[Carlo Lazzaro]

Thomas:
as -company- seems to be nested within -industry-, I would take a look at Example #4 under -mixed-entry in Stata 13.1 .pdf manual.

[Roman Mostazir]

Now you have a 4-level model. Highest level-Industry, Third-level-company, ceo-being at the 2nd level and performance is the lowest level. Year is a level-1 variable. You want to estimate each 'ceo' effect on performance i.e. average effect of each 'ceo' on performance and according to the post #11 you have different idea in mind for getting the each 'ceo' effect.

First, you need to define that you have random intercepts around industry and company level. We ignore the random intercepts for 'ceo' because we are estimating effect for each 'ceo'. However, 'ceo' is a 2nd level variable and 'ceo' performance varies within company year by year. Therefore, you need to tell the model to adjust for the fact that different `ceo' performance varies year by year within company (interaction of 'ceo*year' as random effect within company). You could also allow 'ceo' to vary within 'compnay' but in my sense that won't be necessary as you are estimating each 'ceo' effect and presumably each distinctly belong to a distinct company therefore their individual average effect belongs to that company. After fitting this model the estimated main effect of 'ceo' can be atttributed to average performance of each 'ceo'adjusted for variation in performance they have in different years within company. Try the following commands:

xtset industry company

gen ceoXyear=ceo*year  // Interaction variable for random slopes

xtmixed mixed perform i.ceo i.year || industry: || company: ceoXyear, cov(uns) mle // Without `ceo' slope within company

xtmixed mixed perform i.ceo i.year || industry: || company:ceo ceoXyear, cov(uns) mle // If you need `ceo' slope within company

margins i.ceo

[Thomas Lindner]

Thanks to both of you for your answer!

Roman, I ultimately want to estimate the effect for each CEO (this is also why I am interested in the intercepts) but in a first step I would be glad to measure the overall CEO-effect correctly, i.e. what portion of the overall variance in firm performance can be attributed to CEOs in 'general'.
Trying your suggestion, I first of all have a problem with ‘xtset’:

. xtset industry company
repeated time values within panel
r(451);

Shouldn’t I declare the panel data as follows?

xtset company year
       panel variable:  company (unbalanced)
        time variable:  year, 2002 to 2011, but with gaps
                delta:  1 unit

Anyhow, if I’ll try your command after setting 'xtset' with company and year, I get the following error:

 
. gen ceoXyear=ceo*year
 
. xtmixed performance i.ceo i.year || industry: || company:ceo ceoXyear, cov(uns) mle
 
Performing EM optimization:
 
Performing gradient-based optimization:
 
Iteration 0:   log likelihood = -3871.3508  (not concave)
Iteration 1:   log likelihood = -3865.7413 
…
numerical derivatives are approximate
nearby values are missing
Hessian is not negative semidefinite
conformability error
r(503);

Does this give me some insights? To at least get a feeling for the model fit, I used the ‘emonly’ and ‘var’ (for an approximation of the CEO-effect) option:

 
. gen ceoXyear=ceo*year
. xtmixed performance i.ceo i.year || industry: || company:ceo ceoXyear, var cov(uns) mle emiter(300) emonly


…


Mixed-effects ML regression                     Number of obs      =      1013
 
-----------------------------------------------------------
                |   No. of       Observations per Group
 Group Variable |   Groups    Minimum    Average    Maximum
----------------+------------------------------------------
       industry |       12         20       84.4        308
        company |      138          1        7.3         10
-----------------------------------------------------------
 
                                                Wald chi2(268)     =    944.78
Log likelihood = -3862.4825                     Prob > chi2        =    0.0000
 
------------------------------------------------------------------------------
 performance |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         ceo |
          2  |  -1.823491   6.055495    -0.30   0.763    -13.69204    10.0450


…..



------------------------------------------------------------------------------
  Random-effects Parameters  |   Estimate   Std. Err.     [95% Conf. Interval]
-----------------------------+------------------------------------------------
industry: Identity           |
                  var(_cons) |   .0050247          .             .           .
-----------------------------+------------------------------------------------
company: Unstructured        |
                    var(ceo) |   .0030127          .             .           .
               var(ceoXyear) |   7.48e-10          .             .           .
                  var(_cons) |   .2111445          .             .           .
           cov(ceo,ceoXyear) |  -1.50e-06          .             .           .
              cov(ceo,_cons) |  -.0007336          .             .           .
         cov(ceoXyear,_cons) |  -2.79e-07          .             .           .
-----------------------------+------------------------------------------------
               var(Residual) |    119.937          .             .           .
------------------------------------------------------------------------------
LR test vs. linear regression:       chi2(7) =     0.00   Prob > chi2 = 1.0000
 
Note: LR test is conservative and provided only for reference.
Note: EM algorithm failed to converge

Please correct me if I'm wrong, but judging from the variance of the residual compared to the rest as well as the "Prob > chi2 = 1.000", the fit of the model is rather bad? See for comparison the 4-level-modell output:

. xtmixed performance || industry: || company: || ceo: || year: , var emiter(300) emonly

...

Mixed-effects ML regression                     Number of obs      =      1013

-----------------------------------------------------------
                |   No. of       Observations per Group
 Group Variable |   Groups    Minimum    Average    Maximum
----------------+------------------------------------------
       industry |       12         20       84.4        308
        company |      138          1        7.3         10
            ceo |      261          1        3.9         10
           year |     1013          1        1.0          1
-----------------------------------------------------------

                                                Wald chi2(0)       =         .
Log likelihood = -4129.8384                     Prob > chi2        =         .

------------------------------------------------------------------------------
 performance |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       _cons |   1.447456   .8943263     1.62   0.106    -.3053916    3.200303
------------------------------------------------------------------------------

------------------------------------------------------------------------------
  Random-effects Parameters  |   Estimate   Std. Err.     [95% Conf. Interval]
-----------------------------+------------------------------------------------
industry: Identity           |
                  var(_cons) |   .9955171          .             .           .
-----------------------------+------------------------------------------------
company: Identity            |
                  var(_cons) |    47.3286          .             .           .
-----------------------------+------------------------------------------------
ceo: Identity                |
                  var(_cons) |   28.50041          .             .           .
-----------------------------+------------------------------------------------
year: Identity               |
                  var(_cons) |   141.4887          .             .           .
-----------------------------+------------------------------------------------
               var(Residual) |   20.62787          .             .           .
------------------------------------------------------------------------------
LR test vs. linear regression:       chi2(4) =   134.35   Prob > chi2 = 0.0000

Note: LR test is conservative and provided only for reference.

However, as already mentioned in this model the year-effect is suspiciously high. Do you might have another idea how to specify the HLM model?

Thanks in advance for any help!