1. IV Estimation Instrumental Variables

6. Implication Estimate model by OLS and by IV, and compare estimates If But test INDIRECTLY using Wu-Hausman test.

7. THE INSTRUMENTAL VARIABLES (IV) ESTIMATOR Suppose that one or more of the regressors in X is not independent of the equation error term, even in the limit as the sample size goes to infinity. That is, X is correlated with u, the equation disturbance. However, suppose we have another variable, Z, (an instrument for X) that has the properties: (1)Z and X are correlated (2 ) Z and u are uncorrelated Now define the IV estimator as:

9. Generalised IV estimator (GIVE) A more general form of the IV estimator where we have more instrumental variables than “endogenous” X variables GIVE is potentially more efficient than simple IV, if instruments are well-chosen Test whether instruments are ‘valid’ using Sargan’s test

10. When might a regressor variable be correlated with the error term? Correlated shocks across linked equations Simultaneous equations Errors in variables Model has a lagged dependent variable and a serially correlated error term See Appendix to my notes

11. Simultaneity Consider the simultaneous system Reduced forms