If I have two regressors that should theoretically have opposite signed coefficients, should I switch the sign (i.e. multiply by -1) of one of the variables before creating an interaction term?
In my work, I found the 'correct' signs for the main regressors, one positive and one negative in the non-interacted regression. When I created an interaction term between the two, the main effects kept their original signs but the interaction term was insignificant.
I switched the signs of one of the variables (multiplied each observation by -1) and re-ran the regressions. Obviously, without the interaction term, the absolute value of the coefficient on that variable remained the same but the sign had switched. However, when I added the new interaction term, the coefficient on the interaction term was now significant.
Note that these are all continuous variables and interaction terms were based on mean-centered variables as in Balli & Sorensen (2013).
I'm not sure why this would happen. Is this acceptable? Is it normal? Should I be concerned about my data?