Instrumental Variables in Plain Language

A method that uses an outside factor to isolate the part of a variation that behaves like an experiment, illustrated by the Vietnam draft lottery.

Sometimes we want to know the effect of something that people choose, such as years of schooling or military service, but the choice is tangled up with other factors. An instrumental variable is a clever way to cut through that tangle.

The idea

An instrument is a factor that pushes people toward the choice we care about, but has no other route to affect the outcome. It lets us isolate a slice of the choice that is as good as random.

An instrument must satisfy two conditions:

Relevance: it must actually affect the choice we are studying.
Exclusion restriction: it must affect the outcome only through that choice, not in any other way.

The draft lottery

During the Vietnam War, the United States used a lottery based on birth dates to decide which young men would be called up for military service. Joshua Angrist used this lottery to study how military service affected later earnings.

Comparing veterans with non-veterans directly would be misleading, because the men who volunteered may have differed from those who did not. But the lottery number was random. Men with low numbers were much more likely to serve. The lottery affected earnings only by changing the chance of serving. Angrist found that, years later, white veterans earned noticeably less than they would have without serving, reflecting lost years of civilian work experience.

Distance to college

Some researchers have used how far people grew up from a college as an instrument for how much education they got. Living closer makes college easier to attend. If distance affects earnings only by changing education, it can reveal the effect of education on earnings. Critics note that families near colleges may differ in other ways, which would break the exclusion restriction.

Why it is tricky

The relevance condition can be checked with data. The exclusion restriction usually cannot be proven; it must be argued. Much debate over instrumental variable studies is about whether the instrument truly affects the outcome only through the intended channel. Weak instruments, which barely affect the choice, can also produce unreliable results.

Thinking any correlated factor makes a good instrument

A good instrument is rare. It must strongly affect the choice while having no other link to the outcome. Many proposed instruments fail the second test, because they are connected to the outcome in ways the researcher did not consider.

Key takeaways

An instrumental variable isolates a part of a choice that behaves as if random.
A valid instrument must affect the choice and influence the outcome only through that choice.
Angrist used the Vietnam draft lottery to study the effect of military service on earnings.
The exclusion restriction cannot usually be proven, so instruments are often debated.