Moderation - Panel Data Analysis

[Sjors van Tilburg]

Dear Stata experts,

I am trying to test the influence of my dummy moderator (high tech industry =1, not high tech =0) on the relationship between R&D (lagged with 1 year, lagrd) and Return on Sales (ros100) with panel data ranging from 2005 to 2010. As controls I included a dummy for the company being from the US or not being from the US, year dummies, and a dummy for marketing intensity. Hausman test argues a Fixed effect model.

So far so good. Hereafter I get some difficulties. I am not sure about:

1. which model to use. Using the fixed effects model will omit my US dummy, is it justified to just use random effects model instead?
2. if my input to see the results is correct: xtreg ros100 i.du_high_tech##c.lagrd, re

And when it is correct; what should be interpreted as the overall results.

. xtreg ros100  i.du_high_tech##c.lagrd, re

Random-effects GLS regression                   Number of obs     =      1,620
Group variable: company_id                      Number of groups  =        324

R-sq:                                           Obs per group:
     within  = 0.6199                                         min =          5
     between = 0.9172                                         avg =        5.0
     overall = 0.7350                                         max =          5

                                                Wald chi2(3)      =    4482.85
corr(u_i, X)   = 0 (assumed)                    Prob > chi2       =     0.0000

--------------------------------------------------------------------------------------
              ros100 |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
---------------------+----------------------------------------------------------------
      1.du_high_tech |   .5100225   .0539294     9.46   0.000     .4043229    .6157222
               lagrd |   .0323437   .8364303     0.04   0.969     -1.60703    1.671717
                     |
du_high_tech#c.lagrd |
                  1  |  -3.476529   .8380226    -4.15   0.000    -5.119023   -1.834035
                     |
               _cons |   .0004879   .0430304     0.01   0.991    -.0838501     .084826
---------------------+----------------------------------------------------------------
             sigma_u |          0
             sigma_e |  .84690728
                 rho |          0   (fraction of variance due to u_i)
--------------------------------------------------------------------------------------

Thanks in advance for your help, it would be greatly appreciated!

Sjors

[Felix Bittmann]

First of all, the choice of model just be justified theoretically. You cannot include time-constant independent variables in a FE model. So if the central interest is in these variables, you have to use RE models. As a control, it is not important since FE models control for all time-constant factors implicitly. Another option would be to run the model separately for all levels of your time-constant variable as FE, but this is probably not possible with your current research question. The command you use seems fine to me. Probably it would be helpful for you to learn more about the ideas of the respective models so you can have an informed decision.
https://stats.idre.ucla.edu/stata/fa...g-re-xtreg-fe/
https://www.princeton.edu/~otorres/Panel101.pdf

[Sjors van Tilburg]

Thanks for your help Felix!
I decided to do a subsample analysis in order to see the differences in the coefficient and the significance levels to draw conclusions about the influence of high-tech (not a that advanced assignment). Hausman still suggests Fixed effects, so I keep using it.

Is it correct if I interpret the results as high-tech having a negative influence on the relationship between R&D and firm performance? Possibly meaning that non-high tech firms have more positive results on firm performance on short term.

. xtreg ros100 lagrd employees du_mark du_us du_2005 du_2006 du_2007 du_2008 du_2009 du_2010 if du_high_tech==1, fe
note: du_mark omitted because of collinearity
note: du_us omitted because of collinearity
note: du_2005 omitted because of collinearity
note: du_2010 omitted because of collinearity

Fixed-effects (within) regression               Number of obs     =        788
Group variable: company_id                      Number of groups  =        160

R-sq:                                           Obs per group:
     within  = 0.6239                                         min =          1
     between = 0.9154                                         avg =        4.9
     overall = 0.7350                                         max =          5

                                                F(6,622)          =     171.95
corr(u_i, Xb)  = -0.6746                        Prob > F          =     0.0000

------------------------------------------------------------------------------
      ros100 |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       lagrd |  -4.331467   .1363955   -31.76   0.000    -4.599318   -4.063615
   employees |   2.73e-07   6.05e-06     0.05   0.964    -.0000116    .0000122
     du_mark |          0  (omitted)
       du_us |          0  (omitted)
     du_2005 |          0  (omitted)
     du_2006 |   .0831599   .1406513     0.59   0.555    -.1930491    .3593689
     du_2007 |   .3120235   .1389281     2.25   0.025     .0391986    .5848484
     du_2008 |   .1803332     .13715     1.31   0.189        -.089    .4496663
     du_2009 |   .2199608   .1370667     1.60   0.109    -.0492088    .4891304
     du_2010 |          0  (omitted)
       _cons |   .5385511   .2043005     2.64   0.009     .1373488    .9397534
-------------+----------------------------------------------------------------
     sigma_u |  .77522249
     sigma_e |  1.2149311
         rho |  .28934133   (fraction of variance due to u_i)
------------------------------------------------------------------------------
F test that all u_i=0: F(159, 622) = 1.05                    Prob > F = 0.3455

. xtreg ros100 lagrd employees du_mark du_us du_2005 du_2006 du_2007 du_2008 du_2009 du_2010 if du_high_tech==0, fe
note: du_us omitted because of collinearity
note: du_2005 omitted because of collinearity
note: du_2010 omitted because of collinearity

Fixed-effects (within) regression               Number of obs     =        829
Group variable: company_id                      Number of groups  =        168

R-sq:                                           Obs per group:
     within  = 0.0335                                         min =          2
     between = 0.0353                                         avg =        4.9
     overall = 0.0162                                         max =          5

                                                F(7,654)          =       3.24
corr(u_i, Xb)  = -0.4817                        Prob > F          =     0.0022

------------------------------------------------------------------------------
      ros100 |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       lagrd |  -.0420059   .0129984    -3.23   0.001    -.0675295   -.0164823
   employees |  -6.89e-09   8.38e-09    -0.82   0.411    -2.33e-08    9.55e-09
     du_mark |  -.0003347    .001865    -0.18   0.858    -.0039968    .0033275
       du_us |          0  (omitted)
     du_2005 |          0  (omitted)
     du_2006 |   .0000499   .0002911     0.17   0.864    -.0005217    .0006216
     du_2007 |   .0000109   .0002913     0.04   0.970    -.0005611    .0005829
     du_2008 |  -.0008073   .0002943    -2.74   0.006    -.0013851   -.0002294
     du_2009 |  -.0005502   .0002916    -1.89   0.060    -.0011228    .0000225
     du_2010 |          0  (omitted)
       _cons |   .0041549   .0010967     3.79   0.000     .0020014    .0063083
-------------+----------------------------------------------------------------
     sigma_u |  .00452303
     sigma_e |  .00263147
         rho |  .74711344   (fraction of variance due to u_i)
------------------------------------------------------------------------------
F test that all u_i=0: F(167, 654) = 9.67                    Prob > F = 0.0000

Thanks in advance!!!!

[Sjors van Tilburg]

Anyone to the rescue? Thanks..