If the mills ratio of a Heckman selection model (with/without exclusion restriction) is not significant, shall I prefer to estimate my model with OLS instead?
Or is it better to use the estimates from the heckman model although there seems to be no sample selection?
Solved – Heckman sample selection vs. OLS
heckmanleast squaresmodel selectionregressiontwo-step-estimation
Best Answer
In this case you would have no selection problem, so you could use OLS on the non-censored observations. This can be tested by what you did. So you are correct, see e.g. also wikipedia
"so testing the null that the coefficient on $\lambda$ is zero is equivalent to testing for sample selectivity."