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Is the front-door criterion: 1) a novel alternative to IV, 2) something econs already do, or 3) an oddity with little relevance to econ? I think the answer is 2), although perhaps such strategies are underutilized? (1/131,431)
This post is based on conversations with @autoregress and, as usual, he is to blame for any errors (and the school example). Get your act together @autoregress! (2/131,431)
The front-door criterion is based on the attached DAG. The key exclusion restrictions are: X only causes Y via Z and X "blocks" any confounders that might impact both Z and Y. (3/131,431) 
Suppose someone told you, we have estimated the causal impact of attending different schools on test scores using a lottery (assume homogeneous treatment effects). Now we want to know the causal impact of an assignment mechanism that will assign students to alternative schools.
Can you figure out how to do it? Even a poor DAGless economist can! We would check how the new assignment mechanism changed what school you go to and multiply that by the effect of different schools. This is one half the front-door criterion (and it's obvious and intuitive).
This assumes that the assignment mechanism only impacts test scores via the school you attend (X only causes Y via Z). A completely natural assumption in this setting. Now, what if we don't have a lottery to generate estimates of the impact of school quality on outcomes?
This is the other half of the front-door approach. You might say--now we're stuck! Higher-achieving students will attend better schools and it's hard to control for ability. But perhaps we could control for ability by controlling for how students rank schools?
This is what the front-door DAG would suggest we do here. If any confounders (like ability) only impact what school you go to via your ranking, then we're home free. But this of course begs the question: what *does* generate variation in school attendance conditional on ranking?
If, conditional on ranking a given school highly, whether you are admitted depends on the idiosyncratic popularity of that school in a given year, and if this idiosyncratic popularity doesn't impact your test scores directly through peer effects, we may have something!
So, is this new? No, it's what every paper in the school fixed effect literature does to simulate counterfactual assignment, although they do it better, because they find cases where the school assignment mechanism involves some randomization.
But arguably, we should be more on the look-out for cases such as, "We observe a ranking and residual variation in assignment given rankings is driven by factors which are unlikely to impact outcomes except via assignment."
But this approach can also go badly wrong; consider the example routinely given by @yudapearl to illustrate the front-door. In this case, smoking only impacts cancer via tar, and confounds like whether you are a healthy person only impact tar via whether you smoke. DAG attached.
This seems like a terrible set of assumptions. It simply begs the question: why does tar vary conditional on smoking? Could it possibly have anything to do with other aspects of your diet, exercise, or anything else that impacts your health? Seems very likely.
This illustrates a general contrast between how economists approach identification and the prevailing epidemiology approach. You could approach identification by asking, "Can we rule out confounding stories?" (this is the "backdoor" approach).
The credibility revolution says: "Can we understand what is driving the variation in our treatment variable?" The ideal case is randomization (a special case of IV). If we don't really know what is generating variation in treatment, we can never credibly assess confounds.
This is why it is preferable to have natural experiments. We want to *understand* the variation in our treatment, rather than eliminate a few confounds and desperately hope that what remains is immaculate. This is a fruitless endeavor if the remaining variation is not understood.
(thread continued here, somehow it got split in two: )
