# Re: st: -xtreg, re- vs -regress, cluster ()-

 From "Mark Schaffer" To statalist@hsphsun2.harvard.edu Subject Re: st: -xtreg, re- vs -regress, cluster ()- Date Thu, 5 Dec 2002 17:35:56 -0000

```Enrica,

Date sent:      	Thu, 5 Dec 2002 02:23:47 -0800 (PST)
From:           	Enrica Croda <croda@nicco.sscnet.ucla.edu>
To:             	statalist@hsphsun2.harvard.edu
Subject:        	st: -xtreg, re-  vs  -regress, cluster ()-
Send reply to:  	statalist@hsphsun2.harvard.edu

> 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   0.000    -.2507737    -.198251
>        sak35 |  -.0701418   .0101739    -6.89   0.000    -.0900823   -.0502013
>        sak6g |  -.0407319   .0061695    -6.60   0.000    -.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
>
>
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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