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## Random-effects panel-data estimators

### Highlights

 New estimators Random-effects ordered probit Random-effects ordered logit Random-effects multinomial logit (via generalized SEM) Cluster–robust standard errors Relax distributional assumptions Allow for correlated data Available on new estimators Also available on probit, logit, complementary log-log, and Poisson

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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 4,708 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 age age2 experience Random-effects ordered probit regression Number of obs = 28508 Group variable: idcode Number of groups = 4708 Random effects u_i ~ Gaussian Obs per group: min = 1 avg = 6.1 max = 15 Integration method: mvaghermite Integration points = 12 Wald chi2(4) = 5676.07 Log likelihood = -26032.326 Prob > chi2 = 0.0000
 status Coef. Std. Err. z P>|z| [95% Conf. Interval] educ .333993 .0091215 36.62 0.000 .3161152 .3518707 age .2129696 .0123513 17.24 0.000 .1887616 .2371777 age2 -.004221 .0002029 -20.80 0.000 -.0046188 -.0038232 experience .1918314 .004661 41.16 0.000 .1826959 .2009669 /cut1 7.625209 .2156879 35.35 0.000 7.202468 8.047949 /cut2 8.498753 .217015 39.16 0.000 8.073411 8.924094 /cut3 10.07729 .219697 45.87 0.000 9.646696 10.50789 /sigma2_u 1.498732 .0506867 1.402609 1.601443
LR test vs. oprobit regression: chibar2(01) = 9467.03 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).