The Lucas critique and twin adoption studies
It is odd to cite a twin adoption study, and its results, as a response to a methodological critique of…a twin adoption study. Nonetheless, the paper Alex cites, and the associated graph, show very readily the problems in interpreting such studies.
If you check out the graph, for a variable such as "religious importance" it shows family transmissibility of about thirty percent, with varying estimates of transmissibility for other religious variables. That is the result from a data set involving a) parents who try hard to transmit religion with some idea of what to do, b) parents who don't try very hard, and c) parents who try hard and have no idea of what is an effective technique, as they might be advised by a well-informed social scientist.
Here's the key point. The original "control" question we were debating was about a) alone, yet in response Alex is putting forth a measure of the marginal efficacy for a-c, namely including the families who aren't trying to transmit. Obviously the marginal product of the informed, trying families should be higher than the average marginal product for the group as a whole. At the very least we can take thirty percent as the lower bound here, not the best estimate of the effect we are trying to measure.
The Korean-American Protestant study finds transmissibility of religious fervor, through family influence, of two-thirds. That paper does not control for genetics, and of course because of genetic similarity family influence will run especially easily and this figure is an overestimate of the net family effect. You can think of two-thirds as the upper bound here. If we had commensurable studies (not the case), we would have lower and upper bounds for trying-to-transmit families.
One way to think about the Korean study is to recognize that out of 100 Protestant children, parental inculcation "worked" for 66 of them. The correct marginal product question is: without that inculcation, how many of those 66 kids would have found their way to a comparably observant religion? Of course we don't know, but that's the right question to focus upon.
Twin studies encourage you to think in terms of a different question about marginal products: if you had those Protestant families adopt 100 kids, and try to inculcate the same religion, would 66 of them have ended up observant? Very likely not. Of course the two thought experiments are quite different, and they give you different measures of marginal product, most of all because there are non-linear interactions between parenting, peers, and genes. Since most children are not adopted, it is the first thought experiment which gives the more accurate measure of marginal product of parental inculcation of religion.
What about the religious variables which don't seem very transmissible at all? Alex cites "born agains," drawing on the same paper. But this interpretation again mirrors a major drawback of many interpretations of twin adoption studies, namely that they don't reconcile the cross-sectional and the time series comparisons. Alex is walking a simple pitfall here, as does the paper he cites.
What does this mean in practice? Born agains (or arguably, their revival) are a relatively recent phenomenon in the United States, dating from the 1970s. (There is a similar revival in biblical literalism, although perhaps less extreme.) The study takes adults from the mid-1990s. That means you will have lots of "born again" descendents who had strongly below average prospects of having had "born again" parents. The correlation will appear very weak, but this doesn't show the variable is not transmissible going forward. We simply don't know, at least not from this data set.
To put this final point another way, the father of Abraham was not a Muslim, and so back then the correlation was zero, but this does not show the family cannot transmit Islam in later periods of time.
I'd like to stress again that when it comes to Bryan's book, I agree with most of his points. But on religion in particular I don't think Alex is making sound claims.