Consider the following population regression model relating the dependent variable $Y _ { i }$ and regressor $X _ { i }$,
$$\begin{array} { c }
Y _ { i } = \beta _ { 0 } + \beta _ { 1 } X _ { i } + u _ { i } , i = 1 , \ldots , n . \
X _ { i } \equiv Y _ { i } + Z _ { i }
\end{array}$$ where Z is a valid instrument for X.
(a) $$\text { Exlain why you should not use OLS to estimate } \beta _ { 1 } \text {. }$$

Question

Consider the following population regression model relating the dependent variable $Y _ { i }$ and regressor $X _ { i }$,
$$\begin{array} { c } 
Y _ { i } = \beta _ { 0 } + \beta _ { 1 } X _ { i } + u _ { i } , i = 1 , \ldots , n . \
X _ { i } \equiv Y _ { i } + Z _ { i }
\end{array}$$ where Z is a valid instrument for X.
(a) $$\text { Exlain why you should not use OLS to estimate } \beta _ { 1 } \text {. }$$

Quizplus · Accepted Answer

The Answer of Consider the following population regression model relating the dependent variable $Y _ { i }$ and regressor $X _ { i }$,
$$\begin{array} { c } 
Y _ { i } = \beta _ { 0 } + \beta _ { 1 } X _ { i } + u _ { i } , i = 1 , \ldots , n . \
X _ { i } \equiv Y _ { i } + Z _ { i }
\end{array}$$ where Z is a valid instrument for X.
(a) $$\text { Exlain why you should not use OLS to estimate } \beta _ { 1 } \text {. }$$

Consider the Following Population Regression Model Relating the Dependent Variable YiY _ { i }Yi​

Consider the Following Population Regression Model Relating the Dependent Variable $Y _ { i }$