In the RE model the best quadratic unbiased estimators of the variance
components come directly from the spectral decomp. of the covariance matrix
of the model error. You don't get a direct estimate for sigma_u, but an
estimate for sigma_e and an estimate for sigma_1=T*sigma_u+sigma_e. Then
sigma_u is obtained as sigma_u=(sigma_1-sigma_e)/T
Stata implements two different methods to estimates these variances
components, but both of them estimate sigma_u using this last formula and
there is no guarantee that this estimator will be greater than zero.
Stata replaces sigma_u for zero, whenever it finds a negative estimate. That
is, at the end Stata computes
sigma_u=max{0,(sigma_1-sigma_e)/T} [I don't have the manuals with me but I
am sure this is clearly specified in the reference manual]. And of course
when sigma_u is set to be zero, BetaGLS is reduced to BetaOLS.
There is another estimate for sigma_u that you can use. You estimate sigma_u
using the sample variance of the individual fixed effects obtained from a
dummy variable LS regression.
--------------------------------------------
Universidad Alberto Hurtado
ILADES / Georgetown University
Erasmo Escala 1835
Santiago, Chile
Phono: 671-7130 anexo 267
http://www.ilades.cl/economia/index.html
----- Original Message -----
From: "Mark Schaffer" <[email protected]>
To: <[email protected]>
Sent: Thursday, December 05, 2002 11:35 AM
Subject: Re: st: -xtreg, re- vs -regress, cluster ()-
> Enrica,
>
> Date sent: Thu, 5 Dec 2002 02:23:47 -0800 (PST)
> From: Enrica Croda <[email protected]>
> To: [email protected]
> Subject: st: -xtreg, re- vs -regress, cluster ()-
> Send reply to: [email protected]
>
> > Hello Stata-listers:
> >
> > I am a bit puzzled by some regression results I obtained using -xtreg,
re-
> > and -regress, cluster()- on the same sample.
> >
> > I would appreciate if anybody out there could give me feedback on
whether
> > it possible to obtain the same coefficient estimated by using -regress,
> > cluster(ID)- and -xtreg, re i(ID)- on the same specification on
> > the same sample, and if there are common circumstances in which this may
> > happen.
>
> This will happen only in "degenerate" cases.
>
> -regress- with -cluster- gives you the same coefficients as regress,
> but with standard errors that are robust to intra-group correlation
> (in your case, correlation between observations of the same married
> woman at different points in time).
>
> -xtreg, re- gives you estimates for the "random effects" model. This
> is a different specification, and you'll normally get different
> coefficients.
>
> The issue is "normally". You have, in effect, a collinearity
> problem. What is happening is that the random effects model is
> reducing to standard OLS. You can tell by the following lines at the
> bottom of the -xtreg,re- output:
>
> sigma_u | 0
> sigma_e | .28993302
> rho | 0 (fraction of variance due to u_i)
>
> u_i is the "random effect", and this output is basically telling you
> that it has no role in what you've estimated. The results are OLS.
>
> This is why the MLE results are different - you'll see that the
> sigma_u for that estimation is not zero, and you are getting what you
> expected (ie, not OLS).
>
> I don't remember offhand all the circumstances that can cause this to
> happen with the random effects estimator, but that is what is going
> on.
>
> Hope this helps.
>
> --Mark
>
> NB: I've seen this come up on the list before. Does anyone else
> think that -xtreg,re- should print a warning when random effects
> degenerates into OLS?
>
> >
> > As far as the specifics of my case, I am studying labor force
> > participation of married women.
> > I am using a balanced panel data-set in "long form" (iis: ID, tis year)
> > containing yearly data for the period 1990-1997.
> > I have a total of 8696 observations on 1087 married women.
> >
> > The dependent variable is a binary variable with values 1 or 0.
> >
> > I run
> > 1) pooled OLS regressions with the cluster option (-regress,
cluster(ID)-,
> > and
> > 2) -xtreg, re i(ID)-
> > on the same specification.
> >
> > If I use a static specification and do not include any lagged variable
> > among the explanatory variables, applying the 2 different estimation
methods
> > produces different coefficient estimates and different standard errors.
> > And this is what I was expecting.
> >
> > What is puzzling me is the following.
> >
> > If I use a dynamic specification, i.e. basically I include the lagged
> > value of the dependent variable among the explanatory variables,
applying
> > the two different estimation methods produces exactly the same
> > coefficient estimates and different standard errors. (Estimation results
> > follow)
> > I was not expecting the coefficient estimates to be exactly the same
with
> > the two methods.
> >
> > I tried other panel regressions.
> > -xtreg, mle- provides different estimates and standard errors
from -xtreg,
> > re-.
> >
> > I also tried to construct the random effects estimates by running a
pooled
> > regression on the quasi-differences specification (4) in Volume 4 of
> > the Stata 7 Manual, p.437, with theta estimated as described on p. 452,
> > and I got yet different results.
> >
> > I am reporting below the estimates obtained with
> > I. -regress, cluster(ID)-
> > II. -xtreg, re i (ID)-
> > III.-xtreg, mle i (ID)-
> >
> >
> > Variable definition:
> > curremplo: current employment status
> > lagemplo : lagged employment status
> > perminc : husband's permanent income
> > transinc : husband's transitory income
> > age : age/10
> > agesq : (age/10) squared
> > sak02 : number of kids aged 0-2
> > sak35 : number of kids aged 3-5
> > sak02 : number of kids 6+
> > east : dummy variable =1 if respondent is East German (the data
> > are for East and West Germany)
> > schoolmax: maximum years of schooling
> > yr## :year dummy, equal to 1 if year is ## (##=91,...97).
> >
> > ----------------------------------------------------------------------
> > REGRESS, CLUSTER
> >
> > . regress curremplo perminc transinc sak02 sak35 sak6g lagemplo age
agesq east
> > > schoolmax yr91 yr92 yr93 yr94 yr95 yr96 yr97, cluster(persnr);
> >
> > Regression with robust standard errors Number of obs =
8696
> > F( 17, 1086) =
411.72
> > Prob > F =
0.0000
> > R-squared =
0.5388
> > Number of clusters (persnr) = 1087 Root MSE =
.32573
> >
>
> --------------------------------------------------------------------------
----
> > | Robust
> > curremplo | Coef. Std. Err. t P>|t| [95% Conf.
Interval]
>
> -------------+------------------------------------------------------------
----
> > perminc | -.003359 .0016812 -2.00
0.046 -.0066579 -.0000602
> > transinc | -.0029873 .0017223 -1.73 0.083 -.0063667
.0003921
> > sak02 | -.1735915 .0155283 -11.18
0.000 -.2040605 -.1431226
> > sak35 | -.0343057 .0091977 -3.73
0.000 -.0523531 -.0162584
> > sak6g | -.0222673 .0047493 -4.69
0.000 -.0315862 -.0129483
> > lagemplo | .6713014 .012667 53.00 0.000 .6464469
.6961559
> > age | .010654 .0038414 2.77 0.006 .0031165
.0181915
> > agesq | -.000187 .000048 -3.89
0.000 -.0002813 -.0000927
> > east | .0453875 .0097331 4.66 0.000 .0262897
.0644853
> > schoolmax | .0051449 .0018325 2.81 0.005 .0015493
.0087405
> > yr91 | -.031073 .0159144 -1.95 0.051 -.0622995
.0001534
> > yr92 | -.0133491 .0143174 -0.93 0.351 -.041442
.0147438
> > yr93 | -.02965 .01378 -2.15
0.032 -.0566885 -.0026115
> > yr94 | -.0042043 .0134346 -0.31 0.754 -.030565
.0221563
> > yr95 | -.010533 .013451 -0.78 0.434 -.0369259
.0158599
> > yr96 | -.0319808 .0135433 -2.36
0.018 -.0585548 -.0054069
> > yr97 | -.0140815 .0134361 -1.05 0.295 -.0404453
.0122822
> > _cons | .09109 .073401 1.24 0.215 -.0529337
.2351137
>
> --------------------------------------------------------------------------
----
> >
> >
> >
> > XTREG, RE
> >
> > . xtreg curremplo perminc transinc sak02 sak35 sak6g lagemplo age agesq
east
> > > schoolmax yr91 yr92 yr93 yr94 yr95 yr96 yr97, i(persnr) re;
> >
> > Random-effects GLS regression Number of obs =
8696
> > Group variable (i) : persnr Number of groups =
1087
> >
> > R-sq: within = 0.0984 Obs per group: min =
8
> > between = 0.9408 avg =
8.0
> > overall = 0.5388 max =
8
> >
> > Random effects u_i ~ Gaussian Wald chi2(17) =
10137.10
> > corr(u_i, X) = 0 (assumed) Prob > chi2 =
0.0000
> >
>
> --------------------------------------------------------------------------
----
> > curremplo | Coef. Std. Err. z P>|z| [95% Conf.
Interval]
>
> -------------+------------------------------------------------------------
----
> > perminc | -.003359 .0013716 -2.45
0.014 -.0060473 -.0006708
> > transinc | -.0029873 .002286 -1.31 0.191 -.0074678
.0014932
> > sak02 | -.1735915 .0125305 -13.85
0.000 -.1981509 -.1490322
> > sak35 | -.0343057 .0091113 -3.77
0.000 -.0521635 -.0164479
> > sak6g | -.0222673 .0044685 -4.98
0.000 -.0310254 -.0135091
> > lagemplo | .6713014 .0080104 83.80 0.000 .6556013
.6870015
> > age | .010654 .0038709 2.75 0.006 .0030672
.0182408
> > agesq | -.000187 .0000471 -3.97
0.000 -.0002792 -.0000947
> > east | .0453875 .0087905 5.16 0.000 .0281584
.0626166
> > schoolmax | .0051449 .0016204 3.18 0.001 .0019691
.0083208
> > yr91 | -.031073 .0139985 -2.22
0.026 -.0585096 -.0036365
> > yr92 | -.0133491 .0140428 -0.95 0.342 -.0408724
.0141743
> > yr93 | -.02965 .0140972 -2.10
0.035 -.0572799 -.0020201
> > yr94 | -.0042043 .0141534 -0.30 0.766 -.0319445
.0235358
> > yr95 | -.010533 .0142409 -0.74 0.460 -.0384447
.0173787
> > yr96 | -.0319808 .0143176 -2.23
0.026 -.0600429 -.0039188
> > yr97 | -.0140815 .0144083 -0.98 0.328 -.0423214
.0141583
> > _cons | .09109 .0777215 1.17 0.241 -.0612413
.2434213
>
> -------------+------------------------------------------------------------
----
> > sigma_u | 0
> > sigma_e | .28993302
> > rho | 0 (fraction of variance due to u_i)
>
> --------------------------------------------------------------------------
----
> >
> >
> >
> > XTREG, MLE
> > . xtreg curremplo perminc transinc sak02 sak35 sak6g lagemplo age agesq
east
> > > schoolmax yr91 yr92 yr93 yr94 yr95 yr96 yr97, i(persnr) mle;
> >
> > Fitting constant-only model:
> > Iteration 0: log likelihood = -6568.6464
> > Iteration 1: log likelihood = -5790.8646
> > Iteration 2: log likelihood = -5653.5493
> > Iteration 3: log likelihood = -5646.3662
> > Iteration 4: log likelihood = -5646.3369
> >
> > Fitting full model:
> > Iteration 0: log likelihood = -2559.0813
> > Iteration 1: log likelihood = -2490.0659
> > Iteration 2: log likelihood = -2461.6401
> > Iteration 3: log likelihood = -2461.2976
> > Iteration 4: log likelihood = -2461.2973
> >
> > Random-effects ML regression Number of obs =
8696
> > Group variable (i) : persnr Number of groups =
1087
> >
> > Random effects u_i ~ Gaussian Obs per group: min =
8
> > avg =
8.0
> > max =
8
> >
> > LR chi2(17) =
6370.08
> > Log likelihood = -2461.2973 Prob > chi2 =
0.0000
> >
>
> --------------------------------------------------------------------------
----
> > curremplo | Coef. Std. Err. z P>|z| [95% Conf.
Interval]
>
> -------------+------------------------------------------------------------
----
> > perminc | -.0056741 .0023379 -2.43
0.015 -.0102562 -.0010919
> > transinc | -.0040303 .0020947 -1.92 0.054 -.0081358
.0000752
> > sak02 | -.2245123 .0133989 -16.76
.000 -.2507737 -.198251
> > sak35 | -.0701418 .0101739 -6.89
0.000 -.0900823 -.0502013
> > sak6g | -.0407319 .0061695 -6.60
000 -.0528238 -.02864
> > lagemplo | .4443965 .0139782 31.79 0.000 .4169997
.4717933
> > age | .0100016 .0052861 1.89 0.058 -.0003589
.0203621
> > agesq | -.0002096 .0000642 -3.26
0.001 -.0003356 -.0000837
> > east | .0910558 .0149718 6.08 0.000 .0617116
.1204
> > schoolmax | .0081604 .0027614 2.96 0.003 .0027482
.0135726
> > yr91 | -.0255522 .0127857 -2.00
0.046 -.0506118 -.0004927
> > yr92 | -.011285 .0128852 -0.88 0.381 -.0365396
.0139695
> > yr93 | -.0259762 .01303 -1.99
0.046 -.0515146 -.0004379
> > yr94 | -.0032213 .0132016 -0.24 0.807 -.0290961
.0226534
> > yr95 | -.0055009 .0134236 -0.41 0.682 -.0318108
.0208089
> > yr96 | -.0257715 .0136532 -1.89 0.059 -.0525313
.0009883
> > yr97 | -.0123659 .0139074 -0.89 0.374 -.0396239
.0148922
> > _cons | .2832431 .1087164 2.61 0.009 .0701629
.4963232
>
> -------------+------------------------------------------------------------
----
> > /sigma_u | .1662792 .0073449 22.64 0.000 .1518834
.180675
> > /sigma_e | .2968988 .0025839 114.90 0.000 .2918345
.3019632
>
> -------------+------------------------------------------------------------
----
> > rho | .238768 .0173716 .2060788
.2741066
>
> --------------------------------------------------------------------------
----
> > Likelihood ratio test of sigma_u=0: chibar2(01)= 229.39 Prob>=chibar2 =
0.000
> >
> >
>
> --------------------------------------------------------------------------
-
> >
> >
> > Thank you very much in advance for any idea,
> >
> > Enrica
> >
> >
> > *
> > * For searches and help try:
> > * http://www.stata.com/support/faqs/res/findit.html
> > * http://www.stata.com/support/statalist/faq
> > * http://www.ats.ucla.edu/stat/stata/
>
>
> Prof. Mark E. Schaffer
> Director
> Centre for Economic Reform and Transformation
> Department of Economics
> School of Management & Languages
> Heriot-Watt University, Edinburgh EH14 4AS UK
> 44-131-451-3494 direct
> 44-131-451-3008 fax
> 44-131-451-3485 CERT administrator
> http://www.som.hw.ac.uk/cert
> *
> * For searches and help try:
> * http://www.stata.com/support/faqs/res/findit.html
> * http://www.stata.com/support/statalist/faq
> * http://www.ats.ucla.edu/stat/stata/
______________________________________
Universidad Alberto Hurtado
http://www.uahurtado.cl
*
* For searches and help try:
* http://www.stata.com/support/faqs/res/findit.html
* http://www.stata.com/support/statalist/faq
* http://www.ats.ucla.edu/stat/stata/
