Asymptotic Representation Of The Instrumental Weighted Variables - Theory And Practice: Part I - deriving the formula for the asymptotic representation

Abstrakt

The robust version of the classical instrumental variables, called Instrumental Weighted Variables (IWV) and the conditions for its consistency and $\sqrt{n}$-consistency are recalled. The reasons why the classical instrumental variables as well as IWV were introduced and the idea of implicit weighting the residuals are also very briefly recalled.

Then asymptotic representation and normality of all solutions of the corresponding normal equations is proved. Part II - numerical studies offers a possibility to create an idea how the asymptotic representation works under various frameworks.

Klíčová slova

• Robustness
• instrumental variables
• implicit weighting
• root-consistency of estimate by instrumental weighted variables
• asymptotic representation of the estimate
• numerical study