weak instruments

[john ghi]

hello,
I estimate a model with the command ivregress 2sls. I have two endogenous variables.
Can I conclude that my instruments are not weak if the minimum eigenvalue statistic is above the critical values, although the shea's partial R-sq and the she'a adj partical R-sq are very low?
If the answer is yes, which information does the shes partial R-squares add?



. estat firststage

Shea's partial R-squared
--------------------------------------------------
| Shea's Shea's
Variable | Partial R-sq. Adj. Partial R-sq.
-------------+------------------------------------
x1 | 0.2201 0.2091
x2 | 0.0328 0.0191
--------------------------------------------------


Minimum eigenvalue statistic = 30.4388

Critical Values # of endogenous regressors: 2
Ho: Instruments are weak # of excluded instruments: 4
---------------------------------------------------------------------
| 5% 10% 20% 30%
2SLS relative bias | 11.04 7.56 5.57 4.73
-----------------------------------+---------------------------------
| 10% 15% 20% 25%
2SLS Size of nominal 5% Wald test | 16.87 9.93 7.54 6.28
LIML Size of nominal 5% Wald test | 4.72 3.39 2.99 2.79
---------------------------------------------------------------------

@Joao Santos Silva

[Joro Kolev]

Yes, you can conclude that you can reject the null that your instruments are weak.

As to what Shea's R-squares add, if anything at all, depends on what you are looking for. If you are only looking to test the null of weak instruments, it does not add anything.

[john ghi]

Thank you very much @Joro Kolev !
I want to test my instruments and to test the null of weak instruments, but also to get from this table as much information as I can.
Are there important conclusions from these values? (or from negative values of the she'a adj. partical R-Sq , which I got in another regression)?

[Joro Kolev]

Not only in your context, but everywhere I think that R-squares are just a summary statistic which does not have straightforward and clear interpretation. This is because we typically have no notion of what constitutes good, and what constitutes bad R-squared. I personally report some R-squares in my research because it is customary, but do not lose sleep over my R-squares and what they mean.

Thank you very much @Joro Kolev !
I want to test my instruments and to test the null of weak instruments, but also to get from this table as much information as I can.
Are there important conclusions from these values? (or from negative values of the she'a adj. partical R-Sq , which I got in another regression)?