In Roodman's 2009 paper, he notes that a 'very low instrument count also weakens the Hansen test'. Is there any guidance for how low this is relative to the number of regressors used, for example, if I had 10 instruments and 6 regressors would there be the potential of this test being weakened?

Also, I am unsure how to interpret the difference in Hansen test on Stata. Under the null of joint instrument validity, do I require the 'Hansen test excluding group' result to be over 0.05 (5% significance level) or the 'difference (null h=exogenous)' result to be over 0.05?