Hi everyone! I have a question regarding three-way interaction when my regressors are endogenous.
Let's assume I have x1, x2 and x3 and I assume that, in line with the literature on topic, x2 and x3 are endogenous. Also, let's assume I have convincing instruments for them - z2 for x2 and z3 for x3.
What is the best way to run a model where I would try to estimate the effect of X1*X2 interaction contingent on X3? More specifically, do I construct by hand predicted values for x2 and x3 in the first stage of 2SLS and then include them in the X1*X2*X3 interaction model or is this done otherwise? Is there an advantage to using control function approach in such a setting?
Finally, would a sub-sampling approach work in this case, where I would split the sample based on some value of X3 and then test for differences in coefficient on the (instrumented) X1*X2 interaction term or estimate SUR and do the same
Thank you!
Let's assume I have x1, x2 and x3 and I assume that, in line with the literature on topic, x2 and x3 are endogenous. Also, let's assume I have convincing instruments for them - z2 for x2 and z3 for x3.
What is the best way to run a model where I would try to estimate the effect of X1*X2 interaction contingent on X3? More specifically, do I construct by hand predicted values for x2 and x3 in the first stage of 2SLS and then include them in the X1*X2*X3 interaction model or is this done otherwise? Is there an advantage to using control function approach in such a setting?
Finally, would a sub-sampling approach work in this case, where I would split the sample based on some value of X3 and then test for differences in coefficient on the (instrumented) X1*X2 interaction term or estimate SUR and do the same
Thank you!
