st: OLS equivalence for unbalanced panel

[Silviya Nikolova <Silviya.Nikolova@manchester.ac.uk>]

Dear Statalist,

I am estimating RE model (xtreg) using unbalanced panel dataset. Sigma_u for some reason is 0. My dependent variable is discrete with large variation. To understand why this is the case, I tried:
1. Add some iid normal noise to the data
2. Drop groups with small number of observations in them
These two approaches do not make a difference.
3. Reduce the number of variables (after sufficient number of dropped variables sigma_u became > 0).
4. Expand the data using --expand 2-- command. This generates non-zero sigma_u as well. 
Is there any reasonable explanation for all 4 of these? 2 and 3 in isolation can be explained easily. 

This is a snippet of the output before expand:

. xtreg q2_OHS ISTC q1_OHS ${q1_eq5d_elem_nf} q1_eq5d_health_scale ${other_health_nf} ${comorbs_nf} ${pa
> tients_nf_`severity'} ${provider_nf}, re

Random-effects GLS regression                   Number of obs      =     36090
Group variable: procode1                        Number of groups   =       246

R-sq:  within  = 0.2200                         Obs per group: min =         1
       between = 0.6405                                        avg =     146.7
       overall = 0.2415                                        max =      1017

                                                Wald chi2(45)      =  11473.56
corr(u_i, X)   = 0 (assumed)                    Prob > chi2        =    0.0000


--------------------------------------------------------------------------------------

. . . 

---------------------+----------------------------------------------------------------
             sigma_u |          0
             sigma_e |  8.2124003
                 rho |          0   (fraction of variance due to u_i)
--------------------------------------------------------------------------------------



And after expand:

. preserve

. expand 2
(133799 observations created)

. xtset procode1

. xtreg q2_OHS ISTC q1_OHS ${q1_eq5d_elem_nf} q1_eq5d_health_scale ${other_health_nf} ${comorbs_nf} ${pa

> tients_nf_`severity'} ${provider_nf}, re

Random-effects GLS regression                   Number of obs      =     72180
Group variable: procode1                        Number of groups   =       246

R-sq:  within  = 0.2200                         Obs per group: min =         2
       between = 0.6400                                        avg =     293.4
       overall = 0.2409                                        max =      2034

                                                Wald chi2(45)      =  20798.64
corr(u_i, X)   = 0 (assumed)                    Prob > chi2        =    0.0000

--------------------------------------------------------------------------------------

. . . 

---------------------+----------------------------------------------------------------
             sigma_u |   1.115697
             sigma_e |  8.1965088
                 rho |  .01819121   (fraction of variance due to u_i)
--------------------------------------------------------------------------------------

. restore


Thank you.

Silviya


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