Xtreg output: standard error

[Siham Hari]

Dear Statalists,

I have a basic question for which I can't find an anwer.

I am using the Monte Carlo method to test my mediating effect after running multiple regressions.

In order to run the test, I need the values "cov(a) and cov(b)", which represent the squared standard errors of my variable of interest.

My question is do I use the standard error produced by the regression output or do I have to high square it first.

I don't no if the standard error produced by Stata is originally a squared value or if I am suppose to calculate it manually.

I hope someone can help me with this!!

Kind Regards,
Siham

[Andrew Musau]

I am using the Monte Carlo method to test my mediating effect after running multiple regressions.

In order to run the test, I need the values "cov(a) and cov(b)", which represent the squared standard errors of my variable of interest.

My question is do I use the standard error produced by the regression output or do I have to high square it first.

I do not get the part that the variance is the covariance. In fact, if you refer to a covariance, it cannot be cov(a) but something like cov(a, b). The interesting case is cov(a, a) = var(a). In any case, here is how to get the variance of an estimated coefficient.

Two ways: You can either square the standard error or pick the variance directly from the VCE matrix

webuse grunfeld, clear
xtreg invest mvalue kstock, fe
di (_se[mvalue])^2
mat l e(V)
di e(V)[1, 1]

Res.:

.
. 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)
------------------------------------------------------------------------------
F test that all u_i=0: F(9, 188) = 49.18                     Prob > F = 0.0000

.
. di (_se[mvalue])^2
.00014058

.
. mat l e(V)

symmetric e(V)[3,3]
            mvalue      kstock       _cons
mvalue   .00014058
kstock  -.00007747   .00030118
 _cons  -.13068152   .00066516   155.09442

.
. di e(V)[1, 1]
.00014058