Instrumental Variable
A third variable used in regression analysis to estimate causal relationships when the primary explanatory variable is endogenous.
What is Instrumental Variable?
An instrumental variable (IV) is a tool used to isolate the exogenous variation in an endogenous predictor. A valid instrument must satisfy two conditions: relevance (it must be strongly correlated with the endogenous explanatory variable) and the exclusion restriction (it must affect the dependent variable only through its effect on the endogenous variable, meaning it is uncorrelated with the error term).
Why Instrumental Variable Matters
IV methods allow researchers to estimate consistent and unbiased causal effects even when randomized control trials are impossible and observational data suffers from omitted variable bias or reverse causality.
Example
To estimate the effect of education on earnings (where education is endogenous due to unobserved ability), a researcher might use 'distance to the nearest college' as an instrumental variable, assuming it affects education levels but does not directly affect earnings except through education.
Common Mistakes
- Using weak instruments that are only weakly correlated with the endogenous variable, which can exacerbate bias and lead to huge standard errors.
- Violating the exclusion restriction by choosing an instrument that directly impacts the outcome or is correlated with unobserved omitted variables.