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

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

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

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The Probability Limit of the OLS Estimator in the Case β^1→pβ1+ρXuσuσX\hat { \beta } _ { 1 } \stackrel { p } { \rightarrow } \beta _ { 1 } + \rho _ { X u } \frac { \sigma _ { u } } { \sigma _ { X } }β^​1​→pβ1​+ρXu​σX​σu​​

Definitions:

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