# Interpretation of Interaction Term with Dummy [duplicate]

I am trying to interpret the following model:

                                 y=a1+a2*x+a3*d+a4(x*d)+e


where

y= growth rate

x=debt

d= dummy high debt countries (=1 for high debt countries; =0 low debt countries)

The problem is on the interpretation of the interaction term.

For example, i want to interpret the impact of x*d on the dependent variable (y), what i say is :

"if the x increases by 1% then growth rate of high debt countries increases by (a2+a4)".

Is it correct to say increases or I have to say higher? In addition, should I refer that "if the x increases by 1% then growth rate of high debt countries increases by 0.03 more than low debt countries" or it does not need to refer "low debt countries"?

## marked as duplicate by whuber♦Mar 18 '15 at 21:14

• You can use if...then constructions when you know there is causality. However, regression alone does not imply causality; hence, you must be relying on some outside information when you make causal statements based on regression results. Regarding the last question, yes, you need to refer to low debt countries because a4 shows the effect of x for high debt countries relative to low debt countries (rather than relative to, say, the average of high and low growth countries). – Richard Hardy Mar 18 '15 at 19:31