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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