How to deal with cycles in causal inference?

Question

I’m trying to think about a study that showed that cam girls (yes, seriously) received higher salary with more years of experience. The takeaway from the author of the “study” was that experience had a causal effect on salary, but my immediate thought was that, perhaps, more likely, “good” cam girls simply got more business and thus, were more likely to remain in the business and gain more experience. Thinking about this more, in general, it seems entirely possible there are situations where experience could affect salary and salary could affect experience. My question is how would one go about constructing a causal DAG when these two variables are essentially pointing to each other? Eg there is probably some dependence between them in both directions. How does one avoid a cycle or is this just a hopeless case?

Answer 1

In this particular case, multiple measurements over time would help. From a DAG point of view, current experience can only affect current and future earnings, not past earnings; current earnings can only affect future decision to stay/leave, not past ones.

So, under the hypothesis that it's just experience affecting earnings, current experience will be correlated with future earnings but not (or less so) with past earnings.

Under the hypothesis that it's just earnings affecting the stay/leave decision, current experience will be correlated with past earnings, and will be independent of experience conditional on past earnings.

If (as seems likely) it's a mixture, the correlations will be more complicated.

In general there are are at least two other possible solutions (assuming you can't experiment)

• you could look for an intermediate variable on one of the two causal pathways and see if conditioning on it blocks the association.
• you could look for a natural experiment that affects earnings (eg higher charges on some relevant internet platform) and see what impact it has. You'd still need a good model for how earnings affected the stay/leave decision.