Hello, I have come to a roadblock in my research. I am trying to figure out what type of model to use and how to implement it. I have a binary Y (0 or 1), a variety of exogenous variables, and an ordinal endogenous variable. The endogenous ordinal variable has values from 1 to 4 and is based on a question asking people how much they agree with something from 1 to 4.

I am trying to mitigate endogeneity but don’t know which model to use or how to change the endogenous ordinal variable to fit a model. I have two valid instrumental variables for it.

I tried using Lewbel’s special regression but do not know how to change the ordinal variable to be accurate.

Originally I used a probit and left the ordinal variable as continuous but this is not accurate. Could I simply add each level of the endogenous variable as a dummy variable (one for 1, another for 2, a third for 3, and finally for 4)?

I would appreciate any help or guidance. Thank you.