Suppose y = h(11, 12, q, u) where y, 11, 12, q, and u are all...

 

Transcribed Image Text:

Suppose y = h(11, 12, q, u) where y, 11, 12, q, and u are all scalars and continuous random variables and where and 2 are observed but q and u are not observed. Let C(2,22,9, u)=h(11,12,9, u) denote the causal effect of 2 on y. (a) [5pts] Can the causal effect be measured for particular individuals? Why? (b) [5pts] Write down an expression for the average causal effect of ri on y as a function of observed variables. (c) [5pts] Suppose we know that h(r, x2,q, u) = B + Bx1 + Bx2 + B3q + u and that E[u/1, 12, 9] = 0. In this case, what is the average causal effect of r on y. (d) [5pts] Let m(11, 12) denote the regression derivative where m(11,12)= E[y/r1, 2] is the conditional expectation function. Continuing to suppose that h(11, 12, 9, u) = Bo + B11 + B1 + B39 + u and that Elu 11, 12, 9] 0, provide an expression for the regression derivative in this context. (e) [5pts] In general, does,m(11, 12) equal the average causal effect? If not, provide two conditions under which the regression derivative is equal to the causal effect and explain what each one means. Suppose y = h(11, 12, q, u) where y, 11, 12, q, and u are all scalars and continuous random variables and where and 2 are observed but q and u are not observed. Let C(2,22,9, u)=h(11,12,9, u) denote the causal effect of 2 on y. (a) [5pts] Can the causal effect be measured for particular individuals? Why? (b) [5pts] Write down an expression for the average causal effect of ri on y as a function of observed variables. (c) [5pts] Suppose we know that h(r, x2,q, u) = B + Bx1 + Bx2 + B3q + u and that E[u/1, 12, 9] = 0. In this case, what is the average causal effect of r on y. (d) [5pts] Let m(11, 12) denote the regression derivative where m(11,12)= E[y/r1, 2] is the conditional expectation function. Continuing to suppose that h(11, 12, 9, u) = Bo + B11 + B1 + B39 + u and that Elu 11, 12, 9] 0, provide an expression for the regression derivative in this context. (e) [5pts] In general, does,m(11, 12) equal the average causal effect? If not, provide two conditions under which the regression derivative is equal to the causal effect and explain what each one means.

Answer rating: 100% (QA)

a No the causal effect cannot be measured for particular individuals because it ... View the full answer