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 yi=xi+ui,i=1,,n, where xi=vi+ui, such that E(ui)=E(vi)=0 and E(uivi)=0. The OLS estimator for 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 zi 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=0+1wkearni+2wkhoursi+ui, where outphr ri denotes output per hour for worker i, wkearn ni denotes weekly salary and whers i denotes weekly working hours. Adding hourly pay as a variable would violate assumption MLR.4. (2 marks) 5. Let yi=0+1x1i+2x2i+ui. The OLS estimate for 1 can be obtained using the following twostage procedure: in the first stage, x1i is regressed on x2i and an intercept. In the second stage, yi is regressed on the fitted value obtained from the first-stage, omitting x2i. (2 marks) 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 yi=xi+ui,i=1,,n, where xi=vi+ui, such that E(ui)=E(vi)=0 and E(uivi)=0. The OLS estimator for 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 zi 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=0+1wkearni+2wkhoursi+ui, where outphr ri denotes output per hour for worker i, wkearn ni denotes weekly salary and whers i denotes weekly working hours. Adding hourly pay as a variable would violate assumption MLR.4. (2 marks) 5. Let yi=0+1x1i+2x2i+ui. The OLS estimate for 1 can be obtained using the following twostage procedure: in the first stage, x1i is regressed on x2i and an intercept. In the second stage, yi is regressed on the fitted value obtained from the first-stage, omitting x2i. (2 marks)