Continuous Continuous interaction in panel regressions

[lal mohan kumar]

Dear All,
I am here with some basic questions which which might be very trivial for many in the forum, and my apologies for this. However, please let me know your thoughts and direct me correctly if I am wrong.

Here are results

 reghdfe F.REC_TA_w  ///
> c.EPU##c.PROP_WIP_w ///
> GOVT_EFF GDP BUS_VOL FME  ///
> , absorb (id year) cluster (id)
(dropped 727 singleton observations)
(MWFE estimator converged in 7 iterations)

HDFE Linear regression                            Number of obs   =     86,321
Absorbing 2 HDFE groups                           F(  20,   9207) =      60.00
Statistics robust to heteroskedasticity           Prob > F        =     0.0000
                                                  R-squared       =     0.8147
                                                  Adj R-squared   =     0.7925
                                                  Within R-sq.    =     0.0646
Number of clusters (id)      =      9,208         Root MSE        =     0.0512

                                       (Std. err. adjusted for 9,208 clusters in id)
------------------------------------------------------------------------------------
                   |               Robust
        F.REC_TA_w | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------------+----------------------------------------------------------------
               EPU |  -.0002003   .0016535    -0.12   0.904    -.0034415    .0030409
        PROP_WIP_w |  -.0178172   .0194307    -0.92   0.359    -.0559056    .0202712
                   |
c.EPU#c.PROP_WIP_w |   .0018114   .0039981     0.45   0.651    -.0060258    .0096486
                   |
          GOVT_EFF |   .0011215   .0001084    10.35   0.000     .0009091    .0013339
               GDP |  -.0013491   .0023814    -0.57   0.571    -.0060172    .0033191
           BUS_VOL |   .0001369   .0003306     0.41   0.679    -.0005112    .0007851
               FME |   .0149315    .006771     2.21   0.027     .0016589    .0282041
            
             _cons |   .2225589   .0240751     9.24   0.000     .1753664    .2697513
------------------------------------------------------------------------------------

Absorbed degrees of freedom:
-----------------------------------------------------+
 Absorbed FE | Categories  - Redundant  = Num. Coefs |
-------------+---------------------------------------|
          id |      9208        9208           0    *|
        year |        18           1          17     |
-----------------------------------------------------+
* = FE nested within cluster; treated as redundant for DoF computation

.

test c.EPU#c.PROP_WIP_w

 ( 1)  c.EPU#c.PROP_WIP_w = 0

       F(  1,  9207) =    0.21
            Prob > F =    0.6505

testparm c.EPU##c.PROP_WIP_w

 ( 1)  EPU = 0
 ( 2)  PROP_WIP_w = 0
 ( 3)  c.EPU#c.PROP_WIP_w = 0

       F(  3,  9207) =    2.51
            Prob > F =    0.0568

 testparm c.EPU#c.PROP_WIP_w

 ( 1)  c.EPU#c.PROP_WIP_w = 0

       F(  1,  9207) =    0.21
            Prob > F =    0.6505

In the above regression model (I have omitted a few variables here to show only main things), I am concerned about the continuous-continuous interaction "c.EPU##c.PROP_WIP_w" and I would like to ask following doubts
1) In the regression table, the coefficient of interaction (c.EPU#c.PROP_WIP_w) is insignificant with t Stats of 0.45 and p value 0.651. As is evident that interaction effect is not significant , is it necessary to test the significance of the interaction coeffecient through "test" or "testparm"?
2) I have used test c.EPU#c.PROP_WIP_w to check the significance and I could see almost same p-value (or are the really same) and Prob > F show that we cannot reject the null. Is this testing way correct

3) Among testparm testings, which one is correct?

Looking forward to some answers

[Carlo Lazzaro]

Ial:
1) no, it is not necessary, as the results of -test- mirror exactly the ones reported in the regression table;
2) while the second -testparm- is correct (=-test-=results of the regression table). That said, -testparm- is mainly used to test the joint statistical significance of categorical predictors.

[lal mohan kumar]

Thanks dear Carlo Lazzaro for the swift reply.