How to demonstrate that some variables "do not vary much"? I have a continuous variable (say, sales volume) that I measure for multiple firms over a time period of ten years (but I do not have data across the full ten years for all firms, some drop out, some enter my sample). I want to show that, for each of these firms, there is not a lot of variation in this continuous variable over time, within any given firm.
Added complication: The continuous variable is logged, so it does not have an intuitive interpretation.
What is the best way to show that there is "not much variation," ideally in a single number?
(And yes, I know that there is no technically "correct" answer to this, and "not much variation" is utterly unspecific; I am really just looking for ways to give a reader a quick intuitive sense of whether there is a lot it not a lot of variation over time)
 A: If the variability is "small", the standard deviation of the logs will be a reasonable measure of the typical "percentage deviation" from the geometric mean.
e.g. if the standard deviation of the logs is 0.05, that means that a "typical" amount of deviation from the geometric mean is around 5% above or below. (As this gets to much over 0.10 it starts to be less useful as a direct approximation but it's still a good bit smaller than the distinction between root-mean-square deviation and average absolute deviation of the logs, which we're sort of glossing over; if you're happy with that level of glossing over, it's still reasonable up to about 0.25 or even a bit higher).
This standard-deviation-of-the-logs will also be a good approximation to the coefficient of variation when it's small.
A: Intuitive option:
Given the fact that there is concern about each firm having a different mean wouldn't the R-squared of the following regression give a nice heuristic for the amount of within-firm variance?
$$ log(volume)_{i,t} = \theta_i + u_{i,t}$$
where $\theta_i$ are saturated indicators for the firms. A "high" R-squared means that most of the variance in revenues is happening as across- rather than within-firm variance. If the panel is "close" to balanced my intuition is that the R-squared will tell you the percent of variance that is within vs across firms. Then you can decide what threshold is "not much" within-firm variance.
