Hello. I have panel data. How could we calculate the share of inter and intra variabilities in total variabilities? A reviewer of an econometrics journal recommends reporting such share. Stata’s “xtsum” reports the standard deviations for overall, between, and within. However, the sum of the between (inter) and within (intra) variances is not equal to the overall variance, and the standard deviation for between can be larger than the standard deviation for overall, as follows.

https://www.stata.com/manuals13/xtxtsum.pdf

. use http://www.stata-press.com/data/r13/nlswork
(National Longitudinal Survey. Young Women 14-26 years of age in 1968)

. xtsum hours

Variable | Mean Std. Dev. Min Max | Observations
-----------------+--------------------------------------------+----------------
hours overall | 36.55956 9.869623 1 168 | N = 28467
between | 7.846585 1 83.5 | n = 4710
within | 7.520712 -2.154726 130.0596 | T-bar = 6.04395

. xtsum birth_yr

Variable | Mean Std. Dev. Min Max | Observations
-----------------+--------------------------------------------+----------------
birth_yr overall | 48.08509 3.012837 41 54 | N = 28534
between | 3.051795 41 54 | n = 4711
within | 0 48.08509 48.08509 | T-bar = 6.05689

Then, we cannot calculate a meaningful share of the between or within variabilities in overall variabilities using the xtsum statistics? Is there any way to obtain such share? I am using Stata/SE 16.1. I would appreciate your help.