Smartphones and fertility: a simple model
Preliminary calibrated estimates to explain my skepticism
Previously, I have been a longstanding sceptic of the smartphone theory of everything, including the notion that they are partly responsible for the global fertility decline1. This argument has always struck me as model-free, yet the sort of hypothesis you need a model for2. Phones raise the value of the outside option yet lower search and matching costs whilst increasing the efficiency of matching3. Without a model, we cannot come close to knowing what the net effect is. This post provides such a model using a search-theoretic approach.
Our model
Suppose that the rate at which matches occur is described by an exogenous real-valued φ and match quality (and surplus) an exogenous real-valued q. The number of matches M is a Poisson process of rate φ. For simplicity, q is normally distributed i.i.d with mean zero and variance of one4. Individuals will form matches if q is weakly preferred to their reservation utility, which is a function of their outside options and the expected NPV of all possible matches preferred to this match:
where b is the outside option and F(q) is the C.D.F. of q.
Phones increase the value of the outside option to b’=b0+ε, whilst φ increases. The number of matches is M = φ(1-F(R))N for N being the total number of those seeking a romantic relationship5. So Δφ>-Δ(1-F(R)) for phones to increase matching via my proposed channel of reduced matching barriers, and vice versa for the smartphone theory to hold. Can we introduce some numbers to arrive at a precise conclusion? Yes we can. Let's now turn to a calibration exercise.
Calibration
For over a decade now, online dating has been the most common channel via which relationships form. About 30% of US adults have used online dating apps, and 12% are in romantic relationships as a direct result of online dating. Considering all the online platforms via which matching can occur, and those platonic friendships online that eventually develop into romantic relationships, these numbers understate the extent to which the internet facilitates matching. On the other hand, these figures are heavily US-centric, whilst fertility has fallen worldwide. Nonetheless, I think the overall effect has been to increase the matching rate, and so therefore I will use a rise from φ=1 to φ=1.3 as my choice in parameters for this calibration6.
There is also some evidence that people prefer matches formed online relative to offline, and if anything revealed preferences from dating behaviour shifting to online imply that Ariely et al (2010) likely understate the improved matching efficiency. However this reduces acceptance rates in the model, as people become more selective given that reservation utility is higher. Perhaps a change in 1-F(q) from 0.3 to 0.2 is plausible.
The notion that phones are a substantial gain in the outside option value is uncontroversial, and perhaps this rise is up to around half a standard-deviation point of average match surplus. I will use b0=0.2 and b’=0.5.
From the model, using our chosen parameters, these are the values of reservation utility prior to smartphones. R is 0.494 at a discount rate of 2%, and 0.485 at a 5% discount rate. After smartphones, if β=0.98 then R=0.7548 and if β=0.95 then R=0.747.
Why my priors imply null effects with high uncertainty
With these numbers, the cheaper matching effect roughly outweighs the effect of the gains to the outside option, albeit this result is highly uncertain and sensitive to the choice of parameters involved. Adjusting for this, the model implies that the effects of smartphones on number of matches is close to zero yet almost certainly non-significant and not robust.7
One significant limitation of this exercise however is that I have not estimated a regression structurally to inform these parameter values of match rates, changes to cross-country match rates after smartphone adoption, and an outside-option proxy (aggregating a weighted mix of app usage intensity, time on social media or dating apps, survey data on relationship quality, and so on). If there exists high-quality datasets for this empirical exercise, perhaps a staggered DiD is possible, and one can then feed the estimates into this model. More research on this topic is certainly necessary, otherwise model-free and empirically slack commentary will prevail in this discourse.
So what explains the baby bust?
In general8, I believe that factors such as high housing costs (a result of persistent NIMBY policies across the West) and declining maternal and child mortality (meaning people that previously internalised the risk of death are adjusting their planned births downwards) are the most compelling explanations. Less kids amongst families already giving birth seems to dwarf the impact of rising childlessness.
The cross-country data clearly rejects the thesis that feminism (in particular increased female labour-force participation) is driving the decline, as fertility is collapsing in highly conservative societies such as Italy and China, and generally is declining regardless of how feminist a nation is9. To the extent that the motherhood penalty is higher in such societies, this should actually reduce TFR in equilibrium.
However there are some cultures where TFR is stable and often high. The Amish and Haredi Jewish communities, and to a lesser extent Central Asians, are the most commonly cited examples. Although fertility is declining in sub-Saharan Africa and the Muslim world too, those TFRs tend to be higher than those in Western or East Asian societies. Hence “cultural” factors likely play some role (with spillovers observed), yet at this stage features as nothing more than a residual lacking precise mechanisms or estimates - instead being a kitchen-sink for our (often ideologically motivated) priors.
To be clear, the mechanism commonly proposed is that phones increase the relative pleasure of solitary activity, leading to less relationships forming. Phones can also act as a substitute to sex and raising children within a relationship, but to be tractable, this post will focus entirely on the former mechanism. Incorporating the latter channels probably increases the estimates of the smartphone cost to fertility.
Also improvements in smartphone technology are likely correlated with that in IVF, which is undoubtedly pro-fertility, yet today I want to isolate the impact of smartphones in particular.
In the sense that matches (platonic and romantic relationships alike) reflect preferences better. People who meet online are more likely to have interests, traits, and values in common than random matches. People prefer these matches than those awkward ones where they hardly have anything in common. In this sense, the efficiency is both allocative and Paretian.
Admittedly my results are sensitive to this assumption. Online dating tends to follow a lognormal or power law process, in that matches and response rates tend to be incredibly skewed to the most attractive (so highest quality) matches. The greater the skew and kurtosis, the more likely that online dating reduces total matches. However, dating apps are not the only means via which people interact and meet online. Hence by considering all the (social media) platforms via which matching can occur, my assumption of using a Gaussian process is justified. Alternative social media platforms offset the inequalities inherent in online dating apps.
Of course phones increase the value of nonparticipation too, but for simplicity we'll assume that inactivity is zero, which is sufficient for modelling this margin.
Non-economists would probably consider these chosen values as rather arbitrary, and indeed calibration is a large source of dispute for each particular paper. However this process is at least more precise and rigorous than simply asserting that phones decrease matching, and allows for transparency in assumptions and estimates.
Accounting for footnotes 1 and 4 possibly turns this into a negative effect, however still probably non-significant and not robust given the sensitivity of these estimates to the assumptions, calibration, and mechanisms used.
The links in my link pages inform these conclusions, alongside any others provided here.
Indeed there is an ulterior motive amongst many in the pro-natal crowd to use this as an excuse to control female bodies and subjugate women’s rights and autonomy. Needless to say, none of this is helpful to resolving what I consider to be humanity's greatest existential threat. This is mostly a positive rather than normative exercise though, so my opinion is relegated to the footnotes for those interested.