Significance of regressor effect with and without moderator

[Deepika Deshpande]

Hi, I am running fe panel data regression on a set of companies to explore the effect of firm geographic segment (GS) diversification on firm firm performance (ROA.) My time series includes 2001-2019. I have divided the data into pre-crisis (2001-2006) and post crisis (2010-2019) periods. The regression results show that:
a. the effect of quadratic geographic segment (GS) diversification on firm performance is significant if I include crisis as a moderator - however -
b. if I run the regression for the pre-crisis (2001-2006) period and post crisis (2010-2019) period separately and drop the moderator "Crisis", the effect of geographic segment (GS) diversification on firm performance is no longer significant.

I am wondering how to interpret this result and was hoping I could gets some guidance from this group. I am pasting my results below:

a. Regression effect of quadratic geographic segment (GS) diversification on firm performance is significant with "crisis" as a moderator

. xtreg ROA_win05 LnRev TDTE Co_Age c.l1.GSFinal##c.l1.GSFinal##Crisis if Excl_bynd_delisting !=
> 1 & Year !=7 & Year !=8 & Year !=9, fe

Fixed-effects (within) regression               Number of obs     =      1,486
Group variable: ID                              Number of groups  =        176

R-sq:                                           Obs per group:
     within  = 0.1685                                         min =          1
     between = 0.1286                                         avg =        8.4
     overall = 0.1064                                         max =         15

                                                F(8,1302)         =      32.99
corr(u_i, Xb)  = -0.6592                        Prob > F          =     0.0000

----------------------------------------------------------------------------------------------
                   ROA_win05 |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-----------------------------+----------------------------------------------------------------
                       LnRev |   1.714848   .1508791    11.37   0.000     1.418855    2.010841
                        TDTE |    .000211   .0005493     0.38   0.701    -.0008667    .0012886
                      Co_Age |  -.2314909   .0404682    -5.72   0.000    -.3108809   -.1521009
                             |
                     GSFinal |
                         L1. |  -15.84082   2.337321    -6.78   0.000    -20.42614   -11.25549
                             |
       cL.GSFinal#cL.GSFinal |   11.38014   2.240617     5.08   0.000     6.984526    15.77575
                             |
                    1.Crisis |  -2.421146   .5444138    -4.45   0.000     -3.48917   -1.353121
                             |
           Crisis#cL.GSFinal |
                          1  |   14.38415     2.3525     6.11   0.000     9.769045    18.99926
                             |
Crisis#cL.GSFinal#cL.GSFinal |
                          1  |  -11.83307   2.295733    -5.15   0.000    -16.33681   -7.329325
                             |
                       _cons |   3.553605   .9702083     3.66   0.000     1.650262    5.456947
-----------------------------+----------------------------------------------------------------
                     sigma_u |   5.249395
                     sigma_e |  3.7141179
                         rho |  .66639907   (fraction of variance due to u_i)
----------------------------------------------------------------------------------------------
F test that all u_i=0: F(175, 1302) = 5.82                   Prob > F = 0.0000

b. Regression effect of quadratic geographic segment (GS) diversification for the pre-crisis (2001-2006) period WITHOUT moderator "Crisis" (post crisis period has similar results and hence I am not pasting that.)

. xtreg ROA_win05 LnRev TDTE Co_Age c.l1.GSFinal##c.l1.GSFinal if Excl_bynd_delisting !=1 & Year
>  <7, fe

Fixed-effects (within) regression               Number of obs     =        303
Group variable: ID                              Number of groups  =         98

R-sq:                                           Obs per group:
     within  = 0.0905                                         min =          1
     between = 0.1059                                         avg =        3.1
     overall = 0.0901                                         max =          5

                                                F(5,200)          =       3.98
corr(u_i, Xb)  = -0.1687                        Prob > F          =     0.0018

---------------------------------------------------------------------------------------
            ROA_win05 |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
----------------------+----------------------------------------------------------------
                LnRev |    1.79619   .4877115     3.68   0.000      .834474    2.757907
                 TDTE |  -.0029504   .0026559    -1.11   0.268    -.0081877    .0022868
               Co_Age |  -.0180046   .1883957    -0.10   0.924    -.3895014    .3534922
                      |
              GSFinal |
                  L1. |  -1.234931    4.66017    -0.26   0.791     -10.4243     7.95444
                      |
cL.GSFinal#cL.GSFinal |   2.979751   3.566609     0.84   0.404    -4.053233    10.01273
                      |
                _cons |  -2.280197   3.572285    -0.64   0.524    -9.324373    4.763978
----------------------+----------------------------------------------------------------
              sigma_u |  6.3345603
              sigma_e |  3.0909695
                  rho |  .80769024   (fraction of variance due to u_i)
---------------------------------------------------------------------------------------
F test that all u_i=0: F(97, 200) = 7.96                     Prob > F = 0.0000

[Deepika Deshpande]

In order to better understand the situation I have described above, I would like to run a Chow test for the sample with Crisis as the breakpoint. However, I wanted to know what is the appropriate command to sum a Chow test for a panel data (xtreg fe.) Thank you very much.

[Carlo Lazzaro]

Deepika:
in my opinion you're making things more difficult that they have to be.
Why not running one regression only including a two-level categorical predictor coded 0 (pre-crisis) and 1 (post-crisis) in the right-hand side of the regression equation?
As an aside, please note that the more interactions you plug in, the more difficult the explanation and dissemination of your results is expected to be.

[Deepika Deshpande]

Hi Carlos,

Thank you for your response (#3.) I have in fact run the regression for the pre-crisis and post-crisis sample as you suggested that that is what has resulted in the question I asked.

Let me repeat: I have panel data for a set of companies for 2001-19. I have divided the data as pre-crisis (Crisis = 0 i.e. 2001-06) and post-crisis (Crisis = 1 i.e. 2010-19.) I ran fe panel regression (xtreg fe) and obtained the following results:

1. Overall effect of Geographic Segmentation (squared) on ROA in the TOTAL sample is significant.
2. Effect of Crisis and Crisis*Geographic Segmentation (squared) in the TOTAL sample is also significant.
3. However, if I divide my TOTAL sample into a pre-crisis subsample and a post-crisis subsample, then the effect of Geographic Segmentation (squared) in the two sub-samples is not significant.

I am wondering how to interpret this result. Would you have any suggestions?

[Carlo Lazzaro]

Deepika:
short answer: you ran two different regression models; hence, no wonder that your results differ.
It seems resonable to include -crisis- among the set of your predictors (as in your first regression model).
Including -i.year- is advisable as well.

[Deepika Deshpande]

Thank you Carlos (#5.) Do you believe it will help if i run a Chow test for the (1) TOTAL sample (2) pre-crisis subsample and (3) post-crisis subsample?

PS: I am wondering if a Chow test will help highlight any differences in the regression effects of Geographic Segmentation (squared) on ROA. Hence my question.

[Carlo Lazzaro]

Deepika:
you can perform a Chow test to investigate whether data are poolable or not (https://www.stata.com/support/faqs/s...cs/chow-tests/).
That said, I prefer interaction.