Significance of the main effects when main effects aren't significant but interaction is

[Umito Takao]

Dear Statalisters,

Hi, I have a problem about interpreting significance of the main effects and interaction term.

I have a panel data of X1 and the Y for each country and over a few decades, and I have been analyzing the relationship between these two variables. In my analysis I hypothesized that the X1 does not have significant effect on Y for a few years, but after that it starts to show significant and positive effect on Y. Hence I created a dummy variable X2 that indicates 1 if more than 3 years has passed and 0 otherwise, and introduce an interaction term between X1 and X2. The results shows significant and positive effect of interaction term but insignificant effect of X1. From this I can see that the X1 does not have a significant effect when the X2 is 0, and that the effect of X1 significantly increases when X2 becomes 1. However, from the results, I cannot tell whether the effect of X1 will be significant when X2 becomes 1.

Would it be possible for me to know the significance of the effect of X1 conditional on X2 being 1?

Best,
Umito

[Clyde Schechter]

You do not show your regression output, but assuming that your variables really are named X1 and X2 and that you properly introduced these variables into your regression command as c.x1##i.X2, you can get that with:

lincom _b[X1] + _b[1.X2#X1]

That said, the American Statistical Association now recommends abandonment of the concept of statistical significance. You should be looking at the magnitude of effects of X2 conditional on X1 = 0 and X1 = 1, along with an estimate of their uncertainty, such as the standard error or confidence interval. Comparing a p-value to 0.05 or any other arbitrary threshold is now deprecated. See https://www.tandfonline.com/doi/full...5.2019.1583913. The -lincom- command I have shown here will provide those statistics (as well as a p-value).