I took two courses that explicitly touched on causal inference in college. Both began with the idea that the Rubin average causal effect of treatment D on outcome Y is given by:
The idea here is that many things may determine Y. D determines Y, but so do other things (X). If we can estimate the average Y given D=1 versus Y given D=0 while keeping X constant, then we are in business. Luckily, well-specified, squared-loss regressions are good statistical estimators of the conditional expectation function. So if we have a good model that is fully exogenous, all we would have to do is obtain from the following regression:
In economics, these models often have some endogenous D, so we use instrumental variables, sample selection corrections, matching, etc.
In any case, the Rubin approach can be very useful for solving specific problems. For example, if one can show that race or gender significantly predicts wages while holding other characteristics equal, we have good evidence of discrimination. This is a very direct and practical use for a human resources department trying to keep things fair.
But one can also argue that treating D as orthogonal to X is a sterile approach with a limited normative interpretation. If nearly everyone with D=1 has a different X than those with D=0, then the incremental effect of D=1 may not be of interest to people actually trying to use the research to improve outcomes.
Marriages preceded by a period of cohabitation tend to result in divorce at higher rates than marriages not preceded by cohabitation. This is unintuitive to some because it is reasonable to think that only couples with good cohabitation periods decide to marry; cohabitation serves as a screener for good couples. It turns out that people with less committal personalities generally opt for cohabitation and then ease into marriage later via social convention, while those who are committal tend to go straight for marriage. When researchers statistically isolate personality, they find cohabitation leads to better marriages.
So, if you are one of those couples who are heavily committal, how important is the above for you? You might think that you should cohabitate because, all else equal, it should improve your eventual marriage. But the marginal effect for you, as a committal couple, may be so small that delaying marriage is actually the sub-optimal thing to do. So what is important to you is not the effect of cohabitation or D=1, but D=1 given your personality X.
Excessive attention to the effect of D obscures the usefulness of research to people with known X. Many researchers do and should care about the heterogeneity of the effect of D. Unfortunately, acknowledging heterogeneity does not always make for the punchy (amusingly counter-intuitive ex-ante but almost obvious post-hoc) causality papers that are idolized by “Mostly Harmless Econometrics” fans.