randomized control experiments & adequate treatments

Hello everyone,

I am interested in finding if there are any gender norms differences between immigrants and the native population btw if these norms are indeed transmitted across time and space. I am pretty much a newbie in this topic and my question is: "how would you proceed"? What are possible treatments considering that these randomized experiments can't be too expensive.
I guess one treatment would be if you belong to the immigrant population or not. Right?

Thank you in advance!

I am trying to take a randomized sample of immigrants and natives. I use panel data (btw micro-level survey data) for that. By taking the difference of the means i can find out systematic differences for example for wage etc. and afterwards building a gender gap index for immigrants and natives.
I was just wondering what else I could use for a treatment which would be less expensive to do and with less costs connected. For example parental immigration background? Do you have any idea?