Question

The following equations have been estimated by Ordinary Least Squares (OLS), where Y denotes annual earnings, P job evaluation points, and the subscripts m and f denote male and female respectively:

Y_m = 5000 + 100P_m

Y_f = 4000 + 80P_f

Assume the average job evaluation score was 300 points in male-dominated jobs and 200 points in female-dominated jobs.

1. What is the average pay in male-dominated jobs and in female-dominated jobs?
2. Use a Oaxaca decomposition to determine the average pay differential between male and female dominated jobs into two components: a portion attributable to the difference in job evaluation points (valued according to the male pay for such points) and a portion attributable to differences in pay for the same job evaluation points.
3. Use that same decomposition, but this time evaluate the differences in job evaluation points according to the female pay for such points.

Answer 1

A.

The average pay in male-dominated jobs can be calculated using the given equation and the given average job evaluation points for male-dominated jobs, 300.

Ym = 5000+100*300 = 35000

The average pay in female-dominated jobs can be calculated using the given equation and the given average job evaluation points for female-dominated jobs, 200.

Yf = 4000+80*200 = 20000

B.

Oaxaca decomposition can be explained using the above example

The following three equations illustrate this decomposition. We can use the given estimated different linear wage regressions for individuals in Male and Female groups:

1) Y_m = 5000 + 100P_m

2) Y_f = 4000 + 80P_f

where P is an explanatory variable for average job evaluation points for male (m) and female (f) dominated jobs, 100 and 80 are coefficient.

Then, since the average value of residuals in a linear regression is zero, we have:

3) Mean(Ym) - mean(yf)

= 100*mean(Pm) - 80*mean(Pf)

= 100*(mean(Pm) - mean(Pf)) + mean(Pf)(100-80)

= 100*(300-200) + 200(20)

= 100*100 + 4000, here 10000 is attributable to the difference in job evaluation points (valued according to the male pay for such points) and 4000 is attributable to differences in pay for the same job evaluation points.

= 14000

C.

Same decomposition can be illustrated using eq 3 in the following reprised form;

4) Mean(Yf) - mean(Ym)

= 80*mean(Pf) - 100*mean(Pm)

= 80*(mean(Pf) - mean(Pm)) + mean(Pm)(80-100)

= 80*(200-300) + 300(-20)

= 80*(-100) + (-6000), here -8000 is attributable to the difference in job evaluation points (valued according to the female pay for such points) and -6000 is attributable to differences in pay for the same job evaluation points.

= -14000