Dear Statalists,

I am using -heckman- command to address the self-selection problem. I read from many places that we can use the same elements in both stages of estimation (Z identical to X). However, the constraint of using the same variable is the nonlinearity of inverse Mill's ratio (IMR). My questions are below:

1. How can we measure the nonlinearity of IMR?
2. Can we use VIF to examine the multicollinearity? Then how to estimate VIF for a probit model in the first stage of Heckman?
3. I also spot that some scholars test the normality of first stage probit to verify the nonlinearity, are normality of probit and nonlinearity of IMR the same thing?

Thanks in advance for your help and comments.