Selection between Pooled OLS and RE model in Panel logistic regression

[Suren Perera]

Hello , I am currently engaged in research on the determinants of financial distress among listed companies over the last five years (2018 - 2022). I have chosen a binary variable as my dependent variable, where 1 represents financial distress and 0 signifies financial stability. To analyze this, I employed panel logistic regression, and based on the Hausman test results, a random effect model is deemed appropriate. However, during the process, I encountered an issue while conducting the Breusch–Pagan test using xttest0 command to determine whether to employ panel data or a pooled OLS approach. The result displayed as "last estimates not found," leaving me uncertain about the accuracy of my steps.

I would appreciate clarification on where I might be going wrong in my approach, as well as guidance on the correct steps to conduct the Breusch–Pagan test and decide between panel data and pooled OLS.

Thank You.
Suren

[Carlo Lazzaro]

Suren:
1) -xttest0- is not allowed after -xtlogit-;
2) there's no such a test for -xtlogit-.

[Suren Perera]

Dear Sir,
Thank you so much invaluable guidance and assistance. I am genuinely grateful for the time and effort you have dedicated to assisting me

Suren

[Carlo Lazzaro]

Suren:
Carlo is enough.
Thanks.

[Jeff Wooldridge]

There is an equivalent test for xtlogit. The estimate of rho is an estimate of the share of the variance due to the unobserved effect (with the idiosyncratic variance normalized to one). Stata reports a standard error and a confidence interval. The problem is that the estimate assumes no serial correlation in the time-varying error. In the end, it's just picking up some form of serial correlation. You can just use pooled logit and cluster the standard errors as an alternative.

Below the estimate of rho is very large and quite statistically significant.

xtlogit lfp black educ age kids lhinc i.period, re

Fitting comparison model:

Iteration 0:  Log likelihood = -17709.021  
Iteration 1:  Log likelihood = -16920.497  
Iteration 2:  Log likelihood = -16912.649  
Iteration 3:  Log likelihood = -16912.645  
Iteration 4:  Log likelihood = -16912.645  

Fitting full model:

tau =  0.0    Log likelihood = -16912.645
tau =  0.1    Log likelihood = -16030.926
tau =  0.2    Log likelihood = -15190.261
tau =  0.3    Log likelihood = -14386.718
tau =  0.4    Log likelihood = -13612.243
tau =  0.5    Log likelihood = -12856.237
tau =  0.6    Log likelihood =     -12106
tau =  0.7    Log likelihood = -11345.889
tau =  0.8    Log likelihood = -10555.766

Iteration 0:  Log likelihood = -11346.646  
Iteration 1:  Log likelihood = -9073.2282  
Iteration 2:  Log likelihood = -8861.0322  
Iteration 3:  Log likelihood = -8768.5935  
Iteration 4:  Log likelihood = -8760.4206  
Iteration 5:  Log likelihood = -8760.4206  (backed up)
Iteration 6:  Log likelihood = -8732.0254  
Iteration 7:  Log likelihood = -8731.6635  
Iteration 8:  Log likelihood = -8731.6411  
Iteration 9:  Log likelihood =  -8731.641  

Random-effects logistic regression                   Number of obs    = 28,315
Group variable: id                                   Number of groups =  5,663

Random effects u_i ~ Gaussian                        Obs per group:
                                                                  min =      5
                                                                  avg =    5.0
                                                                  max =      5

Integration method: mvaghermite                      Integration pts. =     12

                                                     Wald chi2(9)     = 363.97
Log likelihood = -8731.641                           Prob > chi2      = 0.0000

------------------------------------------------------------------------------
         lfp | Coefficient  Std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
       black |   1.454505    .381193     3.82   0.000     .7073804    2.201629
        educ |   .6546262   .0474766    13.79   0.000     .5615739    .7476785
         age |  -.1114423   .0150507    -7.40   0.000    -.1409411   -.0819436
        kids |  -.8692121   .0858018   -10.13   0.000    -1.037381   -.7010436
       lhinc |  -.3208495   .0817084    -3.93   0.000     -.480995    -.160704
             |
      period |
          2  |  -.0972577   .0901918    -1.08   0.281    -.2740304    .0795149
          3  |  -.2363488   .0900232    -2.63   0.009    -.4127909   -.0599066
          4  |  -.2697878    .090148    -2.99   0.003    -.4464746    -.093101
          5  |   -.381383   .0901338    -4.23   0.000    -.5580421    -.204724
             |
       _cons |   4.233501   .9883852     4.28   0.000     2.296302    6.170701
-------------+----------------------------------------------------------------
    /lnsig2u |    4.26013   .0469351                      4.168139    4.352121
-------------+----------------------------------------------------------------
     sigma_u |   8.415416   .1974891                      8.037111    8.811527
         rho |   .9556078   .0019911                      .9515376    .9593507
------------------------------------------------------------------------------
LR test of rho=0: chibar2(01) = 1.6e+04                Prob >= chibar2 = 0.000

[Suren Perera]

Dear Jeff,
Thank you so much invaluable guidance. I will try this approach.