Problem 2 (50 points) a) (20 points total for this part) Now suppose instead of having health information on only two people, we have data on health indices and whether the person has health insurance for 500 people. D in this example =1 if the person has health insurance and D=0 if the person does not have health insurance. Y stands for health index. However, remember that we are not talking about a particular person anymore, we have data on 500 people. You will need to use "average when you interpret each term in the equation below. The difference in mean health indices is given by Difference in means = E[Y1|D= 1] - E[Yo:D= 1] + E[YiD. = 1] - E[Y:D = 0] Carefully explain what each term in the equation above mean (5 points each) in the context of this example. You do not have to explain what E[Yo:D= 1] means twice. In addition, explain what E[Y1i|D = 0) would mean in the context of this example (5 points) b) (10 points total for this part) Your friend tells you that the equation for difference in means in part a provides you with the pure causal effect of health insurance on health (ATET - average treatment effect on the treated). Do you agree with your friend? (5 points) Why or why not? (5 points). If you say that you do not agree, your explanation should clearly indicate what the equation for difference in means in part a provides you with c) (10 points total for this part) Suppose you decide to use random assignment to estimate the causal impact of health insurance on health instead. Explain how you would determine that the randomization was done properly. d) (10 points total for this part) Suppose (just like in par c) you decide to use random assignment to estimate the causal impact of health insurance on health. Write down regression model that will provide you with the causal impact of health insurance on health (5 points). Write down regression model that will provide you with Intent-to-Treat (ITT) (5 points) Problem 2 (50 points) a) (20 points total for this part) Now suppose instead of having health information on only two people, we have data on health indices and whether the person has health insurance for 500 people. D in this example =1 if the person has health insurance and D=0 if the person does not have health insurance. Y stands for health index. However, remember that we are not talking about a particular person anymore, we have data on 500 people. You will need to use "average when you interpret each term in the equation below. The difference in mean health indices is given by Difference in means = E[Y1|D= 1] - E[Yo:D= 1] + E[YiD. = 1] - E[Y:D = 0] Carefully explain what each term in the equation above mean (5 points each) in the context of this example. You do not have to explain what E[Yo:D= 1] means twice. In addition, explain what E[Y1i|D = 0) would mean in the context of this example (5 points) b) (10 points total for this part) Your friend tells you that the equation for difference in means in part a provides you with the pure causal effect of health insurance on health (ATET - average treatment effect on the treated). Do you agree with your friend? (5 points) Why or why not? (5 points). If you say that you do not agree, your explanation should clearly indicate what the equation for difference in means in part a provides you with c) (10 points total for this part) Suppose you decide to use random assignment to estimate the causal impact of health insurance on health instead. Explain how you would determine that the randomization was done properly. d) (10 points total for this part) Suppose (just like in par c) you decide to use random assignment to estimate the causal impact of health insurance on health. Write down regression model that will provide you with the causal impact of health insurance on health (5 points). Write down regression model that will provide you with Intent-to-Treat (ITT) (5 points)