Consider the one-variable regression model,Yi = β0 + β1Xi + ui,where the usual assumptions from Chapter 4 are satisfied.However,suppose that both Y and X are measured with error, = Yi + zi and = Xi + wi.Let both measurement errors be i.i.d.and independent of both Y and X respectively.If you estimated the regression model = β0 + β1 + vi using OLS,then show that the slope estimator is not consistent.

Question

Consider the one-variable regression model,Yi = β0 + β1Xi + ui,where the usual assumptions from Chapter 4 are satisfied.However,suppose that both Y and X are measured with error,  = Yi + zi and  = Xi + wi.Let both measurement errors be i.i.d.and independent of both Y and X respectively.If you estimated the regression model  = β0 + β1  + vi using OLS,then show that the slope estimator is not consistent.

Quizplus · Accepted Answer

The Answer of Consider the one-variable regression model,Yi = β0 + β1Xi + ui,where the usual assumptions from Chapter 4 are satisfied.However,suppose that both Y and X are measured with error,  = Yi + zi and  = Xi + wi.Let both measurement errors be i.i.d.and independent of both Y and X respectively.If you estimated the regression model  = β0 + β1  + vi using OLS,then show that the slope estimator is not consistent.

Consider the One-Variable Regression Model,Yi = β0 + β1Xi