I hope this is not too elementary a post for this forum. However, since I am not sure, I thought I would give it a shot.

I would like to know whether the following reasoning regarding the instrumental variable approach is acceptable. I understand there are case-by-case factors that affect the applicability of instruments that I am discussing below. But I just want to know if the general logic is correct or if I am missing something.

I am studying the effect of a state-level policy on a state-level outcome, y1. The simplest strategy would be to run a regression with the policy variable (p1) as a covariate along with a set of controls (x1-x5):

regress y1 p1 x1 x2 x3 x4 x5

But it is possible that there is reverse causality. Let's say that one of the factors driving the reverse causality is that there are special interests that would benefit from the policy, and states with higher values for the outcome variable have stronger special interests that lobby policymakers to implement it. If campaign contributions (camcon) only have an indirect causal influence on the dependent variable through the policy, then it would satisfy the exclusion restriction for instruments.

ivregress 2sls y1 x1 x2 x3 x4 x5 (p1 = camcon)

However, if there are multiple policies that benefit the special interests, it is likely that the special interests lobby for the other policies as well. If these policies were exogenous, then we would just need to include these other policies in the second-stage regression.

ivregress 2sls y1 p2 x1 x2 x3 x4 x5 (p1 = camcon)

But if the special interests are lobbying for the second policy, the policy would not be exogenous; there is reverse causality, as with the first policy. Thus, we need to treat the second policy as an endogenous variable as well. Therefore, we should try to find all the policies that could influence the outcome variable and treat them as endogenous variables. To do so, we would need as many instruments as there are endogenous variables. Assuming that the policies are the only endogenous variables, the instruments have no direct causal impact on the dependent variable, and the instruments are not correlated with the error in the second-stage regression, we should be able to adequately control for endogeneity in the estimation of the second-stage regression. If there are three endogenous policies and thus three instruments (i.e., camcon z2 z3), we would run the following:

ivregress 2sls y1 x1 x2 x3 x4 x5 (p1 p2 p3 = camcon z2 z3)

Note: Crossposted here:
https://stats.stackexchange.com/ques...iable-approach
https://www.reddit.com/r/econometric...e_iv_approach/