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:

with 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

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.

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.

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.