Hi everyone!
I am running a linear regression with wage as dependent variable; education (dummy coded with 1=master; 0=bachelor) and gender (1=female; 0=male) are my categorical predictors. I am interested to see if the effect that gender has on wage is moderated by education education (i.e. comparing the gender wage gap for master and bachelor). Therefore, I have interacted education and gender and obtained the following results:

Code:
reg wage female##edulvl if cntry=="GB"

      Source |       SS           df       MS      Number of obs   =     2,117
-------------+----------------------------------   F(3, 2113)      =     76.15
       Model |  1171.64829         3  390.549429   Prob > F        =    0.0000
    Residual |  10837.4098     2,113  5.12892088   R-squared       =    0.0976
-------------+----------------------------------   Adj R-squared   =    0.0963
       Total |  12009.0581     2,116  5.67535827   Root MSE        =    2.2647

-------------------------------------------------------------------------------
         wage |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
--------------+----------------------------------------------------------------
     1.female |   -.426915   .1275451    -3.35   0.001     -.677042    -.176788
     1.edulvl |   1.406627   .1492304     9.43   0.000     1.113973    1.699281
              |
female#edulvl |
         1 1  |   .1045125   .2019969     0.52   0.605     -.291621     .500646
              |
        _cons |   4.507881   .0947753    47.56   0.000     4.322018    4.693743
-------------------------------------------------------------------------------
Is it correct, given the results, to say that in this case masters education does not moderate the effect that gender has on wage (i.e. masters education does not reduce the gender pay gap). Do I need to do something else (e.g. testing for difference between coefficients)?