The situation is the following:

I have a dataset with 200 assets. For each one, I have a unique price range that the asset can be priced in. The price range specifies an upper and a lower limit. The expected price (Pexpected) of the asset is the average of the upper and the lower limit of the price range. The dataset also contains the actual price set for each asset (Pactual). The price adjustment (PA) between the expected price and the actual price is calculated as (Pactual-Pexpected)/Pexpected.

I have several independent variables (X) that predict the price adjustment. Hence I could run the following OLS regression:

PA ~ X

However, this would lead to biased results, because of the constrains from the price range. My data shows that out of my 200 assets 153 assets are priced at the upper limit of the price range, indicating that the upper limit of the price range is set too low.

I would like to run a censored regression to calculate the unbiased regression coefficients. Based on these coefficients, I then want to predict the actual price (Pactual) of the asset if they were no pricing constraints through the price range.

I know how to run a censored regression if the dependent variable is censored. Here, however, the dependent variable is calculated based on censored data. How would you approach this problem?

Maybe there is also another approach/method to obtain predictions for the price of the assets if no constraints through the price range would exist. In case you have suggestions, I would also be very thankful.

Any help is welcome as I am really lost with this problem.

Thanks a lot!