Weak Instrument test in GMM (time series estimation)

[wolly77]

Dear guys,

I have only a simple question. I would like to say if the Cragg-Donald F Stat reported in the Weak instrument tests" for GMM estimations (with time series data) is correct. In this case I suppose that I have to check the column "Stock-Yogo critical values (size)" for the correct critical values (the first column "Stock-Yogo TSLS critical values (relative bias)" is valid only for the TSLS estiamtions).
This is because in the manual I have read that "Although the Cragg-Donald statistic is only valid for TSLS and other K-class estimators, EViews also reports for equations estimated by GMM for comparative purposes". So, I suppose that Cragg-Donald statistic is not robust for GMM estimations. Thank you in advance.

[cel]

I don't quite know what youre estimating. But I was chewing these issues a while ago when i was estimating some New Keynesian Phillips curve,

pi = f(pi(-1), pi(+1), mc)

in non-linear structural form. I deduced the following about the Cragg-Donald F-statistic, and its comparison to the Stock-Yogo critical values:

a. It is only applicable in the linear (reduced-form) case; by contrast, i estimated the non-linear structural form.

b. However, even if you did estimate the RF case, inference would still not be viable since SY size critical values aren’t available when there is 3 or more endogenous variables (as there was in my case).

c. Finally, the CD-SY framework isn't robust to the presence of heteroskedastic and/or serially correlated errors (see the discussion in Baum et al. 2007).

Hope this is of some help.

[wolly77]

Thank you Cel. So, if I use HAC corrections for heteroskedasticity and serial correlation I cannot use anyway Stock-Yogo critical values tests.

[cel]

Again, I don’t really know your application. So I don't want to lead you astray.

But I think they're really two different things. Robust standard errors are per se a good way of making sure your inference is correct in the (potential) presence of badly behaved residuals.

The SY framework is about the validity of instrument in a GMM setting. As I said in my message their application is pretty limited. One aspect of that limitation is the presence of problematic residuals. But even if these are clean, there are still other limitations of the validity of the SY framework.

The latest tests on inference in the presence of weak instruments (and of course, one almost always has weak instruments) is the tests By Kleinberg and Mavroeidis. I don’t think they've been "added in" to eviews yet, but you can probably implement them under other software.

Hope that helps.