The Probability Limit of the OLS Estimator in the Case

Essay

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