I wanted to know what would be the relevant weak IV tests among the following in case of one endogenous regressor and 2 IVs.
i) Comparing Cragg-Donald F-statistic to Stock-Yogo table
ii) Kleibergen-Paap statictic (should it be compared to Stock-Yogo table?)
iii) CLR test
iv) Montiel-Plueger test
v) Hahn & Hausman forward-reverse TSLS estimators
It would be really helpful if someone could point out the appropriate method. Please also suggest if any other tests are applicable.
Thank you.
I am not familiar with the arguments for using the tests that you list, but in your case of one endogenous regressor and two instruments (n=1, K2=2 in Stock and Yogo (2005) notation) I believe it would be reasonable to use the first-stage F-statistic and the Staiger and Stock (1997) rule of thumb, F<10, unless you have some reason for a very exact definiton of ”weak”.
From Stock and Yogo (2005):
Comparison to the Staiger-Stock (1997) rule of thumb. Staiger and Stock (1997) suggested the rule of thumb that, in the n = 1 case, instruments be deemed weak if the first-stage F is less than ten. They motivated this suggestion based on the relative bias of TSLS. Because the 5% critical value for the relative bias weak instrument test with b = 0.1 is approximately 11 for all values of K2, the Staiger-Stock rule of thumb is approximately a 5% test that the worst case relative bias is approximately 10% or less. This provides a formal, and not unreasonable, testing interpretation of the Staiger-Stock rule of thumb. The rule of thumb fares less well from the perspective of size distortion. When the number of instruments is one or two, the Staiger-Stock rule of thumb corresponds to a 5% level test that the maximum size is no more than 15% (so the maximum TSLS size distortion is no more than 10%). However, when the number of instruments is moderate or large, the critical value is much larger and the rule of thumb does not provide substantial assurance that the size distortion is controlled.
