Too many predictors when using Time fixed effects for panel data

Monica Jaison

Join Date: Aug 2022
Posts: 8

Too many predictors when using Time fixed effects for panel data

16 Mar 2023, 23:21

Hello,
I am running an xtreg-fe cluster(panelvar) on monthly data. I employ time-fixed effects too. However, the regression output contains too many predictors. The number of predictors> the number of clusters. Is there a way out of this predicament?
Here is my code:

Code:

xtreg laod  lnl lpr lt lh lp lwi lf la lpop lndvi i.month, fe cluster(sd)

Result:

Code:

note: lpop omitted because of collinearity

Fixed-effects (within) regression               Number of obs     =      5,826
Group variable: sd                              Number of groups  =         59

R-sq:                                           Obs per group:
     within  = 0.3639                                         min =         80
     between = 0.5746                                         avg =       98.7
     overall = 0.4326                                         max =        102

                                                F(58,58)          =          .
corr(u_i, Xb)  = -0.3306                        Prob > F          =          .

                                    (Std. Err. adjusted for 59 clusters in sd)
------------------------------------------------------------------------------
             |               Robust
        laod |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         lnl |   .0444047   .0189316     2.35   0.022      .006509    .0823003
         lpr |   .0073755   .0040048     1.84   0.071     -.000641    .0153921
          lt |  -3.884795   1.871788    -2.08   0.042    -7.631587   -.1380035
          lh |   .5299972   .0476566    11.12   0.000     .4346021    .6253922
          lp |   4.666758   6.377097     0.73   0.467    -8.098389     17.4319
         lwi |  -.3078047    .058291    -5.28   0.000    -.4244869   -.1911225
          lf |    .565516   .6729575     0.84   0.404    -.7815548    1.912587
          la |    .307257   .1024781     3.00   0.004     .1021247    .5123892
        lpop |          0  (omitted)
       lndvi |  -.2585523   .0444562    -5.82   0.000     -.347541   -.1695636
             |
       month |
        649  |  -.1233491   .0306944    -4.02   0.000    -.1847905   -.0619077
        650  |  -.0332226   .0468975    -0.71   0.482     -.127098    .0606529
        651  |   .1017779   .0643089     1.58   0.119    -.0269503     .230506
        652  |   .0465545   .0721204     0.65   0.521    -.0978102    .1909193
        653  |   .1329436   .1007038     1.32   0.192    -.0686368    .3345241
        654  |   .0536357   .1015976     0.53   0.600     -.149734    .2570054
        655  |  -.1270271   .0812046    -1.56   0.123    -.2895757    .0355216
        656  |  -.3396463   .0666669    -5.09   0.000    -.4730947    -.206198
        657  |  -.1076306   .0529593    -2.03   0.047    -.2136402    -.001621
        658  |   .0830799   .0496674     1.67   0.100    -.0163402       .1825
        659  |   -.121576   .0278431    -4.37   0.000      -.17731    -.065842
        660  |  -.1345138   .0250915    -5.36   0.000    -.1847399   -.0842877
        661  |  -.1078254   .0322146    -3.35   0.001      -.17231   -.0433409
        662  |  -.0871166   .0491051    -1.77   0.081    -.1854111    .0111779
        663  |   .0174388   .0497147     0.35   0.727    -.0820761    .1169536
        664  |   .2145259   .0837729     2.56   0.013     .0468362    .3822157
        665  |    .031304   .1028956     0.30   0.762    -.1746639    .2372719
        666  |   .2418876   .1020404     2.37   0.021     .0376316    .4461436
        667  |  -.0446145    .082237    -0.54   0.590    -.2092298    .1200008
        668  |  -.2410526   .0697299    -3.46   0.001    -.3806322    -.101473
        669  |   -.091523   .0435524    -2.10   0.040    -.1787026   -.0043434
        670  |  -.0992061    .056894    -1.74   0.087    -.2130917    .0146795
        671  |  -.2472565   .0264505    -9.35   0.000    -.3002029   -.1943101
        672  |  -.0079172   .0290274    -0.27   0.786    -.0660218    .0501874
        673  |   .0613458   .0326798     1.88   0.066      -.00407    .1267615
        674  |   .0185414   .0510152     0.36   0.718    -.0835766    .1206594
        675  |   .0246948   .0633253     0.39   0.698    -.1020646    .1514542
        676  |  -.0176356    .084514    -0.21   0.835    -.1868087    .1515375
        677  |  -.1145517   .1096654    -1.04   0.301     -.334071    .1049675
        678  |  -.0882696   .1083409    -0.81   0.419    -.3051375    .1285984
        679  |  -.1288769   .0862318    -1.49   0.140    -.3014886    .0437348
        680  |   -.252661   .0796029    -3.17   0.002    -.4120035   -.0933185
        681  |  -.1868149   .0611212    -3.06   0.003    -.3091622   -.0644676
        682  |   .0267119   .0466807     0.57   0.569    -.0667296    .1201534
        683  |  -.1697311   .0430275    -3.94   0.000    -.2558601   -.0836022
        684  |  -.0028064   .0208123    -0.13   0.893    -.0444668     .038854
        685  |  -.0862943   .0407558    -2.12   0.039    -.1678759   -.0047127
        686  |   -.005816   .0440132    -0.13   0.895    -.0939181    .0822861
        687  |   .2303101    .066068     3.49   0.001     .0980606    .3625596
        688  |   .0515448   .0816173     0.63   0.530    -.1118301    .2149196
        689  |  -.1343553   .1008913    -1.33   0.188    -.3363112    .0676005
        690  |   -.071389   .1032045    -0.69   0.492    -.2779752    .1351972
        691  |  -.0436445    .101499    -0.43   0.669    -.2468168    .1595278
        692  |  -.3623209   .0795405    -4.56   0.000    -.5215385   -.2031033
        693  |   -.137231   .0668359    -2.05   0.045    -.2710177   -.0034443
        694  |   .0502787   .0588681     0.85   0.397    -.0675586     .168116
        695  |  -.0297487   .0249504    -1.19   0.238    -.0796923    .0201949
        696  |   .2128178   .0492536     4.32   0.000      .114226    .3114095
        697  |  -.1318354   .0319908    -4.12   0.000    -.1958719   -.0677989
        698  |   .1500738   .0592733     2.53   0.014     .0314254    .2687222
        699  |   .0708001   .0651461     1.09   0.282    -.0596041    .2012042
        700  |   .1466561   .0819551     1.79   0.079    -.0173948    .3107071
        701  |   .0960467   .1118363     0.86   0.394     -.127818    .3199115
        702  |  -.0199497   .1224544    -0.16   0.871    -.2650688    .2251694
        703  |   .1611545   .1091591     1.48   0.145    -.0573511    .3796602
        704  |  -.3932091   .0616178    -6.38   0.000    -.5165505   -.2698677
        705  |  -.1384157   .0415515    -3.33   0.002    -.2215901   -.0552413
        706  |  -.1232199   .0393126    -3.13   0.003    -.2019126   -.0445272
        707  |   .0229704   .0443862     0.52   0.607    -.0658783    .1118191
        708  |    .003345   .0300747     0.11   0.912     -.056856    .0635461
        709  |  -.1586821   .0255624    -6.21   0.000    -.2098508   -.1075134
        710  |  -.0659489   .0494828    -1.33   0.188    -.1649995    .0331018
        711  |  -.0910197   .0650305    -1.40   0.167    -.2211924     .039153
        712  |   .1705902   .0803942     2.12   0.038     .0096637    .3315167
        713  |  -.0349302   .0975616    -0.36   0.722     -.230221    .1603607
        714  |   .0457064   .1174711     0.39   0.699    -.1894375    .2808503
        715  |   -.091042   .0997719    -0.91   0.365    -.2907573    .1086732
        716  |  -.2498159   .0979934    -2.55   0.013    -.4459709   -.0536608
        717  |  -.3566553    .057478    -6.21   0.000    -.4717101   -.2416006
        718  |   .0368881   .0480439     0.77   0.446    -.0592823    .1330585
        719  |   -.099185   .0316461    -3.13   0.003    -.1625316   -.0358384
        720  |  -.1638996   .0166212    -9.86   0.000    -.1971706   -.1306286
        721  |  -.0645378   .0305725    -2.11   0.039    -.1257354   -.0033402
        722  |  -.1241648    .043424    -2.86   0.006    -.2110874   -.0372422
        723  |  -.0614872   .0544523    -1.13   0.263    -.1704854     .047511
        724  |  -.0086622   .0832141    -0.10   0.917    -.1752334     .157909
        725  |   -.213926   .1238311    -1.73   0.089    -.4618009    .0339488
        726  |  -.2437386   .1041832    -2.34   0.023    -.4522839   -.0351932
        727  |  -.1545941   .1188872    -1.30   0.199    -.3925728    .0833845
        728  |  -.3049369   .0829763    -3.67   0.001    -.4710321   -.1388417
        729  |  -.0042765   .0881209    -0.05   0.961    -.1806697    .1721166
        730  |   .0111962   .0514665     0.22   0.829    -.0918253    .1142177
        731  |  -.0253891   .0363513    -0.70   0.488    -.0981542    .0473761
        732  |   .1024035   .0263547     3.89   0.000     .0496489    .1551581
        733  |   .0508763   .0299352     1.70   0.095    -.0090456    .1107982
        734  |   .2174193   .0536344     4.05   0.000     .1100584    .3247801
        735  |   .2987526   .0671605     4.45   0.000     .1643162    .4331891
        736  |  -.0379749   .0809879    -0.47   0.641    -.2000899    .1241401
        737  |  -.0257866   .1015697    -0.25   0.800    -.2291004    .1775271
        738  |  -.0003278   .1141334    -0.00   0.998    -.2287907    .2281351
        739  |  -.0071986   .0921522    -0.08   0.938    -.1916612    .1772641
        740  |  -.2660276   .0953891    -2.79   0.007    -.4569696   -.0750856
        741  |  -.1511299   .0671898    -2.25   0.028    -.2856248    -.016635
        742  |  -.0220244   .0602739    -0.37   0.716    -.1426757    .0986269
        743  |   .1625696   .0367626     4.42   0.000     .0889812     .236158
        744  |  -.0285415   .0379808    -0.75   0.455    -.1045682    .0474853
        745  |   .0387975    .044154     0.88   0.383    -.0495863    .1271812
        746  |    .322907   .0602675     5.36   0.000     .2022685    .4435455
        747  |   .3102825   .0777607     3.99   0.000     .1546276    .4659374
        748  |   .3304651   .0885366     3.73   0.000     .1532399    .5076904
        749  |   .2293189   .1110574     2.06   0.043     .0070134    .4516244
             |
       _cons |  -21.81826   76.01927    -0.29   0.775    -173.9874    130.3508
-------------+----------------------------------------------------------------
     sigma_u |  .16010163
     sigma_e |  .22657205
         rho |  .33303091   (fraction of variance due to u_i)
------------------------------------------------------------------------------

Last edited by Monica Jaison; 16 Mar 2023, 23:25.

Tags: panel data, time-fixed effects, xtreg

Carlo Lazzaro

Join Date: Apr 2014

Posts: 17854
#2

17 Mar 2023, 01:24

Monica:
this is not an issue (see -help j_robustsingular-).
That said, your panel-wise effect seems limping (if existing at all sigma_u<sigma_e).
In addition, you're probably taking -xtreg- to its limit, as you seem to have a T>N panel dataset (see -xtregar,fe-).

Kind regards,
Carlo
(Stata 19.0)
Comment

Monica Jaison

Join Date: Aug 2022
Posts: 8

17 Mar 2023, 06:20

Dear Carlo,

I decided to run the code:

Code:

xtregar laod lnl lpr lt lh lp lwi lf la lpop lndvi, fe

the results are:

Code:

FE (within) regression with AR(1) disturbances  Number of obs     =      5,767
Group variable: sd                              Number of groups  =         59

R-sq:                                           Obs per group:
     within  = 0.3782                                         min =         79
     between = 0.3283                                         avg =       97.7
     overall = 0.2170                                         max =        101

                                                F(9,5699)         =     385.20
corr(u_i, Xb)  = 0.1013                         Prob > F          =     0.0000

------------------------------------------------------------------------------
        laod |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         lnl |   .0385658     .00847     4.55   0.000     .0219614    .0551702
         lpr |   .0017984   .0022246     0.81   0.419    -.0025627    .0061594
          lt |  -.8268044   .4244654    -1.95   0.051    -1.658918    .0053092
          lh |   .3431221   .0197289    17.39   0.000     .3044459    .3817983
          lp |   1.158246   .2137022     5.42   0.000     .7393089    1.577184
         lwi |  -.1486478   .0201606    -7.37   0.000    -.1881702   -.1091255
          lf |   .9495168   .1730063     5.49   0.000     .6103588    1.288675
          la |   .2914388   .0486246     5.99   0.000     .1961161    .3867615
        lpop |          0  (omitted)
       lndvi |  -.2980514    .019274   -15.46   0.000    -.3358358   -.2602671
       _cons |  -.3072107   .0876244    -3.51   0.000    -.4789879   -.1354335
-------------+----------------------------------------------------------------
      rho_ar |  .28474839
     sigma_u |  .18441393
     sigma_e |  .25078577
     rho_fov |  .35095764   (fraction of variance because of u_i)
------------------------------------------------------------------------------
F test that all u_i=0: F(58,5699) = 16.06                    Prob > F = 0.0000

However I am unsure how I can justify shifting to -xtregar- ignoring time fixed effects. Can you please explain how I can describe this?

Comment

Carlo Lazzaro

Join Date: Apr 2014

Posts: 17854
#4

17 Mar 2023, 08:13

Monica:
the justificatiom rests on the fact that you have a T>N panel dataset (whereas -xtreg- was developed for N>T panel datasets).
xtregar- allows you to calculate whether or not the epsilon residuals follow an AR1 process.

Kind regards,
Carlo
(Stata 19.0)
Comment
Monica Jaison

Join Date: Aug 2022

Posts: 8
#5

20 Mar 2023, 21:45

Thank you Carlo. Now I understand it well.
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Too many predictors when using Time fixed effects for panel data

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