variable selection with LASSO + fixed-effect model. (Alternative: RIDGE)

[Loic DUBOIS]

Hello everyone,

I hope you are well.

I'd like to post a message on the forum about the LASSO and RIDGE methods.

Indeed, the objective of my study is to investigate the impact of different governance dimensions (board independence, CEO duality, governance index membership, board/committee size, etc.) on earnings management (measured by accruals).

Part 1 : LASSO

Here's my basic fixed-effect model:

xtreg ACC CFO2 DCFO CFOxDCFO CADln2 CADlnxCFO CADlnxDCFO CADlnxCFOxDCFO CEO CEOxCFO CEOxDCFO CEOxCFOxDCFO IND2 INDxCFO INDxDCFO INDxCFOxDCFO  AUDln2 AUDlnxCFO AUDlnxDCFO AUDlnxCFOxDCFO COGln2 COGlnxCFO COGlnxDCFO COGlnxCFOxDCFO IGE IGExCFO IGExDCFO IGExCFOxDCFO OWN2 OWNxCFO OWNxDCFO OWNxCFOxDCFO LEVIER2 LEVIERxCFO LEVIERxDCFO LEVIERxCFOxDCFO TAILLEln2 TAILxCFO TAILxDCFO  TAILxCFOxDCFO LITIGE LITIGExCFO LITIGExDCFO LITIGExCFOxDCFO, fe robust

I was unable to make any choices concerning the various governance variables (CAD, IND, etc.). However, when I analyzed the VIF, it turned out to be very high (even after centering reduced variables, etc.).

I therefore opted for a variable selection method, the LASSO method.

I used the following command:

rlasso ACC CFO2 DCFO CFOxDCFO CADln2 CADlnxCFO CADlnxDCFO CADlnxCFOxDCFO CEO CEOxCFO CEOxDCFO CEOxCFOxDCFO IND2 INDxCFO INDxDCFO INDxCFOxDCFO  AUDln2 AUDlnxCFO AUDlnxDCFO AUDlnxCFOxDCFO COGln2 COGlnxCFO COGlnxDCFO COGlnxCFOxDCFO IGE IGExCFO IGExDCFO IGExCFOxDCFO OWN2 OWNxCFO OWNxDCFO OWNxCFOxDCFO LEVIER2 LEVIERxCFO LEVIERxDCFO LEVIERxCFOxDCFO TAILLEln2 TAILxCFO TAILxDCFO  TAILxCFOxDCFO LITIGE LITIGExCFO LITIGExDCFO LITIGExCFOxDCFO, fe

Following this command, the variables selected are as follows: CFO2 DCFO CEO*CFO2*DCFO INDxCFO INDxCFOxDCFO IGExCFO IGExCFOxDCFO LEVIER2 TAILLEln2 TAILxCFO

Next, I forced the inclusion of certain variables present in the triple interactions but not selected by LASSO (e.g. CEO).
I then integrated the retained variables into my fixed-effect model and analyzed the results:

xtreg ACC CFO2 DCFO CFOxDCFO CEO CEOxCFO CEOxDCFO CEOxCFOxDCFO IND2 INDxCFO INDxDCFO INDxCFOxDCFO IGE IGExCFO IGExDCFO IGExCFOxDCFO LEVIER2 TAILLEln2 TAILxCFO, fe robust

With this new order, the VIF has been considerably reduced, with an average of 3.

Part 2: Ridge

For robustness, I'd also like to use the Ridge method to reduce the multicollinearity of my model.

I used the following command:

ridgeregress ACC CFO2 DCFO CFOxDCFO CADln2 CADlnxCFO CADlnxDCFO CADlnxCFOxDCFO CEO CEOxCFO CEOxDCFO CEOxCFOxDCFO IND2 INDxCFO INDxDCFO INDxCFOxDCFO  AUDln2 AUDlnxCFO AUDlnxDCFO AUDlnxCFOxDCFO COGln2 COGlnxCFO COGlnxDCFO COGlnxCFOxDCFO IGE IGExCFO IGExDCFO IGExCFOxDCFO OWN2 OWNxCFO OWNxDCFO OWNxCFOxDCFO LEVIER2 LEVIERxCFO LEVIERxDCFO LEVIERxCFOxDCFO TAILLEln2 TAILxCFO TAILxDCFO  TAILxCFOxDCFO LITIGE LITIGExCFO LITIGExDCFO LITIGExCFOxDCFO

And here are the results:

Ridge regression                       Number of observations     =      1,822
                                       R-squared                  =     0.5094
                                       alpha                      =     0.0000
                                       lambda                     =     0.0968
                                       Cross-validation MSE       =     0.0323
                                       Number of folds            =         10
                                       Number of lambda tested    =        100
---------------------------------------------------------------------------------
            ACC | Coefficient
----------------+----------------------------------------------------------------
           CFO2 |  -.4201313
           DCFO |   .0442865
       CFOxDCFO |  -.2361166
         CADln2 |  -.0085005
      CADlnxCFO |  -.0199712
     CADlnxDCFO |  -.0186018
 CADlnxCFOxDCFO |  -.1104472
            CEO |   .0232471
        CEOxCFO |   .0026195
       CEOxDCFO |  -.0896609
   CEOxCFOxDCFO |  -.5306899
           IND2 |   .0057495
        INDxCFO |  -.7414762
       INDxDCFO |  -.0783018
   INDxCFOxDCFO |  -.6897435
         AUDln2 |  -.0184643
      AUDlnxCFO |  -.0240426
     AUDlnxDCFO |  -.0593989
 AUDlnxCFOxDCFO |  -.1078209
         COGln2 |   .0148307
      COGlnxCFO |  -.0076942
     COGlnxDCFO |  -.0097863
 COGlnxCFOxDCFO |  -.0744067
            IGE |   .0032314
        IGExCFO |  -.1649624
       IGExDCFO |  -.0513084
   IGExCFOxDCFO |  -.2191058
           OWN2 |  -.0032892
        OWNxCFO |   .0702804
       OWNxDCFO |  -.0259848
   OWNxCFOxDCFO |  -.2782928
        LEVIER2 |  -.1592852
     LEVIERxCFO |  -.0819853
    LEVIERxDCFO |  -.0316133
LEVIERxCFOxDCFO |   .0887082
      TAILLEln2 |   .0045048
       TAILxCFO |   .0483754
      TAILxDCFO |   .0191018
  TAILxCFOxDCFO |   .0965565
         LITIGE |   .0031396
     LITIGExCFO |  -.0606596
    LITIGExDCFO |  -.0048072
LITIGExCFOxDCFO |   .1459947
          _cons |  -.0316815
---------------------------------------------------------------------------------

I confess I don't know how to interpret the results and what to do with them ...
I don't have any p-values to tell me which variables are significant in my model.



My questions are as follows:

Is the LASSO procedure empirically correct and well done?

What should I do to exploit the RIDGE method? Is it relevant or is LASSO enough?

Thank you very much for your answers,

Loïc Dubois