Question

Consider a model for individual data to test whether nutrition affects productivity (in a developing country):

log(produc) = δ₀ + δ₁exper + δ₂exper² + δ₃educ + α₁calories + α₂protein + 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 exper, exper² , and educ are all exogenous. The variables calories and protein are possibly correlated with u₁ . 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 proteins ?

(i) Calories and protein must be partially correlated with prices of food. ____ (True or False)

(ii) We must assume prices are exogenous in the productivity equation. ____ (True or False)

(iii) Prices should directly affect productivity. ____ (True or False)

(b) To test the null hypothesis that calories and protein are exogenous in the structural equation,

(i) The only option is to test for endogeneity of each variable separately. ____ (True or False)

(ii) We can use a regression-based procedure and then apply a standard F test or a similar heteroskedasticity-robust test. ____ (True or False)

Answer 1

(a)

(i)calories and protein must be partially correlated with price of food. TRUE

(ii)We must assume prices are exogenous in the productivity equation. TRUE

(iii) Prices shuld directly affect productivity, FALSE (price vary because of things like transportation costs that are not systematically related to regional variation in individual productivity.Price effect the quality of food.)

(b) to test null hyothesis...

(i) The only option is to test for endogeneity of each variable separately. FALSE

(ii) We can use a regression-based procedure and then apply a standard F test or a similar heteroskedasticity-robust test. TRUE