Outliers/choosing the right model

Hey guys,

I have a lot of problems dealing with outliers/choosing the model.

dependent variable:
- already transformed portfolio variable
- a lot of observation with the value = zero plus a lot of outliers on the upper end as usal with wealth data (want to have the ownership decision =zero in my analysis)
independent variables:
- risk
- wealth in general (also transformed)
-polinominal regression because the linktest failed with linear regression (passed with polinominal regression)
-robust standard errors because of heteroscedasticity
-no multicollinarity

My problem is that the residuals look kinda odd and I'm not sure I handled the data correctly/choose the right model.


What do you guys think? Is there another type of model which could fit my data better? Is it reasonable to censor my data even though the outliers aren't there because of measurement errors?

Thanks in advance