility rates have been declining more rapidly in urban areas than in rural areas, and therefore this would lead to overstatement of the measured effect of iPhone coverage on fertility. Specifically, the CDC reports that from 2007 to 2017, the total fertility rate fell by 12 percent in rural counties (many of which will be in the control sample), but by 18 percent in large metro counties (which are almost certainly in the treated sample).
Myers and Hooper try to deal with this problem by re-weighting their data in two ways. The first is by using an "entropy balanced Poisson event study", which effectively re-weights the control counties by giving more weight to those that are most similar to the treated counties in terms of their cross-sectional characteristics at the time of the iPhone launch. The second is by using a "synthetic difference-in-differences estimator", which creates a set of synthetic control counties by re-weighting the control counties so that the time series of fertility most closely matches each of the treated counties.
Using those methods, Myers and Hooper find the results that the news media has picked up. Specifically:
Both estimators imply large, statistically significant declines in births to young women. The post-gestation ATT ranges from −4.5 to −8.0% at ages 15–19 and −3.2 to −6.6% at ages 20–24 (the entropy-balanced Poisson at the lower-magnitude end, SDID at the higher), with smaller effects at older ages. Scaled to the U.S. county universe, these estimates imply the iPhone accounts for between 33 and 52% of the 2007–2011 decline in the general fertility rate. The pattern is similar across race, parity, marital status, and education, with the exception of Black women, for whom we estimate no effect.
The key results are summarised in Figure 3 from the paper (for the entropy balanced Poisson event study):
And in Figure 4 from the paper (for the synthetic difference-in-differences (SDID) estimator):
In both cases, the point estimates from the time before 2008 show no statistically significant difference between treated and control counties, while there is a negative (and increasing) difference between treated and control counties from 2008 onwards. However, notice that in Figure 3 (the first figure above), it seems clear visually that the downward trend starts before 2008, even if it is statistically insignificant. In Figure 4, there is no pre-trend, but remember that in the SDID analysis, the controls are reweighted to replicate the pre-treatment time series of fertility for the treated counties, so there should be no difference in the pre-treatment values by construction.
Myers and Hooper run various robustness checks that address some of the more obvious criticisms of their approach, including sensitivity to the choice of treatment and control cutoffs, using a continuous treatment variable, estimating the model in levels rather than logs, various placebo treatments, and truncating the sample to exclude any contamination from the release of Android phones. Among the placebo tests, they run analyses using Verizon's and Sprint’s pre-2011 coverage, and find no effects. So, their findings are not general to the difference between counties that attract mobile operators and those that don't. They also address the plausibility of the results, noting that:
The iPhone is not a treatment that operates at the individual level. Whether one’s own phone matters likely depends on whether one’s peers have phones; a phone in a friend group full of non-owners is a different intervention than a phone in a group where everyone has one. Spillovers run between phone-owning peers and their non-owning friends, and operate at the level of the group, not just the match: if smartphones reduce friend-group meetups and parties, then matches that would have formed under no-iPhone simply never do—the unformed match is itself the outcome.
That may be so, but the implied size of the spillovers is far larger than is plausible. If, as Cowen suggests, less than 15 percent of the population have iPhones, unless iPhone ownership and the spillovers from iPhone ownership were heavily concentrated among women of childbearing age, the overall effect simply can't be that large.
So, what has gone wrong. The overall approach that Myers and Hooper apply seems valid on the face of it, and re-weighting of controls to better match the treated sample is a common method of causal inference. The problem here is that the weighting is extreme. Myers and Hooper note that, in relation to the entropy balanced Poisson event study approach:
Balance comes at a cost: equalizing the marginal means requires putting high weight on a small number of treated-like controls. The Kish (1965) effective sample size of the balanced control pool is 77 out of 1,399 raw controls...
So, basically the analysis is heavily skewed towards a comparison between the treated counties and a small number of control counties, which are the control counties that are most like the treated counties (which also makes them the most unlike the other control counties). Those control counties are doing a lot of the work in this analysis.
There are also other possible differences between urban and rural counties that are approximately contemporaneous with the release of the iPhone. First among these is the 'Great Recession' and the housing slump around that time. Myers and Hooper do control for county-level changes in house prices, so that reduces concerns about contamination from that source. They also control for unemployment and poverty rates, which might pick up differential changes in labour markets. However, there was a change in contraceptive availability that directly affects young women's fertility, which is expanded access to the 'morning after pill' for 17-year-olds, although that occurred in 2009. Finally, after the 'Great Recession' there was a slowdown in Hispanic immigration, which might have affected urban and rural counties differently. Given that Hispanic immigrants tend to have relatively higher fertility than the US-born, so if the decline in Hispanic immigration was greater in control counties (and especially for the small number of heavily weighted control counties), then that might explain the effect. Myers and Hooper control for county Hispanic population share. However, it would be better to control for Hispanic population share among the age group that is being analysed, or to control for changes in Hispanic immigration.
This paper has certainly gotten people talking. Smartphones might be part of the story of why fertility has declined, but I don't think that we should uncritically take away from this study that the iPhone caused half of the decrease in US fertility between 2007 and 2011. More likely, it had a modest effect (if at all), and is confounded by a number of other changes that differentially impacted rural and urban US counties at around the same time.
[HT: Marginal Revolution]
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