Negative binomial regression: Coefficient gets insignificant when control variable is logged

[Klaus Klausen]

Hi,

please note that this question was cross-posted on StackExchange but didn't receive any feedback so I hope I might have better luck here. Link

My dependent variable is a count variable that takes on the value 0 in most cases (80%) so I am applying a Negative binomial regression model. Depending on the exact model specification my independent variable of interest is significant at 5% or 1%. My model has a total of 16 predictor variables and no interaction term included. It has year and industry-fixed effects. Each observation corresponds to a Merger & Acquisition announced by US companies on some day between 2009 and 2018. For each observation (i.e., each deal) my dependent variable measures the number of press releases the acquiring company has published from one day before to one day after the acquisition was announced. So ultimately my mode examines what determines the number of press releases published by an acquiring firm around the date on which the firm announced an M&A. Most papers I read so far take the natural log of a control variable that I also included in my model (market value of a company). This makes sense to me as the variable usually is skewed to the right. The non-transformed version of the variable is highly significant (1%) and doesn't do much to my independent variable of interest in terms of significance. However, if I include the logged version of the control my independent variable get's highly insignificant. I am not trying to push my data towards significance but want to understand if this could be an absolutely normal thing or indicates some sort of problem.

Please find below the current Stata output of my model. To improve readability I left out the estimates for the fixed effects dummies. CNS is my variable of interest that gets highly insignificant when the variable Acq_Size_MV42 is logged.

Negative binomial regression                            Number of obs =    888
                                                        Wald chi2(34) =      .
Dispersion: mean                                        Prob > chi2   =      .
Log pseudolikelihood = -575.33319                       Pseudo R2     = 0.0926

--------------------------------------------------------------------------------------------------------------------------------------------
                                                                           |               Robust
                                                             IM_Offsetting | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
---------------------------------------------------------------------------+----------------------------------------------------------------
                                                                CEO_tenure |   .0263472   .0138861     1.90   0.058    -.0008691    .0535635
                                                                   CEO_Age |    .020686   .0121678     1.70   0.089    -.0031625    .0445345
                                                                CEO_Gender |  -.4555254   .3685265    -1.24   0.216    -1.177824    .2667733
                                                                Acq_MA_exp |  -.0125482   .0219201    -0.57   0.567    -.0555109    .0304145
                                                                Deal_Value |  -6.53e-11   2.88e-11    -2.27   0.023    -1.22e-10   -8.98e-12
                                                              Deal_AllCash |  -.2488855   .2840594    -0.88   0.381    -.8056317    .3078607
                                                                Deal_Stock |   .1827599   .3102503     0.59   0.556    -.4253195    .7908392
                                                              Targ_Listing |   .0517394   .0560832     0.92   0.356    -.0581817    .1616604
                                                                  FF12_Div |     .42329   .1428464     2.96   0.003     .1433162    .7032638
                                                             Acq_Size_MV42 |   8.30e-12   2.08e-12     4.00   0.000     4.23e-12    1.24e-11
                                                               Acq_Lev_WWU |   .0271976   .0346693     0.78   0.433    -.0407529    .0951482
                                                           Acq_TobinsQ_WWU |   .1080321   .0686858     1.57   0.116    -.0265896    .2426537
                                                                   Acq_FCF |   3.453921   1.930733     1.79   0.074    -.3302461    7.238087
                                                             Acq_Cash_hold |    .154336   .5424386     0.28   0.776    -.9088242    1.217496
                                                                   Acq_ROA |  -4.144292   1.860108    -2.23   0.026    -7.790036    -.498547
                                                                       CNS |   .2598483   .1100374     2.36   0.018      .044179    .4755176

---------------------------------------------------------------------------+----------------------------------------------------------------
                                                                  /lnalpha |  -.7465692   .4326131                     -1.594475    .1013369
---------------------------------------------------------------------------+----------------------------------------------------------------
                                                                     alpha |   .4739899   .2050543                       .203015    1.106649
--------------------------------------------------------------------------------------------------------------------------------------------

. sum IM_Offsetting if sample == 1

    Variable |        Obs        Mean    Std. dev.       Min        Max
-------------+---------------------------------------------------------
IM_Offsett~g |        888    .3085586    .6643227          0          4

[Joao Santos Silva]

Dear Klaus Klausen,

there are several possible reasons for that (e.g. different degrees of collinearity), but I would avoid NB regression with fixed effects. How do the results look like if you use Poisson regression with FE?

Best wishes,

Joao

[Nick Cox]

It's always hard to know what is going on with a dataset too big to post here and a complicated model. In other contexts loss of significance (or importance) when a variable is logged suggests that the effect of one or more outliers or at least values in the tail has been damped. Researchers can jump either way on that: big firms have much higher values, and that is real; or the first result was just a side-effect of distribution shape.

Marginal distributions of predictors are what they are and don't even have to be symmetric, although sometimes as here results are necessarily sensitive to what scale you use for a predictor, original or an alternative. (No one I know of objects to the skewness of an indicator that is say 90% of one value and 10% of the other value.)

It is far from a complete solution but worth better than nothing at all (or just wondering) is to plot

response against that predictor, logged

response against that predictor, original

and see what you can see.

[Klaus Klausen]

Thank you both for providing very helpful answers.
Joao Santos Silva The results look quite similar but I figured out an error in my dataset which seemed to solve my problem.