Problem 1 Consider the following model Yi = 1 + 2Di + ui where Y = annual salary of a college professor X = years of teaching experience D = dummy for gender Consider three ways of defining the dummy variable. a D = 1 for male, 0 for female. b D = 1 for female, 2 for male. c D = 1 for female, -1 for male. Interpret the preceding regression model for each dummy assignment. Is one method preferable to another? Justify your answer. Using the data given in excel verify your answer. Problem 2 A researcher has data on the average annual rate of growth of employment, e, and the average annual rate of growth of GDP, x, both measured as percentages, for a sample of 27 developing countries and 23 developed ones for the period 19851995 He defines a dummy variable D that is equal to 1 for the developing countries and 0 for the others. Hypothesising that the impact of GDP growth on employment growth is lower in the developed countries than in the developing ones, he defines a slope dummy variable xD as the product of x and D and fits the regression (standard errors in parentheses): e = 1.45 (0.36) + 0.119 (0.10) x + 0.78 (0.10) xD R2 = 0.61, RSS = 50.23 He also runs simple regressions of e on x for the whole sample, for the developed countries only, and for the developing countries only, with the following results: 1 Whole Sample e = 0.56 (0.53) + 0.24 (0.16) x R2 = 0.04, RSS = 121.61 Developed countries e = 2.74 (0.53) + 0.50 (0.15) x R2 = 0.35, RSS = 18.63 Developing countries e = 0.85 (0.42) + 0.78 (0.15) x R2 = 0.51, RSS = 25.23 a Explain mathematically and graphically the role of the dummy variable xD in this model. b The researcher could have included D as well as xD as an explanatory variable in the model. Explain mathematically and graphically how it would have affected the model. c Suppose that the researcher had included D as well as xD. What would the coefficients of the regression have been? Problem 3 Use the data savings and consider the following model: ln(Savings)i = 1 + 2 ln(Income)i + 3Di + 4Di ln(Income)i + ui where ln stands for natural log and where Di = 1 for 1970 1981 and 1 for 1982 1995. a What is the rationale behind assigning dummy values as suggested? b What are the intercept and slope values of the savings function in the two sub periods and how do you interpret them? Problem 4 Suppose that a researcher, using wage data on 250 randomly selected male workers and 280 female workers, estimates the OLS regression 2 Wage = 12 \ .52 + 2.12 Male S.E() = (.23) S.E() = (.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. Define the wage gender gap as the difference in mean earnings between men and women. a What is the estimated gender gap? b Is the estimated gender gap significantly different from zero? c In the sample, what is the mean wage of women? Of men? d Another researcher uses these same data but regresses Wages on Female, a variable that is equal to 1 if the person is female and 0 if the person a male. What are the regression estimates calculated from this regression?