consider the following equations designed to

Question

Consider the following equations designed to estimate  a school's test scores (Test) and the school's dropout rate (Drop).

Test_i = B₀ + B₁*Parent Ed_i + B₂*school quality_i + B₃*Drop_i + E_i

Drop_i = a₀ + a₁*Parent Ed_i + a₂*school quality_i + a₃*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.