A subsample from the Current Population Survey is taken, on weekly earnings of i

Question

A subsample from the Current Population Survey is taken, on weekly earnings of individuals, their age, and their gender. You have read in the news that women make 70 cents to the $1 that men earn. To test this hypothesis, you first regress earnings on a constant and a binary variable, which takes on a value of 1 for females and is 0 otherwise. The results were: Eam = 570.70 - 170.72 Times Female, R^2=0.084, SER = 282.12. (9.44) (13.52) (a) Perform a difference in means test and indicate whether or not the difference in the mean salaries is significantly different. Justify your choice of a one-sided or two-sided alternative test. Are these results evidence enough to argue that there is discrimination against females? Why or why not? Is it likely that the errors are normally distributed in this case? If not, does that present a problem to your test? (b) Test for the significance of the age and gender coefficients. Why do you think that age plays a role in earnings determination?

Explanation / Answer

Males earn $570.70, females $399.98. Percentage of average female income to male income is 70.1% in the sample.

a)

Use the difference in means formula to find t.The t-statistic is -12.63, while the critical value is –1.64. The difference is therefore statistically significant. A one-sided alternative was chosen since the claim is that females make less than males. This represents
little evidence of discrimination, since attributes of males and females have not been included. Given that earnings distributions are not normally distributed, the errors will also not be distributed normally, and assuming that they are, results in problematic inference.

b) The t-statistics are 9.36 for the age coefficient, and -13.00 for the gender coefficient. Both of these values are greater than the (absolute) critical value from the standard normal distribution (1.64). Hence you can reject
the null hypothesis that these coefficients are zero. Age proxies “on the job training.” A better proxy that has been used frequently in the past is the Mincer experience variable (Age-Education-6). Obviously this is a better proxy for some subsample of individuals than for others.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.