Consider the following regression that examines the wages of graduating economists:

wage₁ = 𝛽o + 𝛽1ranki + u¡

where rank is the rank of the school the student graduated from (lower is better) and wage is the wage in dollars per hour. A random sample of recent graduates was taken.

a) What is the predicted sign on 𝛽₁? Explain.

b) Suppose that the R² of the model is very poor: R² = 0.01. What does this say about the potential to interpret causality in the model?

c) Suppose that a government experiment sent students to schools of different ranks: that is, rank; is randomly assigned. Is the estimate of ₁ unbiased? Explain.