I want to estimate the effect of socio-economic status on private tuition expenditure (cross section data with cluster) in India using hurdle model. Having gone through a number of literature, I understand that it is a two part model (probit + Ols (lognormal with log (y)) or hurdle model (probit + truncated regression (on y not on log y)). In both models , the equations are not combined and can be estimated separately. However, in the case of a lognormal model, estimating E(y/x, y>0) is not an issue but E(y/x). I want to estimate E(y/x) too.

When I run lognormal regression with district fixed effects, the magnitude (even sign) of the coefficient of few covariates diffres (gets reversed) as compared to the model without fixed effects. To the best of my knowledge , we don't have a command for estimation of truncated normal regression with fixed effects in Stata 14 or 16. so, I can't do such a comparison in this case.

Should I trade off district unobserved heterogeneity in favour of truncated normal regression for estimating E(y/x) ? What if the effects of the unobserved heterogeneity is severe as in the case of lognormal regression?