Consider the one-variable regression model, $Y _ { i } = \beta _ { 0 } + \beta _ { 1 } X _ { i } + u _ { i }$
assumptions from Chapter 4 are satisfied. However, suppose that both Y and X are
measured with error, $\widetilde { Y } _ { i } = Y _ { i } + z _ { i } \text { and } \widetilde { X } _ { i } = X _ { i } + w _ { i }$
and independent of both Y and X respectively. If you estimated the regression model
$\widetilde { Y } _ { i } = \beta _ { 0 } + \beta _ { 1 } \widetilde { X } _ { i } + v _ { i }$ \quad using OLS, then show that the slope estimator is not consistent.

Question

Consider the one-variable regression model, $Y _ { i } = \beta _ { 0 } + \beta _ { 1 } X _ { i } + u _ { i }$
assumptions from Chapter 4 are satisfied. However, suppose that both  Y  and  X  are
measured with error, $\widetilde { Y } _ { i } = Y _ { i } + z _ { i } \text { and } \widetilde { X } _ { i } = X _ { i } + w _ { i }$
and independent of both  Y  and  X  respectively. If you estimated the regression model
$\widetilde { Y } _ { i } = \beta _ { 0 } + \beta _ { 1 } \widetilde { X } _ { i } + v _ { i }$  \quad  using OLS, then show that the slope estimator is not consistent.

Quizplus · Accepted Answer

The Answer of Consider the one-variable regression model, $Y _ { i } = \beta _ { 0 } + \beta _ { 1 } X _ { i } + u _ { i }$
assumptions from Chapter 4 are satisfied. However, suppose that both  Y  and  X  are
measured with error, $\widetilde { Y } _ { i } = Y _ { i } + z _ { i } \text { and } \widetilde { X } _ { i } = X _ { i } + w _ { i }$
and independent of both  Y  and  X  respectively. If you estimated the regression model
$\widetilde { Y } _ { i } = \beta _ { 0 } + \beta _ { 1 } \widetilde { X } _ { i } + v _ { i }$  \quad  using OLS, then show that the slope estimator is not consistent.

Consider the One-Variable Regression Model Yi=β0+β1Xi+uiY _ { i } = \beta _ { 0 } + \beta _ { 1 } X _ { i } + u _ { i }Yi​=β0​+β1​Xi​+ui​

Consider the One-Variable Regression Model $Y _ { i } = \beta _ { 0 } + \beta _ { 1 } X _ { i } + u _ { i }$