Consider the following equations designed to estimate a school's test scores (Test) and the school's dropout rate (Drop).
Test_{i} = B_{0} + B_{1}*Parent Ed_{i} + B_{2}*school quality_{i} + B_{3}*Drop_{i} + E_{i}
Drop_{i} = a_{0} + a_{1}*Parent Ed_{i} + a_{2}*school quality_{i} + a_{3}*Test_{i} + V_{i}
a. Use the order condition to determine if these equations are exactly identified, under-identified, or over-identified (the intuitive version is fine).
b. Suppose another variable (teenage unemployment) is available and is thought to affect dropout rates but not test scores. How will your answer to part (a) change if this unemployment variable is included in the dropout equation?
c. Explain intuitively why OLS will be biased if the equations are estimated separately.