Asymptotics of diagonal elements of projection matrices under many instruments/regressors

Abstrakt

This article sheds light on the asymptotic behavior of diagonal elements of projection matrices associated with instruments or regressors under many instrument/regressor asymptotics. When the diagonal elements do not exhibit variation asymptotically, certain results in the many instrument/regressor literature lead to elegant solutions and conclusions.

We establish conditions when this happens, provide relevant examples, and analyze instrument designs, for which this property does or does not hold.

Klíčová slova

• instrumental variable estimation
• inference
• models
• heteroskedasticity
• approximations
• distributions
• regressors
• estimators