Insignificant predictor in DID Analysis

[Pranshu Tripathi]

I performed a DID analysis in panel data with a fixed-effect regression model. I have two dummy and one continuous predictor. When I run the regression by interacting the two dummies then the continuous predictor is significant but when I interact all the predictors that are group dummy, treatment dummy, and continuous predictor then the coefficient of the continuous predictor is insignificant. How should I interpret it?

[Clyde Schechter]

When the model contains the continuous variable (which, for the rest of this post, I will call x) but x is not interacted with anything else, then the coefficient of x that you get is an estimate of the effect of x on the outcome (adjusted for everything else). However, when you do another model in which x is interacted with other variables (let's call them u and v), then the model is stipulating that there is no such thing as the effect of x on the outcome. Rather the model says that there are many different effects of x on the outcome, corresponding to all possible combinations of values of u and v. The result that you see in the output as the coefficient of x, therefore, is a completely different thing from what the coefficient of x in an uninteracted model. They don't have to be the same, and usually aren't. They don't have to be close to each other, nor even have the same sign, let alone the same significance. The interpretation of the coefficient of x in a model that contains u#v#x interaction is that it is the effect of x on the outcome when u and v are both 0.

Added: By the way, none of the above depends at all on x being continuous, nor does it require two variables u and v. It is all equally true regardless of what type of variable x is, and you can have just one variable, or more than two variables interacting with x.

[Pranshu Tripathi]

Thanks, Clyde.
You cleared my doubt.
Kind Regards