I have a logistic regression model which implicitly estimates the probability that a business will default in each of 8 future quarters conditional upon survival to that quarter. In other words, I have 8 sets of coefficients to give me 8 different conditional probabilities based on the covariates at t=0. (cumulative for each borrower calculated as 1-(1-Pr_conditional_t1)*(1-Pr_conditional_t2)*...(1-Pr_conditional_t8))
Now, I am building a different yet related model, and I want to explicitly estimate the future covariates for the borrowers (same covariates as the first model) as opposed to using the same covariates at t=0 for all 8 quarters. I want to use macroeconomic factors to model these future covariates. I know that Logistic Regression is more intended for use with covariates that have been observed or empirically estimated, but I was wondering if anyone had any suggestions on ways to go about modeling this without creating biases in future observations based on the convex nature of the logit curve and different risk categories, etc... I was thinking OLS would suffice but don't know if I am thinking too simply.
I have re-fit my coefficients explicitly where the defaults (0,1) at t=k are regressed on the covariates at t=k for all businesses who have survived t>=k quarters, as opposed to defaults at t=k being regressed on covariates at t=0 in the original model (same number of observatsions, different time alignment).
Thanks much for any help!