Exercise 1 (sw chapter 5): suppose that a researcher, using wage data on 250 randomly selected male workers and 280 female workers, estimates the ols regression wage= 12.52 + 2.12 * male, r(squared) = 0.06, ser =4.2 (0.23) (0.36) where wage is measured in dollars per hour and male is a binary variable that is equal to 1 if the person is a male and 0 if the person is a female. the wage gender gap is defined as the difference in mean earnings between men and women. a) what is the estimated gender gap? b) is the gender gap significantly different from zero? (compute the p-value for testing the null hypothesis that there is no gender gap. c) construct a 95% confidence interval for the gender gap. d) in the sample, what is the mean wage of women? of men? e) another researcher uses these same data but regresses wages on female, a variable that is equal to1 if the person is female and 0 if the person is a male. what are the regression estimates calculated from this regression? , exercises 2 (sw chapter 5) suppose that satisfy the usual least squares assumptions. a random sample of size n=250 is drawn and yields ^ y = 5.4 + 3.2 * x, r(squared) = 0.26, ser = 6.2 (3.1) (1.5) a) test vs. at the 5% level. b) construct a 95% confidence interval for . c) suppose you learned that and were independent. would you be surprised? explain. d) suppose that and are independent and many samples of size n=250 are drawn, regressions estimated, and a) and b) answered. in what fraction of the samples would h0 from a) be rejected? in what fraction of samples would the value be included in the confidence interval from b)? exercise 3: true or false tell if the following assertions are true or false, and explain your 1. an estimator that is unbiased is necessarily efficient too. 2. an estimator that is efficient is unbiased too. 3. in multivariate regressions using the same dependent variable, when comparing between two specifications one should prefer the one with the largest r-squared. 4. this regression suffers from multicollinearity: in (earnings) = a0 + a1 female + a2 males + school (years) + a4 age + u due date: wednesday april 20, 2011