Interpreting a 3-category dummy variables and interaction terms

[nazlikaramollaoglu]

Dear All,

I run the following model:
Suppose I have a dummy variable: small, medium, large; and the reference category is small.


Interactive Model: y = a + bX + cmedium + dlarge + emediumX + flargeX.

reg Y X medium large mediumX largeX

b is the effect of X on y for the "low" category,
b+e is the effect of X for the “medium “category
b+f is the effect of X for the “large” category.

Are the following interpretations correct?

If e >0, this means that medium sized firms are affected from X more than small sized firms.
If f >0, this means that large sized firms are affected from X more than small sized firms.
If b>0, this means that small sized firms are affected positively from X
If d>c implies that larger firms have larger Y

Also,

1. How can I test whether medium firms are affected (from X) more or less than large sized firms?

1. How can I interpret c&d?

[Clyde Schechter]

Your interpretations are correct.

You can test the contrast between medium and large firms by running -test c = d-.

The interpretation of c is that it is the difference between the effect of X in small firms and the effect of X in medium firms. Similarly, the interpretation of d is that it is the difference between the effect of X in small firms and the effect of X in large firms.