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