Hi,
I have a two step-model (see below) in which all the people answer the question in the first part and only a limited number of people answer in the second step (i.e. based on their response in the first step).

Step 1: Did you demand credit (1) or not(0)?
Step 2: Were you able to obtain credit (1) or not (0)? (Only people who demanded credit (1) answer this)

One way is to run two different probit models (the second model would be run only for people who answered 1 in the first step). But one can argue that the second probit model might suffer from issues pertaining to sample selection bias and autcorrelation. Can someone recommend what type of model would be the most appropriate in this case (other than using heckman process because finding an exclusion variable in this case is near to impossible)? Thanks.