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


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

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.

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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