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:

Dividends

Payments made by a corporation to its shareholder members, usually distributed from the company's profits.

Liquidation

Occurs when a business is terminated, the assets are sold, and liabilities and partners are paid off.

Creditors

Entities or individuals to whom a company owes money or has financial liabilities, often in the context of short or long-term borrowing.

Contract Rate

Rate of interest (based on face value) stated on bond certificate and bond indenture.