Robust Two-Step Confidence Sets, and the trouble with the First Stage F-statistic

When weak identification is a concern, researchers frequently calculate confidence sets in two steps, first assessing the strength of identification and then deciding whether to use an identification-robust confidence set. Unfortunately, two-step procedures of this sort may generate highly misleading confidence sets, and building two-step confidence sets from the first stage F-statistic can have extremely poor coverage when applied to linear instrumental variables models with heteroskedastic errors.

To provide an alternative, Isaiah Andrews introduces a simple approach to detecting weak identification and constructing two-step confidence sets which controls coverage distortions under weak identification in general nonlinear GMM models. The model indicates strong identification with probability tending to one if the model is well-identified. Applying this approach to linear IV shows that it provides similar results to approaches based on the first-stage F-statistic under homoskedasticity while performing far better under heteroskedasticity.