Hi Dear Souaré,

I don't know it will be well-adjusted, probably not.

Maybe could be better if you try to use instrumental variables.

Search about "probit/logit with instrumental variable", maybe it could help you. If you use Stata Software, "ivprobit".

Kind regards.

Luan Bernardelli

Although I am not certain with the details you provided, it sounds like what you are proposing resembles two-stage least squares and applications such as what I think you are proposing is sometimes referred to as forbidden regression.

Look at this link for more details:

https://stats.stackexchange.com/questions/94063/probit-two-stage-least-squares-2sls

I hope this helps. If I am on the wrong track, it might help to provide a bit more detail so other answers can offer more definitive assistance.

Rob

Dear Ismaila, I hope it is not too late to help. I will answer to your question with an affirmative answer, but the model you get will be just a bad approximation of the one you need. There are 2 reasons for this: (1) if the explanatory variables have lags and include lags of the probability, the "predicted probability" cannot be the simple propagation of your logit model because of its nonlinearity (the expected value should be obtained by simulating the model from the estimated error's density (monte carlo, say) and saving the mean of the simulated values), and (2) you must constraint the value of the probability to be inside the interval (0,1) for any circunstance. Therefore, I would recommend you to keep the logit regression and just compute the marginal effects (which are not equal to the logit regression's estimated coefficients): they are impacts on the probability you want! To do so, please read the corresponding chapter in Greene's Econometric Analysis (textbook).