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:

Fixed Rate

A constant interest rate for a loan or mortgage that remains unchanged for the entire term of the loan or for a set period.

Variable Rate

An interest rate that changes periodically over the lifetime of the loan based on an underlying benchmark or index.

Prime Rate

The interest rate that banks charge their most creditworthy customers, often used as a benchmark for other loans.

Risk Profile

An assessment of an entity's or individual's willingness to take risks, as well as the threats to which they are exposed.