Glossary

Instrumental Variables

A method for obtaining consistent estimates when an explanatory variable is endogenous. An instrument must be correlated with the endogenous regressor (relevance) but uncorrelated with the error term (exclusion restriction). Two-stage least squares (2SLS) is the most common IV...

Definition

Why It Matters

Endogeneity arising from omitted variables, measurement error, or simultaneity renders OLS estimates inconsistent. Instrumental variables provide a path to consistent estimation when valid instruments are available. However, finding instruments that satisfy both relevance and the exclusion restriction is challenging; weak instruments can produce worse estimates than OLS, and invalid instruments introduce bias of their own. Diagnostic tests for instrument relevance and overidentifying restrictions are therefore essential.

Example

A researcher studying the effect of education on wages in Turkey faces endogeneity because ability influences both education and earnings. Using distance to the nearest university as an instrument for education, the first-stage regression shows a strong positive relationship (F-statistic > 10), and the 2SLS estimate of the return to education is 12%, compared to 8% from OLS, confirming upward omitted-variable bias in the naive estimate.

Related Terms

Software Notes

SPSS: Use Analyze > Regression > 2-Stage Least Squares for basic 2SLS estimation.
R: Use ivreg() from the AER package for 2SLS estimation with diagnostic tests. The ivtest package provides additional specification tests.
Stata: Use ivregress 2sls for two-stage least squares. After estimation, use estat firststage for weak-instrument diagnostics and estat overid for the Sargan-Hansen test of overidentifying restrictions.