Is there a way of infering causation when you have multiple endogenous regressors?

Instrumental Variables (IV) estimation is used when the model has endogenous ’s.

IV can thus be used to address the following important threats to internal validity:

• Omitted variable bias from a variable that is correlated with but is unobserved, so cannot be included in

the regression;

• Simultaneous causality bias (endogenous explanatory variables; causes , causes );

• Errors-in-variables bias ( is measured with error)

Instrumental variables regression can eliminate bias from these three sources.

Terminology: Endogeneity and Exogeneity

An endogenous variable is one that is correlated with

An exogenous variable is one that is uncorrelated with

Historical note: “Endogenous” literally means “determined within the system,” that is, a variable that is jointly

determined with , that is, a variable subject to simultaneous causality. However, this definition is narrow and IV

regression can be used to address omitted variable bias and errors-in-variable bias, not just simultaneous causality

bias.

Instrumental Variables: Intuition

• An instrumental variable, is uncorrelated with the disturbance but is correlated with (e.g., proximity to

college might be correlated with schooling but not with wage residuals)

• With this new variable, the IV estimator should capture only the effects on of shifts in induced by

whereas the OLS estimator captures not only the direct effect of on but also the effect of the included

measurement error and/or endogeneity

• IV is not as efficient as OLS (especially if only weakly correlated with , i.e. when we have so-called “weak

instruments”) and only has large sample properties (consistency)

o IV results in biased coefficients. The bias can be large in the case of weak instruments.