Question

Question Four marka (a) You are given the following information on 10 dividual Individual Wage 25.00 12.00 Black White 10.00 15.00 21.00 21.63 7.51 11.00 Black to the alle Create dummy variables for the Race variable and add them to the table. 13 marks] (b) Consider the model WAGE=A+, EDUC+8, EDUC+8,FEMALE+ where WAGE is hourly wape in US dollars, EDUC is years of education, FEMALE is a dummy variable that assumes the value for females and the value for males, and is a random com The model is estimated based on a random sample of 150 observations and the following results obtained WAGE 22.6484 - 2.8464 EDUC+0.2337 EDUC - 2.4132 FEMALE Interpret the estimated values of and [4 marks] (c) Consider the model: WAGE- + 4 EDUCA EDUC+ FEMALE FEMALEX EDUC+, FEMALE EDUC where WAGE is hourly wage in US dollars, EDUC is years of education, FEMALE is a dummy variable that assumes the value for females and the value for males, and u is a random error term The model is estimated based on a random sample of 150 observations and the following results obtained WÁGE - 18.61 -1.48 EDUC+0.15 EDUC+15.95 FEMALE-4.83 FEMALE EDUC+0.28 FEMALEX EDUC Ohin the predicted wage for male and females. 15 marks]

please help,it is a revision question for my exam tomorrow and i am stuck

Answer 1

(a) Since there are 3 types of race, we can use 2 dummy variables in the presence of the intercept in the model. The variables created in the table are D_White, which takes a value 1 if the individual is white, else 0. Similarly, the dummy variable D_Black takes a value 1 if an individual is black, else 0. The variables have been shown in the table below. For example, individual 5 is an Asian (i.e., neither white, nor black). Hence, both the dummy variables created have a value 0 for this individual.

Indiviual Wage D_White D_Black 19.23 Education Race 14 White 14 White 13 White 13 Black 9 Asian 9 Black 9 White 13 Asian 9 Black 9 Black H-I--00-00

(b) Wage = B. + B.EDUC + B2EDUC + B,FEMALE + u, and Wage = 22.6484 -2.8464 EDUC +0.2337EDUC? - 2.4132 FEMALE The estimated value of B, i.e.., B, = -2.8464. It means that the wage reduces by 2.8464 with every increase in years of education or wage increases by 2.8464 with every decrease in years of education. Similarly, ehe estimated value of B4, i.e., Be = -2.4132. It means that the average wages for female is 2.8464 less than their male counterpart. (c) Wage = B1 + B,EDUC + BEDUC? +B.FEMALE + BsFEMALE EDUC + BEFEMALE EDUCP+u, and To get the predicted value of wage for male and female, we need the values of the independent variables (at least one observation). These values can be multiplied with respective regression coefficients to get the predicted values. Note that, for female, all the terms need to be considered, whereas for male, only the first three terms would be used and rest of the terms will vanish. Hence, Wage = 18.61 – 1.48 EDUC + 0.15 EDUC' + 15.95 FEMALE – 4.83FEMALE EDUC + 0.28FEMALE * EDUC? For example, let us predict wage for a person who has 10 years of education and is a male. => Wage = 18.61 – 1.48 + 10 +0.15 * 102 + 15.95 * 0 - 4.83 *) * 10 +0.280 * 102 => Wage = 18.61 – 1.48 + 10 + 0.15 10º = 18.81 On the other hand, the predicted wage for a female with 10 years of education would be: => Wage = 18.61 - 1.48 + 10 + 0.15 * 10° + 15.95 1 -4.83 110+ 0.28 * 1 * 102 = 14.46