On Tue, 24 Mar 2009, Ignacio Diaz-Emparanza wrote: Hmm, yes, that is a little obscure. It relates to the work by Sock and Yogo on testing for weak instruments in IV regression. See for instance http://ksghome.harvard.edu/~JStock/pdf/rfa_6.pdf S&Y argue that in case of weak instruments there can be substantial size distortion in tests based on the covariance matrix (more so for TSLS than for LIML). And they produced Monte Carlo critical values for the relevant test statistic (which is either the first-stage F-stat or its matrix counterpart). Their critical values work like this: you choose a maximum size that you're willing to tolerate, for hypothesis tests that are nominally at the 5 percent level, then read off from the S&Y values how big the "weak instruments" test statistic must be to give confidence that your condition is satisfied. Here's an example of the full output in the TSLS case (the LIML output is in the same format; see the --liml option for the tsls command). <quote src="gretl"> Weak instrument test - First-stage F-statistic (7, 24) = 4.36539 Critical values for TSLS bias relative to OLS: bias 5% 10% 20% 30% value 19.86 11.29 6.73 5.07 Relative bias may exceed 30% Critical values for desired TSLS maximal size, when running tests at a nominal 5% significance level: size 10% 15% 20% 25% value 31.50 17.38 12.48 9.93 Maximal size may exceed 25% </quote> Allin.