Suppose $X_{it}^*$ is the demeaned version of $X_{it}$, i.e., $$X_{it}^* = X_{it}- \bar{X}_i$$

In Hansen's econometrics textbook, he says the demeaned variable has reduced variation relative to the original observations, what is the precise meaning for this?

Indeed, can we prove the following inequality: $$ Var[X_{it}^*] \leq Var[X_{it}].$$

  • $\begingroup$ It’s about panel data. The within-group variability is the same. It’s the between-group variability that is eliminated by the within transformation. $\endgroup$
    – chan1142
    Jan 20 at 11:36
  • $\begingroup$ Average of yit minus y double bar squared versus the average of yit minus y_i bar squared. $\endgroup$
    – chan1142
    Jan 20 at 11:38

1 Answer 1


I have this derivation typed up as part of a PowerPoint slide. Forgive my laziness, but I'm going to just post an image of that slide. enter image description here


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.