How Does Gender Interaction with Experience Affect Salary Differences?

[statsfanatic]

hi,
i used stata to regress these two models,
the problem is about gender and wage descrimination and stuff like that.
experience and gender are the predictors for salary.

so here are the multiple regression results, also gender is a dummy variable with 1 = male and 0 = female:

model 1 without interaction:
regress salary exp gender

Source | SS df MS Number of obs = 12
-------------+------------------------------ F( 2, 9) = 112.51
Model | 4.5962e+09 2 2.2981e+09 Prob > F = 0.0000
Residual | 183835117 9 20426124.2 R-squared = 0.9615
-------------+------------------------------ Adj R-squared = 0.9530
Total | 4.7801e+09 11 434552604 Root MSE = 4519.5

------------------------------------------------------------------------------
salary | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
exp | 3534.216 320.6494 11.02 0.000 2808.857 4259.576
gender | 26550.33 2609.35 10.18 0.000 20647.57 32453.09
_cons | 13711.1 3792.469 3.62 0.006 5131.935 22290.26



Model 2 with interaction:

.generate cross=gender*exp

. regress salary exp gender cross

Source | SS df MS Number of obs = 12
-------------+------------------------------ F( 3, 8) = 1813.92
Model | 4.7731e+09 3 1.5910e+09 Prob > F = 0.0000
Residual | 7016925.79 8 877115.724 R-squared = 0.9985
-------------+------------------------------ Adj R-squared = 0.9980
Total | 4.7801e+09 11 434552604 Root MSE = 936.54

------------------------------------------------------------------------------
salary | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
exp | 2590.805 93.96821 27.57 0.000 2374.114 2807.496
gender | 7053.171 1475.829 4.78 0.001 3649.902 10456.44
cross | 1886.822 132.8911 14.20 0.000 1580.375 2193.27
_cons | 23459.68 1043.569 22.48 0.000 21053.2 25866.15


the bold points are the new predictor values. cross is the interaction variable between experience and gender.
please help me understand how to interpret the new values of the variables for model 2 and what they mean for female and male salaries?

 

[EnumaElish]

I will assume exp is measured as a positive continuous variable (e.g. "years employed").

Your 2nd equation is really like two equations:
for gender = 0: salary = 23459 + 2590 exp
for gender = 1: salary = (23459 + 7053) + (2590 + 1886) exp

You should verify that you get the above two equations by setting gender to either of its two possible values.

Therefore:
expected salary for gender = 0 with no experience (exp = 0) is about 23459.
expected salary for gender = 0 increases about 2590 with each additional year.
expected salary for gender = 1 with no experience (exp = 0) is about 23459 + 7053.
expected salary for gender = 1 increases about (2590 + 1886) with each additional year.

 

[tacman]

Sure, I can help you interpret the interaction variables in your regression models. An interaction variable is created by multiplying two predictor variables together, in this case, experience and gender. This interaction variable allows us to see if the relationship between experience and salary differs for males and females.

In model 1 without the interaction, the coefficient for gender is 26550.33, which means that on average, males earn $26,550 more than females. This is a significant difference and suggests that there may be gender discrimination in wages.

In model 2 with the interaction, the coefficient for gender decreases to 7053.171. This means that when we consider the interaction between experience and gender, the difference in salaries between males and females decreases to $7,053. This suggests that the relationship between experience and salary may differ for males and females.

The coefficient for the interaction variable, cross, is 1886.822. This means that for every one unit increase in experience, the difference in salary between males and females increases by $1,886. This suggests that as experience increases, the gender wage gap also increases.

To interpret the results for males and females separately, we can look at the coefficient for experience and the interaction variable. For males, the coefficient for experience is 2590.805 and the coefficient for the interaction variable is 1886.822. This means that for every one unit increase in experience, the salary for males increases by $2,590, and for every one unit increase in experience, the difference in salary between males and females increases by $1,886.

For females, the coefficient for experience is 2590.805, which means that for every one unit increase in experience, the salary for females increases by $2,590. However, the coefficient for the interaction variable is 1886.822, which means that for every one unit increase in experience, the difference in salary between males and females increases by $1,886. This suggests that for females, the gender wage gap widens as experience increases.

In summary, the interaction variable shows us that the relationship between experience and salary differs for males and females, and the gender wage gap may increase as experience increases. This suggests that there may be underlying factors, such as gender discrimination, that contribute to the gender wage gap.