Question

In a hospital there are 2 types of surgeons: average and excellent . averageSur = 1 if patient receives average surgeon and 0 otherwise. success = 1 if no complications occur during surgery and 0 otherwise. Suppose patients with high blood pressure are more likely to develop complications, in anticipation of this issue, patients with high blood pressure tend to be assigned to excellent surgeons.

An researcher would like to determine the effects of a patient receiving an operation from an excellent surgeon. She considers the following two regression models:

Short regression: success = B0 + B1averageSur + ushort

Long regression: success = delta0 + B1averageSur + B2BP + ulong

where BP stands for blood pressure, measured in mmHg

A) do you expect B1 to be positive or negative?

B) do you expect B2 to be positive or negative?

C) Assume zero conditional mean assumption holds in long regression. That is E[ulong | averageSur, BP] = 0. However, the researcher decides to estimate B1 using the short regression. Let B1hat be her estimate. In large samples, do you expect B1hat > B1 or B1hat < B1?

Answer 1

Answer:

A)

B1 is expected to be negative, because as averageSur increases, success should decrease. Average surgeon has more chances of causing complications.

B)

B2 is expected to be negative, because as BP increased, success should decrease. Patients with high blood pressure are more likely to develop complications.

C)

B1hat < B1 is expected.

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