deciding between xtgee and xtreg, re

[Timea De Wispelaere]

Hello,

I have an unbalanced panel data set with N = 185 and T = 5. I have 8 dependent variables of which two do not change over time. Therefore, I think random effects is the one to use to tackle this problem. However, I am still struggling a lot at what command to use. I have been asking questions and have been strolling down the internet a lot, and many times it has been pointed out that for T < N xtreg, re is the way to go. However, I do not find an explanation of why this is the case. I have read the part of xtgee In the pdf manual, and here they state the following:" xtgee, fam(gauss) link(ident) corr(exch) is asymptotically equivalent to the weighted-GLS estimator provided by xtreg, re". However, when I run both models, both are very dissimilar. I have significant regressors for the xtgee, but not for the xtreg, re command.

Could somebody please clarify this for me, as I want to understand what I am doing.

Thank you very much,
Timea De Wispelaere

[Joseph Coveney]

Google "individual specific" "population average" together.

[Jeff Wooldridge]

Please follow the guidelines and post your Stata commands and the output. It would help me give an opinion.

[Timea De Wispelaere]

Hello, thank you for your answer. I am sorry I did provide you with any output. These are the regressions I performed:

. xtgee pctcarbonintensitychange L.firmsize L.profitability L.leverage age L.capitalintensity L
> .CAPEX L.KZindex elektricitygenerator Carbonleakage i.twodigitsNACE i.Province_n publicfirm S
> ME

Iteration 1: tolerance = .02873975
Iteration 2: tolerance = .00055776
Iteration 3: tolerance = 9.029e-06
Iteration 4: tolerance = 1.451e-07

GEE population-averaged model                   Number of obs     =        864
Group variable:               Companynum~r      Number of groups  =        183
Link:                             identity      Obs per group:
Family:                           Gaussian                    min =          1
Correlation:                  exchangeable                    avg =        4.7
                                                              max =          5
                                                Wald chi2(48)     =     122.68
Scale parameter:                  .0233528      Prob > chi2       =     0.0000

----------------------------------------------------------------------------------------------
    pctcarbonintensitychange |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-----------------------------+----------------------------------------------------------------
                    firmsize |
                         L1. |  -.0110114   .0055086    -2.00   0.046    -.0218081   -.0002148
                             |
               profitability |
                         L1. |  -.0652048   .1085569    -0.60   0.548    -.2779723    .1475627
                             |
                    leverage |
                         L1. |   .0427361   .0215191     1.99   0.047     .0005595    .0849127
                             |
                         age |  -.0003844   .0001927    -1.99   0.046    -.0007621   -6.59e-06
                             |
            capitalintensity |
                         L1. |   .0142071   .0266912     0.53   0.595    -.0381067     .066521
                             |
                       CAPEX |
                         L1. |  -.0409272    .070088    -0.58   0.559    -.1782972    .0964428
                             |
                     KZindex |
                         L1. |  -.0032342   .0035533    -0.91   0.363    -.0101985    .0037301
                             |
        elektricitygenerator |  -.2965176   .1057578    -2.80   0.005    -.5037991    -.089236
               Carbonleakage |   .0227824   .0103768     2.20   0.028     .0024443    .0431205
                             |
               twodigitsNACE |
                         10  |  -.0170488   .0253427    -0.67   0.501    -.0667196    .0326219
                         11  |  -.0545278   .0362404    -1.50   0.132    -.1255576    .0165021
                         13  |  -.0769276    .033449    -2.30   0.021    -.1424864   -.0113688
                         16  |  -.0997589   .0433162    -2.30   0.021    -.1846571   -.0148606
                         17  |  -.0363827   .0306086    -1.19   0.235    -.0963745    .0236091
                         19  |   -.017968   .0326387    -0.55   0.582    -.0819386    .0460027
                         20  |   -.035422    .024873    -1.42   0.154    -.0841721    .0133281
                         21  |  -.1458477   .0361044    -4.04   0.000    -.2166111   -.0750843
                         22  |  -.0230857   .0322135    -0.72   0.474     -.086223    .0400516
                         23  |  -.0618224   .0243418    -2.54   0.011    -.1095315   -.0141132
                         24  |   -.054857   .0274241    -2.00   0.045    -.1086072   -.0011068
                         25  |   -.065376   .0449941    -1.45   0.146    -.1535627    .0228108
                         27  |  -.1413144    .105282    -1.34   0.180    -.3476632    .0650345
                         28  |  -.1101605    .047586    -2.31   0.021    -.2034273   -.0168936
                         29  |  -.0786536   .0429498    -1.83   0.067    -.1628336    .0055264
                         30  |  -.1357392    .054646    -2.48   0.013    -.2428434    -.028635
                         35  |   .2916917   .1064745     2.74   0.006     .0830055     .500378
                         42  |  -.0675854   .0324183    -2.08   0.037     -.131124   -.0040467
                         46  |  -.0565031    .027916    -2.02   0.043    -.1112175   -.0017888
                         47  |   .0099568   .0551535     0.18   0.857    -.0981421    .1180557
                         49  |  -.0686854   .0459362    -1.50   0.135    -.1587187    .0213479
                         52  |  -.0673122   .0374821    -1.80   0.073    -.1407757    .0061512
                         61  |  -.1721765   .0837297    -2.06   0.040    -.3362838   -.0080692
                         63  |  -.0261264   .0553437    -0.47   0.637    -.1345982    .0823453
                         70  |  -.0579974   .0599777    -0.97   0.334    -.1755515    .0595567
                         72  |  -.1225925   .0552375    -2.22   0.026    -.2308559    -.014329
                         81  |  -.1404944   .0561836    -2.50   0.012    -.2506122   -.0303766
                             |
                  Province_n |
Brabant Wallon / Waals Br..  |   .0118277   .0228113     0.52   0.604    -.0328817    .0565371
                   Brussels  |   .0364452   .0160283     2.27   0.023     .0050304    .0678601
              East-Flanders  |  -.0186906   .0140005    -1.33   0.182    -.0461311    .0087499
       Hainaut / Henegouwen  |   .0153574   .0151453     1.01   0.311    -.0143268    .0450416
         Limburg / Limbourg  |  -.0137308   .0147966    -0.93   0.353    -.0427317      .01527
               Liège / Luik  |   .0069992   .0197536     0.35   0.723    -.0317171    .0457154
                 Luxembourg  |   .0043567   .0277862     0.16   0.875    -.0501033    .0588167
              Namur / Namen  |   -.014729    .054721    -0.27   0.788    -.1219803    .0925223
Vlaams Brabant / Brabant ..  |  -.0305495   .0234302    -1.30   0.192    -.0764719     .015373
              West-Flanders  |   .0141935   .0178888     0.79   0.428     -.020868     .049255
                             |
                  publicfirm |   .0289798   .0271321     1.07   0.285    -.0241982    .0821578
                         SME |  -.0381241   .0141018    -2.70   0.007    -.0657631    -.010485
                       _cons |   .2408525   .1106325     2.18   0.029     .0240169    .4576882
----------------------------------------------------------------------------------------------

. xtreg pctcarbonintensitychange L.firmsize L.profitability L.leverage age L.capitalintensity L
> .CAPEX L.KZindex elektricitygenerator Carbonleakage i.twodigitsNACE i.Province_n publicfirm S
> ME, re

Random-effects GLS regression                   Number of obs     =        864
Group variable: Companynum~r                    Number of groups  =        183

R-sq:                                           Obs per group:
     within  = 0.0000                                         min =          1
     between = 0.3258                                         avg =        4.7
     overall = 0.0720                                         max =          5

                                                Wald chi2(48)     =      59.93
corr(u_i, X)   = 0 (assumed)                    Prob > chi2       =     0.1159

----------------------------------------------------------------------------------------------
    pctcarbonintensitychange |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-----------------------------+----------------------------------------------------------------
                    firmsize |
                         L1. |  -.0087808   .0079931    -1.10   0.272    -.0244471    .0068855
                             |
               profitability |
                         L1. |  -.0688331   .1265621    -0.54   0.587    -.3168903     .179224
                             |
                    leverage |
                         L1. |   .0244818   .0288423     0.85   0.396    -.0320481    .0810117
                             |
                         age |   -.000399   .0002861    -1.39   0.163    -.0009597    .0001617
                             |
            capitalintensity |
                         L1. |   .0166871   .0379886     0.44   0.660    -.0577691    .0911434
                             |
                       CAPEX |
                         L1. |   -.031154   .0799415    -0.39   0.697    -.1878365    .1255286
                             |
                     KZindex |
                         L1. |  -.0014344   .0040594    -0.35   0.724    -.0093907    .0065218
                             |
        elektricitygenerator |  -.2962133   .1209977    -2.45   0.014    -.5333643   -.0590622
               Carbonleakage |   .0244407   .0155893     1.57   0.117    -.0061139    .0549952
                             |
               twodigitsNACE |
                         10  |  -.0198456    .037485    -0.53   0.597    -.0933149    .0536236
                         11  |  -.0580764   .0534681    -1.09   0.277     -.162872    .0467191
                         13  |  -.0779794   .0489724    -1.59   0.111    -.1739636    .0180047
                         16  |  -.1042684   .0648187    -1.61   0.108    -.2313108     .022774
                         17  |  -.0351081    .045549    -0.77   0.441    -.1243825    .0541663
                         19  |  -.0188102   .0486132    -0.39   0.699    -.1140904      .07647
                         20  |   -.035151   .0367532    -0.96   0.339    -.1071859    .0368839
                         21  |  -.1499324   .0539534    -2.78   0.005    -.2556792   -.0441856
                         22  |  -.0199669   .0482437    -0.41   0.679    -.1145228    .0745889
                         23  |   -.062572   .0360905    -1.73   0.083    -.1333081    .0081641
                         24  |  -.0538698   .0407726    -1.32   0.186    -.1337826     .026043
                         25  |  -.0625568   .0676387    -0.92   0.355    -.1951261    .0700125
                         27  |  -.1413433   .1207934    -1.17   0.242     -.378094    .0954075
                         28  |  -.1204707   .0682325    -1.77   0.077    -.2542039    .0132624
                         29  |  -.0838932   .0642725    -1.31   0.192    -.2098651    .0420786
                         30  |  -.1360928   .0819857    -1.66   0.097    -.2967818    .0245961
                         35  |   .2900476    .122596     2.37   0.018     .0497639    .5303314
                         42  |  -.0625901   .0485432    -1.29   0.197    -.1577331    .0325528
                         46  |  -.0533588   .0414742    -1.29   0.198    -.1346466    .0279291
                         47  |   .0147112   .0826967     0.18   0.859    -.1473714    .1767938
                         49  |  -.0628697   .0686873    -0.92   0.360    -.1974944    .0717549
                         52  |  -.0686771   .0553526    -1.24   0.215    -.1771662     .039812
                         61  |  -.1784293   .1056568    -1.69   0.091    -.3855129    .0286544
                         63  |  -.0098283    .078951    -0.12   0.901    -.1645694    .1449128
                         70  |  -.0488087   .0901599    -0.54   0.588    -.2255187    .1279014
                         72  |  -.1259454   .0824177    -1.53   0.126    -.2874812    .0355903
                         81  |  -.1354842   .0845476    -1.60   0.109    -.3011945    .0302261
                             |
                  Province_n |
Brabant Wallon / Waals Br..  |   .0074386   .0338765     0.22   0.826    -.0589582    .0738353
                   Brussels  |   .0384491    .024031     1.60   0.110    -.0086509     .085549
              East-Flanders  |   -.020295   .0208019    -0.98   0.329    -.0610659     .020476
       Hainaut / Henegouwen  |   .0157239   .0224351     0.70   0.483    -.0282482     .059696
         Limburg / Limbourg  |  -.0148268    .022197    -0.67   0.504     -.058332    .0286784
               Liège / Luik  |   .0067555   .0294684     0.23   0.819    -.0510014    .0645125
                 Luxembourg  |   .0031601   .0410097     0.08   0.939    -.0772175    .0835377
              Namur / Namen  |  -.0135276   .0819917    -0.16   0.869    -.1742284    .1471732
Vlaams Brabant / Brabant ..  |   -.025455   .0351928    -0.72   0.469    -.0944316    .0435216
              West-Flanders  |   .0215827   .0267154     0.81   0.419    -.0307784    .0739439
                             |
                  publicfirm |   .0183022   .0401914     0.46   0.649    -.0604714    .0970759
                         SME |  -.0343842   .0207943    -1.65   0.098    -.0751403    .0063719
                       _cons |   .2012123   .1609969     1.25   0.211    -.1143358    .5167605
-----------------------------+----------------------------------------------------------------
                     sigma_u |   .0195396
                     sigma_e |  .16076216
                         rho |  .01455777   (fraction of variance due to u_i)
----------------------------------------------------------------------------------------------

many thanks!
Timea

[Jeff Wooldridge]

As Joseph is alluding to, what you've done with xtgee is ordinary least squares (often called pooled OLS in econometrics) because the default in xtgee is to assume an uncorrelated structure (which they call independent). xtreg does generalized least squares because the default is random effects estimation. These are different estimators. In your case, the estimates are close because sigma_u is so small. This is not surprising because you have effectively already differenced your dependent variable and that removes much, if not all, of the serial correlation. Do you see the small estimate of rho? That means the estimated correlation due to u(i) is very small. You are almost, but not quite, doing pooled OLS.

If you want comparability, use the "corr(exch)" option for xtgee. But, really, you should just be doing pooled OLS and clustering your standard errors. Or, try fixed effects.

[Timea De Wispelaere]

Thank you for your insights, Jeff!