Professor Hsieh decides to run an experiment to measure the effect of time press

Question

Professor Hsieh decides to run an experiment to measure the effect of time pressure on final exam scores. He gives each of the 50 students in his course the same final exam, but some students have 90 minutes to complete the exam, while the others have 120 minutes. Each student is randomly assigned one of the examination times based on the flip of a coin (25 students will be assigned to the 90 minutes group and vice versa). Let Yi denote the test score of student i and let Xi denote the amount of time assigned to student i (Xi = 90 or 120). Consider the regression model Yi = + Xi + ui .

1. Explain why E[ui |Xi ] = 0 for this regression model.

2. Instead of flipping a coin, Prof. Hsieh decides to assign 90 minutes to junior and 120 minutes to senior. Will this cause any problem?

3. It is reasonable to assume that senior students have higher math ability in general as they might have completed more math-related courses. If so, will the assignment in (2) lead to upward or downward bias of OLS estimation?

Explanation / Answer

1. From the basic assumptions of linear regression, it follows the expected value(mean) of error is zero and has no autocorrelation among themselves

2.Yes, This will create a bias as the performance between junior and senior is different Hence it is recommended to have the random way of picking up by flipping a coin

3.Yes , in general we can assume that the senior students have higher math ability. By this the value of beta will increase causing biasness.

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