Suppose you want to test whether girls who attend a girls' high school do better in math than girls who attend coed schools. You have a random sample of senior high school girls from a state in the United States, and score is the score on a standardized math test. Let girlhs be a dummy variable indicating whether a student attends a girls' high school.
(i) What other factors would you control for in the equation? (You should be able to rea- sonably collect data on these factors.)
(ii) Write an equation relating score to girlhs and the other factors you listed in part (i).
(iii) Suppose that parental support and motivation are unmeasured factors in the error term in part (ii). Are these likely to be correlated with girlhs? Explain.
(iv) Discuss the assumptions needed for the number of girls' high schools within a 20-mile radius of a girl's home to be a valid IV for girlhs.
(v) Suppose that, when you estimate the reduced form for girlshs, you find that the coefficient on numghs (the number of girls' high schools within a 20-mile radius) is negative and statistically significant. Would you feel comfortable proceeding with IV estimation where numghs is used as an IV for girlshs? Explain.