High VIF and presence of interaction terms

[Michael Lee]

Hello everyone,
I hope you are doing well.

Statement of the problem:
-I have long panel (6 groups near 100 months) with heteroskedasticity and serial correlation.
-I have used xtpcse and xtgls commands to check my hypotheses.
-There are 2 interaction terms of variables in model + age and age^2 variables in the model (in fact 3 interaction terms).
-VIF,unc command shows high values (>10) in model.


Question:

1.In this case shall I consider the VIF values in the model with interaction terms and remove variables with high VIF values from model?
2. Or just I should consider the VIF of model without interaction terms?

Thank you in advance.

Best Regards,
Michael

[Carlo Lazzaro]

Michael:
interactions inflate -vif- (and unavoidably so):

. use "C:\Program Files\Stata17\ado\base\a\auto.dta"
(1978 automobile data)

. regress price c.mpg##c.mpg i.foreign

      Source |       SS           df       MS      Number of obs   =        74
-------------+----------------------------------   F(3, 70)        =     15.52
       Model |   253687595         3  84562531.8   Prob > F        =    0.0000
    Residual |   381377801        70   5448254.3   R-squared       =    0.3995
-------------+----------------------------------   Adj R-squared   =    0.3737
       Total |   635065396        73  8699525.97   Root MSE        =    2334.1

------------------------------------------------------------------------------
       price | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
         mpg |  -1298.763   278.4207    -4.66   0.000    -1854.056   -743.4705
             |
 c.mpg#c.mpg |   20.95049   5.706873     3.67   0.000     9.568489    32.33249
             |
     foreign |
    Foreign  |   1702.625   645.9568     2.64   0.010     414.3051    2990.945
       _cons |   23124.82   3237.562     7.14   0.000     16667.71    29581.94
------------------------------------------------------------------------------

. estat vif

    Variable |       VIF       1/VIF  
-------------+----------------------
         mpg |     34.77    0.028764
 c.mpg#c.mpg |     34.72    0.028803
   1.foreign |      1.18    0.844610
-------------+----------------------
    Mean VIF |     23.56

. regress price c.mpg i.foreign

      Source |       SS           df       MS      Number of obs   =        74
-------------+----------------------------------   F(2, 71)        =     14.07
       Model |   180261702         2  90130850.8   Prob > F        =    0.0000
    Residual |   454803695        71  6405685.84   R-squared       =    0.2838
-------------+----------------------------------   Adj R-squared   =    0.2637
       Total |   635065396        73  8699525.97   Root MSE        =    2530.9

------------------------------------------------------------------------------
       price | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
         mpg |  -294.1955   55.69172    -5.28   0.000    -405.2417   -183.1494
             |
     foreign |
    Foreign  |   1767.292    700.158     2.52   0.014     371.2169    3163.368
       _cons |   11905.42   1158.634    10.28   0.000     9595.164    14215.67
------------------------------------------------------------------------------

. estat vif

    Variable |       VIF       1/VIF  
-------------+----------------------
         mpg |      1.18    0.845238
   1.foreign |      1.18    0.845238
-------------+----------------------
    Mean VIF |      1.18

.

That said, a VIF>10 with interaction should not be a reason of concern.

As an aside, please share what you typed and what Stata gave you back (as per FAQ). Thanks.

[Michael Lee]

Thank you Carlo for your response.
After running regression I ran VIF code:

. vif,unc

    Variable |       VIF       1/VIF  
-------------+----------------------
cd |      2.05    0.487467
np |      2.86    0.349621
1.generation |      1.59    0.627913
ap |     22.73    0.043987
transition |      1.14    0.873848
ibc |     26.15    0.038239
seasonality |      1.14    0.878726
-------------+----------------------
    Mean VIF |      8.24

and then I removed ibc from the model and get:

    Variable |       VIF       1/VIF  
-------------+----------------------
cd |      1.90    0.524943
np |      2.59    0.385544
1.generation |      1.47    0.681975
ap |      2.16    0.462282
transition |      1.13    0.887466
seasonality |      1.13    0.887523
-------------+----------------------
    Mean VIF |      1.73

after the model with interactions:

.    vif,unc

    Variable |       VIF       1/VIF  
-------------+----------------------
cd |      5.30    0.188648
np |      7.01    0.142589
c.cd#np |      6.86    0.145711
1.generation |      4.96    0.201701
generation#c.np |      5.00    0.199883
ap |     43.85    0.022808
c.ap#c.ap |     13.40    0.074635
transition |      1.20    0.833749
ibc |     26.93    0.037131
 seasonality |      1.21    0.823164
-------------+----------------------
    Mean VIF |     11.57

and removing ibc:

.    vif,unc

    Variable |       VIF       1/VIF  
-------------+----------------------
cd |      4.95    0.201988
np |      6.45    0.155069
c.cd#c.np |      6.72    0.148847
1.generation |      4.79    0.208685
generation#np|      5.00    0.199905
ap |     20.89    0.047872
c.ap#c.ap |     13.32    0.075051
transition |      1.19    0.839882
seasonality |      1.21    0.826354
-------------+----------------------
    Mean VIF |      7.17

Is there any paper I can cite that shows there is no concern about high VIF in models with interactions?
What's your idea about this results?

[Joro Kolev]

Multicollinearity is either
1. not a problem, in case you get sufficiently precise estimates;
2. or a problem that you can resolved only by collecting more data, in case that you cannot estimate precisely what you are interested in.

[Michael Lee]

Multicollinearity is either
1. not a problem, in case you get sufficiently precise estimates;
2. or a problem that you can resolved only by collecting more data, in case that you cannot estimate precisely what you are interested in.

Thank you for your response Joro.
What is the measure of "precise estimates"? how can I make sure that my estimates are precise?

p.s.: when I add month and year dummies to the model the VIF becomes 7.70...

[Carlo Lazzaro]

MIchael:
see examples # 12 and 13 in -regress postestimation- entry, Stata .pdf manual-
In addition, for a humourous explanantion of multicollineraity, see Chapter 23 in https://www.hup.harvard.edu/catalog....=9780674175440

[Michael Lee]

Thanks Carlo.
The link to hup is not working. I got an error.

[Carlo Lazzaro]

Michael:
my bad; I did not check the link.
The following one shoud work:
https://www.amazon.com/Course-Econom.../dp/0674175441

[Michael Lee]

Thank you very much!