Instrumental Variable

What is an Instrumental Variable?

An instrumental variable is an outside variable that is correlated with and predicts the treatment variable (independent) but not with the dependent variable except through its correlation to the independent variable.

When is it Useful?

Instrumental variables are used to identify the causal link between the independent and dependent variables by accounting for unobserved variables that may impact the independent and dependent variables. They are used in observational studies where there is a problem of endogeneity.

Example

Let’s say that a study wants to measure the effects of smoking during pregnancy on the birthweight of the baby. In this case, the independent variable would be smoking during pregnancy and the dependent variable would be birthweight. While smoking during pregnancy may be correlated with low birthweight, it is not clear if it causes it or if there are other factors that play a role in this outcome, like genetic factors.

In this case, an outside variable (instrumental variable) that has an effect on smoking during pregnancy but no effect on birthweight is needed. In this example, tax on cigarettes can be used as the instrumental variable because cigarette taxes only impact the behavior of smoking during pregnancy and can only impact the birthweight through that behavior. The image below shows this example.