State with brief reasoning whether the following statements are true or false. 1. Let yi 1,...

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State with brief reasoning whether the following statements are true or false. 1. Let yi 1, ..., n, where x = v₁ + u¡, such that E (u;) = E(v;) = 0 and E(u¡v;) = 0. The OLS estimator for ß is biased but consistent. (2 marks) Bxi + U₁, i = = 2. For the same model as in 1., let z; 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 = Po + B₁wkearn; + B₂wkhours; + ui, where outphr; denotes output per hour for worker i, wkearn; denotes weekly salary and wkhours; denotes weekly working hours. Adding hourly pay as a variable would violate assumption MLR.4. (2 marks) 5. Let yi Po + B1x1i + P2₂x2i+ui. The OLS estimate for P₁ can be obtained using the following two- stage procedure: in the first stage, x₁i is regressed on x2; and an intercept. In the second stage, y; 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. 1. Let yi 1, ..., n, where x = v₁ + u¡, such that E (u;) = E(v;) = 0 and E(u¡v;) = 0. The OLS estimator for ß is biased but consistent. (2 marks) Bxi + U₁, i = = 2. For the same model as in 1., let z; 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 = Po + B₁wkearn; + B₂wkhours; + ui, where outphr; denotes output per hour for worker i, wkearn; denotes weekly salary and wkhours; denotes weekly working hours. Adding hourly pay as a variable would violate assumption MLR.4. (2 marks) 5. Let yi Po + B1x1i + P2₂x2i+ui. The OLS estimate for P₁ can be obtained using the following two- stage procedure: in the first stage, x₁i is regressed on x2; and an intercept. In the second stage, y; is regressed on the fitted value obtained from the first-stage, omitting x₂i. (2 marks) =

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