Hello,

I am studying the effect of Foreign Direct Investment (FDI) presence in an industry on the productivity of domestic firms, and want to estimate the following regression: productivity = b0 + b1*foreign_buyers_share + b2*industry_foreign_share + b*X, where both foreign buyers share (each firm's share of foreign buyers) and industry_foreign_share (share of foreign firms in the industry) are endogenous variables. Some prior literature uses industry_foreign_share as an instrument for foreign_buyers_share (because in industries with higher foreign participation firms are expected to have more foreign buyers as well). However, more recently it has been argued that industry_foreign_share affects the productivity of domestic firms directly as well, and not only through its effect on foreign_buyers_share. I have two other variables, z1 and z2, that I believe are good instruments for industry_foreign_share.

My first, more theoretical question is: can I use the predicted values of industry_foreign_share as an instrument for foreign_buyers_share in a 2SLS regression? Is there any benefit to using 3SLS instead? From the way I understood the threads I read already, 3SLS may be more efficient, but if the Hausman test shows significant differences between 2SLS and 3SLS, one should go for 2SLS?

My second question is how I should go about doing this in Stata. Should I use reg3, use ivregress or ivreg2 twice, or follow the instructions from this Stata article about instruments for recursive systems, but then perform this twice as well: https://www.stata.com/support/faqs/s...rsive-systems/?

Any help or suggestions are appreciated.

Regards,
Dea