Hi,
I have 2 potentially endogenous regressors (x1, x2) whose causal effects on y are of interest to me. x1 and x2 are created using 2 variables - A1,A2, where x1 falls below a given threshold of A2 and x2 falls above. So technically they have the same set of instruments - z1,z2,z3,z4. My question is whether to instrument x1 and x2 separately and identify their causal effects in isolation by running the following:
ivreghdfe y x2 b1 b2 b3 b4 (x1 = z1 z2 z3 z4), first
ivreghdfe y x1 b1 b2 b3 b4 (x2 = z1 z2 z3 z4), first
or should I instrument them together by running:
ivreghdfe y b1 b2 b3 b4 (x1 x2 = z1 z2 z3 z4), first
These 2 sets of regression methods are producing very different results - one significant, the other insignificant, one perfectly identified model, the other either weakly/over/under identified model. Could someone please clarify the reason for such differences and which method is more rational to implement? Also, should I consider interacting A1 with A2 and then instrument it with z1,z2,z3,z4?
Thank you!
I have 2 potentially endogenous regressors (x1, x2) whose causal effects on y are of interest to me. x1 and x2 are created using 2 variables - A1,A2, where x1 falls below a given threshold of A2 and x2 falls above. So technically they have the same set of instruments - z1,z2,z3,z4. My question is whether to instrument x1 and x2 separately and identify their causal effects in isolation by running the following:
ivreghdfe y x2 b1 b2 b3 b4 (x1 = z1 z2 z3 z4), first
ivreghdfe y x1 b1 b2 b3 b4 (x2 = z1 z2 z3 z4), first
or should I instrument them together by running:
ivreghdfe y b1 b2 b3 b4 (x1 x2 = z1 z2 z3 z4), first
These 2 sets of regression methods are producing very different results - one significant, the other insignificant, one perfectly identified model, the other either weakly/over/under identified model. Could someone please clarify the reason for such differences and which method is more rational to implement? Also, should I consider interacting A1 with A2 and then instrument it with z1,z2,z3,z4?
Thank you!
