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  • #1

    Heckman approach for panel study

    Hi,

    I hope this message finds you well. please i need an advice and guidance regarding applying Heckman approach for panel study

    This is description to my study variables

    Treatment variable: HARD_FREEZE (dummy)


    HARD_FREEZE is a binary treatment indicator equal to 1 in the firm’s hard-freeze year and 0 in all pre-freeze years. Firms that never hard-freeze are coded 0 in every year. Observations after the hard-freeze year are excluded (i.e., the sample includes only pre-freeze years and the freeze year). Outcome
    • CSR_DISC (continuous)
    Main regressors
    • CSO_PRESENCE
    • HARD_FREEZE × CSO_PRESENCE (interaction)
    • Standard control variables
    • Year and industry fixed effects (i.year and i.ff_12)
    Concern


    I am concerned that HARD_FREEZE may be endogenous (self-selection), so I attempted a Heckman-style correction.
    What I did (Heckman-style approach)
    1. Estimated a Probit model for HARD_FREEZE
    2. Computed the inverse Mills ratio (mills) from the Probit linear prediction
    3. Included mills as an additional regressor in the CSR regression (estimated on all observations)
    probit HARD_FREEZE SIZE LEV MB OCF SD_OCF BOARD_SIZE GENDER_RATIO BOARD_IND FUND_STATUS ///
    FUND_RATIO PLAN_SIZE i.year i.ff_12, vce(cluster id)

    predict lefthat if e(sample), xb
    gen mills = normalden(lefthat) / normal(lefthat) if e(sample)

    reg CSR_DISC HARD_FREEZE CSO_PRESENCE HARD_FREEZEXCSO_PRESENCE SIZE LEV MB OCF SD_OCF ///
    BOARD_SIZE GENDER_RATIO BOARD_IND SUS_SCORE SUS_COMM FUND_STATUS FUND_RATIO PLAN_SIZE ///
    mills i.year i.ff_12, vce(cluster id)

    Questions
    1. Is this a valid way to implement a Heckman correction for “self-selection into HARD_FREEZE” when CSR_DISC is observed for all firm-year observations in the analysis sample?
    2. In other words, is it appropriate to include the inverse Mills ratio from probit(HARD_FREEZE) in an OLS regression estimated on all observations?
    HTML Code:
    . asdoc probit  HARD_FREEZE   SIZE       LEV   MB   OCF   SD_OCF  BOARD_SIZE  GENDER_RATIO  BOARD
> _IND    FUND_STATUS  FUND_RATIO  PLAN_SIZE  i.year    i.ff_12  ,  robust cluster (id) nest repl
> ace  drop(i.year i.ff_12  ) dec(4) tzok    save(qqqqa)

Iteration 0:  Log pseudolikelihood = -358.75999  
Iteration 1:  Log pseudolikelihood = -327.72275  
Iteration 2:  Log pseudolikelihood = -324.57221  
Iteration 3:  Log pseudolikelihood = -324.53113  
Iteration 4:  Log pseudolikelihood = -324.53103  
Iteration 5:  Log pseudolikelihood = -324.53103  

Probit regression                                       Number of obs =  3,900
                                                        Wald chi2(40) =  94.12
                                                        Prob > chi2   = 0.0000
Log pseudolikelihood = -324.53103                       Pseudo R2     = 0.0954

                                   (Std. err. adjusted for 282 clusters in id)
------------------------------------------------------------------------------
             |               Robust
 HARD_FREEZE | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
        SIZE |  -.1925695   .0740725    -2.60   0.009    -.3377488   -.0473902
         LEV |  -.0087306   .4015024    -0.02   0.983    -.7956607    .7781996
          MB |   .0002073   .0073871     0.03   0.978    -.0142711    .0146857
         OCF |  -3.458301   1.245414    -2.78   0.005    -5.899267   -1.017335
      SD_OCF |   3.875817   2.853238     1.36   0.174    -1.716427     9.46806
  BOARD_SIZE |  -.0004025   .0297384    -0.01   0.989    -.0586887    .0578837
GENDER_RATIO |   .3799744   .6574852     0.58   0.563    -.9086729    1.668622
   BOARD_IND |   .2277899   .6650473     0.34   0.732    -1.075679    1.531259
 FUND_STATUS |  -4.173805   2.029593    -2.06   0.040    -8.151735   -.1958759
  FUND_RATIO |  -.0761674   .3856172    -0.20   0.843    -.8319632    .6796285
   PLAN_SIZE |   .0687444   .0637423     1.08   0.281    -.0561882    .1936771
             |
        year |
       2005  |  -.2409666   .4322112    -0.56   0.577    -1.088085    .6061518
       2006  |   .0026222    .381609     0.01   0.995    -.7453177    .7505622
       2007  |   -.220559   .4408242    -0.50   0.617    -1.084559    .6434405
       2008  |   .4790183    .321579     1.49   0.136    -.1512649    1.109302
       2009  |   .6453316    .312803     2.06   0.039      .032249    1.258414
       2010  |   .4765423    .325337     1.46   0.143    -.1611064    1.114191
       2011  |   .2260907   .3614312     0.63   0.532    -.4823015     .934483
       2012  |       .361   .3465188     1.04   0.298    -.3181643    1.040164
       2013  |   .4685907   .3371055     1.39   0.165     -.192124    1.129305
       2014  |   .2758176   .3544123     0.78   0.436    -.4188177    .9704528
       2015  |    .438984   .3475913     1.26   0.207    -.2422823     1.12025
       2016  |   .3682024   .3422007     1.08   0.282    -.3024986    1.038903
       2017  |   .3257874   .3579784     0.91   0.363    -.3758373    1.027412
       2018  |   .7495029   .3326064     2.25   0.024     .0976063    1.401399
       2019  |   .5081082   .3590654     1.42   0.157    -.1956471    1.211864
       2020  |   .7474426   .3516579     2.13   0.034     .0582058    1.436679
       2021  |   .3653477   .4157055     0.88   0.379    -.4494201    1.180115
       2022  |   .0776221   .4568847     0.17   0.865    -.8178554    .9730996
             |
       ff_12 |
          2  |   .0701796   .2884724     0.24   0.808     -.495216    .6355752
          3  |  -.2088294   .2146219    -0.97   0.331    -.6294806    .2118218
          4  |  -.3456759   .3760136    -0.92   0.358    -1.082649    .3912973
          5  |  -.3439714   .2487806    -1.38   0.167    -.8315724    .1436295
          6  |  -.1551492   .2504892    -0.62   0.536    -.6460991    .3358007
          7  |   .1184574   .3654636     0.32   0.746    -.5978381    .8347529
          8  |   -.406023   .2438484    -1.67   0.096     -.883957    .0719111
          9  |   .4415868   .2073734     2.13   0.033     .0351424    .8480312
         10  |  -.0921214   .2570592    -0.36   0.720    -.5959483    .4117054
         11  |   .4643857   .2316409     2.00   0.045     .0103778    .9183935
         12  |  -.3317513   .2383857    -1.39   0.164    -.7989788    .1354762
             |
       _cons |  -1.089957   .7413996    -1.47   0.142    -2.543073    .3631599
------------------------------------------------------------------------------
Click to Open File:  qqqqa.doc

.
. predict lefthat, xb // Get the linear prediction
(4681 missing values generated)

. gen mills = normalden(lefthat) / normal(lefthat) // Generate the inverse Mill's ratio
(4,681 missing values generated)

.
.
. asdoc reg CSR_DISC  HARD_FREEZE  CSO_PRESENCE  HARD_FREEZEXCSO_PRESENCE SIZE     LEV  MB   OCF
>   SD_OCF  BOARD_SIZE GENDER_RATIO BOARD_IND SUS_SCORE SUS_COMM    FUND_STATUS  FUND_RATIO PLAN_
> SIZE mills i.year    i.ff_12 ,   robust cluster (id) nest replace  drop(i.year i.ff_12  ) dec(4
> ) tzok  save(qqqkkq)

Linear regression                               Number of obs     =      3,210
                                                F(45, 265)        =      82.22
                                                Prob > F          =     0.0000
                                                R-squared         =     0.7328
                                                Root MSE          =     9.3367

                                               (Std. err. adjusted for 266 clusters in id)
------------------------------------------------------------------------------------------
                         |               Robust
                CSR_DISC | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------------------+----------------------------------------------------------------
             HARD_FREEZE |   6.515599   2.132253     3.06   0.002     2.317286    10.71391
            CSO_PRESENCE |   4.939757   1.003266     4.92   0.000      2.96437    6.915144
HARD_FREEZEXCSO_PRESENCE |   11.49455   3.826643     3.00   0.003     3.960053    19.02904
                    SIZE |    4.09229   5.714213     0.72   0.475    -7.158747    15.34333
                     LEV |   2.102381   3.312074     0.63   0.526    -4.418947     8.62371
                      MB |  -.0699361   .0285242    -2.45   0.015     -.126099   -.0137732
                     OCF |   96.87772   104.7855     0.92   0.356    -109.4404    303.1958
                  SD_OCF |  -79.18178   117.9957    -0.67   0.503    -311.5102    153.1466
              BOARD_SIZE |   .3082756   .1879625     1.64   0.102    -.0618143    .6783656
            GENDER_RATIO |  -7.006496   12.48325    -0.56   0.575    -31.58548    17.57248
               BOARD_IND |  -7.622757    8.28218    -0.92   0.358    -23.93001    8.684493
               SUS_SCORE |   .4262834   .0276078    15.44   0.000     .3719249    .4806419
                SUS_COMM |   2.094647   .9486439     2.21   0.028     .2268087    3.962485
             FUND_STATUS |   91.43655   127.5723     0.72   0.474    -159.7477    342.6208
              FUND_RATIO |   .0185649   3.531582     0.01   0.996    -6.934966    6.972096
               PLAN_SIZE |  -1.076344   2.037312    -0.53   0.598    -5.087722    2.935033
                   mills |  -25.36645   34.17336    -0.74   0.459    -92.65231    41.91941
                         |
                    year |
                   2006  |  -4.348371   7.819994    -0.56   0.579     -19.7456    11.04886
                   2007  |    1.74697   1.767967     0.99   0.324     -1.73408    5.228021
                   2008  |  -15.04875   22.58033    -0.67   0.506    -59.50843    29.41094
                   2009  |   -18.1667   27.63113    -0.66   0.511     -72.5712    36.23779
                   2010  |  -13.48892   22.55056    -0.60   0.550       -57.89    30.91216
                   2011  |  -7.088641   14.95092    -0.47   0.636    -36.52634    22.34906
                   2012  |  -8.790421   19.06939    -0.46   0.645    -46.33721    28.75637
                   2013  |  -9.726865   22.34771    -0.44   0.664    -53.72853    34.27479
                   2014  |  -3.551944   16.40571    -0.22   0.829    -35.85407    28.75019
                   2015  |  -3.941827   21.39897    -0.18   0.854    -46.07546    38.19181
                   2016  |  -1.287779   19.25275    -0.07   0.947    -39.19561    36.62005
                   2017  |   1.712123   17.94974     0.10   0.924    -33.63014    37.05438
                   2018  |  -7.853679   30.77416    -0.26   0.799    -68.44666     52.7393
                   2019  |  -.8836341   23.43472    -0.04   0.970    -47.02558    45.25831
                   2020  |  -4.965544   30.68252    -0.16   0.872    -65.37809      55.447
                   2021  |   4.183326   19.18272     0.22   0.828    -33.58661    41.95326
                   2022  |   11.08698   10.25616     1.08   0.281    -9.106953    31.28091
                         |
                   ff_12 |
                      2  |  -5.538256   3.405261    -1.63   0.105    -12.24307    1.166553
                      3  |   4.424976   6.692888     0.66   0.509    -8.753029    17.60298
                      4  |   16.15874   11.58751     1.39   0.164     -6.65656    38.97403
                      5  |   14.27102   10.57636     1.35   0.178    -6.553377    35.09542
                      6  |   4.717022   5.013485     0.94   0.348     -5.15431    14.58835
                      7  |  -.2381373   5.372516    -0.04   0.965    -10.81639    10.34011
                      8  |   17.25473    12.5777     1.37   0.171    -7.510207    42.01967
                      9  |  -20.46623   13.74946    -1.49   0.138    -47.53831    6.605856
                     10  |   4.638173   3.763951     1.23   0.219    -2.772882    12.04923
                     11  |  -16.87046   13.97701    -1.21   0.229    -44.39058    10.64967
                     12  |    9.30207   10.47078     0.89   0.375    -11.31443    29.91857
                         |
                   _cons |   32.15166    62.6082     0.51   0.608    -91.12116    155.4245
------------------------------------------------------------------------------------------
Click to Open File:  qqqkkq.doc

.
    Last edited by hussein bataineh; 21 Dec 2025, 03:24.
    Tags: None
  • #2
    Hussein: I see several problems with your analysis; some mechanical, some substantive. First, It looks like all variables in the probit appear in the linear outcome equation. That's not really allowed. And it is unusual to have more variables in the outcome equation than in the probit. To be convincing, you need something that predicts the "treatment" -- HARD_FREEZE -- that does not have a direct effect on CSR_DISC. Second, you've implemented the version of Heckman for sample selection, but you need the version for endogenous treatment because you have treated and untreated units. So, after the probit command, type

    Code:
    predict gen_resid, score
    Then the generalized residual will be the inverse Mills ration for the treated and the untreated. This is what you add to the equation in place of "mills."

    Finally, you are estimating a very restrictive version of the treatment effect model. It is better to interact HARD_FREEZE with all other explanatory variables in the outcome equation, including gen_resid. See my 2015 Journal of Human resources paper on control function methods for details.

    Your first task is to find at least one variable that predicts HARD_FREEZE that can be excluded from the CSR_DISC equation.

    One final thing: Are you really worried about HARD_FREEZE being endogenous? It's a weather variable, right? If you control for other factors -- such as geography -- wouldn't you be able to plausibly argue for exogeneity, and then just use flexible regression? That seems a better route than trying to find an instrumenal variable for HARD_FREEZE.

    Comment

    • #3
      Hi Professor Wooldridge,

      Thank you very much for your helpful guidance.

      Following your comments, I added an excluded predictor in the treatment equation: the percentage of firms in each industry-year that hard-freeze (HARD_FREEZE_Percentage). I then used the generalized residual (score) in place of the Mills ratio:

      probit HARD_FREEZE SIZE ROA LEV MB OCF SD_OCF BOARD_SIZE GENDER_RATIO BOARD_IND /// FUND_STATUS FUND_RATIO PLAN_SIZE HARD_FREEZE_Percentage i.year i.ff_12, vce(cluster id)

      predict gen_resid if e(sample), score


      IIn the outcome equation (CSR_DISC), I excluded HARD_FREEZE_Percentage and added the generalized residual plus its interaction with treatment:

      reg CSR_DISC HARD_FREEZE CSO_PRESENCE HARD_FREEZEXCSO_PRESENCE /// SIZE ROA LEV MB OCF SD_OCF BOARD_SIZE GENDER_RATIO BOARD_IND /// SUS_SCORE SUS_COMM FUND_STATUS FUND_RATIO PLAN_SIZE /// gen_resid 1.HARD_FREEZE#c.gen_resid /// i.year i.ff_12, vce(cluster id)


      HTML Code:
      . asdoc probit  HARD_FREEZE   SIZE   ROA     LEV   MB   OCF   SD_OCF  BOARD_SIZE  GENDER_RATIO    B
> OARD_IND    FUND_STATUS  FUND_RATIO  PLAN_SIZE HARD_FREEZE_Percentage  i.year    i.ff_12  ,    ro
> bust cluster (id) nest replace  drop(i.year i.ff_12  ) dec(4) tzok    save(qqqqa)

Iteration 0:  Log pseudolikelihood = -358.75999  
Iteration 1:  Log pseudolikelihood =  -293.8259  
Iteration 2:  Log pseudolikelihood = -272.74105  
Iteration 3:  Log pseudolikelihood = -270.54603  
Iteration 4:  Log pseudolikelihood = -270.52492  
Iteration 5:  Log pseudolikelihood = -270.52491  

Probit regression                                       Number of obs =  3,900
Wald chi2(42) = 260.60
Prob > chi2   = 0.0000
Log pseudolikelihood = -270.52491                       Pseudo R2     = 0.2459

(Std. err. adjusted for 282 clusters in id)

Robust
HARD_FREEZE  Coefficient  std. err.      z    P>z     [95% conf. interval]

SIZE    -.191723   .0827147    -2.32   0.020    -.3538409   -.0296051
ROA      2.6809   1.647337     1.63   0.104    -.5478223    5.909622
LEV   -.3682851   .4553514    -0.81   0.419    -1.260757    .5241871
MB   -.0025721   .0088341    -0.29   0.771    -.0198867    .0147424
OCF   -6.257656   2.167383    -2.89   0.004    -10.50565   -2.009664
SD_OCF    4.186368   3.428449     1.22   0.222     -2.53327    10.90601
BOARD_SIZE    .0027089   .0336054     0.08   0.936    -.0631565    .0685743
GENDER_RATIO     .479759   .7305578     0.66   0.511    -.9521079    1.911626
BOARD_IND    .2723456   .7705377     0.35   0.724    -1.237881    1.782572
FUND_STATUS   -4.473469   2.166505    -2.06   0.039    -8.719741   -.2271971
FUND_RATIO    -.191093   .4295819    -0.44   0.656    -1.033058    .6508719
PLAN_SIZE    .0756886   .0676282     1.12   0.263    -.0568602    .2082373
HARD_FREEZE_Percentage    16.69156   1.722605     9.69   0.000     13.31531     20.0678

year
2005    -.2199498     .43256    -0.51   0.611    -1.067752    .6278522
2006    -.0223293   .3931684    -0.06   0.955    -.7929253    .7482666
2007    -.1756752   .4452967    -0.39   0.693    -1.048441    .6970902
2008    -.1372997   .3965622    -0.35   0.729    -.9145472    .6399479
2009    -.2920125   .3627687    -0.80   0.421    -1.003026    .4190011
2010     .0944829   .3500592     0.27   0.787    -.5916205    .7805863
2011     .0167411   .3942295     0.04   0.966    -.7559345    .7894166
2012    -.0876988   .3668448    -0.24   0.811    -.8067015    .6313038
2013     .0189593   .3615816     0.05   0.958    -.6897275    .7276462
2014     -.044654   .3688469    -0.12   0.904    -.7675805    .6782726
2015     .1711375   .3720439     0.46   0.646    -.5580552    .9003302
2016     -.064141   .3931335    -0.16   0.870    -.8346686    .7063865
2017     .1988054   .3664213     0.54   0.587    -.5193671     .916978
2018    -.2341542   .4697588    -0.50   0.618    -1.154865    .6865562
2019     .2738486    .374941     0.73   0.465    -.4610223    1.008719
2020     .0226841   .4138578     0.05   0.956    -.7884624    .8338305
2021     .1185928   .4038259     0.29   0.769    -.6728915    .9100771
2022     .0207655   .4711304     0.04   0.965    -.9026331    .9441641

ff_12
2    -1.900485   .4908015    -3.87   0.000    -2.862439   -.9385319
3     .1909851   .3458892     0.55   0.581    -.4869454    .8689155
4     .3235794   .4761518     0.68   0.497     -.609661     1.25682
5     .0340655   .3719613     0.09   0.927    -.6949653    .7630963
6        .3268   .3904152     0.84   0.403    -.4383997       1.092
7    -4.111142   .9413738    -4.37   0.000    -5.956201   -2.266084
8     .2730854   .3679752     0.74   0.458    -.4481327    .9943035
9     .1391836   .3944659     0.35   0.724    -.6339553    .9123226
10     .4279429   .3842295     1.11   0.265     -.325133    1.181019
11     .6779133   .3583562     1.89   0.059     -.024452    1.380279
12     .2612683   .3643115     0.72   0.473    -.4527692    .9753058

_cons   -1.595877   .8496891    -1.88   0.060    -3.261237    .0694832

Note: 51 failures and 0 successes completely determined.
Click to Open File:  qqqqa.doc

.
. * Wooldridge control-function term:
. predict gen_resid if e(sample), score
(5,676 missing values generated)

.
. asdoc reg CSR_DISC HARD_FREEZE CSO_PRESENCE HARD_FREEZEXCSO_PRESENCE ///
>      SIZE ROA LEV MB OCF SD_OCF BOARD_SIZE GENDER_RATIO BOARD_IND ///
>      SUS_SCORE SUS_COMM FUND_STATUS FUND_RATIO PLAN_SIZE ///
>      gen_resid ///
>      1.HARD_FREEZE#c.gen_resid ///
>      i.year i.ff_12, ///
>      robust cluster(id) nest replace drop(i.year i.ff_12) dec(4) tzok save(qqqkkq)

Linear regression                               Number of obs     =      3,210
F(47, 265)        =      80.32
Prob > F          =     0.0000
R-squared         =     0.7340
Root MSE          =     9.3189

(Std. err. adjusted for 266 clusters in id)

Robust
CSR_DISC  Coefficient  std. err.      t    P>t     [95% conf. interval]

HARD_FREEZE    10.83046   6.150563     1.76   0.079    -1.279732    22.94065
CSO_PRESENCE    4.976001   1.002927     4.96   0.000      3.00128    6.950721
HARD_FREEZEXCSO_PRESENCE    11.68377   3.850029     3.03   0.003     4.103229    19.26431
SIZE    -.391624   .6001306    -0.65   0.515    -1.573255     .790007
ROA   -18.52997   9.288467    -1.99   0.047    -36.81855   -.2413803
LEV    2.534681    3.27672     0.77   0.440    -3.917038      8.9864
MB   -.0612857   .0275224    -2.23   0.027    -.1154761   -.0070954
OCF    35.86111   11.36903     3.15   0.002     13.47598    58.24624
SD_OCF    7.688993   19.01702     0.40   0.686    -29.75469    45.13268
BOARD_SIZE    .2960563   .1856001     1.60   0.112    -.0693822    .6614949
GENDER_RATIO    1.328495   4.041673     0.33   0.743    -6.629382    9.286373
BOARD_IND   -2.324497   4.516862    -0.51   0.607      -11.218    6.569007
SUS_SCORE      .42627    .027445    15.53   0.000      .372232     .480308
SUS_COMM    1.985458   .9362808     2.12   0.035     .1419622    3.828954
FUND_STATUS   -.4884019   13.03599    -0.04   0.970    -26.15569    25.17889
FUND_RATIO   -1.921449   2.583392    -0.74   0.458    -7.008035    3.165138
PLAN_SIZE    .5321363   .4377539     1.22   0.225    -.3297819    1.394055
gen_resid     .946976   2.076738     0.46   0.649     -3.14203    5.035982

HARD_FREEZE#c.gen_resid
1    -3.317326   3.483128    -0.95   0.342    -10.17545    3.540801

year
2006     1.346166   1.362211     0.99   0.324    -1.335969    4.028301
2007     2.294664   1.577262     1.45   0.147    -.8108955    5.400224
2008     1.619662   1.602788     1.01   0.313    -1.536158    4.775482
2009     1.838756   1.610297     1.14   0.255    -1.331848     5.00936
2010     3.080103   1.599012     1.93   0.055    -.0682805    6.228487
2011     3.844137   1.666539     2.31   0.022     .5627946    7.125479
2012     5.200983   1.682392     3.09   0.002     1.888428    8.513539
2013     6.612217   1.647464     4.01   0.000     3.368432    9.856002
2014     8.442008    1.62005     5.21   0.000     5.252201    11.63181
2015      11.6894   1.709482     6.84   0.000     8.323507     15.0553
2016     12.70051   1.784103     7.12   0.000     9.187685    16.21333
2017     14.84685   1.784215     8.32   0.000     11.33381    18.35989
2018     14.77008   1.891455     7.81   0.000     11.04588    18.49427
2019     16.28996    1.96157     8.30   0.000     12.42771    20.15221
2020     17.42176   1.991098     8.75   0.000     13.50137    21.34214
2021      18.1637   2.065583     8.79   0.000     14.09666    22.23075
2022     18.68002   2.080779     8.98   0.000     14.58306    22.77698

ff_12
2    -4.538353   2.561006    -1.77   0.078    -9.580862    .5041563
3    -.5676342   2.077935    -0.27   0.785    -4.658997    3.523729
4     7.065756   2.781108     2.54   0.012     1.589876    12.54164
5     6.333201   2.484025     2.55   0.011     1.442264    11.22414
6     .6626072   2.194852     0.30   0.763     -3.65896    4.984175
7      1.66933   3.839943     0.43   0.664    -5.891351     9.23001
8     7.413876   2.031119     3.65   0.000     3.414692    11.41306
9    -10.74948   2.324726    -4.62   0.000    -15.32676   -6.172191
10     2.269651   2.402387     0.94   0.346    -2.460545    6.999847
11    -6.352759   2.273292    -2.79   0.006    -10.82877   -1.876747
12     1.435427   2.247391     0.64   0.524    -2.989588    5.860442

_cons   -11.89848   6.357601    -1.87   0.062    -24.41632    .6193565

Click to Open File:  qqqkkq.doc
      Last edited by hussein bataineh; 21 Dec 2025, 11:57.

      Comment

      • #4
        sorry I'm not sure if the presentation of the table is unclear,

        Hi Professor Wooldridge,

        Thank you very much for your helpful guidance.

        Following your comments, I added an excluded predictor in the treatment equation: the percentage of firms in each industry-year that hard-freeze (HARD_FREEZE_Percentage). I then used the generalized residual (score) in place of the Mills ratio:

        probit HARD_FREEZE SIZE ROA LEV MB OCF SD_OCF BOARD_SIZE GENDER_RATIO BOARD_IND /// FUND_STATUS FUND_RATIO PLAN_SIZE HARD_FREEZE_Percentage i.year i.ff_12, vce(cluster id) predict gen_resid if e(sample), score


        In the CSR equation, I excluded HARD_FREEZE_Percentage and added the generalized residual and its interaction with treatment:

        reg CSR_DISC HARD_FREEZE CSO_PRESENCE HARD_FREEZEXCSO_PRESENCE /// SIZE ROA LEV MB OCF SD_OCF BOARD_SIZE GENDER_RATIO BOARD_IND /// SUS_SCORE SUS_COMM FUND_STATUS FUND_RATIO PLAN_SIZE /// gen_resid 1.HARD_FREEZE#c.gen_resid /// i.year i.ff_12, vce(cluster id)

        HTML Code:
         . asdoc probit  HARD_FREEZE   SIZE   ROA     LEV   MB   OCF   SD_OCF  BOARD_SIZE  GENDER_RATIO  B
> OARD_IND    FUND_STATUS  FUND_RATIO  PLAN_SIZE HARD_FREEZE_Percentage  i.year    i.ff_12  ,  ro
> bust cluster (id) nest replace  drop(i.year i.ff_12  ) dec(4) tzok    save(qqqqa)

Iteration 0:  Log pseudolikelihood = -358.75999  
Iteration 1:  Log pseudolikelihood =  -293.8259  
Iteration 2:  Log pseudolikelihood = -272.74105  
Iteration 3:  Log pseudolikelihood = -270.54603  
Iteration 4:  Log pseudolikelihood = -270.52492  
Iteration 5:  Log pseudolikelihood = -270.52491  

Probit regression                                       Number of obs =  3,900
                                                        Wald chi2(42) = 260.60
                                                        Prob > chi2   = 0.0000
Log pseudolikelihood = -270.52491                       Pseudo R2     = 0.2459

                                             (Std. err. adjusted for 282 clusters in id)
----------------------------------------------------------------------------------------
                       |               Robust
           HARD_FREEZE | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-----------------------+----------------------------------------------------------------
                  SIZE |   -.191723   .0827147    -2.32   0.020    -.3538409   -.0296051
                   ROA |     2.6809   1.647337     1.63   0.104    -.5478223    5.909622
                   LEV |  -.3682851   .4553514    -0.81   0.419    -1.260757    .5241871
                    MB |  -.0025721   .0088341    -0.29   0.771    -.0198867    .0147424
                   OCF |  -6.257656   2.167383    -2.89   0.004    -10.50565   -2.009664
                SD_OCF |   4.186368   3.428449     1.22   0.222     -2.53327    10.90601
            BOARD_SIZE |   .0027089   .0336054     0.08   0.936    -.0631565    .0685743
          GENDER_RATIO |    .479759   .7305578     0.66   0.511    -.9521079    1.911626
             BOARD_IND |   .2723456   .7705377     0.35   0.724    -1.237881    1.782572
           FUND_STATUS |  -4.473469   2.166505    -2.06   0.039    -8.719741   -.2271971
            FUND_RATIO |   -.191093   .4295819    -0.44   0.656    -1.033058    .6508719
             PLAN_SIZE |   .0756886   .0676282     1.12   0.263    -.0568602    .2082373
HARD_FREEZE_Percentage |   16.69156   1.722605     9.69   0.000     13.31531     20.0678
                       |
                  year |
                 2005  |  -.2199498     .43256    -0.51   0.611    -1.067752    .6278522
                 2006  |  -.0223293   .3931684    -0.06   0.955    -.7929253    .7482666
                 2007  |  -.1756752   .4452967    -0.39   0.693    -1.048441    .6970902
                 2008  |  -.1372997   .3965622    -0.35   0.729    -.9145472    .6399479
                 2009  |  -.2920125   .3627687    -0.80   0.421    -1.003026    .4190011
                 2010  |   .0944829   .3500592     0.27   0.787    -.5916205    .7805863
                 2011  |   .0167411   .3942295     0.04   0.966    -.7559345    .7894166
                 2012  |  -.0876988   .3668448    -0.24   0.811    -.8067015    .6313038
                 2013  |   .0189593   .3615816     0.05   0.958    -.6897275    .7276462
                 2014  |   -.044654   .3688469    -0.12   0.904    -.7675805    .6782726
                 2015  |   .1711375   .3720439     0.46   0.646    -.5580552    .9003302
                 2016  |   -.064141   .3931335    -0.16   0.870    -.8346686    .7063865
                 2017  |   .1988054   .3664213     0.54   0.587    -.5193671     .916978
                 2018  |  -.2341542   .4697588    -0.50   0.618    -1.154865    .6865562
                 2019  |   .2738486    .374941     0.73   0.465    -.4610223    1.008719
                 2020  |   .0226841   .4138578     0.05   0.956    -.7884624    .8338305
                 2021  |   .1185928   .4038259     0.29   0.769    -.6728915    .9100771
                 2022  |   .0207655   .4711304     0.04   0.965    -.9026331    .9441641
                       |
                 ff_12 |
                    2  |  -1.900485   .4908015    -3.87   0.000    -2.862439   -.9385319
                    3  |   .1909851   .3458892     0.55   0.581    -.4869454    .8689155
                    4  |   .3235794   .4761518     0.68   0.497     -.609661     1.25682
                    5  |   .0340655   .3719613     0.09   0.927    -.6949653    .7630963
                    6  |      .3268   .3904152     0.84   0.403    -.4383997       1.092
                    7  |  -4.111142   .9413738    -4.37   0.000    -5.956201   -2.266084
                    8  |   .2730854   .3679752     0.74   0.458    -.4481327    .9943035
                    9  |   .1391836   .3944659     0.35   0.724    -.6339553    .9123226
                   10  |   .4279429   .3842295     1.11   0.265     -.325133    1.181019
                   11  |   .6779133   .3583562     1.89   0.059     -.024452    1.380279
                   12  |   .2612683   .3643115     0.72   0.473    -.4527692    .9753058
                       |
                 _cons |  -1.595877   .8496891    -1.88   0.060    -3.261237    .0694832
----------------------------------------------------------------------------------------
Note: 51 failures and 0 successes completely determined.
Click to Open File:  qqqqa.doc

.
. * Wooldridge control-function term:
. predict gen_resid if e(sample), score
(5,676 missing values generated)

.
. asdoc reg CSR_DISC HARD_FREEZE CSO_PRESENCE HARD_FREEZEXCSO_PRESENCE ///
>      SIZE ROA LEV MB OCF SD_OCF BOARD_SIZE GENDER_RATIO BOARD_IND ///
>      SUS_SCORE SUS_COMM FUND_STATUS FUND_RATIO PLAN_SIZE ///
>      gen_resid ///
>      1.HARD_FREEZE#c.gen_resid ///
>      i.year i.ff_12, ///
>      robust cluster(id) nest replace drop(i.year i.ff_12) dec(4) tzok save(qqqkkq)

Linear regression                               Number of obs     =      3,210
                                                F(47, 265)        =      80.32
                                                Prob > F          =     0.0000
                                                R-squared         =     0.7340
                                                Root MSE          =     9.3189

                                               (Std. err. adjusted for 266 clusters in id)
------------------------------------------------------------------------------------------
                         |               Robust
                CSR_DISC | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------------------+----------------------------------------------------------------
             HARD_FREEZE |   10.83046   6.150563     1.76   0.079    -1.279732    22.94065
            CSO_PRESENCE |   4.976001   1.002927     4.96   0.000      3.00128    6.950721
HARD_FREEZEXCSO_PRESENCE |   11.68377   3.850029     3.03   0.003     4.103229    19.26431
                    SIZE |   -.391624   .6001306    -0.65   0.515    -1.573255     .790007
                     ROA |  -18.52997   9.288467    -1.99   0.047    -36.81855   -.2413803
                     LEV |   2.534681    3.27672     0.77   0.440    -3.917038      8.9864
                      MB |  -.0612857   .0275224    -2.23   0.027    -.1154761   -.0070954
                     OCF |   35.86111   11.36903     3.15   0.002     13.47598    58.24624
                  SD_OCF |   7.688993   19.01702     0.40   0.686    -29.75469    45.13268
              BOARD_SIZE |   .2960563   .1856001     1.60   0.112    -.0693822    .6614949
            GENDER_RATIO |   1.328495   4.041673     0.33   0.743    -6.629382    9.286373
               BOARD_IND |  -2.324497   4.516862    -0.51   0.607      -11.218    6.569007
               SUS_SCORE |     .42627    .027445    15.53   0.000      .372232     .480308
                SUS_COMM |   1.985458   .9362808     2.12   0.035     .1419622    3.828954
             FUND_STATUS |  -.4884019   13.03599    -0.04   0.970    -26.15569    25.17889
              FUND_RATIO |  -1.921449   2.583392    -0.74   0.458    -7.008035    3.165138
               PLAN_SIZE |   .5321363   .4377539     1.22   0.225    -.3297819    1.394055
               gen_resid |    .946976   2.076738     0.46   0.649     -3.14203    5.035982
                         |
 HARD_FREEZE#c.gen_resid |
                      1  |  -3.317326   3.483128    -0.95   0.342    -10.17545    3.540801
                         |
                    year |
                   2006  |   1.346166   1.362211     0.99   0.324    -1.335969    4.028301
                   2007  |   2.294664   1.577262     1.45   0.147    -.8108955    5.400224
                   2008  |   1.619662   1.602788     1.01   0.313    -1.536158    4.775482
                   2009  |   1.838756   1.610297     1.14   0.255    -1.331848     5.00936
                   2010  |   3.080103   1.599012     1.93   0.055    -.0682805    6.228487
                   2011  |   3.844137   1.666539     2.31   0.022     .5627946    7.125479
                   2012  |   5.200983   1.682392     3.09   0.002     1.888428    8.513539
                   2013  |   6.612217   1.647464     4.01   0.000     3.368432    9.856002
                   2014  |   8.442008    1.62005     5.21   0.000     5.252201    11.63181
                   2015  |    11.6894   1.709482     6.84   0.000     8.323507     15.0553
                   2016  |   12.70051   1.784103     7.12   0.000     9.187685    16.21333
                   2017  |   14.84685   1.784215     8.32   0.000     11.33381    18.35989
                   2018  |   14.77008   1.891455     7.81   0.000     11.04588    18.49427
                   2019  |   16.28996    1.96157     8.30   0.000     12.42771    20.15221
                   2020  |   17.42176   1.991098     8.75   0.000     13.50137    21.34214
                   2021  |    18.1637   2.065583     8.79   0.000     14.09666    22.23075
                   2022  |   18.68002   2.080779     8.98   0.000     14.58306    22.77698
                         |
                   ff_12 |
                      2  |  -4.538353   2.561006    -1.77   0.078    -9.580862    .5041563
                      3  |  -.5676342   2.077935    -0.27   0.785    -4.658997    3.523729
                      4  |   7.065756   2.781108     2.54   0.012     1.589876    12.54164
                      5  |   6.333201   2.484025     2.55   0.011     1.442264    11.22414
                      6  |   .6626072   2.194852     0.30   0.763     -3.65896    4.984175
                      7  |    1.66933   3.839943     0.43   0.664    -5.891351     9.23001
                      8  |   7.413876   2.031119     3.65   0.000     3.414692    11.41306
                      9  |  -10.74948   2.324726    -4.62   0.000    -15.32676   -6.172191
                     10  |   2.269651   2.402387     0.94   0.346    -2.460545    6.999847
                     11  |  -6.352759   2.273292    -2.79   0.006    -10.82877   -1.876747
                     12  |   1.435427   2.247391     0.64   0.524    -2.989588    5.860442
                         |
                   _cons |  -11.89848   6.357601    -1.87   0.062    -24.41632    .6193565
------------------------------------------------------------------------------------------

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