I am analysing cross-section data from two time points, i.e. before and after an intervention and I am particularly interested in the causal effect of the intervention. The outcome of interest ($Y$) is metric and I have some control variables (all nominal or ordinal) like gender, size of company etc. In order to calculate the effect of the intervention I included a pre/post dummy into a regression model: $Y = a + b1*PrePost + b2*male + b3*small \ enterprise + b4*large \ enterprise$
I need some help with the interpretation: $b1$ is the effect of the intervention when all control var are held constant (in the two groups, pre- and post), right? Is that true even when one category of the dummies is left out?
How to interpret the coeffs on the dummies in relation to $b1$ (the most interesting coefficient of the intervention effect)?
How do I calculate the effect of the intervention ($b1$) for various subgroups defined by the dummies? Do I have to include the interaction of each dummy-categorie and the PrePost dummy - in addition to all group dummies? E.g. $Y = a + b1*prepost + b2*male + b3*small \ enterprise + b4*male*prepost + b5*small \ enterprise*prepost$
How are these coeffs then interpreted?