How to interpret interaction terms with dummies?

[Armand Ndraxi]

Hello,
I have a panel dataset that consists of countries and firms for each county. I want to test the effect of Firm Growth, Asset Tangibility, Profitability and Liquidity on Leverage ratio and whether these variables change from Developing to Developed countries.

My command is as follows.
xtreg LEVERAGE c.l1.LEVERAGE##i.GDP_tv c.GROWTH##i.GDP_tv c.LIQUIDITY##i.GDP_tv c.PROFITABILITY##i.GDP_tv c.ASSETTANGIBILITY##i.GDP_tv i.Country_new, re cluster(Firm_new)

Here, GDP_tv is a dummy I have generated with 0 for Developing countries if GDP<20000 and 1 for Developed countries if GDP>20000

As I run my regression, the results show the following (short illustration):

GDP_tv DEVELOPED

Growth

c.Growth#GDP_tv DEVELOPED


Bottom line, there is a list of all the independent variables and their interactions with the respective coefficients, se, p-values and so on.

Could you please help me with how can I interpret GDP_tv DEVELOPED?

Also, can I say that the coefficient of each variable is the effect of that variable on the dependent one (without distinguishing between Developed and Developing), while the coefficient of the interaction is the effect when talking about Developed countries as compared to Developing?

What if the interactions are insignificant? What does it mean?

Thank you in advance.

P.S I am new in Stata list and have not been able to use the coding option to provide you with my full results properly.

[Jaselyn Taubel]

Hi, Armand,

Since your question is an interpretation (rather than technical) question, I may be able to offer some help. Please let me know if I have misunderstood anything from your question.

For me, the easiest way to think of interpreting coefficients on dummies and interactions is by thinking of the coefficient as telling me the effect on the intercept and the slope, respectively. So if GDP_tv DEVELOPED is a dummy, then the coefficient is telling you how much higher, on average, all else equal, Leverage is in a Developed country than a Developing country. That is, it tells you the average effect on Leverage from switching from a developing to a developed country. For the interaction term, it's telling you the effect on the slope of your regression line. So the coefficient on c.Growth#GDP_tv DEVELOPED is telling you how the effect of Growth on Leverage changes when you go from a Developing to a Developed country. If the interaction is insignificant, then it means that there is no statistical difference in the effect of Growth on Leverage between developed and developing countries. Whether or not statistical significance implies empirical significance is something you'll have to figure out based on your data, results, etc.

I hope that helped!

Jaselyn

[Armand Ndraxi]

Hello Jaselyn,

Your insight was very helpful and very clear.

My only concern is that, aside for the interaction term, say c.Growth#GDP_tv DEVELOPED, I also have Growth as a separate variable.

How can I read the results of this variable (in terms of significance and magnitude)?

[Jaselyn Taubel]

Every coefficient should be interpreted ceteris paribus (all else being held equal). So the coefficient on Growth by itself is telling you the effect on Leverage of a one-unit change in Growth. The coefficient on the interaction term is telling you, essentially, how the coefficient on Growth changes when you go from a developing to a developed country.

[Armand Ndraxi]

Dear Jaselyn,

Many thanks. Your help is very much appreciated.