The Errors-In-Variables Model Analyzed in the Text Results In So That the OLS Estimator Is Inconsistent

Essay

The errors-in-variables model analyzed in the text results in $$\hat { \beta } _ { 1 } \stackrel { p } { \rightarrow } \frac { \sigma _ { X } ^ { 2 } } { \sigma _ { X } ^ { 2 } + \sigma _ { w } ^ { 2 } } \beta _ { 1 }$$ so that the OLS estimator is inconsistent.Give a condition involving the variances of X
and w, under which the bias towards zero becomes small.