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ps5 - Introduction to Econometrics Prof Onatski Problem Set...

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Introduction to Econometrics, Prof. Onatski Problem Set 5. Due in class on October 21 Problem 1. Do problem 5.4 on pages 175-176 of the textbook. Problem 2. Do problem 5.13 on page 178 of the textbook. Problem 3. Consider a model Y i = β 0 + β 1 X i + u i where Y i is the number of minutes person i is late for job. (If person i is early for job then Y i is negative.) Let X i be 1 if person i is man and 1 if person i is woman. Suppose that the OLS 1-3 assumptions hold, but there is a heteroskedasticity so that E ¡ u 2 i | X i = 1 ¢ = 4 but E ¡ u 2 i | X i = 1 ¢ = 1 . a) Prove that the GLS and OLS estimators of β 0 and β 1 will nevertheless be equal. b) Can you explain why GLS and OLS are equal for such a model (hint: imagin a scatter plot for the data with binary X i (that is, such X i which may take on only two values). 1

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Problem 4. I just have simulated data from the regression model Y i = 1 + 0 . 5 X i + u i , where OLS 1-3 assumptions hold. I simulated 10 independent samples, each of length 100. Further, for each of the simulated samples, I considered the subsamples which consist of the fi rst 10 oservations, the fi rst 20 observations, the fi rst 30 observations, etc. For each sample and each subsample I have
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ps5 - Introduction to Econometrics Prof Onatski Problem Set...

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