4. Consider each of the following statements. Is the statement true, false or un

Question

4. Consider each of the following statements. Is the statement true, false or uncertain? Justify your answers carefully. The p-value for a test statistic represents the probability of rejecting the null hypothesis if the null hypothesis is true. (4 marks) (a) (b) In the following equation modelling wages log(wage) - Bo + 8 female + B, educ + 8 female x educ + u female = 1 if the person is female and 0 if the person is male, and educ is years of education. To test the hypothesis that the return to education is the same for men and women we would test Ho: 8-0. However, even if we do not reject Ho, this does not rule out the possibility of a wage differential between men and women with the same level of education. (5 marks] (c) If conventional (homoskedasticity-only) and heteroskedasticity-robust standard errors are the same, there is not much practical gain from using the latter. If the difference is large, it is questionable how valid such robust standard errors actually are. In addition, use of heteroskedasticity-robust standard errors does not change the fact that OLS estimates of the B's remain inefficient. (4 marks) (d) If an estimator is biased, then it cannot be consistent. (4 marks]

Explanation / Answer

a) Yes, true statement , it is the probability of rejecting the null hypothesis assumed null is true

b) Yes, true statement.

c) False

d) Falsed, unbaised and consistent are two different conditions and neither one does not imply another.

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