The Probability Limit of the OLS Estimator in the Case $$\hat { \beta } _ { 1 } \stackrel { p } { \rightarrow } \beta _ { 1 } + \rho _ { X u } \frac { \sigma _ { u } } { \sigma _ { X } }$$

question 40

Essay

The probability limit of the OLS estimator in the case of omitted variables is given in
your text by the following formula: $$\hat { \beta } _ { 1 } \stackrel { p } { \rightarrow } \beta _ { 1 } + \rho _ { X u } \frac { \sigma _ { u } } { \sigma _ { X } }$$ Give an intuitive explanation for two conditions under which the bias will be small.

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Definitions:

Zygomatic Arch

The arch of bone that forms from the temporal process of the zygomatic bone and the zygomatic process of the temporal bone, creating the prominence of the cheek.

Zygomatic Process

A bony projection of the temporal bone that articulates with the zygoma (cheekbone) to form part of the cheek structure.

Temporal Bone

A bone of the skull, situated at the sides and base of the cranium, involved in the protection of the inner ear.

Temporal Process

A projection on the zygomatic bone that helps form the zygomatic arch, connecting the zygomatic bone to the temporal bone of the skull.