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A question to #econtwitter that is motivated by the discussion about DAGs by @causalinf, @Jabaluck, @yudapearl, @nickchk. I always had a hard time to understand the difference between Nonparametric IV and Control Function. I tried to use a DAG to understand this difference. 
The triangular model is common to both approaches and is stated in purple for completeness. The IV identification assumption and DAG are in blue. The CF identification assumption and my attempt of its DAG is in black.
If the latter DAG is correct, I guess I could use CF and IV. Is that the case? Since the identification assumptions are not nested, how can I draw a DAG where I can use control function but not IV?
