TAILIEUCHUNG - Econometric theory and methods, Russell Davidson - Chapter 8

Chapter 8 Instrumental Variables Estimation Introduction ˆ In Section , the ordinary least squares estimator β was shown to be consistent under condition (), according to which the expectation of the error term ut associated with observation t is zero conditional on the regressors Xt for that same observation. | Chapter 8 Instrumental Variables Estimation Introduction In Section the ordinary least squares estimator was shown to be consistent under condition according to which the expectation of the error term ut associated with observation t is zero conditional on the regressors Xt for that same observation. As we saw in Section this condition can also be expressed either by saying that the regressors Xt are predetermined or by saying that the error terms ut are innovations. When condition does not hold the consistency proof of Section is not applicable and the OLS estimator will in general be biased and inconsistent. It is not always reasonable to assume that the error terms are innovations. In fact as we will see in the next section there are commonly encountered situations in which the error terms are necessarily correlated with some of the regressors for the same observation. Even in these circumstances however it is usually possible although not always easy to define an information set Qt for each observation such that E u Qt 0. Any regressor of which the value in period t is correlated with ut cannot belong to Qt. In Section method of moments MM estimators were discussed for both linear and nonlinear regression models. Such estimators are defined by the moment conditions in terms of a matrix W of variables with one row for each observation. They were shown to be consistent provided that the tth row Wt of W belongs to Qt and provided that an asymptotic identification condition is satisfied. In econometrics these MM estimators are usually called instrumental variables estimators or IV estimators. Instrumental variables estimation is introduced in Section and a number of important results are discussed. Then finite-sample properties are discussed in Section hypothesis testing in Section and overidentifying restrictions in Section . Next Section introduces a procedure for testing whether it is actually necessary

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