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  • Unbalanced panel data - Model?

    Dear all,

    I have been trying to figure out which model to use for my (unbalanced) panel data analysis for some time now and I am getting more and more confused, so I hope some of you can help. I ran Pooled OLS, fixed effect and random effects models and then checked with both -xttest0- and -xtoverid- (I am using clustered robust standard errors). Please find my results below:

    Code:
     
    Breusch and Pagan Lagrangian multiplier test for random effects
    
            CAR[panel_ID,t] = Xb + u[panel_ID] + e[panel_ID,t]
    
            Estimated results:
                             |       Var     SD = sqrt(Var)
                    ---------+-----------------------------
                         CAR |   .0017767       .0421511
                           e |   .0016862        .041063
                           u |   .0000532       .0072921
    
            Test: Var(u) = 0
                                 chibar2(01) =     0.23
                              Prob > chibar2 =   0.3169
    
    
    xtoverid // Rejection of null-hypothesis -> fixed effects 
    
    Test of overidentifying restrictions: fixed vs random effects
    Cross-section time-series model: xtreg re  robust cluster(panel_ID)
    Sargan-Hansen statistic  74.807  Chi-sq(29)   P-value = 0.0000
    So as far as I understand, -xttest0- indicates, that basically there are no random effects. i.e. to go for pooled OLS rather than random effects. -xtoverid- tells me to reject the null hypotheses and go for FE. Yet, I am wondering now which model actually to use? Do the -xttest0- results tell me to go for Pooled OLS rather than both FE AND RE? I have read multiple times, that -xttest0- is also a test to determine the presence of fixed effects, but I don't really understand what to make of this.

    Like I said, I am confused and I hope someone can help!

    Thanks in advance!

  • #2
    Amina:
    could you please share the -xtreg,fe- code and outcome table? Thanks.
    Kind regards,
    Carlo
    (Stata 19.0)

    Comment


    • #3
      Sure:

      Code:
      xtreg CAR ESG_score Firm_size Firm_performance Firm_leverage RD_intensity i.Layoff_Reason_New i.Year, fe vce(cluster panel_ID) 
      
      Fixed-effects (within) regression               Number of obs     =        435
      Group variable: panel_ID                        Number of groups  =         77
      
      R-squared:                                      Obs per group:
           Within  = 0.0754                                         min =          1
           Between = 0.0018                                         avg =        5.6
           Overall = 0.0501                                         max =         34
      
                                                      F(29,76)          =       3.01
      corr(u_i, Xb) = -0.1461                         Prob > F          =     0.0001
      
                                     (Std. err. adjusted for 77 clusters in panel_ID)
      -------------------------------------------------------------------------------
                    |               Robust
                CAR | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
      --------------+----------------------------------------------------------------
          ESG_score |   .0002105   .0002972     0.71   0.481    -.0003815    .0008024
          Firm_size |  -.0015802   .0146304    -0.11   0.914    -.0307192    .0275588
      Firm_perfor~e |  -.0250244   .0494634    -0.51   0.614    -.1235394    .0734905
      Firm_leverage |   .0000564   .0000829     0.68   0.498    -.0001087    .0002214
       RD_intensity |   .0150315   .1355763     0.11   0.912    -.2549922    .2850551
                    |
      Layoff_Reas~w |
      Demand slump  |  -.0140832   .0053289    -2.64   0.010    -.0246966   -.0034698
               M&A  |  -.0197466   .0091179    -2.17   0.033    -.0379064   -.0015868
           Missing  |   .0038871   .0082938     0.47   0.641    -.0126314    .0204056
             Other  |   .0000276   .0082975     0.00   0.997    -.0164983    .0165535
      Plant clos..  |  -.0016493   .0048841    -0.34   0.737    -.0113768    .0080783
      Reorganiza~n  |  -.0095612   .0079446    -1.20   0.233    -.0253843    .0062619
                    |
               Year |
              2003  |  -.0049713   .0142184    -0.35   0.728    -.0332898    .0233472
              2004  |  -.0017369   .0143395    -0.12   0.904    -.0302964    .0268226
              2005  |  -.0034556    .014433    -0.24   0.811    -.0322013    .0252902
              2006  |  -.0023498   .0143223    -0.16   0.870    -.0308751    .0261754
              2007  |  -.0230816   .0168954    -1.37   0.176    -.0567318    .0105686
              2008  |  -.0280522   .0187535    -1.50   0.139    -.0654031    .0092986
              2009  |  -.0082316   .0156304    -0.53   0.600    -.0393622    .0228989
              2010  |  -.0002667   .0155817    -0.02   0.986    -.0313002    .0307669
              2011  |   .0188843   .0165401     1.14   0.257     -.014058    .0518267
              2012  |   .0002706   .0169002     0.02   0.987    -.0333891    .0339303
              2013  |  -.0068922   .0145696    -0.47   0.638      -.03591    .0221256
              2014  |   .0124621   .0175332     0.71   0.479    -.0224582    .0473824
              2015  |  -.0036136   .0165743    -0.22   0.828    -.0366241     .029397
              2016  |  -.0103561   .0197055    -0.53   0.601    -.0496031    .0288908
              2017  |  -.0125712   .0182966    -0.69   0.494     -.049012    .0238696
              2018  |   .0022368   .0166239     0.13   0.893    -.0308727    .0353462
              2019  |  -.0000369   .0184094    -0.00   0.998    -.0367023    .0366285
              2020  |  -.0138414   .0169881    -0.81   0.418    -.0476762    .0199934
                    |
              _cons |   .0003875   .0683547     0.01   0.995    -.1357526    .1365277
      --------------+----------------------------------------------------------------
            sigma_u |   .0332205
            sigma_e |  .04106304
                rho |  .39558806   (fraction of variance due to u_i)
      -------------------------------------------------------------------------------
      Thanks in advance!

      Comment


      • #4
        Amina:
        as per:
        1) low within R_Sq;
        2) -sigma_u-<-sigma_e-.

        I fear that there's no evidence of a panel-wise effect.
        Therefore, pooled OLS is in all likelihood the way to go.
        Kind regards,
        Carlo
        (Stata 19.0)

        Comment


        • #5
          Ok thanks a lot Carlo! When I estimate using Pooled OLS my F statistic and associated p-value is missing though, so I fear I don't really know whether the overall model fit is sufficient to use that model. Could you help with that as well?


          Code:
          reg CAR ESG_score Firm_size Firm_performance Firm_leverage RD_intensity i.Layoff_Reason_New i.Industry i.Year, vce(cluster panel_ID) 
          
          
          Linear regression                               Number of obs     =        435
                                                          F(34, 76)         =          .
                                                          Prob > F          =          .
                                                          R-squared         =     0.0906
                                                          Root MSE          =     .04197
          
                                         (Std. err. adjusted for 77 clusters in panel_ID)
          -------------------------------------------------------------------------------
                        |               Robust
                    CAR | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
          --------------+----------------------------------------------------------------
              ESG_score |  -.0000851   .0002243    -0.38   0.706    -.0005318    .0003617
              Firm_size |  -.0004415   .0056935    -0.08   0.938     -.011781     .010898
          Firm_perfor~e |  -.0402311   .0554577    -0.73   0.470    -.1506848    .0702225
          Firm_leverage |   .0000372   .0000684     0.54   0.588     -.000099    .0001733
           RD_intensity |  -.0057652   .0580347    -0.10   0.921    -.1213513    .1098209
                        |
          Layoff_Reas~w |
          Demand slump  |  -.0166195   .0056157    -2.96   0.004    -.0278042   -.0054348
                   M&A  |  -.0162465   .0093055    -1.75   0.085    -.0347801    .0022871
               Missing  |   .0050133   .0077056     0.65   0.517    -.0103338    .0203605
                 Other  |  -.0103468   .0092454    -1.12   0.267    -.0287606     .008067
          Plant clos..  |  -.0000426   .0044671    -0.01   0.992    -.0089396    .0088544
          Reorganiza~n  |  -.0160031   .0077179    -2.07   0.042    -.0313747   -.0006314
                        |
               Industry |
          Manufactur~g  |   .0058839   .0080973     0.73   0.470    -.0102433    .0220111
                Mining  |   .0007946   .0101321     0.08   0.938    -.0193853    .0209744
          Public Adm..  |  -.0050129   .0131769    -0.38   0.705    -.0312569     .021231
          Retail Trade  |   .0026157   .0108565     0.24   0.810    -.0190068    .0242382
              Services  |    .012366   .0090631     1.36   0.176    -.0056848    .0304168
          Transporta..  |   .0104526   .0152286     0.69   0.495    -.0198779     .040783
          Wholesale ..  |  -.0263539   .0150261    -1.75   0.083     -.056281    .0035731
                        |
                   Year |
                  2003  |  -.0004327   .0141773    -0.03   0.976    -.0286691    .0278037
                  2004  |    .003775   .0130592     0.29   0.773    -.0222347    .0297847
                  2005  |   .0030294   .0120566     0.25   0.802    -.0209834    .0270423
                  2006  |  -.0006312   .0130546    -0.05   0.962    -.0266317    .0253693
                  2007  |   -.000908   .0142569    -0.06   0.949     -.029303    .0274871
                  2008  |  -.0231898   .0165964    -1.40   0.166    -.0562444    .0098649
                  2009  |   .0091413   .0145714     0.63   0.532    -.0198803    .0381628
                  2010  |     .00794   .0130584     0.61   0.545    -.0180681     .033948
                  2011  |   .0122199    .013642     0.90   0.373    -.0149505    .0393903
                  2012  |   .0039696   .0157885     0.25   0.802     -.027476    .0354152
                  2013  |  -.0020562   .0125671    -0.16   0.870    -.0270857    .0229734
                  2014  |   .0176033   .0146994     1.20   0.235    -.0116731    .0468797
                  2015  |   .0082113   .0139862     0.59   0.559    -.0196447    .0360672
                  2016  |   .0034785   .0167817     0.21   0.836    -.0299452    .0369023
                  2017  |   .0013887   .0155807     0.09   0.929    -.0296428    .0324203
                  2018  |   .0130975   .0152681     0.86   0.394    -.0173116    .0435065
                  2019  |   .0059102    .016177     0.37   0.716     -.026309    .0381295
                  2020  |  -.0122918   .0156232    -0.79   0.434     -.043408    .0188245
                        |
                  _cons |    .004306   .0205827     0.21   0.835    -.0366879    .0452999
          -------------------------------------------------------------------------------

          Comment


          • #6
            Amina:
            1) see -help j_robustsingular- for the missing F-stat;
            2) most of your coefficient do not reach statistical significance (this result is echoed by a very low R-sq, that basically tells you that the simpler -mean CAR- is not less informative than your regression reults);
            3) I would start it all over again, going for a better specified regression (see the literature in your research field).
            Kind regards,
            Carlo
            (Stata 19.0)

            Comment

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