CATE is conditional average treatment effect

ATE is average treatment effect

the topic is applied econometrics

10. Suppose W 's distribution is symmetric around 0 . Suppose the true model for Y is Y=0+1D+2W+3DW3+ with E(D,W)=0 and D{0,1}. i) Express Y(0) and Y(1) in terms of W, and the s. ii) What is the CATE at W=3 ? iii) Derive ATE. (Hint: You can use the results in Q3.) iv) If you run the following regression Y=0+1D+u, is equal to ATE if D and W are independent? Prove your claim. 3. A distribution is called symmetric around 0 if its density f satisfies f(x)=f(x) for all xR. Assume Y 's distribution is symmetric around 0 . i) Prove that Y and Y have identical distribution but not independent. ii) Calculate E(Y) and E(Y3) (assuming they both exist). 10. Suppose W 's distribution is symmetric around 0 . Suppose the true model for Y is Y=0+1D+2W+3DW3+ with E(D,W)=0 and D{0,1}. i) Express Y(0) and Y(1) in terms of W, and the s. ii) What is the CATE at W=3 ? iii) Derive ATE. (Hint: You can use the results in Q3.) iv) If you run the following regression Y=0+1D+u, is equal to ATE if D and W are independent? Prove your claim. 3. A distribution is called symmetric around 0 if its density f satisfies f(x)=f(x) for all xR. Assume Y 's distribution is symmetric around 0 . i) Prove that Y and Y have identical distribution but not independent. ii) Calculate E(Y) and E(Y3) (assuming they both exist)