Interpreting interactions with dummy variables

[Antonio Miguel]

Dear all.
I’m running a model which has a continuous dependent variable (fees) and 2 binary variables: institutional (1 if institutional; 0 if retail) and international (1 if international; 0 if domestic)

reg fees i.dummy_institutional##i.dummy_international , robust cluster (id)


I’m getting the following results:

Intercept	1.1862***
	(130.14)
Dummy institutional	-0.1438***
	(-3.50)
Dummy international	0.2306***
	(23.75)
Dummy institutional x Dummy international	0.01412
	(0.47)

I’m struggling to interpret the results. The goal is to answer to 2 main questions:

1. Are there significant differences between the fees charged by institutional and retail international firms?
2. Are there significant differences between the fees charged by institutional and retail domestic firms?

Thanks in advance
Antonio

[Clyde Schechter]

margins dummy_international, dydx(dummy_institutional)

will give you a table with two rows of output. The first row, for dummy_international = 0, will show you the expected difference in fees charged by institutional vs retail domestic firms. The second row, for dummy_international = 1, will show you the expected difference in fees charged by institutional vs retail international firms.

[Antonio Miguel]

Dear Clyde,
Thanks for your quick response.
These are the results


Delta-method
dy/dx Std. Err. t P>t [95% Conf. Interval]

0.dummy_institutional (base outcome)

1.dummy_institutional
dummy_international
0 -.1438806 .0849669 -1.69 0.090 -.3104734 .0227121
1 -.1297634 .0393198 -3.30 0.001 -.2068568 -.05267



So, there are significant differences in both cases

Can you please help me to interpret the interaction coefficient (0.01412)?

If I understand, it shows that:
the difference in fees charged by institutional vs retail domestic firms (-0.1438) is not sign. different to the difference in fees charged by institutional vs retail domestic firms (-.1297)

but it also shows that:
the difference in fees charged by retail international firms vs retail domestic firms (0.2306) is not signif. different to the difference in fees charged by institutional international vs institutional domestic firms (0.24478=0.2306+0.01412)

Best regards
Antonio

[Clyde Schechter]

Can you please help me to interpret the interaction coefficient (0.01412)?

The interaction coefficient is a difference in differences. If you were to calculate the difference in expected fees between, say, institutional vs retail companies, the interaction coefficient is the difference between those differences when the companies are international vs domestic. Alternatively, if you were to calculate the difference in expected fees between international and domestic companies, the interaaction coefficient is also the difference between those differences with the companies are institutional vs retail.

I would not pay too much attention to the statistical significance of this. Hypothesis testing for interactions is usually underpowered. So unless you are working with a large sample, the absence of a statistically significant difference may well just represent insufficient information in the data. If you did a power analysis beforehand, then you would know if you have this problem or not.

[Antonio Miguel]

Dear Clyde, thanks very much
Antonio