Many thanks to Marcela Perticara and to Mark Schaffer for their very
helpful replies.
It seems indeed that Stata sets sigma_u to zero because it finds a
negative value for it. (At least, I tried to calculate sigma_u
"manually" following the formula Marcela refers to below, and I got a
negative values).
Thanks a lot again,
Enrica
On Thu, 5 Dec 2002, Marcela Perticara wrote:
> 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/
>
*
* 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/
