Instrumental Variables

Take advantage of some fluke i nthe world, needs to have a direct effect on the outcome.

Example of instrumental variables in the context of research:

#researchlandscape

1. Lottery Wins: In studies examining the impact of income on various outcomes such as health, happiness, or children’s education, one of the issues is that income is not randomly assigned. However, lottery wins provide a source of random income shocks which can be used as an instrumental variable.

2. Weather Patterns: In agricultural research studies, weather patterns can be used as an instrumental variable. For example, rainfall levels could influence crop yields but are not influenced by crop yields.

3. Policy Changes: If a policy change varies across geographical areas or time periods but is unrelated to other factors influencing the outcome variable, it can serve as an instrumental variable. For instance, changes in state minimum drinking age laws in the U.S have been used to estimate the effect of alcohol consumption on mortality rates.

4. Distance to Treatment Centers: In health research, distance to treatment facilities has been used as an instrumental variable to study the effect of treatments on health outcomes. The assumption here is that individuals living closer to such facilities are more likely to receive treatment.

5. Instruments from Natural Experiments: An example would be using changes in traffic laws or infrastructure as an instrument for studying the impact on road safety or pollution levels.

6. Birth Weight: In studies investigating the impact of smoking during pregnancy on child outcomes, researchers have used birth weight as an instrumental variable because it’s affected by maternal smoking but doesn’t affect maternal smoking itself.

7. Genetic Variations: In medical research, genetic variations (also known as Mendelian randomization) can serve as instrumental variables because they are randomly assigned at conception and therefore not confounded by environmental factors.

8. Compulsory Schooling Laws: These laws have been used as instrumental variables in researching the effects of education on various outcomes since they force some people to receive more education than they otherwise would have.

9. Military Draft Lottery Numbers: Researchers have used draft lottery numbers from Vietnam War era in the U.S. as an instrumental variable to study the effect of military service on various outcomes, such as earnings or health.

10. Teacher Assignment: In education research, the random assignment of students to teachers can be used as an instrumental variable to study the impact of teacher quality on student achievement.

#researchlandscape

Always takers, never takers… put these categories in a table with any additional ones that are useful.

Category	Definition	Example
Always Takers	These are individuals who would always take the treatment, regardless of whether they are assigned to the treatment or control group.	A student who would always attend college, whether or not they receive a scholarship.
Never Takers	These are individuals who would never take the treatment, even if they are assigned to the treatment group.	A patient who would never take a certain medication, even if it’s prescribed to them.
Compliers	These are individuals who only take the treatment if they are assigned to the treatment group and don’t take it if they’re in the control group. They follow their assignment.	A person who only attends a job training program if they’re accepted into it and doesn’t seek out similar training elsewhere if they’re not accepted.
Defiers	These are individuals who do the opposite of their assignment. They take the treatment if they’re in the control group and don’t take it if they’re in the treatment group.	A student who only studies extra hours when not instructed to do so, but refrains from studying when told to study extra hours.

The validity of an instrumental variable often depends on two key assumptions:

1. The instrument is relevant i.e., it is correlated with the endogenous explanatory variable.

2. The instrument is exogenous i.e., it is not correlated with the error term in the explanatory equation (also known as “exclusion restriction”).

Violation of these assumptions can lead to biased and inconsistent estimates in research studies using instrumental variables.