5.2. Consider a model for the health of an individual:
health¼ b0 þ b1ageþ b2weightþ b3height
þ b4maleþ b5workþ b6exerciseþ u1 ð5:53Þ
where healthis some quantitative measure of the person’s health, age, weight, height, andmaleare self-explanatory, workis weekly hours worked, and exerciseis the hours of exercise per week.
a. Why might you be concerned about exercisebeing correlated with the error term
b. Suppose you can collect data on two additional variables, disthomeand distwork, the distances from home and from work to the nearest health club or gym. Discuss whether these are likely to be uncorrelated with u1.
c. Now assume that disthomeand distworkare in fact uncorrelated with u1, as are all variables in equation (5.53) with the exception of exercise. Write down the reduced form for exercise, and state the conditions under which the parameters of equation (5.53) are identi?ed.
d. How can the identi?cation assumption in part c be tested?