Control variables for firm size

[Khanh Dinh]

Dear friends in the Stata forum,

I am working with a (strongly balanced) panel data using DiD analysis for my research. I have two control variables for the firm size which are total assets (in $thousands) and the number of employees. However, I am not so sure which control variable is the best one to use. Is there any test in Stata to check this?

Also, when I conducted the Hausman test using the natural logarithm of the number of employees, the test result suggested me to use the fixed model effects --> desirable result. But the Hausman test implied the model was random when I used total assets. Does that mean the natural logarithm of the number of employees, in this case, is a good control variable to use?

Many thanks!

Here is my code:

generate y=ln(1+NoPatents)
generate x1=ln(1+RDE)
generate x2=ln(NoEmployees)

xtset, clear
xtset id1 year

xtreg y x1 x2, fe
estimates store fixed
xtreg y x1 x2, re
estimates store random
hausman fixed random

[Rhys Williams]

Dear Khanh,

Why can you not use both control variables in your regression? If both ought to be included then I don't see why you would not do so unless it seriously affects your degrees of freedom (in which case your sample size is probably too small to be meaningful anyway) or you suffer serious multicollinearity.

I don't believe the Hausman test provides the conclusions you are deriving. Instead, it would suggest that there is little correlation between the individual units and total assets but that there was correlation between number of employees and individual units.

In any case, I would suggest controlling for both variables.

Best,
Rhys

[Khanh Dinh]

Dear Rhys,

Thank you for your answer! I'm using the Hausman test as I'd like to show the research model needs fixed effects that would later be appropriate to test for the parallel trend assumption of DiD analysis. As my statistical test for parallel trend assumption is:

tvdiff y treated, model(fe) pre(1) post(1) vce(robust)

I agree with what you mentioned about the Hausman test but it can also be used to differentiate between fixed effects model and random effects model in panel analysis. When I used both variables, the Hausman test result implies a random effect model which is not a desirable result.

If you could provide me with further thoughts on this matter, that would be great.

Many thanks,
Khanh

[Rhys Williams]

Hi Khanh,

I think there might some confusion somewhere. The Hausman test is used to determine whether you should use fixed or random effects. If you should use fixed effects then this means that your individual observations are correlated with time-invariant characteristics (hence the need to use fixed effects), otherwise if Hausman suggests random effects then it means these two variables aren't correlated and the random effects model uses a weighted average of the between and within estimator.

It shouldn't be considered desirable or not to use a certain model... it depends upon the relationship between the variables. If Hausman suggests using RE then you ought to do this (if you want sound results), regardless of whether it is your prior desire.

The fact that the Hausman test suggests that the model controlling for both variables is RE should not really detract you from using such a method. Otherwise, you are basically saying that I want to do the test this way (only controlling for one variable and using FE) despite what the evidence tells me (unless you have strong theoretical grounds to suggest otherwise). Personally, I would advise against that.

That being said, I'm pretty sure that if you use FE rather than RE it is probably less risky than the reverse - you would increase the size of your standard errors (you might find less statistical significance) but you shouldn't introduce much bias. (However, this last statement shouldn't be used to condone such an approach!)

Best,
Rhys

[Khanh Dinh]

Hi Rhys,

It is clear and I understand now. Many thanks for your help!

Regards,
Khanh