2. You study the relationship between wage and education. Consider the following population regression: wage; = Bo + Biedugi + Wi, Ui = Veduc;. ei where wage; is an hourly wage and educ; is education measured by years. The random variable e; is independent of educ; with E(ei) = 0 and var(e) = a. Suppose you are given a grant to run a controlled experiment. Explain how you would structure the experiment in order to estimate the causal effect of education on wage? [Your answer here) b. Show that the conditional mean zero assumption is satisfied, i.e. E(ui|educi) = 0. [Your answer here) c. Show that the conditional variance of the error term u; is var(uz|educ;) = educ.o. Is the error term homoskedastic or heteroskedastic? [Your answer here) d. Why do you think the variance of wage; increases with educ. [Your answer here) e. Using a sample, you get the following estimation results: wage =10.28 +0.67 x educ, R = 0.24, SER= 7.98 (3.24) (0.42) Conduct a hypothesis test for H: B1 = 0 vs. H: B170 at the 5% significance level. [Your answer here) f. In (d), the sample average of wage; is Y = 17.83. What is the sample average of educt? [Your answer here) 2. You study the relationship between wage and education. Consider the following population regression: wage; = Bo + Biedugi + Wi, Ui = Veduc;. ei where wage; is an hourly wage and educ; is education measured by years. The random variable e; is independent of educ; with E(ei) = 0 and var(e) = a. Suppose you are given a grant to run a controlled experiment. Explain how you would structure the experiment in order to estimate the causal effect of education on wage? [Your answer here) b. Show that the conditional mean zero assumption is satisfied, i.e. E(ui|educi) = 0. [Your answer here) c. Show that the conditional variance of the error term u; is var(uz|educ;) = educ.o. Is the error term homoskedastic or heteroskedastic? [Your answer here) d. Why do you think the variance of wage; increases with educ. [Your answer here) e. Using a sample, you get the following estimation results: wage =10.28 +0.67 x educ, R = 0.24, SER= 7.98 (3.24) (0.42) Conduct a hypothesis test for H: B1 = 0 vs. H: B170 at the 5% significance level. [Your answer here) f. In (d), the sample average of wage; is Y = 17.83. What is the sample average of educt? [Your answer here)