This is probably a very basic questions, but I cannot find a straight forward answer anywhere. I have a series of data were a selection method (like Heckman two-step) is necessary. Is it a basic assumption of Heckman two-step that the selection stage of the model include at least one variable not in the second stage? Similarly, is there any assumptions regarding any variables in the second step NOT being included in the first step?
Info on the specific data: I'm looking at data on the % of bills introduced by state legislators that are reported by a committee, or that become law (two different models). A selection method is needed to address the 0's in the data caused by members who did not introduce any bills at all (in predicting the % reported by a committee) or that did not have any bills reported by a committee (for the % that become law) as these actions have to precede the actions we are trying to predict.