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

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.