2sls - interpretation underidentification and weak identification test

[Lucia Credito]

Hi everyone,
Hereunder are the results of my ivreg2. Can you help me to explain/ confirm if my understanding is correct:

- Underidentification test Kleibergen-Paap rk LM statistic: p.value = 0.000 means my IV cannot represent my endogenous variable. But the first-stage regression, the IV is a significant statistic correlated with endo variable. Does it mean I need to include MORE IV?
- Weak identification test: both Cragg-Donald and Keibergen-Paap F-stat are high, does it mean my current IV is strong enough, that is okay to keep the current IV?

Do you suggest me to do something more?
Thank you very much

[Lucia Credito]

Hi everyone,
I was confused before, but now I see that the pvalue of both Underidentification test and F-value of weak identification test are valid to conclude that my current IV is statistically enough and valid.

However, the F-stat of both Cragg-Donald and Keibergen-Paap rk Wald too high, is it normal that high? It was normal 2sls using ivreg2 with robust standard error cluster at country level, with sample size up to 250,000 observation

Thank you very much