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  • 2SLS with an instrumented variable as an instrument

    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


  • #2
    I wouldn't use a predicted value as an instrument. Since you're including all the exogenous variables as instruments anyway, the estimation for the other endogenous variable will take into account anything (including any linear combination which is what a predicted value is) linear in the exogenous variables. That is, it shouldn't help.
    If you're just instrumenting variables to estimate one main equation, then there is no cross equation covariance for reg3 to take advantage of. So ivregress or ivreg2 are fine.

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