Endogenous Regressors and Instrumental Variables

This is a more serious departure from the assumptions of the classical linear model than was the case for the Generalized Regression model, which maintained E("jX) = 0 but permitted nonconstant variances and/or nonzero correlations across error terms. Unlike the Generalized Regression model, the classical least squares estimator will be inconsistent for if the errors are correlated with the regressors. Writing ̂LS = (X 0X) X 0y = + (X 0X) X 0";