Announcement

Collapse
No announcement yet.
X
  • Filter
  • Time
  • Show
Clear All
new posts

  • xtreg documentation

    https://www.stata.com/manuals13/xtxtreg.pdf is the xtreg documentation. I have two questions.

    1. On page 8 I do not understand the "If sigma squared nu = 0, meaning that nu_i is always 0" part. Why nu_i should always be zero?

    2. Where is the explicit formula of "rho" (fraction of variance due to u_i) given? I cannot find it in this document and wonder why the document presents it.
    Last edited by Tunga Kantarci; 09 Nov 2018, 05:59.

  • #2
    2 (follow-up). I am trying to relate the rho to the lambda = 1 - (sigma_sq_nu / (sigma_sq_nu + T * sigma_sq_mu) )^(1/2) where nu is the idiosyncratic component and mu is the individual component of the composite error term varepsilon_it = mu_i + nu_it. lambda is the transformation parameter used to quasi-demean the variables and the error of the model. lambda and rho got to be related. Therefore I am surprised that xtreg documentation does not provide an explicit expression for rho. I am suspecting that rho = sigma_sq_mu / (sigma_sq_mu + sigma_sq_nu) because the xtreg, fe output defines it as the "fraction of variance due to mu_i". This must be the case, but still the documentation could be more explicit. So what is the reason that it is not?
    Last edited by Tunga Kantarci; 09 Nov 2018, 07:03.

    Comment


    • #3
      1. On page 8 I do not understand the "If sigma squared nu = 0, meaning that nu_i is always 0" part. Why nu_i should always be zero?
      I do not know where the misunderstanding comes from. If we start by stating that

      $$\eta_{i} \sim (0, \sigma^{2}_{\eta})$$

      and then I state that \(\sigma^{2}_{\eta} = \sigma_{\eta}= 0\), then it means that \(\eta_{i}\) is always zero (or has zero variance if you prefer). In other words, what has a mean of zero and a variance of zero? It can only be a group of zeros.

      Where is the explicit formula of "rho" (fraction of variance due to u_i) given? I cannot find it in this document and wonder why the document presents it.
      Isn't "fraction of variance due to u_i" self explanatory?

      Code:
      . xtreg invest mvalue kstock, fe
      
      Fixed-effects (within) regression               Number of obs     =        200
      Group variable: company                         Number of groups  =         10
      
      R-sq:                                           Obs per group:
           within  = 0.7668                                         min =         20
           between = 0.8194                                         avg =       20.0
           overall = 0.8060                                         max =         20
      
                                                      F(2,188)          =     309.01
      corr(u_i, Xb)  = -0.1517                        Prob > F          =     0.0000
      
      ------------------------------------------------------------------------------
            invest |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
      -------------+----------------------------------------------------------------
            mvalue |   .1101238   .0118567     9.29   0.000     .0867345    .1335131
            kstock |   .3100653   .0173545    17.87   0.000     .2758308    .3442999
             _cons |  -58.74393   12.45369    -4.72   0.000    -83.31086     -34.177
      -------------+----------------------------------------------------------------
           sigma_u |  85.732501
           sigma_e |  52.767964
               rho |  .72525012   (fraction of variance due to u_i)
      ------------------------------------------------------------------------------
      
      . local rho =e(sigma_u)^2/(e(sigma_u)^2 + e(sigma_e)^2)
      
      . di `rho'
      .72525012
      Last edited by Andrew Musau; 09 Nov 2018, 07:58.

      Comment


      • #4
        Tunga:
        as an aside to Andrew's helpful reply, you can find the formula you asked for in 2) under -icc- entry, Methods and formulas, One-way random effect, Stata .pdf manual.
        Kind regards,
        Carlo
        (Stata 15.1 SE)

        Comment


        • #5
          Andrew, thanks.

          1. Yes, of course, if you assume that nu_i has zero mean. But where on page 8 is this mentioned?

          2. It is self-explanatory, but I do not see the reason of not mentioning it in the documentation or giving a reference that it is in icc (Thanks Carlo).
          Last edited by Tunga Kantarci; 09 Nov 2018, 08:23.

          Comment


          • #6
            It is always the case that the error components have a mean of zero. Econometrics101

            Comment


            • #7
              For who is Stata? Does it exclude learners of Econometrics 101? Regardless, I do not see the point of not mentioning the assumed distribution. The documentation does mention that the idiosyncratic error has zero mean. Then that should also not be mentioned.
              Last edited by Tunga Kantarci; 09 Nov 2018, 08:10.

              Comment


              • #8
                Fair comment. I will give a more standard reference. The panel data models are covered in detail in the first few chapters of Econometric Analysis of Panel Data by Badi H. Baltagi. A lot of the material in the Stata xtreg manual is drawn from this book if you look at the references. I have the latest (5th Edition) and you will find the assumptions that underlie the error components in Chapter 2, page 20.

                Reference:
                Baltagi, B. H. (2013). Econometric Analysis of Panel Data. Wiley

                Comment


                • #9
                  Thanks Andrew, I was not really aware that the documentation relies heavily on Baltagi.

                  Comment

                  Working...
                  X