# How to justify an instrumental variable?

I am hoping for some tips on what I could do for a term paper in applied econometrics. We are running a 2sls where I want to use a firm's location as an IV. How can I go about justifying it is a valid instrument? More specifically, how would you suggest I can argue the exclusion restriction holds for my instrument. I am thinking of a verbal argument of about a page tops, since I have limited space left. Any suggestions would be greatly appreciated. Thank you.

PS: My endogenous variable is a dummy for whether the business owner is a member of a political party, and my outcome variable is a leverage ra

• Please provide clarifications as regards your proposed instrument. How many different values can it take? What each values signifies? Is it a basic correspondence (say "location A =1, location B = 2")? Are locations ordered in some sense? (Say, "location A = industry center", location B "country capital" or something) or they are just geographical? Please include any clarifications in your answer. Feb 29, 2016 at 19:24
• The instrument is coded as 1 if the firm is in the capital city, and 0 otherwise. There is no order; the location instrument just controls for which city the firm is set up in. Feb 29, 2016 at 21:01
• Thank you. One more important issue: why do you think that your regressor is endogenous? What lives inside the error term with which one can argue correlation with the regressor, so you try to find an IV? Feb 29, 2016 at 22:36
• Justifying an instrumental variable can be backed up partially using some statistical tests but intuition is very important. I would simply discuss the conditions required for a valid instrument and how they do not seem to be violated. Seems to be a common approach. Mar 1, 2016 at 0:07
• Well my regressor is a dummy for whether the subject is a member of a political party. We say it is endogenous because there are things we cannot account for which influence this covariate. For example, the subject could have worked for the government in the past. I think this would be correlated with party membership. However, we do not have data for this kind of info. Therefore we say it is endogenous. I think it is also safe to assume endogeneity as there could be many things in the error term which correlate with the covariate of interest, but may not even come to mind. Mar 1, 2016 at 10:23

The general approach

"there are many things that are in the error term which may correlate with the covariate of interest but don't even come to mind",

is a total dead-end, because exactly the same thing could be argued for any instrument you might choose. It would be my suggestion to not use such vague and general arguments in your paper.

On the other hand, the endogeneity issue is not about whether the suspect regressor is correlated with some other variable. Each and everyone variable in the world can be said to be corrleated with at least one other variable. The issue is whether this other variable is also correlated with the dependent variable.

To consider the example offered in a comment by the OP, "past work for the government" may be correlated with "party membership" indeed. But is "past work for the government" correlated with the OP's dependent variable? Namely, does it really live inside the error term of the regression?

Selection of instruments is one of the few instances in econometric work where the verbal argument dominates. As the answer by @ColeTrumbo excellently put it,

"To motivate a good IV, you need a good story."

To motivate a good IV in a paper, you need a good story. For example: schools build in Indonesia as an instrument for education outcomes, quarter of birth as an instrument for income as a result of compulsory education, in their respective papers.

The IV has to be correlated to the characteristic you're trying to fix and uncorrelated to any of the other observable characteristics.

That way, the IV is only affecting the Y variable through the characteristic you're instrumenting. As far as statistically strong, you can look at examples from a few papers and see what kind of statistical scrutiny they used.