Dear Statalisters,

I am interested in measuring the performance of imitative products. These products might be produced by improving the existing product in the focal product category (i), transferring product technology from a different category (ii) or can be produced by combining two or more products(ii). And I am interested in determining which way is better over the other and I have an IV for second and third cases first one being the baseline

The first problem is only high-quality products are imitated and therefore there might a selection bias. In the first draft of the paper, I was only using the sample of imitative products and controlling for the quality of original products. Initially, I was running the following regression

Code:
xtivreg performance (transfer combination= z1 z2) quality_of_original other_controls i.time, fe vce(cluster firm)

However, reviewers suggested that I should include all the observations and make Hackman two-stage to account for selection bias. My first question is Heckman is necessary if I am only interested in imitated products?

Assuming that Heckman is correct can I run the following regression? :
Code:
probit imitated z3 
predict imitated_hat, p
xtivreg  performance quality_of_original other_controls i.time (imitated##transfer imitated##combination= imitated_hat##z1  imitated_hat##z2 ),  fe vce(cluster firm)
Any help will be greatly appreciated,

Best regards,
Erdem