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Suppose I run an OLS regression as follows:

Y = γ1 + γ2*X + γ3*(D*X)

where D is a dummy variable. I excluded one dummy variable, so the effect is in γ2 and γ3 must be interpreted as the difference in effects between the included and the excluded dummy variable.

Let's suppose the regression results are as follows:

Y = 2 + 3*X + 4*(D*X)

How should I report the effect for the included dummy variable? Should I say 4 or 7 (3 + 4)? What is common in the scientific research to report? And how to assess statistical significance of 7?

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1 Answer 1

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You've included an interaction dummy variable ($D*x$) also know as "change in slope" dummy variable, which is different from a "change in the intercept" (i.e. $γ_4D$). The latter is easier to interpret.

In your model, the presence of the dummy variable ($D=1$) means that the equation is $y = 2 + 3x + 4*(1*x) = 2 + 3x + 4x = 2 + (3 + 4)x = 2 + 7x$. And when $D=0$, then the equation simplifies to $y = 2 + 3x$.

So, the actual marginal effect of the dummy over the slope of $x$ is $γ_3$ (=4), so the significance test should be over that sole coefficient ($γ_3 = 0$). For example, if $γ_3>0$ and $γ_2>0$ that will mean an additional slope for the variable $x$ given that dummy.

(However, if you want to check if the slope of $x$ including the dummy is significant you could test if $γ_3 + γ_2 = 0$ or test simultaneously that $γ_2=0$ and $γ_3=0$. Note that those tests are different, depending on your goal and the nature of the variables).

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