I am working to estimate a demand model for solar installations. Dependent variable is a count variable (number of solar installations) with counts 0 to 7. Independent variables includes: cost, rebate (eg. discount given by government) and other demographic and economic variables. Primarily I use a Logit model to estimate the selection model (hurdle part) and a truncated negative binomial regression to estimate the outcome model. Problem: the rebate in the selection model gives a negative coefficient which means decreasing rebate increases installations. However, this should not be the case.

When I run a heteroscedastic probit model with the same variables and use rebate to model the variance, the rebate becomes positively related.

Is it possible in hurdle models to combine heteroscedastic probit model with a truncated negative binomial regression model (have been searching on the internet but no solutions so far).