Asymptotic Estimation Theory

An estimator is said to be asymptotically efficient in the consistent and asymptotically normal (CAN) class if for any other CAN estimator, the difference of the asymptotic variance matrices is positive semidefinite. Consistency of the method of moments generally follows from the conditions for the law of large numbers being satisfied and an application of Slutsky's theorem. The key idea of instrumental variables is that an orthogonality exists between the instruments and the disturbance that can be exploited to identify the linear relationship. In least squares the regressors play the role of instruments, being the efficient choice when orthogonality holds. The method of maximum likelihood (ML) provides a universal estimation technique that in principle can be applied to any data distribution whatever. The likelihood ratio test is commonly cited as a test of the restrictions in large samples.

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