Thanks, Prof. Cottrell.
Professors, I have one additional question.
Although the coefficient estimates of HIP match those of Stata IV Probit exactly, I have found that the endogeneity test (Wald) result is a little bit different. For example, the HIP give me Wald (t = 4.06864, p = 0.0437), but the Stata gives me Wald (t = 3.68, p = 0.0551). My sample size N = 2204. Cragg-Donald shows 107.096 and both AR and Wald tests reject the null of weak instruments.
As shown, this is a delicate situation. My question is that should I reject or not to reject the null of exogeneity in this case? and What might attribute to the difference in the test? Thanks.