Non significant main terms become significant after interaction

[Chiara Pollio]

Dear Statalists,
I am analysing the elasticity of towns' human development index to some town's characteristics . I have an unbalanced panel and I am using the - xtreg, fe - command. I want to see whether a particulare feature of the town (specialization in ICT) moderates the effects of the government expenditure (Govt_exp) per capita. However, I find that while in the main regression (no interaction) ICT is not significant and Govt_exp is, when I add the interaction ICT becomes significant, Govt_exp keeps its significance but the interaction is not significant. Does this make sense in econometric terms or I should suspect a problem in the data? I attach here the output of the two regression.

Thanks to everybody that will like to help.

Chiara

 xtreg log_HDI_rel ICT nospec log_SIPO_Pat log_local_firms log_total_trade log_Govt_exp_pc log_Nrofmarkets, fe

Fixed-effects (within) regression               Number of obs      =       267
Group variable: TOWN_ID                         Number of groups   =        32

R-sq:  within  = 0.2822                         Obs per group: min =         4
       between = 0.5202                                        avg =       8.3
       overall = 0.4274                                        max =        10

                                                F(7,228)           =     12.81
corr(u_i, Xb)  = 0.3027                         Prob > F           =    0.0000

---------------------------------------------------------------------------------
    log_HDI_rel |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
            ICT |    .060298   .0496503     1.21   0.226    -.0375341      .15813
         nospec |   .0253942   .0392888     0.65   0.519    -.0520213    .1028097
   log_SIPO_Pat |   .0992477   .0210757     4.71   0.000     .0577197    .1407757
log_local_firms |   .0127314   .0157105     0.81   0.419     -.018225    .0436879
log_total_trade |   .0269722   .0243544     1.11   0.269    -.0210163    .0749607
log_Govt_exp_pc |   .0546401   .0265604     2.06   0.041      .002305    .1069753
log_Nrofmarkets |   .0250622   .0304422     0.82   0.411    -.0349219    .0850462
          _cons |  -2.510315   .2985892    -8.41   0.000    -3.098662   -1.921968
----------------+----------------------------------------------------------------
        sigma_u |  .26241143
        sigma_e |  .14537252
            rho |  .76516854   (fraction of variance due to u_i)
---------------------------------------------------------------------------------
F test that all u_i=0:     F(31, 228) =    20.37             Prob > F = 0.0000




***Adding the interaction****

xtreg log_HDI_rel ICT nospec log_SIPO_Pat log_local_firms log_total_trade log_Govt_exp_pc log_Nrofmarkets ICT#c.log_Govt_exp_pc, fe

Fixed-effects (within) regression               Number of obs      =       267
Group variable: TOWN_ID                         Number of groups   =        32

R-sq:  within  = 0.2907                         Obs per group: min =         4
       between = 0.5076                                        avg =       8.3
       overall = 0.4240                                        max =        10

                                                F(8,227)           =     11.63
corr(u_i, Xb)  = 0.2876                         Prob > F           =    0.0000

---------------------------------------------------------------------------------------
          log_HDI_rel |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
----------------------+----------------------------------------------------------------
                  ICT |   .7648675   .4299937     1.78   0.077    -.0824219    1.612157
               nospec |     .04217    .040441     1.04   0.298    -.0375178    .1218578
         log_SIPO_Pat |   .0978732   .0210131     4.66   0.000     .0564675    .1392789
      log_local_firms |   .0150249   .0157132     0.96   0.340    -.0159375    .0459873
      log_total_trade |   .0258371   .0242728     1.06   0.288    -.0219917    .0736658
      log_Govt_exp_pc |   .0933109   .0353522     2.64   0.009     .0236504    .1629714
      log_Nrofmarkets |   .0249337   .0303281     0.82   0.412    -.0348269    .0846942
                      |
ICT#c.log_Govt_exp_pc |
                   1  |  -.0835534   .0506535    -1.65   0.100    -.1833646    .0162578
                      |
                _cons |  -2.833464   .3561838    -7.96   0.000    -3.535314   -2.131615
----------------------+----------------------------------------------------------------
              sigma_u |    .263293
              sigma_e |    .144827
                  rho |   .7677153   (fraction of variance due to u_i)
---------------------------------------------------------------------------------------
F test that all u_i=0:     F(31, 227) =    20.58             Prob > F = 0.0000

[Marcos Almeida]

You may wish to take a look at this thread.

Also, bear in mind that - albeit non-significant in "frequentist terms" - the interaction terms has a negative sign.

I gather some interaction plot would show better what is happening, but the negative interaction term (still "significant" if we set the alpha to 0,1) may give a clue.

[Carlo Lazzaro]

Chiara:
Marcos gave a helpful insight.
I would stay with your first regression code (ie, without interaction).
As an aside, please note that your second code (by the way -ICT- does not seem to reach statistical significance in both codes) could have been written more efficiently (I assume that -ICT_ is categorical):

xtreg log_HDI_rel nospec log_SIPO_Pat log_local_firms log_total_trade  log_Nrofmarkets i.ICT##c.log_Govt_exp_pc, fe

Eventually, please note that is -log_Govt_exp_pc- that is statistical significant, whereas, in its original metric, -Govt_exp_pc- might fail to reach a statistical significant coefficient (for what the term "significant" worths; I'm not a great fan of it).

[Chiara Pollio]

Dear Marcos and Carlo,
thanks for the useful hints. In particular for Carlo, I wish to specify that ICT is a dummy variable.
Carlo: I was particularly interested by you final comment and gave a try with a regression in semi-elasticity form rather than elasticity. The results are far more stable, which I suspect it is because the model now takes in due account of the observation that present zero in some of the variables that were previously in log form.

Kind regards,
Chiara