heckman two-step and maximum likelihood method

[LEE CHAN]

I am implementing Heckman model with 2 methods: Two-step and ML. and I am very confused about which model is more suitable. I read a study that says if Mill ratio is at two-step significant, the Two-step model is chosen. Is that really true, i'm very confuse about this?

[George Ford]

ML is more efficient, Heckit more robust. There are some strong distribution assumptions with ML (joint normality) and can be sensitive to specification. ML won't always converge. The significance of the Mills Ratio tells you there is meaningful selection bias, but both account for that. OLS might be appropriate if IMR insignificant. I'd report both, unless they are close to the same result.