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I have a regression as follows:

log(Wage) = B1Female + B2Non-white + B3(Female X Non-white) + Fixed-effect + e

My understanding is that,

  1. the change in the wage for white-male = 0 (baseline)
  2. the change in the wage for non-white-male = B2
  3. the change in the wage for white-female = B1
  4. the change in the wage for non-white-female = B1+B2+B3

Thus, for female, being non-white would change the wage = B2+B3 Also, for male, being non-white would change the wage = B2 So, the effect of being non-white in male and female on wage change is different by (B1+B2+B3) - B2 = B1 + B3

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  • $\begingroup$ Seems correct... $\endgroup$
    – Roger V.
    Commented Nov 28 at 18:51

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Yes this is the usual dummy encoding for an interaction. I have 2 minor notes on what you wrote:

a) You model is on the log-scale, which means you solved for the mean of logs which is not the log of the mean.

b) Be careful with the causal language like effect. Really you are describing observed differences which may or may not be effects of the variables.

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