Dear Statalists

I'm in the final phase of my research and I want to look into the interaction effect of two variables.
I'm having trouble with multicollinearity because of the interaction between one of the two variables and the interaction variable.

I know mean centering variables is often used with this problem.
However, I must be doing something wrong because my variable doesn't change after substracting the mean at every observation as well as my vif values do not change.
I didn't know how to solve this in one step so I tried doing it with multiple steps.
1) I asked for the mean value of the interaction variable
2) I generated a new variable with this value in every cell/observation
3) I substracted the initial interaction variable by the mean of the variable

Am I doing something wrong here? Can someone please help me out.

My coding process is below.

Kind regards
Kletser Jok



Code:
. gen Interaction= UAI* Altman_high

. reg CAR_win Interaction UAI Altman_high LnSize Leverage LnDealValue Domestic Horizontal Japan US

      Source |       SS           df       MS      Number of obs   =       176
-------------+----------------------------------   F(10, 165)      =      1.80
       Model |  .038689375        10  .003868937   Prob > F        =    0.0650
    Residual |  .355554565       165  .002154876   R-squared       =    0.0981
-------------+----------------------------------   Adj R-squared   =    0.0435
       Total |  .394243939       175  .002252823   Root MSE        =    .04642

------------------------------------------------------------------------------
     CAR_win |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
 Interaction |  -.0000212   .0000375    -0.56   0.574    -.0000953     .000053
         UAI |   .0004438    .000323     1.37   0.171     -.000194    .0010816
 Altman_high |   .0003951   .0023014     0.17   0.864    -.0041489     .004939
      LnSize |  -.0047945   .0023444    -2.05   0.042    -.0094233   -.0001657
    Leverage |  -.0230251   .0208805    -1.10   0.272    -.0642525    .0182023
 LnDealValue |   .0052026   .0024621     2.11   0.036     .0003412     .010064
    Domestic |  -.0058679   .0095064    -0.62   0.538    -.0246378    .0129019
  Horizontal |  -.0071467   .0072896    -0.98   0.328    -.0215395    .0072462
       Japan |  -.0237803   .0124236    -1.91   0.057      -.04831    .0007493
          US |  -.0265029   .0131432    -2.02   0.045    -.0524535   -.0005522
       _cons |   .0488307   .0304801     1.60   0.111    -.0113505    .1090119
------------------------------------------------------------------------------

. vif

    Variable |       VIF       1/VIF  
-------------+----------------------
 Interaction |     10.29    0.097223
 Altman_high |     10.03    0.099713
         UAI |      4.12    0.242708
      LnSize |      3.70    0.270312
 LnDealValue |      3.29    0.304259
       Japan |      2.76    0.362260
    Leverage |      1.33    0.753473
          US |      1.30    0.771970
    Domestic |      1.15    0.869232
  Horizontal |      1.08    0.921773
-------------+----------------------
    Mean VIF |      3.90

. mean (Interaction)

Mean estimation                   Number of obs   =        176

--------------------------------------------------------------
             |       Mean   Std. Err.     [95% Conf. Interval]
-------------+------------------------------------------------
 Interaction |    243.902   22.60059      199.2972    288.5068
--------------------------------------------------------------

. gen Meaninteraction= 243.902

. gen MC_Interaction=Interaction- Meaninteraction

. reg CAR_win MC_Interaction UAI Altman_high LnSize Leverage LnDealValue Domestic Horizontal Japan US

      Source |       SS           df       MS      Number of obs   =       176
-------------+----------------------------------   F(10, 165)      =      1.80
       Model |  .038689375        10  .003868937   Prob > F        =    0.0650
    Residual |  .355554565       165  .002154876   R-squared       =    0.0981
-------------+----------------------------------   Adj R-squared   =    0.0435
       Total |  .394243939       175  .002252823   Root MSE        =    .04642

--------------------------------------------------------------------------------
       CAR_win |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
---------------+----------------------------------------------------------------
MC_Interaction |  -.0000212   .0000375    -0.56   0.574    -.0000953     .000053
           UAI |   .0004438    .000323     1.37   0.171     -.000194    .0010816
   Altman_high |   .0003951   .0023014     0.17   0.864    -.0041489     .004939
        LnSize |  -.0047945   .0023444    -2.05   0.042    -.0094233   -.0001657
      Leverage |  -.0230251   .0208805    -1.10   0.272    -.0642525    .0182023
   LnDealValue |   .0052026   .0024621     2.11   0.036     .0003412     .010064
      Domestic |  -.0058679   .0095064    -0.62   0.538    -.0246378    .0129019
    Horizontal |  -.0071467   .0072896    -0.98   0.328    -.0215395    .0072462
         Japan |  -.0237803   .0124236    -1.91   0.057      -.04831    .0007493
            US |  -.0265029   .0131432    -2.02   0.045    -.0524535   -.0005522
         _cons |    .043672   .0328617     1.33   0.186    -.0212115    .1085556
--------------------------------------------------------------------------------

. vif

    Variable |       VIF       1/VIF  
-------------+----------------------
MC_Interac~n |     10.29    0.097223
 Altman_high |     10.03    0.099713
         UAI |      4.12    0.242708
      LnSize |      3.70    0.270312
 LnDealValue |      3.29    0.304259
       Japan |      2.76    0.362260
    Leverage |      1.33    0.753473
          US |      1.30    0.771970
    Domestic |      1.15    0.869232
  Horizontal |      1.08    0.921773
-------------+----------------------
    Mean VIF |      3.90

.