Tag Archives: fertility

Some More Thoughts on Human Development and Fertility

I'm no longer on vacation which means that I have much less time to devote to blogging.  I just wanted to follow up on the last couple posts though before I jump back into the fray. I received some very stimulating comments from Edward Hugh and Aslak Berg, who are economists and contributers to the Demography Matters blog. They pointed to a recent blog post that Aslak wrote in response to my defense of the recent Nature paper by Myrskylä et al. Given how hysterical debate (ostensibly) over health care in the United States has been of late,  it is very refreshing to have a rational debate with intellectual give and take, arguments backed up by evidence, concern over truth, etc. You know, all those things that don't seem to matter in contemporary American political discourse? So, my thanks to my interlocutors.

My basic reply is that I don't disagree with much Ed and Aslak have said.  I nonetheless think that the Myrskylä et al. paper is of fundamental interest.  How can that be?  Well, I think that this turns on the question of causality. Does high HDI cause higher fertility? I think that this is unlikely in the strict sense.   We can use a handy graphical formalism called a directed acyclic graph (DAG) to illustrate causality (Judea Pearl, who pioneered the use of DAGs in causal analysis, has some very nice slides explaining both causal inference and the use of simple DAGs.  There is a whole group at Carnegie Mellon including Peter Spirtes, Richard Scheines, and Clark Glymour who work on the use of statistics and causal inference. Causal DAGs, as discussed in Pearl (1995), are a non-parametric generalization of path analysis and linear structural relations models first developed by Sewell Wright and familiar to geneticists, psychometricians, and econometricians).  The idea that HDI somehow causes fertility can be encapsulated in the following simple graph:


An arrow leads from HDI directly to fertility, indicating that HDI "causes" fertility. The thing is, I don't believe this at all in the strictest sense.  HDI is a composite measure that includes six quantities (life expectancy at birth, log-per capita GDP at PPP in $US, adult literacy, and primary, secondary and tertiary school enrollment fractions).  This alone leads me to think that the results described by Myrskylä et al. are really (interesting) correlations and not causal relations. I suspect that Myrskylä and colleagues also think this.  In the discussion, the authors speculate on what it is about very high HDI that allows fertility to increase from its lowest levels generally seen at intermediate-high HDI. Their leading hypothesis relates to social structures that allow women to simultaneously be part of the workforce and have children: "analyses on Europe show that nowadays a positive relationship is observed between fertility and indicators of innovation in family behaviour or female labour-force participation." They further suggest that the more conservative social mores of the rich East Asian countries may be why their fertility continues to plummet: "Failure to answer to the challenges of development with institutions that facilitate work–family balance and gender equality might explain the exceptional pattern for rich eastern Asian countries that continue to be characterized by a negative HDI–fertility relationship."  The causal graph here might look like this:


I've made the line between HDI and fertility dashed to indicate that the direct influence is reduced -- it's possible that its only influence is indirectly through childcare.  Now HDI causes changes in childcare structures and these are what have the major causal impact on fertility.  Really, I suspect it is more than that, of course.  One possibility is the existence of relatively high-fertility immigrants in many of these high-HDI countries. In the United States, the fertility of foreign- and native-born women (based on the most recent analysis of the Census Bureau's Current Population Survey) was 2.1 and 1.8 respectively.   So foreign-born women in the United States have (period) TFRs that are nearly 20% higher than native-born women.  Similar results apply to European countries.  Is it possible that it's not childcare arrangements but the fraction of foreign-born that is different between the high-HDI European and East Asian countries?  If that's true, what's going on with Canada? It's not difficult to construct a story relating HDI to immigration: as development continues to increase and the skills of a workforce (and wages demanded by it) increase there are two forces increasing further immigration.  First of all, the country becomes a more attractive destination.  Secondly, as the skills/wages of the native labor force increase, there is need to find people who are willing to do the less highly skilled and lower paid labor.  The existence of high fertility migrants is an example of unmeasured heterogeneity, which is the bugaboo of demography and causal inference.  In this case, I think the heterogeneity might really be the object of interest and not simply a nuisance for causal inference.

My guess is that there are multiple causes.  Something like this seems likely to me:

dag-migration-childwith a number of other causes almost certainly contributing (either directly or indirectly) as well.

What I think is so valuable about the paper by Myrskylä and colleagues is that it makes us ask what the causal stories might be. What these scholars have done is initiate a chain of abductive reasoning.  Charles Sanders Pierce first identified abduction as a form of logical inference. Describing abduction, he wrote, "The surprising fact, C, is observed; But if A were true, C would be a matter of course, Hence, there is reason to suspect that A is true" (Collected papers: 5.189). Abduction is basically the process through which new hypotheses are created. Myrskylä have just revealed surprising fact C, namely, that fertility appears to increase with very high HDI.  We are surprised because all the previous literature on the relationship between economic development and fertility showed that the two were negatively related. Our goal now is to elucidate what A (almost certainly a multi-factorial quantity) is.  I like this paper because I see it as starting a new and productive area of research not because it identifies the cause of increased fertility in low-fertility countries.

The problematic correlations that Aslak notes (i.e., that the countries that show J-shaped HDI-TFR curves longitudinally are culturally related) may actually aid us in our quest to uncover the causal mechanism(s) that explains the HDI-TFR relation (more unmeasured heterogeneity). This, of course, would be a miserable situation if we thought that HDI was strictly causal since then HDI and whatever this latent cultural variable would be almost completely confounded.  But their very relationship may aid us in identifying what the actual causal mechanism is.

I look forward to more work in this exciting and important area of demographic research.  Maybe one of these days I'll write more on causal directed acyclic graphs. It's a pretty cool approach to science and one that I think merits much more attention in the social sciences

Follow-Up to the Reversal in Fertility Decline

In my last post, I wrote about a new paper by Myrskylä and colleagues in this past week's issue of Nature.  Craig Hadley sent me a link to a criticism of this paper, and really more the science reporting of it in the Economist, written by Edward Hugh on the blog A Fist Full of Eruos within a couple hours of my writing.  Hugh levels three criticisms against the Myrskylä et al. (2009) paper:

  1. The authors use total fertility rate (TFR) as their measure of fertility, even though TFR has known defects.
  2. The reference year (2005) was a peculiar year and so results based on comparisons of other years to it are suspect.
  3. Even if fertility increases below its nadir in highly developed countries, median age of the population could increase.

The first two of these are criticisms of the Myrskylä et al. (2009) Nature paper and it is these that I will address here. The third is really a criticism of the Economist's coverage of the paper.

TFR is a measure of fertility and in demographic studies like these, what we care about is people's fertility behavior.  In a seminal (1998) paper, John Bongaarts and Griffith Feeney pointed out that as a measure of fertility TFR actually confounds two distinct phenomena: (1) the quantum of reproduction (i.e., how many babies) and (2) the tempo of reproduction (i.e., when women have them).  Say we have two populations: A and B.  In both populations, women have the same number of children on average. However, in population B, women delay their reproduction until later ages perhaps by getting married at older ages.  In both populations, women have the same number of offspring but we would find that population A had the higher TFR. How is that possible? It is a result of the classic period-cohort problem in demography.   As social scientists, demographers care about what actual people actually do. The problem is that measuring what actual people actually do over their entire lifetimes introduces some onerous data burdens and when you actually manage to get data for individual lifetimes, it is typically horribly out-of-date. For example, if you want to look at completed fertility, you need to look at women who are 50 years old or older at the time.  This means that most of their childbearing happened between 20 and 30 years ago. Not necessarily that informative about current trends in fertility.

To overcome this problem, demographers frequently employ period measures of fertility, mortality, marriage, migration, etc.  A period measure is essentially a cross-sectional measure of the population taken at a particular point in time.  Rather than measuring the fertility of women throughout their lifetimes (i.e., looking at the fertility of a cohort of women where they are age 20, 30, 40, etc.), we measure the fertility of 20 year-olds, 30 year-olds, 40 year-olds, and so on at one particular point in time. We then deploy one of those demographers' fictions.  We say that our cross-section of ages is a reflection of how people act over their life course.  TFR is a period measure.  We take the fertility rates measured for women ages 15-50 at a particular point in time (say, 2005) and sum them to yield the number of children ever born to a woman surviving to the end of her reproductive span if she reproduced at the average rate of the aggregate population.

Here is a simple (highly artificial) example of how this works.  (Demographic purists will have to forgive me for reversing the axes of a Lexis diagram, as I think that having period along the rows of the table is more intuitive to the average person for this example.)  The cells contain annual age specific fertility rates for each period. We calculate the period TFR by multiplying these values by the number of years in the age-class (which I assume is 5 for classes 10 and 40 and 10 for the others).  In 1940, we see the beginning of trend in delayed fertility -- no women 15-20 (i.e., the "10 year-old" age class) have children.  This foregone early fertility is made up for by greater fertility of 20-30 year-olds in 1940.  Eventually, overall fertility declines -- at least in the periods for which we have full observations since the 1950, 1960, and 1970 cohorts have not completed their childbearing when the observations stop.


When we measure the TFR in 1930, we see that it is higher than the TFR in 1940 (3 vs. 2.5).  Nonetheless, when we follow the two cohorts through to the end of their childbearing years (in blue for 1930 and red for 1940), we see that they eventually have the same cohort TFRs. That is, women in both cohorts have the same total number of children on average; it's just that the women in 1940 begin childbearing later.  The behavior change is in tempo and not quantum and the period measure of fertility -- which is ostensibly a quantum measure since it is the total number of children born to a woman who survives to the end of her childbearing years -- is consequently distorted.

Bongaarts and Feeney (1998) introduced a correction to TFR that uses measures of birth order to remove the distortions.  Myrskylä et al. (2009) were able to apply the Bongaarts/Feeney correction to a sub-sample (41) of their 2005 data.  Of these 41 countries, they were able to calculate the tempo-adjusted TFR for 28 of the 37 countries with an HDI of 0.85 or greater in 2005. The countries with adjusted TFRs are plotted in black in their online supplement figure S2, reproduced here with permission.

Myrskyla_etal-figS2As one can easily see, the general trend of increasing TFR with HDI remains when the corrected TFRs are used.  This graphical result is confirmed by a formal statistical test: Following the coincident TFR minimum/HDI in the 0.86-0.9 window, the slope of the best-fit line through the scatter is positive.

Hugh notes repeatedly that Myrskylä et al. (2009) anticipated various criticisms that he levels.  For example, he writes "And you don’t have to rely on me for the suggestion that the Tfr is hardly the most desireable [sic] measure for what they want to do, since the authors themselves point this very fact out in the supplementary information." This seems like good honest social science research to me. I'm not entirely comfortable with the following paraphrasing, but here it goes.  We do science with the data we have, not the data we wish we had.  TFR is a widely available measure of fertility that allowed the authors to look at the relationship between fertility and human development over a large range of the HDI. Now, of course, having written a paper with the data that are available, we should endeavor to collect the data that we would ideally want.  The problem with demographic research though is that we are typically at the whim of the government and non-government (like the UN) organizations that collect official statistics.  It's not like we can go out and perform a controlled experiment with fixed treatments of human development and observe the resulting fertility patterns. So this paper seems like a good-faith attempt to uncover a pattern between human development and fertility.  When Hugh writes "the only thing which surprises me is that nobody else who has reviewed the research seems to have twigged the implications of this" (i.e., the use of  TFR as a measure of fertility), I think he is being rather unfair.  I don't know who reviewed this paper, but I'm certain that they had both a draft of the paper that eventually appeared in the print edition of Nature and the online Supplemental material in which Myrskylä and colleagues discuss the potential weaknesses of their measures and evaluate the robustness of their conclusions. That's what happens when you submit a paper and it undergoes peer review.  The pages of Nature are highly over-subscribed (as Nature is happy to tell you whenever it sends you a rejection letter).  Space is at a premium and the type of careful sensitivity analysis that would be de rigeur in the main text of a specialist journal  such as Demography, Population Studies, or Demographic Research, end up in the online supplement in Nature, Science, or PNAS.

On a related note, Hugh complains that the reference year in which the curvilinear relationship between TFR and HDI is shown is a bad year to pick:

Also, it should be remembered, as I mention, we need to think about base years. 2005 was the mid point of a massive and unsustainable asset and construction boom. I think there is little doubt that if we took 2010 or 2011, the results would be rather different.

The problem with this is that the year is currently 2009, so we can't use data from 2010 or 2011.  It seems entirely possible that the results would be different if we used 2011 data and I look forward to the paper in 2015 in which the Myrskylä hypothesis is re-evaluated using the latest demographic data.  This is sort of the nature of social science research.  There are very few Eureka! moments in social science.  As I note above, we can't typically do the critical experiment that allows us to test a scientific hypothesis.  Sometimes we can get clever with historical accidents (known in the biz as "natural experiments"). Sometimes we can use fancy statistical methods to approximate experimental control (such as the fixed effects estimation Myrskylä et al. use or the propensity score stratification used by Felton Earls and colleagues in their study of firearm exposure and violent behavior).  If we waited until we had the perfect data to test a social science hypothesis, there would never be any social science.  Perhaps things will indeed be different in 2011.  If so, we may even get lucky and by comparing why things were different in 2005 and 2011, gain new insight into the relationships between human development and fertility. Until then, I am going to credit Myrskylä and colleagues for opening a new chapter on our understanding of fertility transitions.

Oh, and I plan to cite the paper, as I'm sure many other demographers will too...

Reversal of Fertility Decline

In a terrific paper in the latest issue of Nature, Myrskylä and colleagues (including my sometime collaborator Hans-Peter Kohler) demonstrate that total fertility rate (TFR) -- which we typically think of as declining with economic development -- actually increases at very high levels of development.  One of the fundamental challenges of social science remains explaining the unprecedented decline in fertility witnessed in the twentieth century.  This fertility decline has gone hand-in-hand with economic development.  As Myrskylä et al. write, "The negative association of fertility with economic and social development has therefore become one of the most solidly established and generally accepted empirical regularities in the social sciences."

For those social scientists with an evolutionary bent, this observation has been particularly vexing since it appears to violate our expectations regarding resource-holding and reproductive success.  In a great many traditional societies, researchers have documented a positive relationship between wealth and reproductive success.  However, as soon as people are embedded within (and actually integrated with) the structures of a state-level society, this relationship apparently changes: rich people in states appear to have fewer children than poor people.  And as the overall level of wealth of a state increases, the aggregate pattern of fertility also decreases.  Now there are plenty of caveats here.  Many scholars have committed the ecological fallacy in attributing causal explanations at the individual level based on aggregate ("ecological") data. There is some evidence that the wealthy and well educated actually have marginally higher fertility in certain contexts, but the overwhelming weight of evidence shows that -- at least at the aggregate level -- increased wealth leads to decreased fertility. Until now.

The authors use the Human Development Index (HDI), a widely used measure of progress in human development.  The HDI combines three dimensions: (1) health, as measured by life expectancy at birth, (2) standard of living, as measured by the logarithm of per capita gross domestic product at purchasing power parity in US dollars, and (3) human capital as measured by adult literacy and the enrollment fraction in primary, secondary, and tertiary school.  HDI is now standardized so that it varies between zero and one.  This makes it easy to compare HDI across countries and through time.  The measure of fertility that Myrskylä and colleagues use is total fertility rate.  This is also probably the most commonly used measure of fertility.  It is the sum of a population's age-specific fertility rates across a woman's reproductive years, assuming that the woman survives this span.  It is a demographic fiction, but it is a useful fiction.

What Myrskylä et al. (2009) show (in their figure 1) is that TFR largely declines with HDI in 1975, as expected. The cool, unexpected finding that their paper reports is that in 2005, TFR declines with HDI to a point. When the HDI exceeds 0.9 though, fertility again increases. This plot is cross-sectional: it is a scatter plot of all countries' HDI-TFR pairs for a particular time period. One reason why we don't see this upward turn at the highest levels of human development in 1975 is that no countries had achieved this apparent threshold of HDI=0.9. Of course, from this plot we can't rule out the existence of some "period effect." That is, maybe there was just something different in society or the economy in 2005 compared to 1975.

back half template
Myrskylä et al. (2009) figure 1 (used with permission of the authors).

In figure 2, the authors plot longitudinal data for individual countries. They show that once HDI enters a window between 0.86-0.9 and TFR bottoms out, further increases in HDI lead to increases in TFR.

Myrskylä et al. (2009) figure 2 (used with permission of the authors)
Myrskylä et al. (2009) figure 2 (used with permission of the authors)

This greatly increases our confidence that there is, in fact, a causal relationship between increased human development and fertility.  The really cool thing about this plot, however, is the exceptions to the general trend that it shows. In particular, Japan, South Korea, and Canada (and to a lesser extent Austria, Australia, and Switzerland) do not show this pattern.  For these countries, further increases in HDI are associated with further declines in TFR. A distinct possibility is that for some countries, increasing human welfare also leads to institutions that permit people (particularly women) to have children and be educationally and economically successful at the same time -- that is, not just people who were lucky enough to be born rich.  It's a shocking idea. The authors write:

[A]n improved understanding of how improved labour-market flexibility, social security and individual welfare, gender and economic equality, human capital and social/family policies can facilitate relatively high levels of fertility in advanced societies is needed. For instance, analyses on Europe show that nowadays a positive relationship is observed between fertility and indicators of innovation in family behaviour or female labour-force participation. Also, at advanced levels of development, governments might explicitly address fertility decline by implementing policies that improve gender equality or the compatibility between economic success, including labour force participation, and family life. Failure to answer to the challenges of development with institutions that facilitate work–family balance and gender equality might explain the exceptional pattern for rich eastern Asian countries that continue to be characterized by a negative HDI–fertility relationship.

These are important problems and this is a fundamental contribution to our understanding of the relationships between economic development, human welfare, and reproductive behavior.