Change in the sign of a variable in a regression output

Dear all,

I am currently working on a regression. My aim is to assess whether ESG scores affect the cost of bank loans (variable "AllinDrawn" which is the spread of the loan interest rate over LIBOR, adding any annual (or facility) fee paid to the lender, and it is measured in basis points for each dollar drawn). Below you can find my model:

AllinDrawn_i,_t = f(ESGEnvironmentalPillarScore_i,t-1, ESGSocialPillarScore_i,t-1, ESGGovernancePillarScore_i,t-1, Book_value_of_borrower_assets_i,t-1,Price-to-book_ratio_i,t-1, Debt-equity_ratio_i,t-1, Altman-z_score_i,t-1, EBIT_i,t-1, ROE_i,t-1, Interest_Coverage_ratio_i,t-1, CurrentAssets/CurrentLiabilities_{i,t-1, PPE/TotalAssets}_i,t-1,Book_value_of_lender_assets_i,t-1, Dealsize_t, Maturity_t, Number_of_lenders_t,dummy_collateral_t, dummy_loantype_t, dummy_corporate_purpose_t, dummy_country, dummy_time)

My dataset is composed by 1354 observations over the time period 2010-2020. I do not have a balanced panel as different loans are granted to different firms every year; thus, it may occur that the same firm is present throughout the whole period or for one year only. For this reason, I was thinking of using pooled ols as estimation method. In order to understand which is the best option I have used:
1. the command reg combined with the command robust
2. the command reg combined with vce(cluster borrower company id) to account for the cluster effect
3. the command reg combined with vce(robust)

I was also thinking that I could apply a log-transformation to the variables AllinDrawn, Book_value_of_borrower_assets, Maturity and Dealsize as they are positively skewed.

Code:


* Example generated by -dataex-. For more info, type help dataex
clear
input double(AllinDrawn ESGEnvironmentalPillarScore ESGSocialPillarScore	ESGGovernancePillarScore)
250 77.5557011795543 64.7579193328731 88.7326388888888
630 5.41978129948686 3.53632478632478 0
275 18.564126394052 65.9194214876033 13.5558069381598
250 31.8097413602534 17.4276859504132 23.1316137566137
275 31.8097413602534 17.4276859504132 23.1316137566137
300 10.7844598613613 6.05716253443526 2.51572327044024
460 21.18 31.11 8.33
200 17.24 31.16 25.01
250 17.5230674087816 74.7279614325069 0
225 44.7532467532467 50.2441860465116 0
225 44.7532467532467 50.2441860465116 0
325 14.8953267935558 4.64531680440771 0
300 69.7174447174446 42.1959358617987 31.4429824561403
325 69.7174447174446 42.1959358617987 31.4429824561403
300 69.7174447174446 42.1959358617987 31.4429824561403
300 69.7174447174446 42.1959358617987 31.4429824561403
325 69.7174447174446 42.1959358617987 31.4429824561403
300 69.7174447174446 42.1959358617987 31.4429824561403
325 69.7174447174446 42.1959358617987 31.4429824561403
37.5 27.3032002127565 36.7112304037709 18.9411157024793
end

Code:

* Example generated by -dataex-. For more info, type help dataex
clear
input double(BookvalueoftotalassetsFirm Pricetobookratio DebttoEquityLeverage	Altmanzscore EBIT ROE InterestCoverageRatio BVofCABVofCLLiquidity PPETotalassetsTangibility)
24032 1.0432595133933986 1.406099290780142 1.280729860186418 1247	.06594186576534986 3.681214421252372 2.1813494732122845 .07739680426098536
1572.123 1.447634142903065 .07418778253489806 1.2572250390077622 181.934	.07680436156491312 10.343469568047611 3.861882603848577 .677739591622284
786.401 6.312142016730666 .015752023662174805 .5796776708066242 87.059	.06793264871184676 24.618894123481276 4.380098988998617 .20942369096682228
8094.3 1.2947419015853134 1.4887629546248495 1.1027599668902808 525.9	.029708127253270204 2.4519056261343013 1.8862742241002477 .193617730995886
8094.3 1.2947419015853134 1.4887629546248495 1.1027599668902808 525.9	.029708127253270204 2.4519056261343013 1.8862742241002477 .193617730995886
5937.156 2.7769083937119223 .33365353539984816 .36842434323773876 673.24	.040207092608939246 9.660145073783433 .6675808980320502 .0398877846564921
4645.943 1.997013829529877 2.4163164860084185 .13777250388134338 41.896	.030533362893849964 2.247503143654155 .4604915937554856 .8303532781181344
359.4 -6.364957170420625 -.16689280868385345 2.136366165831942 71.5	.09742114432565924 29.866666666666664 1.4602230483271377 .22120200333889817
5234.318 4.109158671361969 .7731561886119267 2.084586320510141 884.737	.08095669371134429 12.320208982852689 1.1410925133890246 .06600095752684496
5407.3 1.427857787689333 1.0857068426536993 2.886581103323285 386.9	.06020710056697605 5.900889453621346 1.2077922077922076 .3197899136352708
5407.3 1.427857787689333 1.0857068426536993 2.886581103323285 386.9	.06020710056697605 5.900889453621346 1.2077922077922076 .3197899136352708
1200.269 6.296495347642471 .7488521977848601 1.183230259216892 150.992	.02562144501510765 9.576944571457602 2.059774358974359 .024478679362709525
2339.679 1.7450898699218107 .34194769086211746 2.1581339576924865 269.709	.07939763211947916 9.374060374656962 2.7416232869728647 .07157990476471345
2339.679 1.7450898699218107 .34194769086211746 2.1581339576924865 269.709	.07939763211947916 9.374060374656962 2.7416232869728647 .07157990476471345
2339.679 1.7450898699218107 .34194769086211746 2.1581339576924865 269.709	.07939763211947916 9.374060374656962 2.7416232869728647 .07157990476471345
2339.679 1.7450898699218107 .34194769086211746 2.1581339576924865 269.709	.07939763211947916 9.374060374656962 2.7416232869728647 .07157990476471345
2339.679 1.7450898699218107 .34194769086211746 2.1581339576924865 269.709	.07939763211947916 9.374060374656962 2.7416232869728647 .07157990476471345
2339.679 1.7450898699218107 .34194769086211746 2.1581339576924865 269.709	.07939763211947916 9.374060374656962 2.7416232869728647 .07157990476471345
2339.679 1.7450898699218107 .34194769086211746 2.1581339576924865 269.709	.07939763211947916 9.374060374656962 2.7416232869728647 .07157990476471345
16081.984 2.736890126343609 .3551863619917197 2.244584617171612 1491.547	.039283398572413544 12.497946481111873 2.0011704596990167 .13285220281278728
end

Code:


* Example generated by -dataex-. For more	info,	type	help	dataex
clear
input double FacilityAmt int Maturity
3.000e+09 10
1.500e+08 36
50000000 36
6.500e+08 41
3.000e+08 65
7.500e+08 36
1.000e+08 40
240496000 48
1.700e+09 40
581582051.61 51
479417948.39 51
1.275e+09 72
2.650e+08 60
167407404.52 60
9521089.21 60
3.677e+08 60
126560000 60
1.0031e+09 72
379680000 72
1.000e+09 12
end

I have first run a regression of AllinDrawn on ESGEnvironmentalPillarScore_i,t-1, ESGSocialPillarScore_i,t-1, ESGGovernancePillarScore_i,t-1.

Code:

reg AllinDrawn ESGEnvironmentalPillarScore ESGSocialPillarScore ESGGovernancePillarScore, robust

Linear regression                               Number of obs     =      1,354
                                                F(3, 1350)        =      36.61
                                                Prob > F          =     0.0000
                                                R-squared         =     0.0698
                                                Root MSE          =      98.88

---------------------------------------------------------------------------------------------
                            |               Robust
                 AllinDrawn | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
----------------------------+----------------------------------------------------------------
ESGEnvironmentalPillarScore |  -.0753313    .118659    -0.63   0.526    -.3081074    .1574448
       ESGSocialPillarScore |  -.3126749   .1829552    -1.71   0.088    -.6715823    .0462324
   ESGGovernancePillarScore |   -1.01193   .1307176    -7.74   0.000    -1.268362   -.7554986
                      _cons |   238.8086   7.892187    30.26   0.000     223.3263    254.2909

When I then add more variables the coefficient of the variable ESGEnvironmentalPillarScore_i,t-1 becomes positive, contrary to my expectations. Could it be an issue of omitted variables? Or is there any other possible explanation? It is the first time I have used Stata so it could very well be I have made other mistakes when constructing my model.

Code:

reg AllinDrawn ESGEnvironmentalPillarScore ESGSocialPillarScore ESGGovernancePillarScore BookvalueoftotalassetsFirm Pricetobookratio
>  DebttoEquityLeverage Altmanzscore EBIT ROE InterestCoverageRatio BVofCABVofCLLiquidity PPETotalassetsTangibility, robust

Linear regression                               Number of obs     =      1,322
                                                F(12, 1309)       =      28.71
                                                Prob > F          =     0.0000
                                                R-squared         =     0.2597
                                                Root MSE          =     86.596

---------------------------------------------------------------------------------------------
                            |               Robust
                 AllinDrawn | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
----------------------------+----------------------------------------------------------------
ESGEnvironmentalPillarScore |   .0739704   .1128945     0.66   0.512    -.1475035    .2954443
       ESGSocialPillarScore |  -.1242622   .1538227    -0.81   0.419    -.4260281    .1775037
   ESGGovernancePillarScore |   -.801108   .1166373    -6.87   0.000    -1.029924   -.5722915
 BookvalueoftotalassetsFirm |   .0001103   .0000908     1.21   0.225    -.0000678    .0002884
           Pricetobookratio |  -.8398775   .2880863    -2.92   0.004    -1.405039   -.2747162
       DebttoEquityLeverage |   1.745794   .9277623     1.88   0.060    -.0742692    3.565858
               Altmanzscore |  -14.10079   2.155519    -6.54   0.000    -18.32944   -9.872142
                       EBIT |  -.0065537   .0015351    -4.27   0.000    -.0095652   -.0035421
                        ROE |  -6.562555   2.130634    -3.08   0.002    -10.74239   -2.382725
      InterestCoverageRatio |   .0207107   .0416538     0.50   0.619    -.0610048    .1024262
      BVofCABVofCLLiquidity |  -3.882811   2.132499    -1.82   0.069    -8.066301    .3006782
  PPETotalassetsTangibility |   5.673791   11.57927     0.49   0.624    -17.04216    28.38974
                      _cons |   251.7368    8.69042    28.97   0.000     234.6881    268.7855
---------------------------------------------------------------------------------------------

Thanks a lot in advance for your time.

Kind regards.
Giulia Bonacina

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Change in the sign of a variable in a regression output