# Intuitive understanding of instrumental variables for natural experiments

I am wondering if my understanding of Instrumental vairables to exploit natural experiments is correct, or if I am misunderstanding something.

Is the logic as follows: by using an instrument, you are now comparing the outcomes of those who recieved higher levels of treatment because they had higher exposure to the instrument to those who received lower levels of treatment because they had lower exposure to the instrument, but these latter units would have recieved higher treatment had they been more exposed to the instrument?

so should I think intuitively as if it is to some degree a random experiment on a subset of units?

• Perhaps, but one of the main ways IV are used is for de-confounding. Suppose $A\to X\to Y,$ but also $X\leftarrow Z\to Y.$ Then you may be able to use $A$ to de-confound $Z.$ – Adrian Keister Dec 10 '20 at 20:12
• Sure, and i meant this as one of the uses of IV for natural experiments for precisely this reason. But I am more wondering- beyond the causal paths and technical details, what intuitively are the comparisons we are making in the data when running an IV? – Steve Dec 13 '20 at 21:12

I interpret the background to be, you are interested in evaluating the effect of some (endogenous) "treatment" on some "outcome," and we assume that there is a valid "instrumental variable" for "treatment."

so should I think intuitively as if it is to some degree a random experiment on a subset of units?

Basically, yes. A valid instrument should be very much like a random experiment as follows:

• With a valid experiment, treatment is randomly assigned, therefore treatment is independent of potential outcomes

• With a valid instrument, the instrument is randomly assigned, therefore the instrument is independent of potential outcomes (and potential treatments).

Generally when you use instrumental variables, you are no longer estimating the effect of "treatment" on the "outcome." Instead, you are estimating the effect of "treatment" on the "outcome" for those units whose "treatment" can be changed by the "instrument."

The italicized part is the subset.

Is the logic as follows: by using an instrument, you are now comparing the outcomes of those who recieved higher levels of treatment because they had higher exposure to the instrument to those who received lower levels of treatment because they had lower exposure to the instrument, but these latter units would have recieved higher treatment had they been more exposed to the instrument?

Regarding the logic, for simplicity assume a binary instrument. You are comparing the outcomes of those exposed to the instrument, to the outcomes of those not exposed to the instrument. You then divide this comparison by the difference in the treatments of those exposed to the instrument, to the treatments of those not exposed to the instrument.

This ratio estimates the effect of "treatment" on the "outcome" for those units whose "treatment" can be changed by the "instrument."

• Thank you for this answer. Just a quick follow up on the logic part- this still is exactly the logic with a continuous instrument, correct? it is just that thinking of it in terms of a binary one makes it clearer/more intuitive? – Steve Mar 11 at 21:34
• With a continuous instrument, you are still estimating the effect of "treatment" on the "outcome" for those units whose "treatment" can be changed by the "instrument." However, the interpretation is no longer as simple/intuitive as in the binary instrument case. – Peter Mar 12 at 20:11