Small Variance estimating coefficients

[Darcy Hill]

I would just like to confirm my understanding is correct.

I am running a panel regression. One of my variables changes very little over the sample period.

'Including this variable with low variability will lead to an imprecise estimation of the coefficient on this variable?'

Or is it to do with the standard error of this coefficient?

Thank You

[Maarten Buis]

Why do you think the two statements are different?

[Darcy Hill]

Hi Maarten, I don't know. I have decided not to include this variable in my regression because It doesn't change much over the period. I wanted to know what the consequence of including it- would my coefficient be unreliable as it would have a large standard error?

[Phil Bromiley]

At the extreme, if it doesn't vary at all you can't estimate a parameter. But, even extremely low variance will usually give you legit parameter estimates.You might find a very large parameter on this variable since a one unit change is an extremely large change for a variable with low variance. You can usually rescale x's without changing statistical significance or anything substantive - a one unit change just has a different meaning.