申論題

Question III (20 points, 10 points each)

 Consider the case where the true population model has two explanatory variables and an error term:
 and we assume that this model satisfies Gauss-Markov assumptions.

5. Suppose we specify the model as

However, x₃ has no effect on y after x₁ and x₂ have been controlled for. Because we do not know thatβ₃ = 0 in practice, we still estimate the equation including x₃:
 Notc that the variable x₃ may or may not be correlated with x₁ or x₂. What is the effect, if any, of including x₃ in the model on the estimated β₁? Explain.