Binary logit regression and ordered binary logit regression

[Jessica Thacker]

Hi,
I am working on an unabalanced panel of firms for time period of 2011-19.
The dependent variable is binary 0 for unhealthy firms and 1 for healthy firms.
The aim is to understand the drivers of unheathy firms and healthy firms using various forms of independent variables using logit model.

I have the following questions:

(1) The broader question that I would like to ask is that if the dependent variable is binary, does an ordered logit matter?
(1a) How different will be running an ordered logit regression from logit regression when the dependent variable is binary? Also, will the interpretation of the beta coefficients change?
(1b) Please provide a good refrence for (1a)

(2) I ran a panel logistic regression using xtlogit, fe command and panel ordered logistic regression using feologit command. I get the same coefficients as well as standard errors. I was wondering why did that happen. I would be grateful if I get any suggestions regarding the same?

[FernandoRios]

Hi Jessica
I think all your questions have the same answer. When the dep variable is binary, logit and ologit will produce the same results (with same interpretation), with the only difference being the constant (flipped sign if i recall correctly).
You can verify that by simple going over the function of ologit, and derive it for the case of binary case. You will find the expression is the same.

For that reason, it makes sense that xtlogit and feologit also produce the same results.
F

[Jessica Thacker]

Dear FernandoRios, I would first like to thank you for helping me out on this.
I would be grateful if you could help me in interpreting the beta coefficients of xtlogit. I have read that if we find the odds ratio in xtlogit, it will be inconsistent. Is it true?