Causation and Manipulation II: The Causal Effect of Gender? 

 In a  recent post , Jim Greiner asked whether we adhere to the principle of "no causation without manipulation." This principle, if true, raises the question of whether it makes sense to talk about the causal effect of gender. 

 The Rubin/Holland position on this is clear: it makes no sense to talk about the causal effect of gender because what manipulation and thus what counterfactual one has in mind (a sex-transformation surgery?) is clearly ill-defined. One can ask related questions like sending resumes to employers randomizing female and male names and see whether one gender is more likely to be invited to a job interview, but it makes no sense to think about a causal effect of gender  per se . 

 The contrasting view is presented by one of their main foils, James Heckman, who writes in a  recent paper  (Andrew Gelman also had a  blog post  on this): "Holland claims that there can be no causal effect of gender on earnings. Why? Because we cannot randomly assign gender. This confused statement conflates the act of definition of the causal effect (a purely mental act) with empirical difficulties in estimating it. This type of reasoning is prevalent in statistics. As another example of the same point, Rubin (1978, p. 39) denies that it is possible to define a causal effect of sex on intelligence because a randomization cannot in principle be performed. In this and many other passages in the statistics literature, a causal effect is defined by a randomization. Issues of definition and identification are confused. [...] the act of definition is logically separate from the acts of identification and inference." Heckman sees this as a "view among statisticians that gives rise to the myth that causality can only be determined by randomization, and that glorifies randomization as the ‘‘gold standard’’ of causal inference."  

 So what do you make of this? Does it make sense to think about a causal effect of gender or not? Does it make sense to try to estimate it, i.e. interpret a gender gap in wages as causal (balance on all confounders except gender). How about the causal effect of race, etc.? Just to be precise here notice that Rubin/Holland admit that "even thought it may not make much sense to talk about the 'causal' effect of a person being a white student versus being a black student, it can be interesting to compare whites and blacks with similar background characteristics to see if there are differences" in some outcome of interest.