In this chapter we first discuss possibilities that the orthogonality condition E(εt|Xt) = 0 may fail, which will generally render inconsistent the OLS estimator for the true model parameter. We then introduce a consistent Two-Stage Least Squares (2SLS) estimator, investigating its statistical properties and providing intuitions for the nature of the 2SLS estimator. Hypothesis tests are constructed. We consider various test procedures corresponding to the cases for which the regression disturbance is an MDS with conditional homoskedasticity, an MDS with conditional heteroskedasticity, and a non-MDS process, respectively. The latter case will require consistent estimation of a long-run variance-covariance matrix. It is important to emphasize that the t-test and F-test statistics obtained from the second stage regression estimation cannot be used even for large samples. Finally, we conclude this chapter by presenting a summary of econometric theory for linear regression models developed in Chapters 2 to 7.
