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  • How to Present Pseudo R² for First and Second Equations in biprobit?

    Hi all,

    I’m estimating a biprobit model in Stata with a binary endogenous regressor (first equation) and a binary outcome (second equation). Since the model is estimated via maximum likelihood, traditional R² doesn’t apply.

    I'd appreciate advice on:
    1. How to report pseudo R² for First and Second stage.

    HTML Code:
    . asdoc biprobit (hard_final_Exact_new = csopresence1 Firm_Size_w   ROA_w     Leverage_w   M
    > arket_book_four_w   Non_pension_CFO_w   STD_CFO_w  board_size_w  female_percentage_w  inde
    > pendent_percentage_w SUSTAIBILITY_COMITEE_FU    Fund_Status_w  FUNDING_RATIO_w  Platn_Size
    > _w    i.year i.ff_12) (csopresence1 = CSO_Percentage Firm_Size_w   ROA_four_w     Leverage
    > _w   Market_book_four_w   Non_pension_CFO_w   STD_CFO_w  board_size_w  female_percentage_w
    >  independent_percentage_w SUSTAIBILITY_COMITEE_FU    Fund_Status_w  FUNDING_RATIO_w  Platn
    > _Size_w  i.year i.ff_12), vce(cluster id) 
    (File qqqq.doc already exists, option append was assumed)
    
    Fitting comparison equation 1:
    
    Iteration 0:  Log pseudolikelihood = -358.57341  
    Iteration 1:  Log pseudolikelihood = -320.88538  
    Iteration 2:  Log pseudolikelihood = -316.95227  
    Iteration 3:  Log pseudolikelihood = -316.89537  
    Iteration 4:  Log pseudolikelihood = -316.89519  
    Iteration 5:  Log pseudolikelihood = -316.89519  
    
    Fitting comparison equation 2:
    
    Iteration 0:  Log pseudolikelihood = -2262.5849  
    Iteration 1:  Log pseudolikelihood = -1713.9695  
    Iteration 2:  Log pseudolikelihood = -1697.3072  
    Iteration 3:  Log pseudolikelihood = -1697.2217  
    Iteration 4:  Log pseudolikelihood = -1697.2217  
    
    Comparison:   Log pseudolikelihood = -2014.1169
    
    Fitting full model:
    
    Iteration 0:  Log pseudolikelihood = -2014.1169  
    Iteration 1:  Log pseudolikelihood = -2013.5498  
    Iteration 2:  Log pseudolikelihood = -2013.4208  
    Iteration 3:  Log pseudolikelihood = -2013.4205  
    Iteration 4:  Log pseudolikelihood = -2013.4205  
    
    Seemingly unrelated bivariate probit                    Number of obs =  3,890
                                                            Wald chi2(86) = 604.03
    Log pseudolikelihood = -2013.4205                       Prob > chi2   = 0.0000
    
                                                   (Std. err. adjusted for 282 clusters in id)
    ------------------------------------------------------------------------------------------
                             |               Robust
                             | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
    -------------------------+----------------------------------------------------------------
    hard_final_Exact_new     |
                csopresence1 |   .8617745    .391411     2.20   0.028      .094623    1.628926
                 Firm_Size_w |  -.1853392    .079074    -2.34   0.019    -.3403215    -.030357
                       ROA_w |   1.342457   1.270696     1.06   0.291    -1.148062    3.832976
                  Leverage_w |   -1.36359   .4786134    -2.85   0.004    -2.301655   -.4255246
          Market_book_four_w |  -.0019166   .0095825    -0.20   0.841    -.0206979    .0168648
           Non_pension_CFO_w |  -4.731627   1.715921    -2.76   0.006    -8.094771   -1.368483
                   STD_CFO_w |   .9877623   3.248423     0.30   0.761    -5.379031    7.354555
                board_size_w |  -.0168825   .0283382    -0.60   0.551    -.0724244    .0386594
         female_percentage_w |  -.0674595   .6789809    -0.10   0.921    -1.398238    1.263319
    independent_percentage_w |   .2455994   .7079091     0.35   0.729    -1.141877    1.633076
     SUSTAIBILITY_COMITEE_FU |   .0479525   .1377992     0.35   0.728     -.222129     .318034
               Fund_Status_w |  -5.143616   2.077803    -2.48   0.013    -9.216034   -1.071198
             FUNDING_RATIO_w |  -.0741083   .3908778    -0.19   0.850    -.8402148    .6919982
                Platn_Size_w |   .0129418   .0664207     0.19   0.846    -.1172404    .1431241
                             |
                        year |
                       2005  |  -.3291102   .4308951    -0.76   0.445    -1.173649    .5154287
                       2006  |  -.0228991   .3877842    -0.06   0.953    -.7829422     .737144
                       2007  |  -.2596732   .4329916    -0.60   0.549    -1.108321    .5889748
                       2008  |   .4378972   .3283538     1.33   0.182    -.2056644    1.081459
                       2009  |   .6160889   .3227791     1.91   0.056    -.0165465    1.248724
                       2010  |   .4387853   .3344238     1.31   0.189    -.2166734    1.094244
                       2011  |   .1566102   .3721201     0.42   0.674    -.5727318    .8859522
                       2012  |   .2542079   .3607261     0.70   0.481    -.4528023     .961218
                       2013  |   .3616794   .3474024     1.04   0.298    -.3192169    1.042576
                       2014  |   .1459519   .3729648     0.39   0.696    -.5850456    .8769495
                       2015  |   .3231429    .370547     0.87   0.383    -.4031159    1.049402
                       2016  |   .2246956   .3608486     0.62   0.533    -.4825547    .9319459
                       2017  |   .1556381   .3744357     0.42   0.678    -.5782425    .8895186
                       2018  |   .5671508   .3484532     1.63   0.104    -.1158049    1.250107
                       2019  |   .3323077   .3798107     0.87   0.382    -.4121077    1.076723
                       2020  |   .5776984   .3762007     1.54   0.125    -.1596414    1.315038
                       2021  |   .1692187   .4191868     0.40   0.686    -.6523723    .9908096
                       2022  |  -.2173292   .4552191    -0.48   0.633    -1.109542    .6748838
                             |
                       ff_12 |
                          2  |    .167177   .3294582     0.51   0.612    -.4785493    .8129033
                          3  |  -.0105762   .2512164    -0.04   0.966    -.5029514     .481799
                          4  |  -.0953744    .420305    -0.23   0.820    -.9191569    .7284082
                          5  |  -.2516323   .3005004    -0.84   0.402    -.8406023    .3373377
                          6  |  -.1495748   .2802281    -0.53   0.594    -.6988117    .3996621
                          7  |   .3953585   .4553319     0.87   0.385    -.4970756    1.287793
                          8  |   -.084483   .2952769    -0.29   0.775    -.6632152    .4942492
                          9  |   .5784868   .2309531     2.50   0.012      .125827    1.031147
                         10  |   .0317781   .2707231     0.12   0.907    -.4988294    .5623855
                         11  |   .4325062   .2500559     1.73   0.084    -.0575943    .9226068
                         12  |  -.0317484   .2851415    -0.11   0.911    -.5906155    .5271188
                             |
                       _cons |   -.401612   .8140341    -0.49   0.622     -1.99709    1.193866
    -------------------------+----------------------------------------------------------------
    csopresence1             |
              CSO_Percentage |   4.288871   .6483055     6.62   0.000     3.018216    5.559527
                 Firm_Size_w |   .0143239   .1023808     0.14   0.889    -.1863387    .2149866
                  ROA_four_w |  -1.572496    3.69308    -0.43   0.670    -8.810801    5.665808
                  Leverage_w |   .5822143   .5057611     1.15   0.250    -.4090592    1.573488
          Market_book_four_w |   .0044918   .0052439     0.86   0.392     -.005786    .0147696
           Non_pension_CFO_w |   2.084435   4.023461     0.52   0.604    -5.801405    9.970275
                   STD_CFO_w |   7.189673    2.89779     2.48   0.013      1.51011    12.86924
                board_size_w |   .0585557   .0283132     2.07   0.039     .0030629    .1140485
         female_percentage_w |    1.46189    .616302     2.37   0.018     .2539605     2.66982
    independent_percentage_w |   1.420479   .7291936     1.95   0.051    -.0087145    2.849672
     SUSTAIBILITY_COMITEE_FU |    .197292   .1527171     1.29   0.196    -.1020279     .496612
               Fund_Status_w |   2.802765   2.276191     1.23   0.218    -1.658488    7.264017
             FUNDING_RATIO_w |   .0056822    .428719     0.01   0.989    -.8345917    .8459561
                Platn_Size_w |   .1982689   .0735633     2.70   0.007     .0540874    .3424503
                             |
                        year |
                       2005  |   .1582635     .11616     1.36   0.173     -.069406     .385933
                       2006  |   .1798129   .1531858     1.17   0.240    -.1204257    .4800515
                       2007  |   .1992696   .1770909     1.13   0.260    -.1478222    .5463613
                       2008  |   .4022686   .2066423     1.95   0.052    -.0027429      .80728
                       2009  |   .3315491    .203975     1.63   0.104    -.0682345    .7313327
                       2010  |   .2814466   .2076725     1.36   0.175     -.125584    .6884772
                       2011  |   .2477848    .219729     1.13   0.259     -.182876    .6784457
                       2012  |   .2383711   .2339087     1.02   0.308    -.2200814    .6968237
                       2013  |   .1611642   .2361992     0.68   0.495    -.3017778    .6241062
                       2014  |   .1174306   .2495388     0.47   0.638    -.3716565    .6065178
                       2015  |   .1055554   .2658536     0.40   0.691    -.4155082    .6266189
                       2016  |   .0941263   .2854882     0.33   0.742    -.4654203    .6536729
                       2017  |  -.0526493    .301213    -0.17   0.861     -.643016    .5377173
                       2018  |  -.2064691    .338196    -0.61   0.542    -.8693211    .4563828
                       2019  |  -.3711404   .3743367    -0.99   0.321    -1.104827     .362546
                       2020  |  -.5649029   .4089045    -1.38   0.167    -1.366341    .2365352
                       2021  |  -.7492744   .4321883    -1.73   0.083    -1.596348    .0977991
                       2022  |  -.6415122   .4660423    -1.38   0.169    -1.554938     .271914
                             |
                       ff_12 |
                          2  |  -.4032449   .4219972    -0.96   0.339    -1.230344    .4238544
                          3  |   .0445373   .3243181     0.14   0.891    -.5911144    .6801891
                          4  |   .1290963   .4430044     0.29   0.771    -.7391763    .9973689
                          5  |  -.2190148   .3218857    -0.68   0.496    -.8498992    .4118695
                          6  |   .4402585    .327009     1.35   0.178    -.2006674    1.081184
                          7  |   .3281896   .4688779     0.70   0.484    -.5907943    1.247173
                          8  |    .013678   .3189432     0.04   0.966    -.6114392    .6387952
                          9  |   .2375559   .3221404     0.74   0.461    -.3938277    .8689394
                         10  |   .4122343   .3243956     1.27   0.204    -.2235694    1.048038
                         11  |   .0156571   .3313167     0.05   0.962    -.6337116    .6650258
                         12  |    .286629   .3460465     0.83   0.408    -.3916096    .9648676
                             |
                       _cons |  -6.161665   1.055611    -5.84   0.000    -8.230625   -4.092705
    -------------------------+----------------------------------------------------------------
                     /athrho |  -.2897392   .2262834    -1.28   0.200    -.7332465    .1537682
    -------------------------+----------------------------------------------------------------
                         rho |  -.2818947   .2083019                     -.6250475    .1525676
    ------------------------------------------------------------------------------------------
    Wald test of rho=0: chi2(1) = 1.63949                     Prob > chi2 = 0.2004
    Click to Open File:  qqqq.doc
    
    . 
    . 
    end of do-file
    
    . 

  • #2
    biprobit is simultaneous, so not really a first and second stage. You can get the system pr2 using McFadden or Nagelkerke approach. I don't know of any good methods to get equation by equation pr2 in biprobit.

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