Suppose y = h(11, 12, q, u) where y, 11, 12, q, and u are all...
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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.
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a The causal effect cannot be measured for particular individuals in this scenario because we have b... View the full answer
Related Book For
Microeconomics An Intuitive Approach with Calculus
ISBN: 978-0538453257
1st edition
Authors: Thomas Nechyba
Posted Date:
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