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Puzzled by an "omitted variable" question

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Dear members,

I am conducting a study where the coefficient of interest is the one of an interaction term (dummy##continuous).

One of the control variables is "experience" (the years of experience of an individual in a certain industry, integers).

A version for "experience" is "no_experience", a dummy taking the value 1 if the individual has zero years of experience, and zero otherwise.

As you can see from the regressions below, the p-value of the coefficient of the interaction term goes up from 0.020 when I use the "c.experience" to 0.073 when I use "i.no_experience".

I was told (by someone much more experienced than I) that the change in the p-value was indicating an omitted variable.

I am taking this comment very seriously, and I have been thinking about this for days now, but I am puzzled - I cannot think of a variable that would be related to "no_experience" and not to "experience".

I would really use any comment or reference you could have on this one.
What am I missing?


Thank you very much in advance!

MM

Code:
probit part i.dummy##c.continuous c.experience time_elapsed popularity type

Iteration 0:   log likelihood = -472.92546  
Iteration 1:   log likelihood = -375.12789  
Iteration 2:   log likelihood =  -373.9209  
Iteration 3:   log likelihood = -373.91832  
Iteration 4:   log likelihood = -373.91832  

Probit regression                               Number of obs     =     741
                                                LR chi2(13)       =     198.01
                                                Prob chi2       =     0.0000
Log likelihood = -373.91832                     Pseudo R2         =     0.2094

-------------------------------------------------------------------------------
         part |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
--------------+----------------------------------------------------------------
              |
    dummy     |  -3.329878   .9732082    -3.42   0.001    -5.237331   -1.422424
    continous |  -.1627043   .1041651    -1.56   0.118    -.3668642    .0414555
              |
       dummy# |
continuous    |   .2587861    .110819     2.34   0.020      .041585    .4759873
              |
 c.experience |   .0937605   .0312805     3.00   0.003     .0324519    .1550691
 time_elapsed |  -.0532365   .0177352    -3.00   0.003    -.0879969   -.0184761
   popularity |   .0524593   .0395867     1.33   0.185    -.0251293    .1300479
              |
         type |
           2  |  -.8001533   .2560044    -3.13   0.002    -1.301913   -.2983939
           4  |  -.0078864   .1471351    -0.05   0.957     -.296266    .2804931
           5  |  -.3953362   .1735647    -2.28   0.023    -.7355167   -.0551556
           6  |  -.3139073   .3798108    -0.83   0.409    -1.058323    .4305081
           7  |   -.008509   .1919858    -0.04   0.965    -.3847943    .3677763
           8  |  -.2624637   .3092251    -0.85   0.396    -.8685337    .3436063
           9  |   .2764111   .2174467     1.27   0.204    -.1497766    .7025989
              |
        _cons |   1.903462   .8897393     2.14   0.032     .1596047    3.647319
-------------------------------------------------------------------------------



probit part i.dummy##c.continuous i.no_experience time_elapsed popularity type

Iteration 0:   log likelihood = -472.92546  
Iteration 1:   log likelihood = -376.54574  
Iteration 2:   log likelihood = -375.98521  
Iteration 3:   log likelihood = -375.98374  
Iteration 4:   log likelihood = -375.98374  

Probit regression                               Number of obs     =        741
                                                LR chi2(13)       =     193.88
                                                Prob chi2       =     0.0000
Log likelihood = -375.98374                     Pseudo R2         =     0.2050

-------------------------------------------------------------------------------
         part |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
--------------+----------------------------------------------------------------
       dummy  |   -2.70438   .9308157    -2.91   0.004    -4.528745   -.8800147
   continuous |  -.1006177   .0993523    -1.01   0.311    -.2953445    .0941092
              |
      dummy#  |
  continuous  |   .1901668   .1062418     1.79   0.073    -.0180632    .3983968
              |
i.no_exper    |  -.2857927   .1133559    -2.52   0.012    -.5079663   -.0636192
 time elapsed |  -.0519214   .0175974    -2.95   0.003    -.0864117   -.0174312
   popularity |    .057135   .0395783     1.44   0.149    -.0204371    .1347071
              |
         type |
           2  |  -.7549467   .2562922    -2.95   0.003     -1.25727   -.2526233
           4  |  -.0360474   .1470612    -0.25   0.806     -.324282    .2521873
           5  |  -.3904853   .1736325    -2.25   0.025    -.7307987   -.0501718
           6  |  -.3563329   .3817795    -0.93   0.351    -1.104607    .3919411
           7  |  -.0131869   .1910058    -0.07   0.945    -.3875513    .3611775
           8  |  -.2367377   .3053641    -0.78   0.438    -.8352404     .361765
           9  |   .2734384   .2158454     1.27   0.205    -.1496108    .6964876
              |
        _cons |    1.55703   .8543099     1.82   0.068    -.1173863    3.231447
-------------------------------------------------------------------------------

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