IVREG 2 and weakivtest

[Eric Winkler]

Dear Statalist

I am running a 2SLS analysis with the ivreg2 command (Stata 13.1), which looks as follows:

ivreg2 $y1list ($y2list = $x2list) $x1list i.year, first robust cluster(identifikator)
weakivtest

In order to test if my instrument is a weak one (and due to the fact that I am using the robust cluster() option), I use the post estimation command "weakivtest".
However, I have some trouble to correctly understand the output of the weakivtest command. Even after reading the article of Olea and Pflueger (2013) cited below.

My output looks as follows:

. weakivtest, level(0.05)
(obs=714)

Montiel-Pflueger robust weak instrument test
--------------------------------------------
Effective F statistic: 15.229
Confidence level alpha: 5%
--------------------------------------------

--------------------------------------------
Critical Values TSLS LIML
--------------------------------------------
% of Worst Case Bias
tau=5% 37.418 37.418
tau=10% 23.109 23.109
tau=20% 15.062 15.062
tau=30% 12.039 12.039
--------------------------------------------

Now the cited paper of Olea and Pflueger (2013) they used a threshold (tau) of 10% and a alpha of 5%. Hence, I used the same measure. Do I understand this correctly that in this case I would need to conclude that my instrument is weak (even though at the first stage it is highly significant with a t-value of 3.8?
Furthermore, I do not completely understand when I should use which tau. Could somebody please clarify this to me?

Thanks a lot in advance for your help!!

Best,
Eric

Montiel Olea, J. L. and C. E. Pflueger (2013) “A robust test for weak instruments,” Journal of Business and Economic Statistics, Vol. 31, pp. 358–369.

[Mark Schaffer]

Have you looked at the paper that accompanies weakivtest? It's cited in the help file:

Montiel Olea, J. L., C. E. Pflueger, and Su Wang. 2013. A robust test for weak instruments in Stata.
http://papers.ssrn.com/sol3/papers.c...act_id=2323012.

The choice of tau is up to you: the interpretation is that it's the percentage of a "worst-case" bias, and you choose what percentage you're willing to tolerate.

The fact that your instrument is "significant" in the first stage - in other words, significantly different from zero - is not enough. That's a test of whether the model is underidentified. But you can reject underidentification (as you do) and still have a weak identification problem.

[Eric Winkler]

Thanks for your reply Professor Schaffer! Yes, I have also read this paper before posting my question. The one I posted is just a little more detailed.
I have to admit that I am a beginner with handling Stata commands / statistical analysis. Right, both of the papers talk about the hypothesis that the estimator approximate asymptotic bias exceeds a fraction tau of a "worst-case" benchmark (which is when the instrument is not informative at all). Maybe I only do not understand it, because English is not my mother language. But how can it exceed the worst case benchmark?
In your opinion would you say a tau of 10% (as in the example of Olea, Pflueger (and Wang) 2013) seems reasonable or should I increase it to let's say 30%?
I see, so not only the Kleinbergen-Paap rk LM statistic tests for underidentification but rather also the significance level of the instrument at the first stage.
I have consulted some other papers which claimed to have a good instrument when the robust t-value for the instrument on the first stage is highly statistically significant. So this would not be appropriate to say. (To be fair, the paper where published before 2013. Hence they could not use this Stata command.)

Thanks again for your reply!

[Mark Schaffer]

I think the worst-case benchmark means this. (a) O-P establish what the bias would be in a worst-case scenario of completely weak instruments. This is the benchmark. (b) You choose tau; say 10%. So you're willing to tolerate a bias that is up to 10% of the worst-case bias. (c) You choose the test size; say 5%. (d) The null hypothesis is that the bias in your estimator is greater than 10% of the worst-case bias. (e) If your O-P test statistic is greater than the critical value, you reject the null at the 5% level and conclude that your instruments are strong in the sense that the bias is no more than 10% of the worst-case bias.

[Eric Winkler]

Thanks for your clarification Professor Schaffer!