Under the <partially linear model>,
$$
\mathbb E[Y\mid A=1,X]-\mathbb E[Y\mid A=0,X]
=\beta_2.
$$
Inserting this constant conditional contrast into the identification formula from part i gives
$$
\beta_1=\mathbb E[\beta_2]=\beta_2.
$$

Solution

Past exam of the mathematics course of the University of Cambridge / 2022 / iii / Paper 221 / 3 / ii / Solution

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2022/iii/paper-221/3/ii/solution