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@yudapearl Take the example above. You want to find a good research design to study the impact of military service on earnings. If you try to enumerate the variables that cause military service, there will be hundreds. Your DAG will grow and grow and you'll never find a backdoor strategy.
@yudapearl If instead you say, "Can I think of any variables that fit the template of a good IV?" Then you will say, "Aha!" The Vietnam draft fits that template. And now you have the core of an identification strategy which you can refine with an explicit DAG.
@yudapearl If you might say, "How can I study the impact of class size on student achievement?" You write a DAG listing all the determinants of class size. After the first 150,000 variables, you start to worry. Maybe there isn't any back-door strategy. There are too many confounders!
@yudapearl But then you get to variable 150,001. In classrooms in Israel, there is "Maimonides rule" which creates a discontinuous relationship between enrollment and class size. If enrollment crosses a threshold, class size changes dramatically. A natural experiment! (RD)
@yudapearl If you just try to write down a DAG with the determinants of class size, you will never find this natural experiment because you won't get to it until you list the first 150,000 variables you can think of as determinants of class size.
@yudapearl However, if you search your brain (and institutional details) for examples fitting the precise template of a regression discontuity... eureka! Your natural experiment is found. So to summarize, you must start by searching for variables that fit the template of a quasi-experiment.
