# st: RE: Random effects and pooled models

 From "Elena Giarda" To Subject st: RE: Random effects and pooled models Date Fri, 28 Jul 2006 12:17:16 +0200

Dear Mark and Stas,

thank you for your answers. I still have some doubts, though! This is my full model:

ln_wage = f(age, age_squared, cohort_dummies, age*cohort_dummies, control_variables)

In my fixed effects model I got some results which I thought were interesting on the age-specific cohort effects: the coeffs associated to age*cohort_dummies were all significant and decreasing for younger cohorts, so I concluded that younger workers, despite getting higher entry wages (higher cohort dummies for youngsters), are facing worse prospects of wage increases (the wage to age gradient decreases by cohort).

This is the output:

Regression with robust standard errors Number of obs = 283533
F( 29,283503) =11916.87
Prob > F = 0.0000
R-squared = 0.5309
Root MSE = .28886

------------------------------------------------------------------------------
| Robust
lny_sqa | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
age | .1000156 .0039534 25.30 0.000 .0922671 .1077642
age2 | -.0008488 .0000343 -24.78 0.000 -.0009159 -.0007816
dco2 | .4248919 .0685042 6.20 0.000 .2906256 .5591581
dco3 | .6136547 .0704763 8.71 0.000 .475523 .7517863
dco4 | .9172512 .0736344 12.46 0.000 .7729299 1.061573
dco5 | 1.229381 .0821107 14.97 0.000 1.068446 1.390315
dco6 | 1.432516 .0903494 15.86 0.000 1.255434 1.609599
dco7 | 1.546192 .0978922 15.79 0.000 1.354326 1.738058
dco8 | 1.714787 .1038395 16.51 0.000 1.511265 1.91831
dco9 | 1.920803 .1074514 17.88 0.000 1.710201 2.131405
agedco2 | -.0077984 .0012549 -6.21 0.000 -.0102579 -.0053389
agedco3 | -.0112156 .0013104 -8.56 0.000 -.013784 -.0086472
agedco4 | -.0172092 .0013863 -12.41 0.000 -.0199264 -.0144921
agedco5 | -.0244174 .0016154 -15.12 0.000 -.0275836 -.0212512
agedco6 | -.0293587 .0018647 -15.74 .000 -.0330134 -.025704
agedco7 | -.0324999 .00213 -15.26 0.000 -.0366747 -.0283252
agedco8 | -.038488 .0023843 -16.14 0.000 -.0431611 -.0338148
agedco9 | -.044862 .0025906 -17.32 0.000 -.0499395 -.0397845
lncontr | .1105694 .0016846 65.63 0.000 .1072676 .1138713
ptime | .0258564 .011688 2.21 0.027 .0029483 .0487645
areaimp2 | -.0362929 .0014986 -24.22 0.000 -.0392301 -.0333556
areaimp3 | -.1658439 .0019885 -83.40 0.000 -.1697414 -.1619464
d_sect1 | .0149592 .0054922 2.72 0.006 .0041945 .0257239
d_sect3 | .209279 .0025675 81.51 0.000 .2042467 .2143112
d_dim1 | -.116826 .0014852 -78.66 .000 -.119737 -.113915
d_dim3 | .0843824 .0013347 63.22 0.000 .0817664 .0869984
dapp | -.5654553 .0043867 -128.90 0.000 -.5740532 -.5568574
dop | -.3351478 .0014345 -233.63 0.000 -.3379594 -.3323362
ddir | .801534 .003875 206.85 0.000 .793939 .8091289
_cons | 3.0813 .1209896 25.47 0.000 2.844164 3.318436
------------------------------------------------------------------------------

A referee told me to run a random effects regression on the same model and from here the question I posted yesterday and to which you replied.

Now, I tried -xtreg, mle- on the same model and obtained:

iis cohort

Random-effects ML regression Number of obs = 283533
Group variable (i): coorte Number of groups = 4

Random effects u_i ~ Gaussian Obs per group: min = 14575
avg = 22891.8
max = 28101

LR chi2(21) = 214110.71
Log likelihood = -50457.383 Prob > chi2 = 0.0000

------------------------------------------------------------------------------
lny_sqa | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
age | .02889 .0005915 48.84 0.000 .0277306 .0300494
age2 | -.0002464 7.61e-06 -32.38 0.000 -.0002614 -.0002315
agedco2 | -.0001612 .0000609 -2.65 0.008 -.0002806 -.0000418
agedco3 | .0000393 .0000679 0.58 0.562 -.0000937 .0001723
agedco4 | .0005008 .0000764 6.55 0.000 .000351 .0006506
agedco5 | .0008362 .0000911 9.18 0.000 .0006577 .0010148
agedco6 | .0016009 .0001037 15.44 0.000 .0013977 .0018041
agedco7 | .0020657 .0001144 18.06 0.000 .0018416 .0022899
agedco8 | .0021981 .0001283 17.13 0.000 .0019466 .0024496
agedco9 | .0049974 .0001534 32.58 0.000 .0046968 .005298
lncontr | .1105102 .0012093 91.39 0.000 .1081401 .1128803
ptime | .024671 .0065363 3.77 0.000 .01186 .0374819
areaimp2 | -.0362974 .0014908 -24.35 0.000 -.0392192 -.0333755
areaimp3 | -.165722 .0016252 -101.97 0.000 -.1689073 -.1625366
d_sect1 | .0153275 .0054552 2.81 0.005 .0046355 .0260195
d_sect3 | .2076016 .0029165 71.18 0.000 .2018853 .2133179
d_dim1 | -.1092841 .0014408 -75.85 0.000 -.1121081 -.1064601
d_dim3 | .0917709 .0013192 69.56 0.000 .0891852 .0943565
dapp | -.5615198 .003812 -147.30 0.000 -.5689912 -.5540483
dop | -.3352911 .0013491 -248.52 0.000 -.3379354 -.3326468
ddir | .8012167 .0044278 180.95 0.000 .7925384 .8098951
_cons | 5.167075 .0105458 489.96 0.000 5.146406 5.187745
-------------+----------------------------------------------------------------
/sigma_u | 0 .0006151 0.00 1.000 -.0012055 .0012055
/sigma_e | .289101 .000384 752.96 0.000 .2883485 .2898536
-------------+----------------------------------------------------------------
rho | 0 . . .
------------------------------------------------------------------------------
Likelihood-ratio test of sigma_u=0: chibar2(01)= 0.00 Prob>=chibar2 = 1.000

Again, as with -xtreg, re- I get rho = 0. But even worse, the coeffs associated with the age*dummies are increasing!!!

BUT, if I run the above model WITHOUT agedco2-agedco9 (the age*cohort dummies) by -xtreg,mle-, the rho is different from zero (whereas with -xtreg,re- it was equal to 0):

iis cohort
Random-effects ML regression Number of obs = 283533
Group variable (i): coorte Number of groups = 4

Random effects u_i ~ Gaussian Obs per group: min = 14575
avg = 22891.8
max = 28101

LR chi2(13) = 169701.84
Log likelihood = -50444.914 Prob > chi2 = 0.0000

------------------------------------------------------------------------------
lny_sqa | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
age | .0340645 .0005697 59.79 0.000 .0329479 .0351811
age2 | -.0002976 7.42e-06 -40.13 0.000 -.0003122 -.0002831
lncontr | .1107702 .001211 91.47 0.000 .1083968 .1131437
ptime | .0243944 .006535 3.73 0.000 .0115862 .0372027
areaimp2 | -.0362132 .0014906 -24.29 0.000 -.0391347 -.0332917
areaimp3 | -.165622 .0016253 -101.90 0.000 -.1688076 -.1624364
d_sect1 | .0153858 .0054541 2.82 0.005 .0046959 .0260758
d_sect3 | .2076719 .002916 71.22 0.000 .2019566 .2133873
d_dim1 | -.1102143 .0014428 -76.39 0.000 -.1130423 -.1073864
d_dim3 | .0910264 .0013197 68.98 0.000 .08844 .0936129
dapp | -.5652369 .0038215 -147.91 0.000 -.572727 -.5577469
dop | -.3352971 .001349 -248.56 0.000 -.337941 -.3326532
ddir | .8011392 .0044269 180.97 0.000 .7924626 .8098157
_cons | 5.087226 .0201143 252.92 0.000 5.047803 5.12665
-------------+----------------------------------------------------------------
/sigma_u | .050197 .0119324 4.21 0.000 .0268098 .0735841
/sigma_e | .2890571 .0003839 753.03 0.000 .2883047 .2898094
-------------+----------------------------------------------------------------
rho | .0292742 .0135105 .0110474 .0675347
------------------------------------------------------------------------------
Likelihood-ratio test of sigma_u=0: chibar2(01)= 1406.53 Prob>=chibar2 = 0.000

What would you conclude on the interactions between age and cohort?

Also: why when using the optino -mle-, the number of groups (cohorts) is reduced from 9 to 4?

Thanks a lot again!
Elena

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