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PART B Question 1 (10 marks) Page limit: 1 page State with brief reasoning whether the following statements are true or false

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PART B Question 1 (10 marks) Page limit: 1 page State with brief reasoning whether the following statements are true or false. (Note: failure to provide reasoning, or providing invalid reasoning, yields 0 marks even if you chose the right answer). 
1. Let = fix + ui, i = 1,...,n, where xi = vi + ui, such that E(u,) = E(vi) = 0 and E(u:v:) = O. The OLS estimator for ,6 is biased but consistent. (2 marks) 2. For the same model as in 1., let zi be a random variable such that corr(zi, xi) = 1, where corr( , .) is the correlation coefficient between two random variables. The IV estimator that uses z, as an instrument is consistent. (2 marks) 3. The normality assumption in the errors is violated in models where the dependent variable is binary. (2 marks) 
4. Consider the following linear model outphri = iqo + fliwkearni + 132wkhoursi + ui, where outphr, denotes output per hour for worker i, wkearni denotes weekly salary and wkhoursi denotes weekly working hours. Adding hourly pay as a variable would violate assumption MLR.4. (2 marks) 5. Let yi = 130+ + ,g2x2, + ui. The OLS estimate for /31 can be obtained using the following two-stage procedure: in the first stage, is regressed on x2i and an intercept. In the second stage, y, is regressed on the fitted value obtained from the first-stage, omitting x2i. (2 marks) 
Question 2 (10 marks) Page limit: I page 
1. Let y, = 131x, + ui, i = 1, ..., n, where Assumptions 1-5 of the simple linear regression model are satisfied. Define 
Pi = 
Explain whether Pi is consistent or not in this setup. (2 marks) 2. For the same model as above, show that the variance of Pi is larger than the variance of where A. denotes the OLS estimator. Please refrain from referring to the Gauss-Markov theorem as part of your answer. (4 marks) 
3. Consider the following estimated regression model: outphr, = 431.25 — 9.264wkhoursi, where outphri denotes output per hour for worker i, i = 1, ...,n, and wkhours, denotes weekly working hours. Let t(outphri) = 82.92, Var(outphri) = 307.45, E(wkhoursi) = 37.6 and Var(wkhoursi) = 3.217, where E(. ) denotes the sample average and liar() denotes the sample variance. 
Find the expected weekly output of a typical worker, i.e. estimate E(outphri x wkhoursi). (4 marks)