Interaction terms and statistical significance

[Kristian Pal]

Hello Statalisters,

I have an enquiry related to my thesis work on corporate governance. My current model, after discussion with my supervisor and realising the existence of heteroskedacity, autocorrelation, and interclass correlation, uses clustered (by ID) standard errors. Since I am a beginner in Stata and the field, I was confused when the clustering of id's led to most estimates to become insignificant compared to a non-clustered robust model, but I do understand that the latter can lead to too low p-values which are in a sense "normalized" when clustering. The regression output becomes:
Ex1.

regress rdintassets d_institutional d_family d_government d_foundation d_corporate lowtech midlowtech midhightech hightech firmage lemployees salestoassets si
> ze HHI5  i.year, vce(cluster id)
note: d_corporate omitted because of collinearity

Linear regression                                      Number of obs =     821
                                                       F( 16,   207) =    9.83
                                                       Prob > F      =  0.0000
                                                       R-squared     =  0.3794
                                                       Root MSE      =  .04095

                                      (Std. Err. adjusted for 208 clusters in id)
---------------------------------------------------------------------------------
                |               Robust
    rdintassets |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
d_institutional |  -.0083898   .0069731    -1.20   0.230    -.0221372    .0053577
       d_family |  -.0013148   .0075511    -0.17   0.862    -.0162017    .0135721
   d_government |  -.0022413    .009686    -0.23   0.817    -.0213372    .0168545
   d_foundation |   .0201897   .0205137     0.98   0.326    -.0202529    .0606322
    d_corporate |          0  (omitted)
        lowtech |   .0054401   .0077778     0.70   0.485    -.0098937    .0207739
     midlowtech |  -.0011466    .005253    -0.22   0.827    -.0115028    .0092096
    midhightech |    .011555   .0058523     1.97   0.050     .0000172    .0230929
       hightech |   .0381415   .0060274     6.33   0.000     .0262587    .0500244
        firmage |  -.0017071   .0032186    -0.53   0.596    -.0080525    .0046382
     lemployees |   .0029649   .0019039     1.56   0.121    -.0007887    .0067186
  salestoassets |  -.0000491   .0000128    -3.83   0.000    -.0000744   -.0000238
           size |  -.0146623   .0028813    -5.09   0.000    -.0203429   -.0089818
           HHI5 |  -.0255175   .0133956    -1.90   0.058    -.0519268    .0008917
                |
           year |
          2014  |  -.0005828   .0011025    -0.53   0.598    -.0027563    .0015908
          2015  |   .0011059    .002167     0.51   0.610    -.0031664    .0053781
          2016  |   .0030669   .0020493     1.50   0.136    -.0009733     .007107
                |
          _cons |   .1403256   .0253757     5.53   0.000     .0902977    .1903534
---------------------------------------------------------------------------------

Now, there have been suggestions that I can interact the owner concentration variable HHI5 with the owner identity (d_...) variables, to seek for joint effect. Doing so yields the following: Ex2.

. regress rdintassets c.HHI5#i.(d_institutional d_family d_government d_foundation d_corporate) lowtech midlowtech midhightech hightech firmage lemployees sales
> toassets size HHI5  i.year, vce(cluster id)
note: 1.d_corporate#c.HHI5 omitted because of collinearity

Linear regression                                      Number of obs =     821
                                                       F( 16,   207) =   10.89
                                                       Prob > F      =  0.0000
                                                       R-squared     =  0.3695
                                                       Root MSE      =  .04128

                                             (Std. Err. adjusted for 208 clusters in id)
----------------------------------------------------------------------------------------
                       |               Robust
           rdintassets |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-----------------------+----------------------------------------------------------------
d_institutional#c.HHI5 |
                    1  |   .0010219   .0177645     0.06   0.954    -.0340006    .0360444
                       |
       d_family#c.HHI5 |
                    1  |   .0409142   .0173951     2.35   0.020       .00662    .0752085
                       |
   d_government#c.HHI5 |
                    1  |   .0378852   .0229844     1.65   0.101    -.0074284    .0831987
                       |
   d_foundation#c.HHI5 |
                    1  |   .0524052   .0324649     1.61   0.108    -.0115991    .1164096
                       |
    d_corporate#c.HHI5 |
                    1  |          0  (omitted)
                       |
               lowtech |   .0078691   .0072993     1.08   0.282    -.0065214    .0222596
            midlowtech |    .002982   .0052806     0.56   0.573    -.0074286    .0133926
           midhightech |   .0161474   .0054195     2.98   0.003     .0054629    .0268319
              hightech |    .043383   .0069076     6.28   0.000     .0297647    .0570012
               firmage |  -.0014441   .0034059    -0.42   0.672    -.0081587    .0052706
            lemployees |   .0034837    .002268     1.54   0.126    -.0009876     .007955
         salestoassets |  -.0000542   .0000158    -3.43   0.001    -.0000854   -.0000231
                  size |  -.0150694   .0032153    -4.69   0.000    -.0214084   -.0087304
                  HHI5 |  -.0435472   .0173527    -2.51   0.013    -.0777577   -.0093366
                       |
                  year |
                 2014  |  -.0005942   .0011114    -0.53   0.593    -.0027854     .001597
                 2015  |   .0011665     .00217     0.54   0.591    -.0031117    .0054447
                 2016  |   .0031284   .0020456     1.53   0.128    -.0009045    .0071613
                       |
                 _cons |   .1296923    .024291     5.34   0.000     .0818029    .1775817
----------------------------------------------------------------------------------------

I am not sure how to make sense of this as trying margins command on d_family and d_government show that they are "non estimatable". Furthermore, the point of my study was to add country level factors to a baseline model, as shown above, by adding and interact country level factors to any significant effects from first regression in a second and third model. However, if I were to use the interaction model in Ex2 with ownertype and HHI5, could I then include a further interaction with a country variable i.e. Ownertype#HHI5#Countryvar. I can imagine that it would be tricky to explain such effect.

Thank you for considering this lengthy post!

[Phil Bromiley]

You'll increase your chances of a useful answer by following the FAQ on asking questions - provide Stata code in code delimiters, readable Stata output, and sample data.

I am having trouble understanding what you are asking and what you are doing. In the second estimate, you can't do margins on d_family since d_family is not a variable in the model - it only appears in the interactions. Indeed, many would say you need the main effects for the variables you're including in the interactions.