Comments (1)
This is an interesting failure mode - if the estimates for E[T|Z,X,W] are always identical to E[T|X,W] then since the final model weights the rows by the estimated variance (E[T|Z,X,W]-E[T|X,W])^2, all the weights are zero which leads to this problem.
In this particular case, Lasso is regularizing all weights to 0 so the estimators always (correctly) predict E[T] = 0 regardless of whether we condition on Z,X,W or just on X,W.
Hopefully with real world data this is less likely to occur, but we could at least throw a more meaningful error message if we do run into this scenario. But I think it is a real error condition in that we depend on the instrument affecting treatment for identification, so I don't think ignoring it and producing an estimate (say, by using all 1s for the weights if they turn out to all be 0s) would be appropriate.
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