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I am using an instrument variable approach where I have access to several valid (but many times weak instruments) to instrument for a singe endogenous variable. My question is how to think about which instruments to use, is there any good links to papers or step-by-step procedures on how to choose between instruments? I guess there will be a trade off between using multiple instrument (where their linear combination gives a good IV) and the fact that if the instruments are weak using more instrument will increase a potential bias. More specifically my questions are: 1. May I be better off just using one of the instrument or is it always better to use more (given that they are at least somewhat relevant and exogenous)? 2. What test in Stata are most useful to discriminate between the instruments?

Thank you for your help!

Best, C

charlie
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  • there are no recipes for IV selection, unfortunately. the whole thing is a voodoo science to me – Aksakal Jan 06 '22 at 15:23

1 Answers1

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  1. There is no general result that says that it is always better to use more than one instrument. If you have more instruments than endogenous regressors, you can test the exogeneity of the instruments using the so-called overidentifying restrictions test. However, the validity of that test ignores the fact that each instrumental variable may capture a different so-called local average treatment effect (please search and read about this if you have not heard about the term). If each instrument is valid, then each instrument will individually pick up a local average treatment effect that is specific to some group of compliers, which is often a subsample of your total sample.

  2. With ivregress in Stata one can do an overidentifying restrictions test. The best way to generate important tests, however, is to base your instruments on some theory/story, and derive testable implications concerning your instruments from the theory/story.

Elias
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