Low variations in the independent variable

[Jovana Ju]

Hello Stata users!
I would like to ask for your help regarding a dilemma I have. Namely, the independent variable I plan to use in my panel data model has low variations; specifically, I mean that 95% of its values are between 0 and 0.06. I have a total of 650 observations. Is there a problem with this, and if so, what could be a potential solution?
Thank you

[Nick Cox]

No more than if you changed the units to a range from 0 to 6 or from 0 to 600 or ...

A plot of your dependent variable against this one would surely be instructive.

You say "my independent variable". Are there others?

[Maarten Buis]

We don't know if you have low variation from what you have told us. That depends on how that variable is scaled. It could be monthly income of an individual measured in trillions of euros. In my infinite kindness I will accept a monthly income of 0.06 trillion euros... So a range of 0 to 0.06 trillion euros is not low variation. In short, numbers on their own (not saying what they mean, what the unit is, etc.) are meaningless. For an example, look up what the answer is to the ultimate question of life, the universe, and everything.

But for the sake of argument, lets assume there is low variation. At it's core most statistical analyses are comparisons: people with a lot of some variable x tend to have more of some variable y compared to people with less of the variable x. To get a reliable estimate you need people with a lot of x and people who have less of x. That is the problem with low variability: you cannot compare if everybody is the same. Moreover, there is no solution. The purpose of statistical techniques is to allow you to extract information from the data. If the information does not exist in the data, then no technique can extract things that do not exist.

You also mentioned that this is panel data. In that case the more pressing question is whether change in x over the duration of the study. The real power of panel studies is that you can really see how a change in x is associated with a change in y, assuming x does change enough over the duration of the study to reliably estimate that comparison.

John Tukey summarized the problem you have in John Tukey (1986), "Sunset salvo". The American Statistician 40(1):72-76. as: "The combination of some data and an aching desire for an answer does not ensure that a reasonable answer can be extracted from a given body of data."

[Jovana Ju]

Thank you very much for your response!
Yes, Mr Cox, I also have several control variables in the model. Besides what I mentioned, is it problematic that some values of this independent variable are zeros? I have that value in 29 observations. These values pertain to emissions of certain pollutants, and the zeros occur in the years when there were no emissions

[Maarten Buis]

is it problematic that some values of this independent variable are zeros? I have that value in 29 observations.

No, there is nothing special about the value 0 (as long as you are not taking logarithms or divide anything by it).

[Jovana Ju]

Thank you very much!

[Nick Cox]

Plotting the outcome against all other variables is recommended.