When the regression coefficient of the interaction term is 1

[Sang-Bum Park]

Hi

Can the regression coefficient of the interaction term be exactly 1? I am not sure whether I should take the result as reliable.

I analyze the interaction effect between x1 and x2 after residual centering of the interaction term. The process and the results are as follows. These are fixed effects models including year dummies.
First, the coefficients of the lower terms between the independent variable (x1) and moderation (x2) are estimated.

xtreg F.y y x1 x2 i.year, fe vce (robust)

Then, the interaction term between x1 and x2 is added to the model.

xtreg F.y y x1 x2 x1x2 i.year, fe vce (robust)

Residual centering is conducted by following Sauer (2014). The residuals option is replaced with the option epsilon (e), following the suggestion from Statalist (the link attached below).

predict x1x2_rc, e

Then, I run the model again with the centered interaction term.

xtreg F.y y x1 x2 x1x2_rc i.year, fe vce (robust)

The coefficients of the lower terms (x1, x2) are identical to those from the first estimation. But, the regression coefficient and the significance is changed dramatically.
Can I take this result?


Reference
Sauer, C. 2014. Orthogonalizing powered and product terms using residual centering. Stata Journal, 14(1): 226–229.
https://www.statalist.org/forums/for...-a-fe-re-model