Random-effects panel-data estimators

It is difficult to say panel data without saying random effects. Panel data are repeated observations on individuals. Random effects are individual-level effects that are unrelated to everything else in the model.

Say we have data on 4,711 employees of a large multinational corporation. We have repeated observations on these employees over the years. On average, we have 6 years of data. For some employees, we have 15 years.

Our data include professional status (1, 2, 3, or 4), age, education, and years of job experience.

We fit the following model:

. xtset idcode year

Panel variable: idcode (unbalanced)
 Time variable: year, 68 to 88, but with gaps
         Delta: 1 unit

. xtoprobit status educ c.age##c.age experience

Random-effects ordered probit regression            Number of obs    =  28,099
Group variable: idcode                              Number of groups =   4,697

Random effects u_i ~ Gaussian                       Obs per group:
                                                                 min =       1
                                                                 avg =     6.0
                                                                 max =      15

Integration method: mvaghermite                     Integration pts. =      12

                                                    Wald chi2(4)     = 7793.29
Log likelihood = -20469.593                         Prob > chi2      =  0.0000



      status 
 
 Coefficient  Std. err.      z    P>|z|     [95% conf. interval]
 

        educ 
 
   .4777564   .0110886    43.09   0.000     .4560231    .4994896
         age 
 
   .0269213   .0148939     1.81   0.071    -.0022703    .0561129
             
 

 c.age#c.age 
 
  -.0044188   .0002616   -16.89   0.000    -.0049315   -.0039061
             
 

  experience 
 
   .4873618   .0056847    85.73   0.000       .47622    .4985036
 

       /cut1 
 
   4.593579   .2416309                      4.119992    5.067167
       /cut2 
 
   6.057881   .2435617                      5.580509    6.535253
       /cut3 
 
   7.030559   .2451983                      6.549979    7.511138
 

   /sigma2_u 
 
   1.834779   .0693548                       1.70376    1.975874

LR test vs. oprobit model: chibar2(01) = 6454.02      Prob >= chibar2 = 0.0000

We find that the probability of the highest status level increases with education and experience. We also find that individuals have a large permanent component (/sigma2_u, the variance of the random effect, is both large and significant).