You can make future population decline disappear just by changing the way you categorise people and fertility

Fertility has been on a long-term declining trajectory worldwide and, apart from the occasional blip, in every country. There seems to be no prospect of a reversal of this trend, and no prospect of fertility returning to the replacement level of approximately 2.1 births per woman. So, when you see a research paper claiming that "high-fertility, high-retention groups persist, gain share, and lead the total population to grow", you should sit up and take notice. That is, at least, until you've carefully thought about the paper in question.

That's what happened to me with this 2025 NBER Working Paper by Sebastian Galiani (University of Maryland, College Park) and Raul Sosa (Universidad de San Andres). They create and calibrate models of fertility based on two different subgroupings (by race, and by religion), and taking account of cultural transmission of fertility rates from mothers to daughters. They then use their calibrated models to simulate population change going forward for ten generations. What they find when the population is categorised by race is a decreasing population, as shown in Figure 1 Panel A from the paper:

And when Galiani and Sosa categorise the population by religion, they instead find an increasing population, as shown in Figure 2 Panel A from the paper:

Now, this struck me as really odd. We’re talking about the same country and the same underlying population. If you split that population into subgroups and take a weighted average of what happens in each subgroup, you should get back the outcome for the population as a whole. If you are measuring the same underlying thing consistently, changing the subgroups (race in one analysis, and religion in another) shouldn’t magically create or destroy population growth in the model. At most, it should change which groups are growing faster and therefore how the composition by group changes over time, with high-fertility groups making up a larger share of the population and lower-fertility groups making up a smaller share. But the headline result here is much stronger than that, with the direction of population growth in aggregate changing direction entirely depending on the groupings that are employed. Galiani and Sosa use those results to conclude that:

...whenever at least one group remains above replacement on the female line and transmits identity effectively, its share rises and turns the aggregate path upward.

The first part of that conclusion makes sense, but the second part stretches credibility. It made me wonder whether the results were being driven by unusual features of the model, or by different modelling choices in the two analyses. 

So, I dug into the paper, which is not an easy task as it is quite theoretical. And there are consequential differences between the two analyses (by race and by religion) that drive the difference in results. First, they use different measures of fertility, with the analysis by race based on the total fertility rate (TFR), while the analysis by religion is based on completed fertility (see this post for a brief discussion on the difference between those two measures). There is a consequential difference between the two measures. By definition, completed fertility can only be observed for women who have finished their childbearing years, so it covers a period over the last twenty or more years. In contrast, the total fertility rate that Galiani and Sosa use was measured in 2023, after a long period of fertility decline. By construction then, the analysis using completed fertility (the analysis by religion) will be assuming higher fertility than the analysis using the total fertility rate (the analysis by race). This is highlighted by Table 1 in the paper, which shows that nearly every racial group has a total fertility rate that is below replacement (Hispanic is highest among the large groups at a TFR of 1.946, while Native Hawaiian and Pacific Islanders have a TFR of 2.218), whereas there are several religious groups with completed fertility rates above replacement (including Mormons at 3.4, and Muslims at 2.4). 

Second, their calibration implies much bigger gaps across religious groups than across racial groups. Specifically, they assume greater dispersion in fertility and retention by religion than by race. That means that the forces driving fertility change within population groups are much stronger in the analysis by religion than the analysis by race. So, essentially this doubles down on the effect of higher fertility that arises from the different data sources.

Overall, I don't find the comparison across the two models to be credible. They are employing different measures, taken from different points in time, and applying different modelling assumptions. In contrast, the results within each model showing that the relative group proportions change over time to favour groups that have higher fertility are plausible and are worth taking account of. For instance, Galiani and Sosa conclude that:

Although the objective is not to forecast outcomes for particular groups, our world simulations imply not only a more religious composition but also that, within the horizon we study, Muslims become the largest tradition by share.

That seems like a sensible conclusion to draw based on the evidence, especially as they explicitly note that they aren't trying to forecast the population. Nevertheless, they do forecast the population, and their results are not entirely consistent with what is expected to happen. World population is set to start declining later this century in large part because of declining overall fertility, and their results based on religion suggest that this is suddenly going to reverse course, and remain upward over a time horizon of ten generations. In reality, the long-run trend in fertility is difficult to change in the real world, and applying some complicated economic modelling in a way that appears to overturn the on-the-ground reality is not going to contribute to a change.

[HT: Marginal Revolution]

Read more:

• The pandemic 'baby bust' in other countries
• Cohort effects and the downturn in US fertility since the Great Recession
• The new economics of fertility
• The economics of the falling total fertility rate in New Zealand
• The economics of fertility in high-income countries
• Can fertility return to replacement levels?

Why specialist vape retailers may tend to locate in more socially deprived areas

When I first started studying the social impacts of alcohol outlets, one of the things my research team and I were interested in was where alcohol outlets located. We found (see here) that off-licence outlets tended to locate in areas of high deprivation in Manukau City. I've since replicated that analysis a couple of times in unpublished work, for both South Auckland and Hamilton.

I was interested to see that this new article by Robin van der Sanden (Massey University) and co-authors, published in the New Zealand Medical Journal (sorry, no ungated version online, but you can sign up for open access for free), finds very similar results for specialist vape retailers (which are defined here). They used Google Maps and Google Street View data to locate all of the specialist vape retailers across 14 Auckland suburbs, then categorised them into three types: (1) upmarket; (2) budget; and (3) 'store-within-a-store' (which are located inside or attached to convenience stores, petrol stations or liquor stores. The main results in terms of the relationship between store numbers and social deprivation are shown in Figure 1 from the paper:

This figure shows the median number of specialist vape retailers (in total and by type) by social deprivation. In their sample, stores tend to be more likely to be located in the most deprived two deciles (9-10), and least likely to be in the least deprived two deciles (1-2). Aside from that, I wouldn't draw too much from the analysis here. Because these are median counts per suburb group (not per capita or per land area), differences could reflect population size, commercial zoning, or land area rather than ‘density’. So if high deprivation suburbs also tend to have higher populations, or to be larger in area, then the apparent relationship between social deprivation and the number of specialist vape retailers is confounded. However, at the highest level there does seem to be some tendency. Van der Sanden et al. worry about this, concluding that:

The concentration of SVRs in high-deprivation suburbs in Auckland may warrant further regulatory responses that better balance the needs of predominately adults to access vaping products as a means to stop smoking with limiting vape products to young people who have never smoked...

However, Van der Sanden et al. don't really explore why specialist vape retailers may locate in areas of high deprivation. I've done quite a bit of exploration and thinking on this in relation to off-licence alcohol outlets, and I suspect that the reasons might be similar. And it doesn't require retailers to be 'targeting' high deprivation communities in some predatory business strategy. I have a few hypothesised reasons for more specialist vape retailers in more socially deprived areas can be explained with some simple economics.

First, if a prospective retailer is looking to run a retail store that maximises profits, one of the aspects that they must consider is the costs of operating the business. Ceteris paribus (all else held constant), a store with lower costs will be more profitable. Areas of high deprivation tend to have lower commercial rents, and are therefore less costly to operate, and will generate higher profits from the same revenue.

The second hypothesis is a little more complex, and involves a bit of economic geography. Each store may have a particular 'catchment area', which is the area from which its customers come to the store. In a low deprivation area, where everyone owns a car, and often commutes a fair distance for work, the catchment area for a store might be quite large. So, stores that are located close together will be in direct competition for consumers, since their 'catchment areas' will substantially overlap. In contrast, in a high deprivation area, fewer people might own cars, or they may not run reliably, or they may only be able to afford to drive them to and from work without long side-quests to buy vapes. So, the 'catchment area' for a store will be much smaller, and stores can be located closer together without being in direct competition for consumers. And so, we might expect to see more vape stores in areas of high deprivation than in areas of low deprivation, because the retailers are trying to minimise competition with other stores (although they may then need to balance a smaller catchment, which has less spending power, against the costs of operating the store).

Finally, the differences may reflect differences in demand. If vaping rates are higher in more socially deprived areas, then demand for vaping products may also be higher in those areas, and attract more vape retailers. I don't really know whether there is a social gradient in vaping, although the New Zealand Health Survey suggests that there is, with more vaping among people living in areas in the most socially deprived quintile. Of course, there is a potential reverse causation problem with the demand-side explanation, because more specialist vape retailers located in socially deprived areas might drive more vaping in those areas.

None of that is to say that having more specialist vape retailers in more socially deprived areas is a desirable outcome (especially if they do indeed drive more vaping). Van der Sanden's proposed policy response may be appropriate. However, the situation we observe could be explained by some simple economics. So if policymakers want to reduce retail availability of vaping products, they can focus on practical levers (licensing, zoning, proximity rules) without relying on arguments about predatory business practices, or vilifying store owners (both of which I have seen in the case of alcohol retailers).

This week in research #115

Here's what caught my eye in research over the past week (another slow week):

• Mortágua gets deep into the theoretical weeds on the question of whether crypto-assets are money
• Carpenter et al. (with ungated earlier version here) use 2021 Canadian Census data to look at earnings disparities experienced by nonbinary people, and find that nonbinary individuals assigned male at birth, transgender men, transgender women, and cisgender women all earn significantly less than comparable cisgender men

Also new from the Waikato working papers series:

• Valera, Lubangco, and Holmes propose a new measure of revisions to consumer inflation expectations that uses repeated cross-sections rather than panel data, and show that individual inflation expectations are sensitive to price changes across 14 food and energy goods

Tuition fees, incentives, and 'ghost students'

When the New Zealand government introduced 'first-year fees free' in 2018, the universities expected a big uptick in student numbers. It didn't happen (as I discussed in this 2023 post). As the figure below (source) shows, the mild downward trend in domestic student numbers (equivalent full-time students, or EFTS) continued for at least a couple of years past 2018:

My colleagues were worried that we would see an increase in the number of students who enrol, and then do nothing at all (what we call 'ghost students'). My impression was that this didn't happen, but until now I never looked intentionally at the numbers. However, the figure below shows the proportion of each of my A Trimester ECON100 classes (up to 2017) or ECONS101 classes (for 2018 onwards) that were ghost students (I didn't teach the class in 2022, which is why there is no observation for that year). Here, I define a 'ghost student' as any student who didn't attempt any of the tests or exams (although they may have attended some classes during the trimester). In each trimester, the class had between 250-350 enrolments in total. [*]

As the figure shows, there was a big jump in 'ghost students' in 2021, but that is attributable to the COVID pandemic and the weirdness of that whole time period, rather than anything to do with fees-free. In most years, somewhere between three and five percent of students are 'ghosts'. In 2025, the government shifted from first-year fees free to final-year fees free. There's no evidence that change affected the proportion of 'ghost students' either. Or it's too early to tell - the proportion in 2025 was lower than either of the previous two years.

Why might we expect the changes in fees to affect the number of 'ghost students'? It comes down to incentives. As my ECONS101 students will hear next week, when the cost of something decreases, we tend to do more of it. First-year fees free decreased the cost of being a 'ghost student', so ceteris paribus (holding all else constant), we would expect to see more 'ghost students'. Final-year fees free (with first-year fees reintroduced) increased the cost of being a 'ghost student', so ceteris paribus, we would expect to see fewer 'ghost students'. The fact that didn't happen is interesting, and we'll come back to that a bit later.

To see why the New Zealand effect might be negligible, it helps to compare with a setting where student status comes with larger immediate benefits. To do that, I want to discuss this recent article by Johannes Berens (RH Köln), Leandro Henao, and Kerstin Schneider (both University of Wuppertal), published in the journal Labour Economics (ungated earlier version here). They look at the impact of the removal of tuition fees in North Rhine-Westphalia in Germany in 2011. Tuition fees were a very modest EUR500 per year (for every year of study), and Berens et al. essentially compare students who were more or less affected by the policy (depending on how many years they didn't have to pay fees for), looking at a range of academic outcomes including exam registrations and withdrawals, credit points earned, grades, and dropout probabilities, as well as the number of 'ghost students'.

Their data come from a single university, with over 11,000 students who first enrolled between 2008 and 2011. The students in the 2008 cohort would have graduated before the fees were removed, while those in the 2011 cohort would not have faced any fees at all. The other cohorts would have had fees in their later year/s, but not earlier year/s. Applying a difference-in-differences approach, Berens et al. find that:

...abolishing tuition fees significantly affected student behavior and academic outcomes. Active students reduced their academic performance by 1.7 credit points per semester (12 % relative to baseline), despite maintaining similar exam registration patterns... Additionally, the reform increased the prevalence of ghost students by 10 percentage points...

So, removing fees in this context substantially increased the proportion of 'ghost students' by 10 percentage points, from a baseline that was already over 10 percent (Berens et al. present the data by study semester, and the 'ghost student' proportion varies between 10 percent and 20-25 percent, depending on year and study semester).

What explains the high impact of removing fees in Germany? Berens et al. highlight the role of incentives, and in particular the generous nature of public assistance available to students. Specifically:

...student status confers substantial benefits, generally independent of academic performance... These benefits include subsidized health insurance (until age 25), state-wide public transport access (worth EUR 2900 annually), and parental child allowance (EUR 2450 annually). About 16 % of students also receive need-based grants averaging EUR 6800 annually...

So, being classified as a student can be quite lucrative in Germany, even if the student is a 'ghost'. That might also explain the lack of effect of first-year fees free in New Zealand. While the fees are higher in New Zealand than in Germany, being a student in New Zealand is hardly a pathway to great riches (at least, not during the time spent as a student - see this post, and the links at the end of it). The student allowance is not very generous, and while there are some other perks to being a student, cheap movie tickets and public transport are not exactly worth a lot of money. So, it shouldn't be much surprise that the impact in Germany was much larger than for a similar policy change in New Zealand.

Another reason that the impact was not apparent in New Zealand could be that many students do not pay their tuition fees immediately. Instead, many (perhaps most) students' tuition fees are paid by student loans. 'Student Greg' is probably quite content to say that the student loan is 'Graduated Greg's' problem, and not worry about it today. So, from the perspective of 'Student Greg', first-year fees free doesn't really impact the decision to become a student or not. It doesn't change the costs of being a student for 'Student Greg', because they don't consider paying back the student loan as part of the costs of studying today. [**] And that might explain why there was no incentive effect of first-year fees free in New Zealand (also, fees-free papers are not free if students fail them, as I noted in this 2023 post).

The incentives in Germany and New Zealand, when the tuition fees were changes, resulted in quite different impacts. In Germany, where the benefits of being a student were higher, lower costs of being a 'ghost student' induced many people to enrol, whereas in New Zealand, where the benefits of being a student are lower, and the costs of tuition are typically deferred to the future, lower costs of being a 'ghost student' appear to have made no difference.

The nature of incentives, and the costs and benefits around the decision, definitely matter. The policy takeaway from this is that tinkering with fees alone may induce more (or less) 'ghost students', so the other immediate benefits and costs associated with student status also need to be considered. 

*****

[*] The data are for only one paper, but ECON100 and ECONS101 have been, for the most part, compulsory papers for business students. In a couple of years, some students could avoid the paper by taking all of the other first-year business papers. However, unless 'ghost student' status was more likely for students who did not take first-year economics, these results should be broadly representative.

[**] Essentially, 'Student Greg' is heavily discounting the future. In my ECONS102 class, we say that 'Student Greg' exhibits present bias, and is therefore only quasi-rational, not purely rational. Of course, not all students will have acted like 'Student Greg', but if enough of them did, that would explain the lack of incentive effects of the changes in first-year fees.