Generalized IV

Summary

Setup

• The linear regression model with random sampling,

\[y_i=β_1+β_2x_{i,2}+β_3x_{i,3}+…+β_kx_{i,k}+ε_i, i=1,…,n\]

• For any endogenous variable \(x_j\) we at least one an instrument \(z_j\) but we may have more than one.
• If \(x_j\) is exogenous, it will be an instrument for itself, \(z_j=x_j\) .
• The complete set of instruments is \(z_2,z_3,…,z_l\) where \(l≥k\) .

The generalized IV-estimator (GIVE) and its properties

• The generalized IV-estimator is generally biased.
• The generalized IV-estimator is consistent under mild conditions.
• It is possible to find consistent estimates of the standard errors of the GIVE.
• The generalized IV-estimator is generally more efficient than the IV-estimator.