A residual-prediction test with user-chosen ML and sample splitting delivers asymptotic type I error control for linear IV model specification under mean independence of structural errors and instruments, with extensions to weak instruments.
Next, we need some kind of uniform central limit theorem and law of large numbers
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Machine-Learning-Powered Specification Testing in Linear Instrumental Variable Models
A residual-prediction test with user-chosen ML and sample splitting delivers asymptotic type I error control for linear IV model specification under mean independence of structural errors and instruments, with extensions to weak instruments.