Grouped Regressions

[Stijn Machtelinckx]

I am new to Stata so my apologies for any inconvenience regarding the standard structure of Stata Posts.

I have performed some regressions (OLS & Fixed effects) based on different groups for example:
OLS:
by SG, sort : regress lnMFP downturn##Zombie recovery##Zombie

FE:
by SG, sort : xtreg lnMFP downturn##Zombie recovery##Zombie, fe

Where SG stands for Size Group: large firms have received the dummy 1 and small firms have received the dummy 0.

My data is panel data where I have for every company each year observations.

I would like to know whether the coefficients are significantly different for the different regressions and the different size groups.

Is there some code that I could apply to know this in Stata?

Thank you very much for your time and help. If something is not clear, please let me know.

[Øyvind Snilsberg]

maybe you'll find the following example useful,

sysuse auto, clear

*instead of separate regressions for domestic and foreign cars,
bysort foreign: reg price mpg turn

*do one regression that includes foreign as well as interactions between foreign and the other covariates in the model,
reg price (c.mpg c.turn)##i.foreign

*that way, you can use lincom to test whether the coefficient on, e.g., mpg differs based on car origin,
lincom c.mpg#0.foreign - c.mpg#1.foreign

[Stijn Machtelinckx]

I understand what you are saying but I am afraid that the number of interactions will become too big resulting in difficult interpretability I assume. Therefore I would like to run separate regressions and check whether the coefficients are significantly different or not from each other.

[Leonardo Guizzetti]

Øyvind has already shown you how to run separate regressions, as well as a sound method for formally testing significance between related coefficients. Assuming you have enough observations in each subgroup of firm size to model the 3-way interaction above, there should be no difficulty in interpreting coefficients. One big advantage of modeling the separate subgroups in a single model in which group size is interacted with all other variables is that you can use a likelihood ratio test to jointly test this model versus a simpler model that assumes that coefficients are the same in both sizes of firm plus the coefficient for firm size. That is, testing the reduced model in which the interactions with group size are assumed to be zero.