strength of IV from Anderson -Rubin confidence interval provided by weakiv package

[Tariq Abdullah]

With my one endogenous variable and one instrumental variable, I'm testing the strength of IV by seeing the confidence interval of Anderson -Rubin.

Since the p-value of AR ( 0.0447 ) is less than 0.05, I can say that my instrument is strong, right?

 weakiv
Estimating confidence sets over 100 grid points
----+--- 1 ---+--- 2 ---+--- 3 ---+--- 4 ---+--- 5 
..................................................    50
..................................................   100

Weak instrument robust tests and confidence sets for linear IV
H0: beta[dep_variable:endogen_var] = 0
------------------------------------------------------------------------------
 Test |       Statistic         p-value |  Conf. level        Conf. Set       
------+---------------------------------+-------------------------------------
   AR | chi2(1)   =     4.03     0.0447 |      95%       [ .000921,   ...  ]  
------+---------------------------------+-------------------------------------
 Wald | chi2(1)   =     6.09     0.0136 |      95%       [ .003573, .031205]  
------------------------------------------------------------------------------
Confidence sets estimated for 100 points in [-.010243, .045021].
Number of obs N = 1954820.
Method = lagrange multiplier (LM).
Tests robust to heteroskedasticity and clustering on county (N_clust=406).
Wald statistic in last row is based on ivreg2 estimation and is not robust to weak
instruments.

[Fei Wang]

No. You need to test the strength of IVs using other commands (like weakivtest from SSC). The weakiv command shows that the endogenous regressor has statistically significant effects on the dependent variable even though your IVs are weak.

[Joro Kolev]

Pretty much what Fei said, but slightly different: No, this is not a test whether your instrument is weak or strong. This is a correct test of whether your endogenous regressor is significant, and correct confidence interval, regardless of the strength of your instrument.

[Tariq Abdullah]

Thanks to both of you for giving me your time and helping me to have a deeper understanding of the rationale behind the weakiv and weaivtest packages. Sincerely thankful for your time and patience!

[Pino Savana]

A related question: why is the confidence interval open ? Does it mean that the interval is unbounded?
[ .000921, ... ]

[Tariq Abdullah]

It's an unofficial consensus that if after doing weakiv test your CI is unbounded like the above, then that might be an indication that your IV is weak. However, this is my opinion only, you can search on google about the whole thing to know in depth.