Hi, I am currently using a panel data-set to identify ethnic pay differentials. My dependent variable is log monthly income and my explanatory variables include race and number of dependent children, amongst other control factors. I have completed my regression using OLS, random effects and the Mundlak approach.

I am also attempting to look at the potential additional effect of increasing the number of dependent children by ethnicity. Therefore, I have estimated my regression and used the following command to estimate the effect of my interaction term which is race*dependent_children:
margin race ,dydx(dependentchildren)

I wanted to see if this was the best method to use to estimate this and how to interpret the dy/dx below? In my regression analysis the base group was 'british/english/scottish/welsh/northern irish (white)', which was therefore excluded from the regressions, therefore do my results need to be interpreted relative to the base group still?

Also, the co-efficients in my regression analysis on each race category and dependent children were both negative, where this has generated positive results. Could there be a potential reason for this?

Table:
dy/dx w.r.t dependentchildren dy/dx Std. Err t P>|t|
95% Conf. Interval]
race
british/english/scottish/welsh/northern irish (white) .0668368 .004582 14.59 0.000 .0578556 .075818
indian (asian or asian british) .0315714 .012957 2.44 0.015 .0061745 .0569683
pakistani (asian or asian british) .0367387 .0134726 2.73 0.006 .0103312 .0631462
bangladeshi (asian or asian british) .0325315 .0142156 2.29 0.022 .0046676 .0603954
any other ethnic group (other ethnic group) .0470928 .0127087 3.71 0.000 .0221825 .0720031



Thanks