# Interpreting significance of Cragg-Donald F-Statistic for weak instruments

I have a first-stage F value of 9 for a model with 1 instrument and 1 endogenous variables, the mechanical rule of thumb of 10 would say my instruments are weak. However, I am reading the 2005 paper by Stock and Yogo, who have tabulated the critical values and I don't understand the interpretation of the following in the note to the table:

the desired maximal size (r) of a 5% Wald test of β = β0

Also, would Anderson CC , Cragg-Donald, or KP tests for under identification be of any use in a just identified model with only one endogenous variable so there is no matrix rank to test as such.

Also could anybody suggest any other tests?

With one endogenous variable the Cragg-Donald test should give you a similar result as Stock and Yogo. This test differs from the previous one if there are several endogenous variables for which you will have multiple first stages. Anderson's canonical correlation test works similar to Cragg-Donald with the difference that Anderson's CC is a likelihood ratio test whilst Cragg-Donald is a Wald statistic but both tests are applicable with one endogenous variable and one instrument. However, in the end Stock Yogo, Cragg-Donald and Anderson all rely on an iid assumption on the errors. If you used heteroscedasticity robust standard errors for instance these tests will not work but the Kleinbergen-Paap test is robust against violations of the iid assumption. It also works with one endogenous variable and one instrument as long as the model is identified. There is a nice discussion on these tests in these notes by Baum (2007). Other robust tests for weak instruments are also offered in Stata's rivtest package.
If you end up with a weak instrument you can use the conditional likelihood ratio test by Moreira (2003) in order to perform weak instrument robust inference. A paper by Andrews et al. (2008) shows that the CLR test is approximately optimal. Weak robust instruments regressions are available for instance in Stata's condivreg package.