Weak instruments test in xtivreg2

[Costas Lambrinoudakis]

Dear all

I am using command xtivreg2 and I have a couple of questions about the weak instruments test.

I estimate a regression with two-way clustering, so this means that the Cragg-Donald-based weak instruments test is no longer valid. The proper test for that case is the Kleibergen-Paap test.
So, the Stata reports the Kleibergen-Paap F-stat. However, the critical values reported by xtivreg2 for the Kleibergen-Paap statistic are the critical values for the Cragg-Donald test (i.i.d. case).

My questions are the following:
- Is it correct to use the Cragg-Donald critical values for the Kleibergen-Paap test? (an extra info: when I estimate my regression, the result I get for the Kleibergen-Paap F-stat is very high (140) compared to the Cragg-Donald critical values)
- If not, does anyone know the critical values for the Kleibergen-Paap test?

Any help would be greatly appreciated!

[Mark Schaffer]

Strictly speaking, the Kleibergen-Paap statistic can be used for tests of underidentification, but not for weak identification, at least until someone works out the critical values for the latter.

That said, Montiel-Olea and Pflueger have developed a test for weak instruments for case of estimation by IV/2SLS or LIML in the non-iid case (robust, cluster, etc.) with a single endogenous regressor. This has been implemented in Stata by them + Wang in a routine called "weakivtest" that is available from SSC in the usual way. If you your fixed-effects or first-differences estimation by hand and then call their routine, you should get a weak identification test stat you can use.

And that said, 140 is very high. The K-P stat is unlikely to be so very different from the MO-P stat that you will get different results. In other words, you are very likely to reject the null of weak instruments when you use their test.

[Costas Lambrinoudakis]

I 'll try "weakivtest". Many thanks for your help!

[Ellen Sterk]

Mark Schaffer Hi Mark! I am currently trying to apply a test of weak instruments after my xtivreg2, fe command (thanks for writing that btw!), but it only works after ivreg(2)... If I get your previous reply correctly, one can do the fixed-effects estimation by hand and then apply the weakivtest. Could you elaborate on that? What would that look like?

[Mark Schaffer]

Hi Ellen. It's pretty easy. Just apply the "within transformation" to all your variables (i.e. de-mean by panel, center by panel, all means the same thing). You can use -xtdata- for this (or Ben Jann's -center- if you have an older version of Stata). You'll know you did it correctly if you get the same coefficients for your model using xtivreg2,fe on untransformed data and IV using ivreg2 or ivregress on transformed data (the SEs will be different but that doesn't matter if you are clustering). Then use weakiv + ivreg2 or ivregress on the transformed data.

[Ellen Sterk]

Mark Schaffer I see, that makes sense! Thanks a lot!