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2. Consider a model for individual data to test whether nutrition affects productivity (in a devel- oping country): log(produe) = 80 + 8jerper + d2exper2 + 8zeduc + alcalories + o2protein + u1, where produc is some measure of worker productivity, calories is caloric intake per day, and protein is a measure of protein intake per day. Assume here that erper, erper?, and educ are all exogenous. The variables calories and protein are possibly correlated with u. Possible instrumental variables for calories and protein are regional prices of various goods, such as grains, meats, breads, dairy products, and so on. (a). Under what circumstances do prices make good IVs for calories and protein? What if prices reflect quality of food? (b). How many prices are needed to identify the model parameters? (c). Suppose we have M prices, pi... Pm. Explain how to test the null hypothesis that calories and protein are exogenous in the model. 2. Consider a model for individual data to test whether nutrition affects productivity (in a devel- oping country): log(produe) = 80 + 8jerper + d2exper2 + 8zeduc + alcalories + o2protein + u1, where produc is some measure of worker productivity, calories is caloric intake per day, and protein is a measure of protein intake per day. Assume here that erper, erper?, and educ are all exogenous. The variables calories and protein are possibly correlated with u. Possible instrumental variables for calories and protein are regional prices of various goods, such as grains, meats, breads, dairy products, and so on. (a). Under what circumstances do prices make good IVs for calories and protein? What if prices reflect quality of food? (b). How many prices are needed to identify the model parameters? (c). Suppose we have M prices, pi... Pm. Explain how to test the null hypothesis that calories and protein are exogenous in the model

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