Consider the following ordinary least squares regression output of the determina
ID: 3223389 • Letter: C
Question
Consider the following ordinary least squares regression output of the determinants of the hourly wages of a group of factory workers. {Standard errors are presented in parentheses): wage_i = 12.52 + 1.27 ex[er_i + 0.89 age_i + 1.90 male_i (3.21_ (0.413) (0.329) (0541) n = 150 R^2 = 0.123 R^2 = 0.117 The variable wage is the hourly wage, exper is the years of experience of the worker, age is measured in years and male is a dummy variable that takes on a value of one of the participant is male and zero if female. i) All other factors being equal, is there evidence of a wage differential between men and women? How strong is the evidence? ii) The model is extended to include an interaction term between exper and male. The regression output is as follows: wage_i =12.39 + 1.09exper_i, + 0.91age_i + 130male_i + 0.59male_i, times exper_i (3.12) (0.490) (0.36l) (0.412) (0.122) n = 150 R^2 = 0.123 R^2 = 0.117 Interpret the coefficient on male and the coefficient on the interaction term between exper and male. What do these estimated coefficients tell you about the gender wage differential?Explanation / Answer
Part-i
To know a wage differential between men and women we will test the significance of coefficient of male in regression model.
Test statistic t= beta/SE =1.90/0.541=3.51
Degree of freedom=n-k-1=150-3-1 =146
p-value=0.000596255 using excel function =TDIST(3.51,146,2)
As p-value<0.001, so we conclude that the coefficient of male is significant and there is strong evidence as p<0.001. So, all other factors being equal there is strong evidence of a wage differential between men and women and men on an average earn $1.90 higher than women, ceterius peribus.
Part-ii
Coefficient of male is 1.30 which means that for zero experience people, men earn on an average $1.30 per hour more than women. The interaction coefficient is 0.59 which means that for men, corresponding to a one year increase in experience there is on an average $0.59 per hour more income than women of same experience. This tells wage differential as for same experience men earn more than women.