check multicollinearity

[hussein bataineh]

please i have two variable i need to check the multicollinearity between them

1. csopresence1 independent variable is binary variable [ is coded as 1 if the firm has a CSO and 0 otherwise
2. csopresence1XWorkforceScore moderator variable

i have high multicollinearity between csopresence1 independent variable and csopresence1XWorkforceScore moderator variable



does this mean that mean our result is wrong or what?

Thanks

reg   hard_final_Exact_new  csopresence1 CSOXWorkforceScore Firm_Size_w   ROA_w     Leverage_w   Market_book_four_w   Non_pension_CFO_w   STD_CFO_w  Board_Independence_w BoardSize_w Gender_Diversity_w  Fund_Status_w  FUNDING
> _RATIO_w  Platn_Size_w     CSR_Committee WorkforceScore_w   Environmental_Score_w

      Source |       SS           df       MS      Number of obs   =     3,150
-------------+----------------------------------   F(17, 3132)     =      2.35
       Model |  .935998249        17  .055058721   Prob > F        =    0.0013
    Residual |   73.230351     3,132  .023381338   R-squared       =    0.0126
-------------+----------------------------------   Adj R-squared   =    0.0073
       Total |  74.1663492     3,149   .02355235   Root MSE        =    .15291

---------------------------------------------------------------------------------------
 hard_final_Exact_new | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
----------------------+----------------------------------------------------------------
         csopresence1 |   .0617797   .0221089     2.79   0.005     .0184303    .1051291
  csopresence1XWorkforceScore |  -.0005919   .0002924    -2.02   0.043    -.0011652   -.0000187
          Firm_Size_w |  -.0006714   .0037406    -0.18   0.858    -.0080056    .0066629
                ROA_w |   .1508008   .0717624     2.10   0.036     .0100947    .2915069
           Leverage_w |  -.0509017   .0213967    -2.38   0.017    -.0928547   -.0089486
   Market_book_four_w |  -.0001519   .0004231    -0.36   0.720    -.0009815    .0006778
    Non_pension_CFO_w |  -.2827189   .0875633    -3.23   0.001    -.4544062   -.1110315
            STD_CFO_w |    .059265   .1691524     0.35   0.726    -.2723958    .3909259
 Board_Independence_w |    .000179   .0003103     0.58   0.564    -.0004294    .0007874
          BoardSize_w |  -.0006049   .0014291    -0.42   0.672     -.003407    .0021972
   Gender_Diversity_w |   1.53e-06   .0003147     0.00   0.996    -.0006155    .0006186
        Fund_Status_w |  -.3121349   .1166176    -2.68   0.007    -.5407897   -.0834802
      FUNDING_RATIO_w |  -.0037862   .0211474    -0.18   0.858    -.0452504     .037678
         Platn_Size_w |  -.0027324   .0031926    -0.86   0.392    -.0089923    .0035274
        CSR_Committee |   .0053732   .0074643     0.72   0.472    -.0092623    .0200086
     WorkforceScore_w |   .0002057   .0001653     1.24   0.213    -.0001185    .0005299
Environmental_Score_w |  -.0000664   .0001571    -0.42   0.673    -.0003744    .0002416
                _cons |   .0462305   .0438337     1.05   0.292    -.0397151    .1321761
---------------------------------------------------------------------------------------

. vif

    Variable |       VIF       1/VIF  
-------------+----------------------
CSOXWorkfo~e |     15.11    0.066191
csopresence1 |     13.78    0.072576
Non_pensio~w |      3.62    0.276141
Platn_Size_w |      3.52    0.284138
 Firm_Size_w |      3.37    0.296557
       ROA_w |      3.37    0.296923
Environmen~w |      2.26    0.442813
Fund_Statu~w |      2.14    0.466307
WorkforceS~w |      2.13    0.469199
FUNDING_RA~w |      1.81    0.551573
CSR_Commit~e |      1.56    0.639474
 BoardSize_w |      1.31    0.761307
Gender_Div~w |      1.24    0.805756
  Leverage_w |      1.20    0.835067
   STD_CFO_w |      1.18    0.850150
Board_Inde~w |      1.13    0.885105
Market_boo~w |      1.12    0.894002
-------------+----------------------
    Mean VIF |      3.52

.

[Richard Williams]

You'll frequently have high collinearity between a variable and an interaction term that is computed from it.

High collinearity in and of itself does not mean the model is wrong. It may just be that the model is correct and variables in it are highly correlated.

I would worry more about whether or not my model is correct.

For more on collinearity, see https://www3.nd.edu/~rwilliam/stats2/l11.pdf

Finally, unless you have an ancient version of Stata, I would use factor variable notation rather than compute the interactions myself.

[Carlo Lazzaro]

Hussein:
see also https://www.hup.harvard.edu/books/9780674175440 Chapter 23.

[Jeff Wooldridge]

In my experience this kind of collinearity is almost always due to the nature of the moderator, in this case, WorkforceScore. If zero is not a possible or likely value, the coefficient you're estimating on csopresence1 is not meaningful. What is the range of values for WorkforceScore, and what is its mean value?

The solution is to center WorkforceScore about a reasonable value, usually the average, before interacting with csopresence1. Then, the main effect on csopresence1 will be the average partial effect, which is usually much more relevant than the effect when WorkforceScore = 0. If this case is impossible, your original regression is estimating an undefined parameter, and a symptom of that is high collinearity.

I discuss these issues in Chapter 6 of my introductory econometrics text.

[Maarten Buis]

If this case is impossible, your original regression is estimating an undefined parameter, and a symptom of that is high collinearity.

I would not say that the main effect is undefined in that case, but just that it is a silly extrapolation.

[Jeff Wooldridge]

I would not say that the main effect is undefined in that case, but just that it is a silly extrapolation.

Perhaps semantics, but if I'm trying to estimate the effect of taking a financial fitness course on retirement savings and evaluating it at age = 0 then I'm estimating an effect for a nonexistent part of the population. That's what I mean by undefined. That we can use a linear model over undefined ranges of the population is true, but we should agree ahead of time that we won't.

[Maarten Buis]

Jeff Wooldridge Agreed, but I find it didactically easier to explain the problem as silly extrapolation. In my experience, students often tend to get a better feel for the problem that way. For that I like the year of birth example even better: Babies exist, but people born in the year 0 do not (to avoid confusion I will typically ignore the fact that the year 0 does not exist in commonly used (western) calendars). Students can draw a line and extend it, and extend it, and extend it even more till they finally reach 0. They can see that that is what linear regression does, and that that is just silly.