please answer a b and d part

Q 1 The archipelago nation of Tuvalu has enlisted you to study its school choice policies. Because the nation consists of a series of small islands, typically there was little school choice. However, the government recently implemented a charter school policy that led to a large increase in charter school prevalence. Assume you have several years of student-level longitudinal data on math test scores, demographic characteristics, and what school each student enrolls in each year.

a. What would be the problem with simply comparing the math test scores of students attending a traditional public school with the outcomes of students who attend a charter school, even controlling for student demographic characteristics? Would this comparison yield the causal effect of attending a charter school on math test scores?

b. Explain how controlling for student fixed effects might overcome the problems you discussed in part a. In what way is this a difference-in-difference method? Under what assumptions will this method allow you to estimate the causal effect of charter school attendance?

d. Using a variety of methods, you find that charter school enrollment leads to large increases in student math test scores. The government of Tuvalu uses this information to argue that it should expand charter school access to more students. Does this policy conclusion necessarily follow from your results? Explain.