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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"?

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  • $\begingroup$ 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). $\endgroup$
    – Richard Hardy
    Commented Mar 18, 2015 at 19:31

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You've got it right. Say "increases", rather than "higher" because x is continuous.

Whether you refer to the low-debt countries comes down to whether you want to discuss the presence of an interaction. If you do, then talk about them, if not, then don't.

Also notice that you can recode the contrasts to be 1 and 0, instead of 0 and 1, and a2 will give you the effect of x on y for high-debt countries.

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