Fixed Effects and Dummy Variable

[Wanqi Luo]

Hi,

I have a question related to using dummy variable in fixed effects model. The data set I used includes 10 companies in 15 years. I intend to examine the difference between two groups of companies in terms of the relationship between profitability and service quality, therefore, I want to interact a dummy variable with an independent variable to see the difference. However, in my understanding, the time-invariant dummy variable will be automatically dropped out during regression, how can I solve this problem?

The model I set up is shown as below:
R_it = β1Q_it-1 + β2(D_i*Q_it-1) + ε_it

Thanks in advance! Looking forward to your reply!

Best regards,
Crystal

[Clyde Schechter]

That is correct, the time-invariant indicator ("dummy variable") that identifies the two groups of companies will be dropped out of the model. That is not a problem. The effect of that dummy variable is not identifiable in a fixed effects model, but it is also irrelevant to your goal. The difference between the two groups of companies in the relationship of profitability and service quality will be given by the coefficient of the interaction term. The interaction term will not be dropped, and it is all you need.

By the way, the equation you show is not a fixed-effects model, because it lacks a fixed effect at the company level. A correct equation would look like:

R_it = β1Q_it-1 + β2(D_i*Q_it-1) + u_i + ε_it

[Wanqi Luo]

Dear Clyde,

Thanks so much for your reply! Just want to confirm my understanding that if I interact the dummy variable with an independent variable, then the interaction item will not be dropped because the interaction item is not time-invariant? but if I use a single dummy variable in the equation, then it will be dropped, right?

Again, thanks for pointing out the error, I'll fix it!

Best regards,
Crystal

[Clyde Schechter]

Thanks so much for your reply! Just want to confirm my understanding that if I interact the dummy variable with an independent variable, then the interaction item will not be dropped because the interaction item is not time-invariant? but if I use a single dummy variable in the equation, then it will be dropped, right?

Assuming that your data is correct and the service quality variable itself is not time-invariant, then this is correct. However, the dummy variable by itself will be dropped: if you include it and Stata doesn't drop it that tells you that there is a mistake in your data!